* Of course, it all begins with ARISTOTLE, who was quoted by Maltézos
* (1912). The oldest account of mirages seems to be Aristotle's brief
* mention in the "Meteorologica" (c. 340 or 350 BC) at 373 b in Book III
* (p.253 of the Loeb Library edition):
* "Distant and dense air does of course normally act as a mirror . . . ,
* which is why when there is an east wind promontories on the sea appear
* to be elevated above it and everything appears abnormally large;. . . "
* but unfortunately he then drags in the Moon illusion.
* So both MIRAGE and LOOMING were known to him.
* As Lee notes there, a similar (but much briefer) mention occurs in
* "Problems" XXVI. 53: "Why, when the east wind blows, do all the things
* seem larger?" Here are the Loeb Library editions:
* THEOPHRASTUS was Aristotle's successor; he's cited by A. von Humboldt.
* The fragment given in the footnote suggests he was familiar with
* superior mirages as well: "si mons versus aquilonem extenditur . . . ",
* though the translator obviously is not ("with what meaning I cannot
* see.")
* However, it is the inferior-mirage passage that Humboldt refers to:
* "If promontories seem to stand high out of the sea, or a single island
* looks like several . . . ."
* This is the Loeb Library edition; the "weather signs" section is
* apparently just tacked on, after "on odours". The subtitle is
* "with an English translation by Sir Arthur Hort, Bart., . . . ."
* AGATHARCHIDES (2nd Century BC) is known only from fragments of his
* historical work on the areas around the Arabian peninsula quoted or
* paraphrased by the later writers (Diodorus, Strabo, and Photius) who
* cite him as a source. The book cited here is an attempt to collect what
* remains of his work.
* Let's start with a mangled account of mirages in the desert. On p. 116
* (Book 5, Chapter 66 of Agatharchides) we have:
* "At the furthest reaches of Egypt and Trogodytice, . . . because of
* the extreme heat produced by the sun at noon people standing next to
* one another are unable to see each other because of the density of the
* air resulting from its condensation." [Evidently the original story was
* "people standing *near* each other" -- meaning, perhaps, "within hailing
* distance" as opposed to "far away". This is a correct observation of the
* shrinking of the apparent horizon by the inferior mirage, and the hiding
* of objects a few hundred meters away by the mirage. The distortion of the
* sense of the passage in re-copying is quite typical of what copy editors
* do today; it is particularly common in re-told accounts of mirages and
* other refraction phenomena by someone who has not personally seen them.]
* The next passage appears in both Photius and Diodorus, though in
* quite different forms. Here's Burstein's version of Photius; after
* commenting on the supposed lack of twilight at low latitudes: "Second,
* the sun appears to rise from the middle of the sea." [cf. Le Gentil's
* "whale" remark.] "Third, when it does rise, it is like a blazing coal,
* scattering great sparks, some into the disc of light and some beyond."
* [cf. the GF observers who speak of "flames" shooting out of the Sun.]
* "Fourth, people also say that the shape of the sun is not like a disc
* but most closely resembles a thick column which appears fatter at the
* end as if it had a head." [Ch. 107, p. 171] Here Burstein cites Salt,
* (1814) p. 93, for a similar description (q.v., below).
* DIODORUS SICULUS has the next earliest (c. 30 BC) known description of
* mirages. Oldfather's translation makes good sense, but he seems not to
* have appreciated the significance of this passage:
* "And both in this land and in Libya which lies beyond the Syrtis there
* takes place a marvellous thing. For at certain times, and especially when
* there is no wind, shapes are seen gathering in the sky which assume the
* forms of animals of every kind; and some of these remain fixed, but
* others begin to move, sometimes retreating before a man and at other times
* pursuing him, and in every case, since they are of monstrous size, they
* strike such as have never experienced them with wondrous dismay and
* terror. . . . although the natives, who have often met with such things,
* pay no attention to the phenomenon."
* "As for the movements which these shapes make in both directions, these
* . . . indicate no volition on their part, since it is impossible that
* voluntary flight or pursuit should reside in a soulless thing. And yet
* the living creatures are, unknown to themselves, responsible for this
* movement through the air; for, if they advance, they push by their violent
* motion the air which lies beneath them, and this is the reason why the
* image which has formed retreats before them and gives the impression of
* fleeing; whereas if the living creatures withdraw, they follow in the
* opposite direction, the cause having been reversed . . . . Consequently it
* has the appearance of pursuing men who withdraw before it, for the image
* is drawn to the empty space and rushes forward in a mass under the
* influence of the backward motion of the living creature. . . ."
* (from Book III.50 and .51)
* The need for calm air is repeated three times.
* QUINTUS CURTIUS RUFUS (History of Alexander, Book VII; c. 40 A.D.)
* The reference here is Curt. 7.5.4:
* "Then too a mist [caligo], aroused by the excessive warmth of the ground,
* obscures the light, and the aspect of the plain is not unlike that of a
* vast and deep sea."
* Many thanks to Prof. J.C.Yardley of the University of Ottawa for finding
* this passage!
* PLINY in the Loeb Library edition
* This passage from the "Natural History" is obviously not what Kircher
* had in mind: (from Book II, section LVIII)
* "In the third consulship of Marius the inhabitants of Ameria and Tuder
* saw the spectacle of heavenly armies advancing from the East and the West
* to meet in battle, those from the West being routed." (Vol. I, p. 285)
* William Whiston's translation of FLAVIUS JOSEPHUS (c. 78 A.D.)
* This translation has been widely reprinted, up to the present day.
* It is also available on the Perseus website at http://www.perseus.tufts.edu
* and at http://www.coel.wheaton.edu.
* The passage suggestive of a mirage is in Book VI, Chapter V, section 3
* of the "Wars of the Jews" (near paragraph 289). He enumerates several
* omens around the time of the feast of unleavened bread, almost a week
* before Passover:
* "Besides these, a few days after that feast, on the one-and-twentieth
* day of the month Artemisius, [Jyar,] a certain prodigious and incredible
* phenomenon appeared; I suppose the account of it would seem to be a fable,
* were it not related by those that saw it, and were not the events that
* followed it of so considerable a nature as to deserve such signals; for,
* before sun-setting, chariots and troops of soldiers in their armour were
* seen running about among the clouds, and surrounding of cities."
* This does indeed sound much like a superior mirage or Fata Morgana.
* Cf. l'Astronomie 7, 392-393 (1888).
* Very EARLY MIRAGE descriptions (1558) by Antonius de Ferrariis (1444-1517)
* or Antonio de Ferarri, also known as Antonio Galateo, Galateus Antonus, etc.
* after his place of birth (Galatone).
* Supposedly written in 1507-1509, but only published in 1558.
* Japygia is the old name; it became Apulia, and then Puglia.
* This passage is translated from the recent (2005) Latin/Italian version
* "La Iapygia" edited by Domenico Defilippis (Mario Congedo, Galatina):
* [18 10] (pp. 92/93): "In these swamps [near Nardò, on the Gulf of
* Taranto], as also in the fields of Manduria and Baleso and Copertino,
* certain apparitions are seen, which are called Mutationes or Mutata .
* The common people tell tales of I don't know what, vampires or witches or,
* as they say in Naples, janare [fairies], or as the Greeks say, nereids.
* It's amazing: this nonsense takes possession of the whole region and
* misleads the poor people. With no reliable authority, no reason, no
* demonstration, everyone believes in things they have not seen and are
* not true. And we oppose the testimony of the most ignorant people; we
* believe they are childish fantasies and old wives' tales, giving more
* trust to the ear than the eye. No one is an eye-witness, all accept
* what they have heard from others." (He then goes off to condemn popular
* beliefs in magic potions that can turn women into various animal forms
* at night; vampires; and other superstitions.) Then: "But let us return
* to those apparitions."
* [18 18] (pp. 96/97) "And sometimes you will see cities and castles and
* towers, and sheep and different colored cattle and images or specters of
* other things, where there is no city, no sheep, not even a thorn bush.
* I myself have sometimes had the pleasure of seeing these plays, this
* lusus naturae .
* "They do not last long, but change as the vapors in which they appear,
* from one place to another, from one form to another, whence perhaps they
* are called Mutata , or because the sky is changed from sunny to rain
* by these apparitions.
* "This happens in the morning, with calm air, beginning with a light
* breath of air (customarily) from the south. For as the strong south
* wind ceases, so at first it is gentlest and, as it is warm, it raises
* tenuous mists, which reflect images of cities, flocks, and other things
* like a mirror.
* "And like the vapors, those images are moved, as things are seen
* moving in mirrors that are moved and shaken. And because the things
* directly face the vapors, they are seen directly, just like a shadow
* which falls opposite a luminous body; those that are oblique and turned
* produce images, which we also see turned, as also in water we see the
* tops of mountains and roofs at the bottom. For when some things are
* closer to the surface of the water, such as a foundation, to our vision
* they would appear far off; the images of rooftops, which are farther
* from the water, come nearer to us, and therefore are seen below.
* "And so we find that in a closed building, with a little light coming
* through the slits, everything is seen reversed, such as the head of a man
* downward, feet above. For the lines of shadows do not proceed directly,
* but are transposed and intersect in the middle. This same thing happens
* in a concave mirror, so that the upper part of the mirror reflects the
* lower part of the thing seen, and the lower the upper.
* "These apparitions that I have mentioned often deceive the gaze of
* travelers, who, when they suppose they are near a city, are very far away.
* And there have been seen in this region images in the air of men riding
* horses and marching on foot. And so writers have recorded that armed
* troops arrayed for battle have been seen in the sky, and these (as I
* think) images were of those far away from that place in which the images
* were seen, and could not be seen [directly].
* "And thus we don't see a coin in the bottom of a vessel, but if the
* same vessel is filled with water, we see not the coin, but its image at
* the surface of the water, which is touching the air. For the surface
* of the water is analogous to the surface of a mirror, but whether these
* images may belong to the mirror, or the outer surface of the air, is
* another question." And he cites Aristotle. [18 24] (pp. 98/99)
* "And as these figures are of mists, they give likenesses of ships
* and sails, where there is no fleet. These apparitions deceive not only
* the inexperienced. It is not long since the whole coast, from Hydrunto
* [Otranto] to Monte Gargano, at one and the same hour before sunrise,
* saw a fleet sailing from the east. It was thought to have been that
* of the Turks, and before that specter or delusion was revealed by
* the lightening dawn, various letters were composed here and there and
* messengers were sent concerning the approach of this imposing fleet."
* [NOTE: a Turkish fleet had just sacked Otranto in 1480, a few years
* before this was written; he assisted in its liberation.] He continues:
* "Perhaps in this way or another of which we shall speak, as I believe,
* someone (I don't know who) from Lilibeo [Marsala] saw a fleet leaving
* the port of Carthage."
* The 1558 edition was recently republished by Forni.
* Thomas Facellus (Tommaso Fazello) briefly mentions mirages
* Cited by Minasi; and, following him, P&E (p.170). They give the citation
* as Dec. 1, lib. II, cap. 1.
* The title page is imaged at
* http://edit16.iccu.sbn.it/scripts/iccu_ext.dll?fn=60&i=18660#1
* The passage appears on p. 42 of the edition at the HathiTrust website:
* http://babel.hathitrust.org/cgi/pt?id=ucm.5325123864;view=1up;seq=64
* "Sed & alia in hoc freto res mira frequenter apparet. Nam mitigato
* turbine, quietoq; aere, circa diei exortum illucescente aurora, variæ
* animantium, hominumq; formæ in aere crebrò cernuntur. Quarum aliæ
* penitus immotæ sunt, pleræq; vel in aere discurtunt,vel inter se
* dimicant, quousq; Sole incalescente, è conspectu eripiantur:Harum
* Polycletus lib. de Reb.sicul.& Aristoteles lib.de mirab.aud. memi-
* nerunt, quarum etiam haec à Philosophis redditur ratio : quod cùm in
* ijs regionibus,eo præsertim tempore,quo haec cernuntur,ventos, aut
* omnino non spirare,aut exiles admodum,& aerem quietum esse constet,
* in ipso aere denso atq; obtuso diuersæ animantium effigiantur species,
* quibus formam aer, quem tenues & leues quandoq; mouent auræ, variam
* præbet (quemadmodum æstate in nubibus fieri videmus) qua tandem sol
* incalescens in ventos resoluit."
* (Panormi = Palermo)
* MARC'ANTONIO POLITI -- the first to use the term "Fata Morgana"
* Briefly quoted by Costanzo (1903), p. 106.
* ATHANASIUS KIRCHER (1646)
* This is the work cited by Castberg. The discussion of mirages and other
* meteorological phenomena is in Liber decimus, Pars secunda, pp. 800-804.
* "Liber decimus. Magia Lucis & Vmbrae . . . Pars Secunda. Magia
* Parastatica, siue de repræsentationibus rerum prodigiosis; per Lucem &
* Vmbram . . . Caput 1 De Repræsentationibus aeris: mentions "in libris
* Machabeorum" (p. 800)
* "Parastatis I Naturae, siue de Morgana Rheginorum in Freto Mamertino,
* siue Siculo" -- here, on p. 801, we have "Vocant autem Rhegini hoc
* spectaculum Morganam," followed by Ignatio Angelucci's letter to Leone
* Sanzio, describing a Fata Morgana display on Aug. 15, 1643. [Angelucci's
* letter is also quoted by Capozzo (1840).] Note that Angelucci says he
* saw his F.M. "La mattina dell' Assontione della Beatissima Vergine,"
* and does not give a calendar date. This led to some confusion later.
* [His letter is "Di Reggio", dated the 22. of August.]
* p.802 mentions "Scipio Mazzellus, Regni Neapolitani; fol. 117".
* p. 803: "Refert Pomponius Mela, in Mauritania retro Atlantem regiones
* esse, in quibus circa meridiem inter montes varia spectra comparere
* soleant, quae gestus hominu' in omnibus æmulentur: videas ibi choreas,
* audias tubarum, tympanorumque strepitus. Refert quoque Plinius, intra
* Imaum in Scythia regionem esse, in qua quot-annis in vasta planitie
* appareant varia spectacula rerum sub figura hominum animaliumque, &
* instar exercitus; quibus viatores non rarò in auia, & deuia
* præcipitia ac denique in manifestam perniciem deducantur. Ad
* flumen Oby refert Haithon Armenus regionem esse, ad quam nullus adhuc
* penetrauerit, ob formidabilium, spectrorum, quae ex illa fluminis parte
* comparent, multitudinem."
* The reference to Pomponius Mela seems to be nonsense; there is nothing
* like this in his book. I have not found the Pliny passage, either.
* (For more evidence of Kircher's unreliability, see Lohne's 1959 paper
* on Harriot.)
* NOTE: a revised edition of this was printed in Amsterdam in 1671.
* Due to the removal of some material, Angelucci's letter appears in
* it on pp. 704-705 rather than p. 801. Many later commentators have
* referred to that edition instead of the original; see the entries for
* Giardina (1758), Minasi (1773), Boccara (1902), etc.
* Placido Reina quotes Politi, Facellus, etc.
* The Fata Morgana begins on p. 64, and "similar things" on p. 65.
* Politi is cited on pp. 65 and 67. See Costanzo's (1903) discussion
* at his p. 107; esp. the footnotes there.
* Available at Google Books.
* EDME MARIOTTE's short monograph on the optical level and its use
* Mainly of historical interest; first, because of Forel's use of his
* technique for the easy measurement of absolute altitudes; and second,
* for his discussion of temporal VARIATIONS in TERRESTRIAL REFRACTION.
* That discussion is mainly on pp.19-20; but it arises from the calculations
* on p. 18, where the diameter of the Earth is taken to be 40 million feet.
* His concern there is that the height of a distant object on the tangent
* plane at the observer is above the observer's height. But, he says,
* "Il est encore necessaire de sçavoir que dans les grandes distances
* un mesme objet paroist de differentes hauteurs par les refractions,&
* change presq'uà toutes les heures du jour,c'est à dire que s'il est le
* matin au lever du Soleil en une mesme ligne droite avec un objet prochain,
* il paroistra plus bas une heure aprés le Soleil levé, & encore plus bas
* quand l'air sera plus échauffé,& plus les matinées seront fraisches &
* l'air serain, plus les objets éloignez paroistront élevez, & quelques
* fois les objets qui sont à une distance d'environ 500 pas paroistront
* s'élever, & en mesme tems ceux qui sont beaucoup éloignez s'abaisser,
* principalement lors que le Soleil luit, comme on a reconnu par plusieurs
* observations faites en divers lieux & diverses saisons,mesme à l'égard
* des objets moins élevez que observateur,ou d'égale hauteur ; & on a
* remarqué quelquefois, qu'un objet qui avoir paru à midy plus bas que
* le plan de niveau, paroissoit le lendemain matin plus de 20 pieds plus
* haut que ce plan, en une distance d'environ 2 lieuës, d'où il s'ensuit
* que le plus seur moien pour bien niveller de grandes distances, est
* de le faire à plusieurs fois: . . . " whereupon he gives an example,
* referring to Figs. 12 and 13 at the end of the volume. This discussion
* of refraction continues on to p. 22.
* He mentions refraction again on p. 27 and p. 31, where he remarks that
* the refractions are "irregular" when the Sun shines; on the next page,
* he says that reliable measurements can be made when the sky is covered
* with clouds. So, although he give no systematic measurements, it's clear
* from the numerous examples that he was familiar with the variations and
* regularities in terrestrial refraction.
* A good PDF of this work is available at
*
* https://gallica.bnf.fr/ark:/12148/bpt6k6514207h?rk=21459;2
*
* which scrupulously puts "[sic]" after Mariotte's odd title spelling.
* However, BNF's OCR frequently renders the long-s as "f".
* HEVELIUS (1674)
*
* "Under the Sun, towards the Horizon, there hung a somewhat dilute small
* Cloud, beneath which there appear'd a Mock-Sun, of the same bigness (to
* sense) with the true Sun, and under the same Vertical, of a somewhat red
* colour. Soon after, the true Sun more and more descending to the Horizon,
* towards the said Cloud (as may be seen Fig. 4) the spurious Sun beneath it
* grew clearer and clearer, so as that the reddish colour in that apparent
* Solar disk vanish'd, and put on the genuine Solar light, and that the more,
* the less the genuine disk of the Sun was distant from the false Sun: Till
* at length the upper true Sun passed into the lower counterfeit one, and so
* remained alone; as appears Fig. 5.
*
* "Which Appearance being unusual, and having never been seen by me, I took
* the freedom of imparting it unto you, especially since here the Mock-Sun
* was not found at the side of the true Sun, as 'tis wont to be in all
* Parhelia's seen by me, but perpendicularly under it; not to mention the
* Colour, so different from that which is usual in Mock-Suns; nor the great
* length of the Tayl, cast up by the genuine Sun, and of a far more vivid and
* splendid light, than Parhelia's use to exhibit. Upon this appearance there
* soon follow'd here an exceedingly intense and bitter Frost, whereby the
* whole Sinus Puzensis was frozen up from this Town of Dantzick, as far as
* Hela in the Baltick Sea, which lasted unto the 25th of March; and the Bay
* was frozen so hard, that with great safety people run out into it with Sleds
* and Horses, for several of our Miles. Whether the recited Phaenomenon have
* had any influence for this extream Cold, I know not, but leave it for
* Astrologers to examine. Whether the like Appearance have ever been
* observ'd in England, I should be glad to be informed of."
* Translation of Pierre Perrault's "De l'origine des fontaines" (1674)
* and so filed here instead of at 1967. Orig. pub. by Pierre le Petit,
* Paris (1674).
* "Moreover the astronomers are certain that humid vapors either of the
* Sea, or of the Earth, cause much refraction, and cause many things to be
* seen otherwise than they really are: as when the Sun or the Moon
* sometimes appear to be oval, when they rise or set; . . . ." He then
* mentions their appearance "on the horizon before they have risen up to
* it," and offers the coin in a basin filled with water as an illustrative
* demonstration. In section (111): "I have made another more elaborate
* experiment, which shows that the vapors of the earth, according to their
* arrangement, can make distant objects appear now higher now lower, as if
* these objects were really raised or lowered. . . . I took as an object a
* pavilion about thirty-two feet in height half a league away, which I
* observed with a spyglass attached to and rendered motionless on a window
* sill in a large wall; and having aimed it at the top of this pavilion,
* which was on the thread of my spyglass, and level with it; I found that
* from two o'clock in the afternoon, when I began my observation, until
* night, the top of this roof had seemed to rise by eight feet, so that
* more than half this roof was above the thread of my spyglass." [He goes
* on to relate several days' observations, during which the building rose
* and fell by more than its full height.] "I have repeated the same
* experiment at another time when there was a great drought, which had
* lasted more than six weeks without respite, and I have always seen the
* same thing . . . the rising of my object happened regularly from noon to
* evening, and the lowering from morning to noon. . . ." (pp. 58-60)
* The translator suggests (p.182) that "this may be the earliest study"
* of such DIURNAL VARIATIONS in atmospheric refraction. N.B.: "half a
* league" is about 2 km; the building was about 10 m high; so the variations
* cover a range of about 1/200 radian or some 16' of arc.
* Note that the book is dedicated to Christiaan Huygens, who picked up
* the refraction variations in his "Traité de la Lumière" (1690).
* Jean Picard's inferior mirage seen at Tycho's old observatory
* "Je mets à part les changemens qui arrivent à cause des Réfractions,
* & je diray seulement une chose que nous remarquasimes en faisant
* les Observations que nous venons de rapporter. Il y a proche de
* Copenhague une Isle appellée Amac, dont le terrain qui est assez bas
* nous estoit caché par la rondeur de la mer, en sorte néanmoins que nous
* y découvrions les sommets de quelque arbres. Or venant à pointer le
* quart de cercle vers l'endroit où ces arbres me paroissoient tranchez,
* j'estois asseûré que mon Rayon visuel recontroit l'extrémité visible
* de la surface de la mer, & néanmoins on auroit dit que ces arbres
* estoient dans le Ciel, & que la mer estoit terminée bien au dec,à de
* l'endroit où nous sçavions qu'il falloit pointer. La raison de cette
* apparence, est que la mer estoit fort unie, faisoit à nostre égard si
* exactement l'effet du miroir, que nous la confondions avec le Ciel."
* (Probably this is the island of Amager, where Copenhagen's airport is
* today -- about 30 km south of Hven.)
* This memoir contains much else of interest: an eyewitness account of
* Tycho's original records, and his celestial globe: "nonobstant toutes
* les fortunes qu'il a couruës, ayant esté premiérment transporté de
* Dannemarck en Boheme, puis en Silesie, & enfin rapporté in Dannemarck,
* il est en dans son entier comme s'il venoit d'estre fait : son diametre
* est précisément de quatre pieds, sept pouces & une ligne, mesure de
* Paris." (p. 4)
* Picard also enjoyed the collaboration of Erasmus Bartholin, who
* accompanied him to Uraniburg, as well as "un jeune Danois nommé
* Olaüs Romer, que M. Bartholin m'avoit fait connoitre, & qui estant
* ensuite venu en France avec moy, fut de l'Académie des Sciences, où
* il a donné plusieurs marques de son rare génie & se son esprit." (p.5)
* He found Tycho's observatory completely destroyed, and the remains
* scattered. Placing his instruments on the surviving foundations of
* Tycho's observatory, he determined its location: the ground was about
* 27 toises [52.6 m] above the sea (p. 7); a latitude of 55° 54' 15''
* (p. 25); and a longitude 42m 10s or 10° 32' 30'' E of Paris. (p.28)
* His stay in November 1671 was so difficult that "enfin le travail des
* veilles durant un froid auquel je n'estois pas accoustumé, & l'air de
* la Mer Baltique me causerent une langueur qui renoit un peu de scorbut,
* & qui me fit à la fin résoudre à quitter cette solitude, pour me
* retirer dans un lieu de secours avant que les glaces me fermassent
* le passage." (p.12) (He notes on the next page that scurvy was common
* "aux personnes sedentaires".) But he sent Romer back in the spring,
* to finish the observations.
* Then, on p. 18, we find he has noticed (but not understood) the
* effects of annual aberration, "que j'observe depuis dix ans." Not bad!
* Thanks to Sharron Huling for providing a photocopy!
*
* Earliest mention seems to be in JOHN WINTHROP's Journal
* In the entries for 1648, we find on p. 346:
* ``There appeared over the harbor at New Haven, in the evening, the
* form of the keel of a ship with three masts, to which were suddenly
* added all the tackling and sails, and presently after, upon the top of
* the poop, a man standing with one hand akimbo under his left side, and
* in his right hand a sword stretched out toward the sea. Then from the
* side of the ship which was toward the town arose a great smoke, which
* covered all the ship, and in that smoke she vanished away; but some saw
* her keel sink into the water. This was seen by many, men and women, and
* it continued about a quarter of an hour.''
* [cf. the FOG FILE for the "smoke".]
* A footnote says: "The spectral ship of New Haven, the tradition of
* which was taken up and characteristically developed by Cotton Mather, is
* one of the most weird of New England legends, and has become familiar to
* the later generations."
* Leonard Bacon's account, largely taken from Winthrop's
* Here, after describing the loss of the ship sent out in January, 1646,
* he says: ``Two years and five months from the sailing of that ship, in
* an afternoon in June, after a thunder storm, not far from sunset, there
* appeared over the harbor of New Haven, the form of the keel of a ship
* with three masts, to which were suddenly added all the tackling and
* sails; and presently after, upon the highest point of the deck, a man
* standing with one hand leaning against his left side, and in his right
* hand a sword pointing towards the sea. The phenomenon continued about a
* quarter of an hour, and was seen by a crowd of wondering witnesses, --
* till at last, from the farther side of the ship, there arose a great
* smoke, which covered all the ship; and in that smoke she vanished
* away.''
* A footnote calls it an "atmospheric phenomenon"; mirages were well known
* by 1839, when this was published.
* COTTON MATHER's belated third-hand account
* This quotes a secondary source -- a letter from James Pierpont, who
* was pastor of the First Congregational Church of New Haven from 1685 to
* 1714, and therefore could not himself have been a witness. His
* second-hand account, reported to Mather in a letter, has the year of the
* original sailing wrong; and the details are by now vastly exaggerated by
* the fading memories of the (unnamed) witnesses:
* "In Compliance with your Desires, I now give you the Relation of
* that Apparition of a Ship in the Air , which I have received from the
* most Credible, Judicious and Curious Surviving Observers of it.
* "In the Year 1647, besides much other Lading, a far more Rich
* Treasure of Passengers, (Five or Six of which were Persons of chief Note
* and Worth in New-Haven ) put themselves on Board a New Ship , built at
* Rhode-Island , of about 150 Tuns; but so walty, that the Master,
* (Lamberton ) often said she would prove their Grave. In the Month of
* January , cutting their way thro' much Ice, . . . they set Sail. Mr.
* Davenport in Prayer with an observable Emphasis used these Words,
* Lord, if it be thy pleasure to bury these our Friends in the bottom
* of the Sea, they are thine; save them! The Spring following no
* Tidings of these Friends arrived with the Ships from England:
* New-Haven's Heart began to fail her: This put the Godly People on
* much Prayer , both Publick and Private, That the Lord would (if it was
* his Pleasure) let them hear what he had done with their dear Friends,
* and prepare them with a suitable Submission to his Holy Will. In
* June next ensuing, a great Thunder-storm arose out of the
* North-West : after which, (the Hemisphere being serene) about an Hour
* before Sunset a SHIP of like dimensions with the aforesaid, with her
* Canvas and Colours abroad (tho' the Wind Northernly) appeared in the Air
* coming up from our Harbour's Mouth, which lyes Southward from the Town,
* seemingly with her Sails filled under a fresh Gale, holding her Course
* North, and continuing under Observation, Sailing against the Wind for
* the space of half an Hour. Many were drawn to behold this great Work
* of God; yea, the very Children cry'd out, There's a Brave Ship! At
* length, crouding up as far as there is usually Water sufficient for
* such a Vessel, and so near some of the Spectators, as that they imagined
* a Man might hurl a Stone on Board her, her Maintop seem'd to be blown
* off, but left hanging in the Shrouds; then her Missen-top ; then all
* her Masting seemed blown away by the Board: Quickly after the Hull
* brought unto a Careen , she overset, and so vanished into a smoaky
* Cloud, which in some time dissipated, leaving, as everywhere else, a
* clear Air."
* To which, Mather adds: "Reader, There being yet living so many
* Credible Gentlemen, that were Eye-Witnesses of this Wonderful thing, I
* venture to Publish it for a thing as undoubted , as 'tis wonderful ."
* (Mather's book originally appeared in 1702.)
* Mather's account enshrined by the poet Longfellow
* (Thanks to Penny Porter for pointing this out!)
* A brief modern mention by Isabel MacBeath Calder
* On pp. 160-161 there is a description of "the attempt to build
* transatlantic vessels on Long Island Sound." The launch of the first
* ship, ``ill built and very `walt-sided,' '' in January, 1646, is
* described. On p. 161: ``After the lapse of many months a mirage of
* the ship was said to have appeared over the harbor at New Haven, but the
* vessel itself neither reached its destination nor returned to its port
* of departure.''
* Numerous citations are offered: New Haven Colonial Records,
* 1638-1649 , pp. 147, 283, 329-333, and ``Roxbury Land and Church
* Records,'' Record Commissioners of the City of Boston, Sixth Report ,
* p. 190 are not available to me; the others are cited here.
* (see also "Crocker Land" and "W.H.Lehn" files)
*
* ORIGIN of the word "MIRAGE":
*
* The 1687 French dictionary that defines "La terre se mire":
* "Cela se dit lors que les vapeurs font paroître les terres comme si
* elles étoient élevées sur de basses nuées." (p. 352)
* by Nicolas Desroches
* At
* https://www.livres-anciens-et-modernes.fr/accueil/300-nicolas-desroches-dictionnaire-des-termes-propres-de-marine-1687.html
* we read that "Nicolas Desroches fut lieutenant de vaisseau en 1671 et
* capitaine en 1693."
* Thanks to Eric Frappa for finding this reference!
* available at Google Books;
* https://books.google.fr/books?id=HcoeqZRLeKsC&printsec=frontcover&hl=fr#v=onepage&q&f=false
*
* ORIGIN of the word "MIRAGE":
* The old French/Dutch dictionary by Nicolas Aubin
* Defines "La terre se mire" on p. 565. The wording given there is almost
* identical to that used by Le Gentil (1789), who says he got it from the
* 1736 edition; there was also a 1742 (3rd) edition. The first edition was
* this one, in 1702. Its definition seems taken from the 1687 dictionary by
* Desroches, with minor changes.
* Thanks to Eric Frappa for finding this reference!
* available at Google Books
* Modern comments on the origin of "mirage"
* Jacques Gronier, Attaché to the French Consulate at Malta, responds to
* Richard Beck's article (16 March), supplying good English translations:
* "In the report of Monge, entitled `On the optical phenomenon known
* under the name of mirage', and published in the Reports of the
* Institute of Cairo, one reads textually the following: 'It [the
* phenomenon] is well known to sailors, who frequently observe it at sea
* and who have given it the name of mirage. In truth, the cause which
* produces the mirage at sea may well be different from that which produces
* it on land; but the effect being absolutely the same in the two cases,
* I did not believe it necessary to employ a new word.'
* "It is plainly apparent from this that the term had not been
* invented by Monge and that it was in previous use. Some years later,
* the physicist Biot, also a member of the Academy of Sciences, gave the
* theory of the phenomenon. His report, read on 8 August, 1808, began thus:
* "'Physicists and astronomers have for a long time observed that
* objects which are seen very near to the horizon sometimes transmit to
* the observer two images, one upright, the other inverted. No one is
* better placed than sailors to observe this phenomenon and it is well
* known to them: they designate it by a very expressive name in calling
* it the mirage, because indeed it then seems that objects are reflected
* as in a mirror.
* 'In the volume of the History of the Royal Academy of Sciences, for the
* year 1753, printed in 1757, one finds on page 253, in the account made to
* the Academy by M. de Chabert, Lieutenant-Commander, of the voyage which he
* made by order of the King, in 1750 and 1751, to rectify the maps of Acadia
* and of Newfoundland, the following paragraph:
* 'While M. de Chabert was occupied in drawing up the plans of which we
* spoke above, he was often stopped by a singular phenomenon, that is called
* a mirage: it is an apparent change in the aspect of the shores a little
* way away, which the inhabitants attribute to the reflection of the sky
* which, mirrored in the water, makes the shore appear lifted in the air
* and which M. de Chabert believes, with great probability, is caused by
* the irregularities of refraction often undergone by terrestrial objects.'
* "These extracts open the way to new researches. In effect,
* this phenomenon of refraction, although it has often given place to
* interpretations scientifically incorrect, seems to have been observed,
* from very distant times, by the navigators who have certainly not omitted
* to report it.
* "It is probable that in the archives of the Musee de la Marine in
* Paris and, in particular, in the old 'log books' which are preserved
* there, the oldest references to the word mirage may be discovered."
* MIRAGE OBSERVATIONS
*
* EARLIEST LOOMING? (Maraldi, cited by de Chabert, 1755); and indirectly
* referred to by Biot (1805).
* Giacomo Filippo Maraldi -- by now, Jacques Philippe Maraldi -- was
* the nephew of Giovanni Domenico (or Jean Dominique) Cassini.
* This is indeed mostly about determining the coordinates of several
* places on and near Corsica; but our interest is in the introductory
* remarks:
* "On voit des Côtes de Genes & de Provence les Montagnes de l’Isle de
* Corse, qui paroissent quelquefois élevées au-dessus de l'horison
* sensible , comme si elles sortoient de l’eau , & qui disparoissent
* en d'autre temps par un Ciel également pur & serein , comme si elles
* s’étoient plongées dans la Mer.
* "Il y a des saisons plus propres pour découvrir cette Isle des
* côtes de Genes, qui sont le Printemps & l’Automne. On la voit aussi
* quelquefois l‘Hiver; & les heures du jour qu’elle paroît , sont le
* matin au lever du Soleil , & un peu avant , ou bien le soir , un peu après
* son coucher. On la voit aussi quelquefois dans le même jour le matin &
* le soir , & elle se perd entierement de vûe le reste de la journée.
* "Toutes ces apparences se font sur les Côtes de Genes, par rapport
* à un Observateur qui esi toujours dans la même situation & à la même
* hauteur sur la surface de la Mer.
* "On pourroit attribuer cette diverfité d’apparence à la variation
* qui arrive à la hauteur des eaux de la Mer , qui sont entre Genes &
* la Corse; car quoique , suivant l’opinion commune des Philofophes , la
* surface de la Mer soit sphérique, il faut avouer que cette figure est
* sujette à des variations qui lui arrivent par des causes extérieures ,
* dont les principales font les courants, aussi-bien que le flux &
* le reflux, & qui font varier confiderablement la hauteur de l’eau
* dans le même lieu.
* "Suivant cette idée, on pourroit dire que l’Isle se découvre
* lorsque la mer est basse : au contraire la Corse se doit perdre de vûe
* du même lieu , lorsque la Mer s’éleve & se place entre deux.
* "Mais cette explication n’est pas la plus naturelle , & il est
* plus vrai-semblable d‘attribuer ces apparences aux réfractions ,
* & de supposer que les rayons visuels qui viennent de cette Isle à
* l‘Observateur qui est sur les Côtes opposées, se rompent diversement
* dans les vapeurs qui sont entre deux; ainsi, lorsque les vapeurs sont
* plus denses ou en plus grande quantité, les réfractions des rayons
* sont plus grandes, & font paroître l'Isle au-dessus de la Mer, &
* lorsque les vapeurs sont moins denses , ou qu’il y en a une moindre
* quantité répandue dans l’air , les réfractions des rayons étant
* plus petites , l’Isle reste cachée par la Mer.
* "Cette explication paroît d’autant plus vrai-femblable , qu’elle
* est également propre à rendre raison des apparences semblables qui
* arrivent au milieu des Terres ; car on a remarqué depuis longtemps à
* l’Observatoire, des maisons éloignées de fept ou huit lieues ves [sic]
* le Nord , qui étant cachées pendant le jour par d’autres maisons qui
* sont plus proches, & placées seulement à une demi-lieue de distance,
* paroissent souvent le matin au lever du Soleil, élevées au-dessus de
* celles qui sont proches. Ces maisons éloignées s’abaissent ensuite
* peu à peu , jusqu'à ce qu’elles se cachent entierement pendant le
* jour par les Maisons qui sont proches. Cette apparence est donc une
* preuve évidente , que les rayons se courbent dans l’air différemment ,
* suivant les différentes densités de l’air, ou suivant la différente
* quantité de vapeurs par où ces rayons passent. Cela prouve aussi que
* le matin les vapeurs sont plus denses , ou bien qu’il y en a dans
* l’air une plus grande quantité que le reste du jour. L’apparence
* que fait la Corse , vûe de Genes , étant semblable à celle que nous
* venons de rapporter , on en peut rendre raison de la même maniere.
* "M. le Marquis Saluago a observé très souvent ces apparences que
* fait l’Isle de Corse , d’une Maison qu’il a proche de Genes vers
* le Nord . . . ." -- and here he takes up the details of the surveying,
* remarking that the height of that observatory was 50 toises (about
* 97 meters) above sea level.
* On p. 351, he says that this height, together with the size of the
* Earth's radius determined by the Academy, predicts a geometrical dip
* of the horizon of 18 minutes; but the observed dip is only 16' 0" to
* 17' 30", which is smaller. This difference should be attributed to the
* refraction of the rays between the horizon and the quadrant.
* The first paragraph describes an appearance corresponding to inferior
* mirages. Subsequent descriptions of variations in terrestrial refraction
* correspond to looming and sinking; and the diurnal variations are a more
* detailed description of those reported in Perrault's "De l'origine des
* fontaines" (1674).
* The best visibility of the distant mountains (over 260 km from Genoa)
* just before sunrise and just after sunset is due to the illumination
* of the intervening lower atmosphere by the Sun, when it is above the
* observer's horizon. When the Sun is just below the horizon, the distant
* peaks are silhouetted against the brightly illuminated upper troposphere.
* The apparent motion of distant houses relative to nearer ones that are
* visible at daybreak and sink out of sight in the middle of the day, is
* direct observation of changes in the apparent curvature of the Earth's
* surface, due to changes in lapse rate in the boundary layer.
* In short, lots of good observations of DIURNAL VARIATIONS in refraction
* that are understandable today, but were remarkably mysterious four
* centuries ago.
* Cited by de Chabert (1753), and mentioned by Le Gentil (1789).
* [cf. Perrault (1674); Delambre (1814); Williams, Mudge, and Dalby (1795);
* Atkinson (1826); etc.]
* Dated 28. Mars, 1722.
* Available at BHL., and at Gallica:
*
* https://gallica.bnf.fr/ark:/12148/bpt6k3524k/f1.item
*
* EARLIEST LOOMING? (THOMAS SHAW, D.D.; cited by T.Jefferson, 1787)
* On the title page, Shaw is merely "Fellow of Queen's-College in
* Oxford, and F.R.S."; but on the title page of the 1746 Supplement
* (bound together with the original in the copy I managed to borrow), he
* is also "Principal of St. Edmund Hall, and Regius Professor of Greek,
* in the University of OXFORD."
* In Chap. III, p. 358, "Physical Observations &c. or an Essay towards
* the Natural History of Syria, Phœnice, and the Holy Land," we find
* the passage cited by Jefferson:
* "We are likewise to observe further with Regard to these strong
* Easterly Winds, that Vessels or any Objects which are seen, at a
* Distance, appear to be vastly magnified, or loom , according to the
* Mariners expression." [N.B.: p. 362 -- not 302!]
* But more surprising is the passage in Chap. IV, "Physical Observations
* &c. or an Essay towards the Natural History of Arabia Petræa" (p.377):
* "Where any Part of these Deserts is sandy and level, the Horizon
* is as fit for astronomical Observations as the Sea, and appears,
* at a small Distance, to be no less a Collection of Water1. It was
* likewise equally surprizing, to observe, in what an extraordinary Manner
* every Object appeared to be magnifyed within it; insomuch that a Shrub
* seemed as big as a Tree, and a Flock of Achbobbas might be mistaken
* for a Caravan of Camels. This seeming Collection of Water, always
* advances, about a Quarter of a Mile before us, whilst the intermediate
* Space appears to be in one continued Glow, occasioned by the quivering
* undulating Motion of that quick Succession of Vapours and Exhalations,
* which are extracted by the powerful Influence of the Sun." [pp.378-379]
* P.378 footnote at "Water": "The like Observation is taken notice of
* by Diodorus Siculus in his Account of Africa, l. 3, p. 128" -- and the
* passage is quoted in the original Greek.
* This theme is continued in the Supplement, which is dated 1746;
* pp. vi and vii of its Preface contain a Note to p. 378:
* "To Note 1. add this learned Remark, and corroborating Proof,
* from Dr. Hyde ; who in his Annotations on Peritsol's Itinerary,
* p. 15 deduces the Name of Barca and Libya , from this Phænomenon .
* [Quotation italicized in the original:] Et quidem (ut denominationis
* causam & rationem exquiramus) dictum nomen [Arabic transcription]
* [Hebrew transcription] splendorem seu splendentem regionem notat,
* cum ea regio radiis solaribus tam copiose collustretur, ut reflexum
* ab arenis lumen adeo intense fulgens, a longinquo spectantibus (ad
* instar Corporis Solaris) aquarum speciem referat; & hicce arenarum
* splendor & radiatio Arabibus dicitur [Arabic] serâb i.e. aquæ
* superficies , seu superficialis aquarum species . --- Hinc etiam
* nominis [Greek] ratio peti potest - cum [Hebrew] contractum sit pro
* [more Hebrew], a [Hebrew] flamma - a fulvescentibus arenis ardore
* pene inflammatis."
* The full title of the Supplement is: A Supplement to a Book Entituled
* Travels, or Observations, &c. wherein Some Objections, lately made
* against it, are fully considered and answered: with several additional
* Remarks and Dissertations."
* The long s is used throughout; curious spellings such as "antient"
* are regularly used. Note the capitalized Nouns as well. . . .
* Note that Jefferson's editor (William Peden) appears to have mis-read
* the page reference from TJ's MS note: it is 362, not 302.
* EARLY LOOMING (cited by Cranz)
* "Fuer einen gewissen Vorboten eines bevorstehenden großen Sturmes in
* der See, oder auch in den unteren Gegenden des Jenisei wird dieses
* gehalten, wenn Inseln oder jaehe Felsen, die bey stillem Wetter niedrig
* aussehen, groeßer als gewoehnlich zu seyn scheinen."
* NOTE: the umlauts are written as a small letter e over each vowel.
* FIRST appearance of "MIRAGE" in print? (1753)
* Chabert's full account: the 'mirage' explanation is on p. 136.
* It is taken from his journal entry for 23 Juin 1751, when he was
* observing:near Cape Sable (the southern tip of Nova Scotia).
* "Je m'occupai pendant trois jours à la suite des opérations de la
* carte, commencées le 23 à la pointe du cap, & dans lesquelles je fus
* souvent arrêté par l'effet du mirage . C'est ainsi que plusieurs
* marins appellent un changement qui, quelquefois se fait en apparence
* dans l'aspect des côtes un peu éloignées, parce qu'ils l'attribuent
* à la réflexion du ciel, qui se peignant dans la mer au dessous de la
* côte, fait paroitre cette côte comme élevée dans le ciel. Ce même
* phénomène semble bien plûtôt venir de la grande réfraction à
* laquelle sont sujets les objets vûs à travers des vapeurs fort denses :
* cette densité n'étant point égale dans toute l'étendue d'une côte,
* les rayons diversement brisés la rendent méconnoissable. C'est la
* raison qu'en a donné feu M. Maraldi, dans les Mémoires de l'Académie
* de l'année 1722."
* The remark about the mirage stopping his surveying operation is
* very similar to the report by Boscovich & Maire (1755). Notice that in
* this version, the word comes from "several sailors"; in the abstract in
* "Hist.", the word is attributed to "the inhabitants" of the coast.
* This page is cited in the Index as a peculiar entry: "Mirage. Idée
* de cette illusion d'optique, 136."
* Note that Bouguer was one of the referees who approved this work for
* publication (pp.i and iv).
* The first page has a nice woodcut showing the surveyors with all their
* equipment, observing the Moon with their quadrant to determine the time.
* This was reprinted in 1966; copies of the original sell for over $1000.
* Available at Google Books. The example digitized by Google bears the
* stamps of the National Library of Naples.
* https://www.google.com/books/edition/Voyage_fait_par_ordre_du_roi_en_1750_et/lJzIEAa6cuwC?hl=en&gbpv=1&dq=mirage&pg=PA136&printsec=frontcover
* ROGER BOSCOVICH sees some EARLY INFERIOR MIRAGEs, and looming
* The mirage observations are in paragraphs 173 and 174.
* These seem to be the first circumstantial descriptions of mirages.
* To understand para.173, some explanation is required:
* They were starting the triangulation at the mouth of the Ausa river
* (near Rimini) in July, 1752, using a baseline measured along the shore
* some months previously. The "sign" used at each end of the baseline
* was three posts stuck in the ground, with a whitewashed sheet wrapped
* around their upper ends as a target to sight on. The angles were
* measured with a portable quadrant. Now read on:
* "As soon as the signs were erected, we went there to take angles, and
* at least at the Ausa's mouth everything went quite well. But as soon as
* we reached the other end, a quite wonderful phenomenon appeared to us.
* The second sign is separated from the first by only eight thousand
* paces [about 12 km in modern units], and more than 20 spans [1.5m] high;
* we had seen it quite plainly first thing in the morning. But when we
* arrived at this second end a little after noon, allowing for the
* curvature of the sea (for a straight line about eight miles long joining
* the two heads would pass well above the sea) could only hide much less
* of its height in this interval, for it was raised 20 spans; yet now with
* the telescope pointed to a place we knew very well, corresponding to
* a place at the port of Rimini next to the building where those who are
* accustomed to be cared for are liberated to health from a fear of
* pestilence [i.e., the quarantine hospital], nothing appeared at all.
* Really only the highest part of the buildings was seen, and even that
* wonderfully contracted, as also the sails of ships in the harbor, many
* of which were spread and appeared completely distorted. Struck by the
* novelty of the thing, I brought a ladder to the post of the sign, and
* having climbed up a few steps, with the telescope pointed to the place,
* I saw the webbing of the sign at Ausa, not emerging from the waters
* gradually, though it was broad, but all at once, at first as through a
* haze, then much clearer, and at first the thinnest line, then as I
* climbed higher it enlarged more, until it returned to its own form,
* as did that building I have mentioned, and the sails of the ships. Both
* Maire and I have watched this phenomenon quite astonished, again and
* again, now raised up higher by the steps, now lowering the eye; but toward
* sunset we had to return to our angles, which we could take even at this
* sign, by moving a wagon, which fortunately was there, to the very place of
* observation, and raising up the quadrant in it, we saw the sign quite
* plainly, and we completed our observations."
* [This is a fine description of an inferior mirage; the "all at once"
* business being a particularly nice touch; cf. Hardcastle (1905).]
* In para.174, he remarks that he has often seen "the ends of
* promontories, or the points of islands, as if raised in the air," and
* that this is a phenomenon of the same kind. He has noticed that this
* occurs only when the line of sight grazes the surface of the sea, and
* that it vanishes if viewed more obliquely from a higher location.
* In section 175, he mentions an instance of variable looming, which he
* correctly attributes to an "inequality" of the horizontal refraction.
* Thanks to Classics Prof. James Smith for assistance with the translation!
* According to the E.B., Christopher Maire was an English Jesuit.
* O'C #9
* Early use of the word "MIRAGE" by Joseph-Bernard de Chabert
* "Cette année M. de Chabert, Lieutenant des vaisseaux du Roi, Chevalier
* de l'Ordre de Saint-Louis, Membre de l'Académie de Marine, de celle de
* Berlin & de celle de l'Institut de Bologne, présenta à l'Académie la
* Relation du voyage qu'il a fait par ordre du Roi en 1750 & 1751 dans
* l'Amérique septentrionale, pour rectifier les cartes des côtes de
* l'Acadie, de l'isle Royale & de celle de Terre-Neuve, & pour en fixer
* les principaux points par des observations astronomiques." (pp.242-243)
* "Pendant que M. de Chabert étoit occupé à lever les plans dont nous
* venons de parler, il fut souvent arrêté par un phénomène singulier,
* qu'on appelle mirage : c'est un changement apparent de l'aspect des
* côtes un peu éloignées, que les habitans attribuent à la réflexion du
* ciel, qui, se mirant dans l'eau, fait paroître la côte comme élevée
* en l'air, & que M. de Chabert croit, avec plus d'apparence, causé
* par l'irrégularité de la réfraction qu'ont souvent à souffrir les
* objets terrestres." (p. 253)
* (See Gronier, 1961, for a good translation.)
* From the collected tables of contents, it appears that this text is
* on p.358 of the reprinted edition of Hist. Acad. Roy. Sci.
* This account in the Hist. Acad. Roy. Sci. is just an extended abstract
* of the book published in 1753.
* Many thanks to Éric Frappa for discovering this at Gallica:
*
* http://gallica.bnf.fr/ark:/12148/bpt6k3551g/
* DOMENICO GIARDINA explains the Fata Morgana of Aug. 1643
* The day here (the 14th) is the day before Angelucci's FM observation
* quoted by Kircher (1646); but the two accounts are substantially
* identical, as noted by Consolo; Allegranza seems to be the only source
* for the 14th as the date.
* [Cf. Boccara's (1902) denunciation of Kircher, Giardina, and Allegranza.]
*
* The motivation for publishing all this nonsense seems to have been the
* ambition of the publisher, Gioachimo Pulejo, a printer in Catania who
* published several works promoting the reputations of local cities and
* their inhabitants -- e.g., "L'ardenza e tenacità dell'impegno di
* Palermo, nel contendere a Catania la gloria di aver dato alla luce la
* regina delle vergini, e martiri siciliane Sant'Agata" (1747). The
* present case is another example: in the dedication, and on the prefatory
* pages I and II, "from the publisher to the reader", we see how he
* is concerned with promoting Sicilian works.
*
* The full title preceding Giardina's text is:
*
*
* D I S C O R S O
*
* S O P R A
* L A
*
* F A T A M O R G A N A
*
* DI MESSINA, COMPARSA
* NELL' ANNO MDCXLIII. AL DI XIV. D'AGOSTO
*
* DEL
* P. DOMENICO GIARDINA
*
* DELLA COMPAGNIA DI GESU'
*
* CON ALCUNE NOTE
* DELL' ERUDITISSIMO
* SIG. ANDREA GALLO
* MESSINESE.
*
*
* (which takes up all of p. 117.)
*
* Giardina and Gallo are briefly described in pp. II and III of the preface.
* As Giardina died in 1747, in his 50th year, he could not have observed
* the 1643 display he tries to interpret here; Marina Warner is confused.
* Unfortunately, her confusion has become a "viral" sensation on the Web.
* This falsehood continued to be spread by other readers who believed the
* fabrications added to the story by Capozzo (1840), such as Consolo
* (1993) and Séstito (2011).
*
* The numerous informative footnotes were inserted by Gallo; they refer to
* "the author" (Giardina) in the third person.
* In particular, note [c] (p. 121) criticizes the author for not being
* "concordant with modern Philosophy" which distinguishes the real ascent
* of sulfurous and bituminous material in the air from the "apparent,
* formed by the refraction of the solar rays."
*
* Giardina's essay ends on p. 143, where a letter from Giuseppe Allegranza
* begins. Allegranza attempts to derive "Morgana" from the German "Morgen".
* Strangely, he has the page wrong in "Ars Magna", and calls Angelucci
* "Andreucci". In fact, the page number given (704) corresponds to the
* 1671 edition published in Amsterdam in; but that one still has
* "Angelucci" correctly. Apart from minor editorial changes in spelling
* and punctuation, Allegranza's text here is exactly the same as a text
* published without attribution in "Giornale de' Letterati" for the year
* 1755, dated "Messina 15. Feb. 1751", pp. 46 - 55. In particular, both
* that version and this one have the "Andreucci" error. So Allegranza's
* 1751 text appears to be the origin of both the "Andreucci" error and the
* dubious date: he says the observation was made "in una Vigilia dell'
* Assunzione" -- i.e., the 14th. (p. 144) Boccara (1902) dismisses all
* of them: Kircher, Giardina, and Allegranza.
*
* The attribution of the Fata Morgana to reflections by "polyhedral
* crystals" seems to be inspired by Mariotte's explanations of halos
* by refraction and reflection in ice crystals, in 1679.
*
* Available in two copies from Google Books. One, from Oxford:
* https://books.google.com/books?id=3r0TAAAAQAAJ&vq=Giardina&source=gbs_navlinks_s
* is lower quality; the other, from U.Michigan:
* https://books.google.com/books/about/Opuscoli_di_autori_Siciliani_Dunning.html?id=LvgDAAAAMAAJ
* has had the name "Dunning" unaccountably appended to the title, and is
* also available at the HathiTrust site. Note that Vol. 2 is bound
* together (and scanned) with Vol. 1.
* This is the work Brydone (1773) mentions but was unable to find.
* Cited by P&E in a footnote on p.186.
* MARINA WARNER's garbled account (placed here for her citation of Giardina)
* Chapter 7 is devoted to "Fata Morgana ; or, Castles in the Air".
* Her Fig. 9b on p. 94 was the best reproduction of Fortuyn's engraving for
* Minasi that I had seen in print, until Séstito's (2011). But she failed
* to get the facts right:
* "Kircher described one instance in his book . . . , in response to a
* fellow Jesuit who had written to him [sic!] . . . about a . . . fata morgana
* he had witnessed himself in Sicily [sic!]." (p. 95)
* So she confuses Giardina with Angelucci, and Kircher with Sanzio.
* "Giardina . . . goes on to describe how he saw [sic] `a city all floating
* in the air . . .'" (p. 96)
* Note 2 on p. 96 links to p. 391; the note there cites both Giardina
* and Minasi -- who explained that Giardina was referring to Angelucci.
* She also parrots much common nonsense about mirages: "Technically
* now known as a `superior' or `looming mirage', fata morgana appears
* above the horizon, often rising to great heights among the clouds." (p. 97)
* Then follows: "Layers of the atmosphere at different temperatures develop
* [sic] different densities, and the sun's rays, hitting the surface
* of the sea and the layers of air at a certain angle (45 degrees) turn
* them into an infinite recession of mirrors, multiplying and inverting
* reflections, diffracting [sic] and refracting the light so as to project
* images of far distant scenes and objects onto the clouds; these images,
* turned upside down and superimposed [sic] on one another, then mingle
* and change rapidly as the layers move up and down from the observer's
* vantage point." Well, this is all nonsense! She has thrown some words
* together without understanding their meaning, and produced gibberish.
* On top of this, she cites as references on fata-morgana mirages some
* so-so websites, rather than the standard references on these topics
* (e.g., P&E; Humphreys; not even Minnaert or Greenler are cited.)
* A pretty sorry showing.
* (snippet view on Google Books)
*
* Much of this is taken from her Tanner lecture in 1999; see
* http://tannerlectures.utah.edu/_documents/a-to-z/w/Warner_01.pdf
* [all reprinted in Raritan 21, No.4, pp. 264-301 (Spring, 2002)]
* where she cites both Giardina and Minasi in note 3 on p. 67. There,
* she explicitly refers to Angelucci's letter in Kircher's book, and even
* says that Giardina's "Discorso" came "More than a hundred years later".
* So how did she later arrive at the wrong chronology?
* Note that her Tanner lecture contains more errors of its own; e.g.,
* her mistranslating of the phrase "delle sustruttioni di Salomone" as
* "the somersaults of Salome" instead of "the constructions of Solomon."
* This "Salome" appears as a typo in the text of the 1671 Amsterdam
* edition of "Ars Magna"; apparently she got it from that:
* https://books.google.com/books?dq=Kircher+%22Ars+Magna%22&jtp=704&id=wYlDAAAAcAAJ#v=onepage&q=Kircher%20%22Ars%20Magna%22&f=false
* -- and she gave 1646 as the date of Kircher's book, but cited the page
* (701) where this error appears in the 1671 edition. Evidently, she
* only consulted the later edition, citing the earlier one without
* actually reading it.
* Furthermore, she attributes Minasi's term "l'iride fregiata" (1773)
* to Giardina, who died in 1747, when Minasi (born in 1736) was still a
* schoolboy. (Giardina used "iride", but only in the phrase "iride
* marina".) And she mis-translates Minasi's phrase as "the festooned
* rainbow." Some historian!
* [And in the introductory Acknowledgments in the book, she gives the date
* of her 1999 lecture as 1992.]
* ARCHANGIOLO LEANTI's mention of Fata Morgana, based on Giardina
* This is the source of Brydone's (1773) exaggerated account.
* Although modern references to Leanti spell his given name "Archangelo",
* his historical monograph uses "Archangiolo" consistently. The title
* page describes him as "sig. Abate Arcangiolo Leanti da Palermo".
* The reference to the Fata Morgana is on pp. 3 and 4; he cites mainly
* the Giardina/Gallo/Allegranza work, but mentions Kircher, Fazello,
* Pliny, and Pomponius Mela as earlier sources.
* BOSCOVICH translated into French
* The same section numbering is used as in the original. There is a
* detailed map included, showing the region surveyed.
* NOTE on UNITS: There is a handy Table for converting between
* Roman feet and palms and Paris toises and feet on p. viii.
* Typographical note: The use of the accented "E" is extremely
* haphazard. On the title page, it only occurs in "État". In the
* preface and table of contents, no uppercase E is accented; but the
* lowercase é is abundant. The heading on p.1 of the main text says
*
* V O Y A G E
*
* ASTRONOMIQUE ET GÉOGRAPHIQUE
*
* DANS L'ÉTAT DE L'ÉGLISE
*
* and the body type all has accents where you'd expect them.
*
* See
* https://gallica.bnf.fr/ark:/12148/bpt6k9629131h/f25.item.texteImage
* John Byron's probable superior mirage
* Nov. 12, 1764: "At 4 PM it thunder'd & Lightened very much, & looked
* very black almost round the Horizon, I was then walking the Quarter Deck
* when all the People upon the Forecastle called out at once Land right a
* head, I looked under the Foresail & upon the Lee Bow, & saw it to all
* appearance as plain as ever I saw Land in my life, It made at first like
* an Island with two very scraggy Hammocks upon it, but looking to Leeward
* we saw the Land joining it & running along way to the SE, we were then
* steering SW. I sent Officers to the Mast head to look out upon the
* weather Beam & they called out immediately they saw the Land a great way
* to Windward. I brought too & sounded & had 52 fm -- I now thought I was
* embay'd & as it looked very wild all round I wished myself out before
* night. We made Sail & steered ESE. All this time the appearance of the
* Land did not alter in the least, the Hills looked very Blue as they
* generally do at some little distance in dark rainy weather, & many of the
* People said they saw the Sea break upon the Sandy Beaches. After steering
* for about an hour, what we took for Land all at once disappeared to our
* great astonishment, & certainly must have been nothing but a Fog Bank.
* Tho' I have been at sea now 27 years & never saw such a Deception before,
* & I question much if the oldest Seaman breathing ever did, except it was
* some in that Ship when the Master made Oath of seeing an Island between
* the West End of Ireland & Newfoundland, & even distinguishing the Trees
* upon it, & which since has never been heard of tho' Ships have been sent
* out on purpose to look for it. And had the weather come on very thick
* after the sight we had for some time of this Imaginary Land so that we
* could not have seen it disappear as we did, I dare say there is not a Man
* on board but would have freely made Oath of the certainty of it's being
* Land. Course So 47° Wt. Dist 108 Ms Latt in 43° 46' So.
* Longde made 19° 47' Wt."
* Note the reference to (evidently) "St. Brendan's island".
* [mentioned in Beauford's 1802 review of mirages.]
* VERY EARLY MIRAGE seen by David Cranz (FATA MORGANA + SUPERIOR MIRAGE)
* "Aber nichts hat mich mehr surprenirt und artiger anzusehen geduenkt,
* als wenn bey heiteren, warmen und stillen Sommer-Tagen die Kookoernen,
* oder die zwey Meilen von Godhaab gen Westen gelegenen Inseln, eine ganz
* andere Gestalt, als sie natuerlich haben, vorstellen. Nicht nur sieht man
* sie, wie durch einen Tubum , weit groesser, und alle Steine und die mit
* Eis angefuellten Ritzen so deutlich, als ob man nahe dabey stuende;
* sondern wenn dieses eine Weile gewaerht hat, so sehen sie alle wie ein
* einiges Land aus, und stellen einen Wald, oder eine geschorne Baum-Wand
* vor. Darauf sieht man sie allerley seltsame Figuren, als Schiffe mit
* Segeln, Wimpeln und Flaggen, alte Berg-Schloesser mit ruinierten Thuermen,
* Storch-Nestern und hundert dergleichen Dingen, vorstellen, welche sich in
* die Hoehe oder Weite ziehen und sodann verschwinden. Die Luft is alsdann
* zwar ganz still und klar, aber doch, wie bey sehr heissem Wetter, mit
* subtilen Duensten angefuellt, durch welche sich, nach meinen Gedanken,
* wenn sie zwischen dem Auge und den Inseln in einem gehoerigen Abstand
* sich befinden, die Objecte, wie durch ein convexes Glas, weit groesser
* vorstellen; und gemeiniglich folgt ein paar Stunden darauf ein sanfter
* West-Wind mit einem sichtbaren Nebel, da dann dieser Lusus naturae
* gleich ein Ende hat.(*)"
* FOOTNOTE: "(*) Etwas dergleichen habe ich bey Bern und Neufchatel von
* denen gegen Sueden gelegenen Gletschern observirt. Wenn sich dieselben
* naeher, deutlicher und groesser als gewoehnlich vorstellen, so rechnet
* der Landmann auf einen baldigen Regen, der sich auch gemeiniglich den
* folgenden Tag einstellt. Und die Tartern an der Muendung des
* Jenisei-Flusses in Sibirien haltens fuer einen Vorboten des Sturms, wenn
* die Inseln groesser scheinen. Gmelins Reise Th. III S. 129."
* Orthographic note: All double-s's are simply spelled out, using the long
* s for both. Umlauts are written as a raised e over the vowel.
* HUGH HAMILTON
* Early mirage publication (mentioned by Huddart.)
* Footnote, pp.43-44: "This Fleece of vapourous Air that some times hangs
* over Water, is very discernable when we stand by the Sea-side in a hot
* calm Day, and is the Cause of some odd Appearances. For the lower Part
* of the Air, which is then much impregnated with Water, refracts the Rays
* of the Light more strongly than at other Times, and by this unusual Degree
* of Refraction, Houses on the Shore at a Distance from us appear almost as
* high as Steeples, remote Ships and Islands and the extreme Parts of
* Head-lands or Promontories appear to be raised quite out of the Water, and
* to hang in the Air above its Surface."
* WILLIAM WALES reports looming in "haze" (i.e., "FOG") at Hudson's Bay
* Observations of LOOMING, CONCAVE surface, NEGATIVE DIP, etc.:
* pp. 115-116: "August 7th. About 5 saw the low land of Cape Churchill,
* bearing from the S to S. W. b. S. but the haziness of the horizon made
* the land put on a different appearance every 4' or 5'. I cannot help
* taking notice of one circumstance, as it appears to me a very remarkable
* one. Though we saw the land extreamly plain from off the quarter deck,
* and, as it were, lifted up in the haze, in the same manner as the ice
* had always done; yet the man at the mast head declared he could see
* nothing of it. This appeared so extraordinary to me, that I went to the
* main-top-mast-head myself to be satisfied of the truth thereof; and though
* I could see it very plain both before I went up, and after I came down,
* yet could I see nothing like the appearance of land when I was there.
* I had often admired the singular appearance of the ice in these parts,
* which I have seen lifted up 2° or 3° at a distance of 8 or 10 miles,
* although when we have come to it, we have found it scarcely higher than
* the surface of the water."
* P. 131: "The prodigious difference between the latitude of Churchill
* factory, as laid down from observations made by Hadley's quadrant, and
* that deduced from the observations made with our astronomical quadrant on
* shore, has often employed my most serious attention; but I cannot think on
* any probable cause for such difference, unless it lie in the very great
* refractive power of the air in these parts. I have mentioned how the
* ice and land appear to be lifted up, when we stand on the ship's deck:
* and if the visible horizon be lifted up in like manner, it must make its
* apparent distance from the sun, or, which is the same thing, the sun's
* apparent altitude less than it otherwise would be; and consequently,
* the latitude greater than the truth; and also greater than it will be
* shewn by a land quadrant, which depends not on the horizon, agreeable
* to what we find it in the case before us*."
* The footnote (*) continues onto p. 132:
* "*Having mentioned this circumstance to the reverend Mr.
* Maskelyne, it immediately occurred to him, that the longitude
* deduced from observations of the moon’s distance from the sun or a
* star, would be considerably affected by this cause, as not only
* the altitudes of the sun, from whence the time at the ship is
* found ; but also the latitude of the ship, found by an observa-
* tion of the sun’s meridional altitude, or otherwise, will conspire
* to encrease the sun’s distance from the meridian, or angle at the
* pole.
* "I have therefore recomputed the longitude from my observa-
* tion of the moon's distance from the sun, taken August the 5th,
* 1768, on a supposition that the mean error in any altitude taken
* by Hadley's quadrant, arising from this cause, is 10 minutes;
* and find that, on such a supposition, which it must be allowed
* appear to be extremely well founded, the longitude will be 11'¼
* less than what I found it at the time when I made the observa-
* tion, and therefore the longitude of Churchill will in this case be
* only be 94° 30'¾ W. And by making a similar correction of 15' to
* Mr. Dymond’s observation of the 6th, it will give the longi-
* tude of Churchill 95° 18' W." [Modern long. = 94° 13'.]
* [This may be the EARLIEST mention of this problem.]
* William Wales later made similar observations in the Antarctic, as
* one of the astronomers on Captain James Cook's second voyage. A good
* biography is at
*
* http://biographi.ca/009004-119.01-e.php?id_nbr=2203
*
* and a complete bibliography of his publications is at
*
* http://www.captaincooksociety.com/home/detail/articleid/95/manuscripts-and-published-work-involving-william-wales
*
* Available from JSTOR; but their OCR is worse than tesseract's.
* Their URL is
* http://www.jstor.org/stable/105882?seq=1#page_scan_tab_contents
* JOSEPH VIERA Y CLAVIJO (1772) -- Early mirage observations in CANARIES
* After recounting the legend of the mythical island, and quoting some
* first-hand observations, he concludes it is all due to atmospheric
* refraction.
* The mirage section is unusually long and detailed. It is Chapter 28 of
* Book 1.
* (Originally published by La Imprenta de Blas Roman, Madrid, 1772-1783)
* Thanks to Guy Vincent for calling this to my attention!
* PATRICK BRYDONE's account of the Sicilian mirages
* Though this is clearly a description of the Fata Morgana, that name
* never appears; instead, the apparitions are attributed to Old Nick
* [Note: "this place" is Messina]:
* "Do you know, the most extraordinary phœnomenon in the world is often
* observed near to this place? -- I laugh'd at it, at first, as you will do;
* but I am now thoroughly convinced of its reality; and am persuaded too,
* that if ever it had been thoroughly examined by a philosophical eye,
* the natural cause must long ago have been assigned.
* "It has often been remarked, both by the antients and moderns, that
* in the heat of summer, after the sea and air have been greatly agitated
* by winds, and a perfect calm succeeds, there appears, about the time of
* dawn, in that part of the heavens over the Straits, a vast variety of
* singular forms, some at rest and some moving about with great velocity.
* These forms, in proportion as the light increases, seem to become more
* aerial; till at last, some time before sun-rise, they entirely disappear.
* "Some of the Sicilian authors represent this as the most beautiful
* sight in nature; Leanti, one of their latest and best writers, came here
* on purpose to see it: He says, the heavens appear crowded with a variety
* of beautiful objects: He mentions palaces, woods, gardens, &c. besides
* the figures of men, and other animals, that appear in motion amongst
* these objects. -- No doubt the imagination must be greatly aiding, in
* forming this aerial creation; but as most of their authors, both antient
* and modern, agree in the fact, and many give an account of it from their
* own observation, there certainly must be some considerable foundation
* for the story. There is a Jesuit, one Giardina, that has lately writ
* a treatise on this phœnomenon, but I have not been able to find it:
* The celebrated Messinese Gallo has likewise published something on this
* singular subject; if I can procure them in the island, you shall have
* a more perfect account of it. The common people, according to custom,
* give the whole merit of it to the devil; and indeed it is by much the
* shortest and easiest way of accounting for it: Those who pretend to
* be philosophers, and refuse him this honor, are greatly puzzled what
* to make of it. They think it may be owing to some uncommon refraction,
* or reflection of the rays, from the water of the Straits; which, as it
* is at that time carried about in a variety of eddies and vortexes, must
* of consequence, say they, make a variety of appearances on any medium
* where it is reflected. -- This, I think, is nonsense; or at least very
* near it; and till they can say more to the purpose, I think they had
* much better have left it in the hands of the old gentleman. I suspect
* it is something in the nature of our Aurora Borealis; and, like many of
* the great phœnomena of nature, depends upon electrical causes; which,
* in future ages, I have little doubt, will be found to be as powerful an
* agent in regulating the universe, as gravity is in this age, or as the
* subtile fluid was in the last." (Vol. I, pp. 86-89)
* (Brydone's scientific specialty was electrical phenomena.)
* NOTE: Brydone's comments on Leanti are off the mark: Leanti was born
* in Sicily, and spent his whole life there; so the ". . . came here on
* purpose to see it" part is bogus [he probably confused Leanti with
* Kircher in this case]. Likewise, "the heavens appear crowded with"
* the images is Brydone's invention; Leanti merely says "in the air".
* [Brydone's references to Giardina and Gallo correspond to Gallo's
* notes added to Giardina's useless rediscussion of Angelucci's letter.]
* This went through dozens of editions, in English and several other
* languages. In the "new edition" of T. Cadell and W. Davies (1806), the
* text has been tidied up a bit by minor editing, and changes in punctuation
* and spelling (making "ancients" and "phænomenon" instead of the variants
* above, for example); and the passage then falls on pp. 50-52.
* I read somewhere that this originally appeared in the Gentleman's Magazine
* in 1773, but find no reference to it.
* Copies of the 1773 London (1st) and 1806 editions are on Google Books.
* ANTONIO MINASI's account of the Fata Morgana
* There are many interesting details here that were omitted by Nicholson
* in his translation. This 102-page monograph is more informative than
* some later reviews (Nicholson; Reinecke; Büsch; Gilbert; P&E) suggest.
* The last 4 all depend on German translations of Nicholson's English.
* In the footnote on p. 18, he says "I have observed a little Fata
* Morgana near Rome. . . " at 11:30 on April 21, in the lake of Castel
* Gandolfo.
* In the discussion, he reviews all earlier accounts, including de
* Ferrariis, Angelucci, Kircher, etc. -- even including the Maccabees.
* He reprints (with some minor changes) almost all of Angelucci's letter,
* from the 1671 (Amsterdam) edition of Kircher.
* Notice his extensive discussion of Giardina's paper (§4, pp. 21 ff.)
* Minasi makes plain his disbelief of the Giardina discussion in Cap. IV;
* see the additional discussion in his footnotes 2 and 7 to this chapter.
* See his footnotes on p. 35, and the derivation of the "45°" on p.41.
* Minasi buried much valuable information in his footnotes. For
* example, the note on p.17 in Cap. III mentions the "spring, and the
* first months of summer" as the time when the images are reflected;
* and these are exactly the classical superior-mirage season (cf. Forel!)
* And on the next page, he cites the months of April through August as
* most favorable for these reflections.
* Note that Minasi's footnotes are numbered consecutively on each page .
* This leads to some confusion in their cross-references: the note at the
* foot of p. 17, where § 8 begins, is actually referenced in § 7, and
* numbered 1. The "nota 1" of § 8 that is referenced in the notes in
* later chapters is the note numbered 1 on p. 18, but continued on p. 19.
* The next note, cited as "§8. nota 2" in later chapters, is numbered 1 on
* p. 19, but continues on p. 20.
* Note on UNITS: the "Italian palms" used by Minasi are probably the same
* as the "Roman palms" that are converted to Paris measures in the Table on
* p. viii of the 1770 French translation of Maire & Boscovich.
*
* This is available at Google Books:
*
* https://books.google.com/books?id=yh3SLkLf9NYC&printsec=frontcover&dq=Minasi+%22Fata+Morgana%22&hl=en&sa=X&ved=0ahUKEwi_-vuR3f7dAhWlct8KHSiCCCIQ6AEILDAB#v=onepage&q=Minasi%20%22Fata%20Morgana%22&f=false
*
* but unfortunately the text of the PDF file they provide is badly
* garbled. Apparently, because of the mixture of Italian, Latin, Greek,
* and Hebrew in the text, everything available in UTF-8 encoding turns up.
* There are snatches of Chinese and Japanese characters, as well as
* Cyrillic. This makes any kind of machine translation impractical.
* A more practical re-publication of Minasi's text is in Consolo's
* 1993 book "Vedute dello Stretto di Messina"; but that is marred by
* his credulous acceptance of Capozzo's (1840) fallacious inventions.
* (Evidently, Consolo never bothered to read Minasi.) Yet another
* republication of Minasi's text is in Séstito's book (2011); it copies
* errors from Consolo, and appears to be copied from his version rather
* than from Minasi's original.
*
* A high-resolution scan of Fortuyn's engraving is available at
*
* http://dr.casanatense.it/drviewng.html#action=jumpin;idbib=1582;idpiece=-1;imageNumber=1;idpiece=-1
*
* [click on the "IIP" icon in the header to see the full resolution.]
*
* The engraving is discussed in Maria Toscano's thesis:
* http://www.fedoa.unina.it/777/1/Tesi_Toscano.pdf
* and in her article:
* "Lo strano caso di Guglielmo Fortuyn. Un tentativo di attribuzione"
* Neoclassico, No. 23/24, pp. 39-68 (2003)
*
* Finally, a biography of Minasi written by Enrico Pescatore was published
* in the "Scilla News" on 20 April, 2020, and archived on the publisher's
* website:
*
* http://www.strettoweb.com/2020/04/scilla-storia-don-antonio-minasi/1003141/
*
* Possible mirages in the Antarctic in JOHN MARRA's Journal (1775)
* [Dec. 15, 1773:] "Here the ice islands presented a most romantic
* prospect of ruined castles, churches, arches, steeples, wrecks of ships,
* and a thousand wild and grotesque forms of monsters, dragons, and all the
* hideous shapes that the most fertile imagination can possibly conceive."
* (p. 111)
* [Jan. 26, 1774:] "At nine in the morning every body on deck imagined
* they saw land; and accordingly preparations were made for getting all
* things in readiness to cast anchor. At eleven crossed the antarctic
* circle to the southward for the 2d time, and hauled up S. E. by E. where
* they were persuaded land was. But to their great disappointment, the
* farther they sailed, the farther the land seemed to bear from them;
* and at length it wholly vanished." (p. 123)
* [Jan. 30, 1774:] "Came in sight of a fog bank, which had a great
* appearance of land, and many who were thought the best judges asserted
* that it was land; however it proved upon trial a deception, as well as the
* former. . . . Taking a view from the mast-head nothing was to be seen but
* a dreary prospect of ice and sea. Of the former might be seen a whole
* country as far as the eye could carry one, diversified with hills and
* dales, and fields and imaginary plantations, that had all the appearance
* of cultivation; yet was nothing more than the sports of chance in the
* formation of those immense bodies of congregated ice." (p. 125)
*
* This is a heavily-edited account, nowadays attributed to the journal of
* John Marra, a gunner's mate on the Resolution . Supposedly his editor
* was David Henry, of the Gentleman's Magazine . No author appeared
* on the title page of this when it was originally published, 18 months
* before Cook's official account (which does not mention these appearances,
* but only ice fields). The original title was:
*
* J O U R N A L
* of the
* RESOLUTION's VOYAGE,
* In 1772, 1773, 1774, and 1775.
* on
* DISCOVERY to the SOUTHERN HEMISPHERE,
* by which
* The Non-Existence of an undiscovered Continent,
* between the Equator and the 50th Degree of Southern
* Latitude, is demonstratively proved.
*
* Sources on the Web indicate that a French translation was published
* in Amsterdam in 1777, and it is evidently that which Biot had read.
* This modern edition is Bibliotheca Australiana #15.
* WALES & BAYLY (astronomers with James Cook's second voyage)
* William Wales was the editor of this volume, which contains various
* sections written by himself and by William Bayly; Wales was aboard
* the Resolution (James Cook's flagship); Bayly, on the Adventure.
* Our interest is in Wales's "Meteorological Journal", pp. 335-366.
* The excerpt reprinted by Sir Napier Shaw in 1930/1942 was from
* p. 351; cf. Pernter (1902).
* The publication details are complex: the volume was printed by
* W. & A. Strahan, and sold by J. Nourse, in the Strand, and J. Mount
* and T. Page, on Tower-Hill, Booksellers to the Board of Longitude,
* which paid for the observations:
* "Published by order of the Board of Longitude, at the Expence of which
* the Observations were made."
* See
*
* http://acms.sl.nsw.gov.au/album/albumView.aspx?itemID=852703&acmsid=0
*
* for the Introduction and Contents.
*
* LE GENTIL's observations in India
*
* There are several sections of interest here, all in the Seconde Partie
* of Vol. 1:
*
* Ch. I, Art. III. Observations sur les Réfractions horizontales (p. 393)
* Remarques sur l'Observation des Hollandois dans la nouvelle Zemble en
* 1596 & 1597 (p. 416)
* Ch. I, Art. IV. Observations sur les Réfractions, à différens
* degrés de hauteur (p. 426)
* Then, after the Supplément:
* Observations sur les Réfractions terrestres (p. 701)
*
* Full title:
* VOYAGE
* dans
* LES MERS DE L'INDE,
* FAIT PAR ORDRE DU ROI ,
* A l'occasion du Passage de Vénus,
* sur le Disque du Soleil, le 6 Juin 1761,
* & le 3 du même mois 1769.
*
* TOBIAS GRUBER's letter
*
*
* An amazingly perceptive summary of the salient points: flat, smooth
* ground; the hiding of objects below a limiting ray; the dependence
* on season, height of the eye and distance to the object --
* all here in just a few pages. P. 55 has a nice ray diagram, too.
* "Ein merkwürdiges Phänomen, welches ich auf meinen Reisen im
* Temeswarer Bannate so oft gesehen, und hier auf dem ebenen Seeboden
* samt meinen Gefährten wieder zu bemerken Gelegenheit hatte, kann ich
* unmöglich ganz vorbeylassen. Blos in sehr flachen, und auf viele
* Meilen weit sich erstreckenden Gegenden, besondere, wenn sich der
* ebene Horizonte in dem Himmel hinaus verliert, habe ich den über die
* Erde etwa 6 Schuh hoch liegenden Theil der Atmosphäre also verdicket
* gefunden, daß die unter einem sehr spitzigen Winkel darauf einfallenden
* Lichtstrahlen nicht durchgelassen, sondern abgeprellet werden; welches zu
* vielen optischen Blendungen Anlaß giebt. Also habe ich in einer Ferne
* von 1000 bis 2000 Klaftern blos die Dächer von Dorfgebäuden gesehen,
* welche mir wie ein durchsichtiges Wäldchen vorkamen. Also erschienen
* die hie und da auf der Ebene stehenden Warthügel ohne Grundlage.
* Also wurden die etwas höher emporragenden Objecte, als Bäume, Gebäude,
* Thürme, u. s. w. doppelt so hoch gezeigt, weil sie nämlich wie auf
* einer Wasserebene gespiegelt wurden. Also sah ich in der weiten Ferne
* zerstreute große Seen, die bis an den Horizont hinaus wie Meere wurden.
* Nach Maaß der Annäherung verschwanden sie, und entfernten sich immer.
* Ja so gar, wenn ich von meinem Sitze im Kalesche, wo ich sie noch sah,
* aufstund, und mich etwa 3 Schuhe in die Höhe richtete, so nahmen sie
* ab, oder erschienen nicht mehr. Als ich die Ursache dieses Spielwerkes
* der Lichtstrahlen noch nicht kannte, ward ich überdiemaßen durch diese
* Seltsamkeiten gerührt. Die öftere Ansicht in verschiedenen Umständen,
* das Erscheinen und Verschwinden nach Verhältniß der Erhöhung und
* Erniedrigung, und die Analogie aus optischen Experimenten entdeckten
* mir endlich das ganze Geheimniß." He explains it, with the use of the
* ray diagram. "Es ist eine ganz natürliche Sache, daß, wenn ein
* Lichtstrahl sehr schief in ein Mittelding einfällt, dessen Verdickung
* verhältnißmässig anwächst, derselbe den Grund des Mitteldings
* nicht erreiche, sondern in einer Entfernung vom Grunde, unter eben
* dem Winkel, unter welchem er einfiel, abgeprellet werde. Newton hat
* diese Eigenschaft bey allen spiegelnden Flächen aus der Theorie der
* abstossenden Kräfte erwiesen. Kommt nun die Direction ch vom Himmel,
* oder aus einer lichtgrauen Ferne, (wie es beym Zirknitzer See geschah,)
* so sieht man nichts von den Objecten, die unter der Linie ch stehen,
* und die reflektirte wird dem Wasser ähnlich seyn. . . .
* "Auf diese Art erklärte ich mir alle ähnliche Erscheinungen.
* Die Sache fordert aber eine nähere Bestimmung, zu welcher ich zu
* wenig Zeit für diesmal habe. Ueberhaupt scheine ich mir mit Grunde
* schließen zu können, daß die durch gröbere Dünste nahe an der Erde
* verdickte Luft (welches ich meistens im Frühjahr bemerkte) bloß auf
* einer gewissen Höhe über den weiten Flächen (vielleicht auf 6 bis 7
* Schuhe) diese optischen Betrügereyen hervorbringen könne."
* [The line ch mentioned is not Minnaert's "vanishing line," but the
* lowest ray of an erect image. Thus Gruber failed to appreciate that
* there are in fact bits along the way that lie above Biot's caustic but
* below this ray, and so are visible. He neglects the general curvature
* of the rays, as well as that of the Earth.]
* This is actually a Postscript (Nachschrift ) to the Fifth Letter,
* beginning on p. 40, and dated 20 April 1779, from Zirknitz.
* The "Kalesche" was an open horse-drawn carriage with a folding top,
* usually rendered as "calash" or "caleche" in English.
* Typographical note: this is all set in Fraktur, with little e's over
* the vowels as umlauts. There are numerous ligatures: ch, ck, ff, fi, fl,
* si, ss, st, sz, tz. ["Krausz" is actually set with the tz ligature,
* which differs from the ß used in "durchgelaßen" and "abstoßenden".]
* Proper names are set in a slightly broader and less angular font than
* the Fraktur body text.
*
* Full title page reads:
*
* Herrn Tobias Grubers,
* Weltpriesters und k. k. Bau- und Navigationsdirektors
* im Temeswarer Banat,
*
* B r i e f e
* hydrographischen
* und
* physikalischen Inhalts
* a u s K r a i n
* an
* Ignaz Edlen von Born,
* k. k. wirklichen Hofrath
*
*
* Available today at
*
* https://books.google.com/books?hl=en&lr=&id=zehnX5qi9YIC&oi=fnd&pg=PA3&dq=Grubers+Briefe+1781&ots=KZk9HfEjaY&sig=NspSHz-thBbqj_Tczwe-EBfI3Uk#v=onepage&q=Grubers%20Briefe%201781&f=false
*
* [Pogg. says "eigentlich Grüber."] See also Acta Carsologica 33,
* 277-298 (2004), available at
* http://www.zrc-sazu.si/izrk/Carsologica/Acta332/Pdf3332/juznic.pdf
* for more information about Gruber and his book.
* Ignaz von Born is profiled in European History Quarterly 36, 61 (2006);
* see
* http://ehq.sagepub.com/cgi/reprint/36/1/61.pdf
*
* Despite the name on the title page, this was often cited as written by
* Johann Gruber. There are also obscure references to a "patriotic"
* commentary on Gruber's letters, published the same year in Laibach.
* Joh. Georg BÜSCH's TRACTATUS DUO OPTICI ARGUMENTI (1783)
*
* Only the first 78 pages deal with mirages; the second "argument"
* of the tract is devoted to myopia -- which is how I discovered that
* the Becker Medical Library of Washington University (St. Louis) has
* a copy (see their website).
* The preface explains that he was inspired to write by the problem
* posed by the Royal Danish Academy of Sciences ("Societas Hafniensis")
* in 1781. He also says he has translated his observations into Latin to
* make them available to the learned societies.
* Here the "miles" are specifically German ones; and the barometric
* readings are explicitly in Paris inches and lines. Unfortunately,
* he scrupulously gives barometric readings, but no temperatures!
* On pp. 9 and 10, he discusses Fig. 1, which shows the difference
* between the apparently calm reflecting surface in the distance, and the
* surface roughened by the wind in the foreground. This effect is also
* shown in Figs. 3, 4, and 6 (discussed on pp. 16, 17, and 36).
* On p. 12, he notes that this mirage is more likely to be seen in the
* morning, with a clear sky, and warm air. And he does discuss the effect
* of changing the height of the eye.
* On p. 20 is the original "chamberpot" quotation in the original
* English: "Indeed, it looks like a Chamberpot turn'd upside down."
* The first 38 pages are observations; then comes his theory: he
* thinks it has to do with electricity, and lightning. . . . He also
* supposes that (because only distant objects are miraged) the curvature
* of the ray depends on distance. . . .
* Still, on p. 39 he says ". . . refractionem, quae indubia causa est,
* . . . "
* Interestingly, he does invoke total internal reflection (p. 53).
* But (p. 59) "there must be something by which the light is reflected."
*
* On p. 61, he quotes from Gruber's 1781 letter, translated from German
* to Latin. (For a while we have "Gruner" for "Gruber"; but the given
* name "Tobias" certainly identifies him, as well as the reference to
* Carniola; apparently Büsch confused Gruber with the Swiss naturalist
* and geologist G. S. Gruner, who also worked about that time.) Büsch
* discusses Gruber's letter extensively, saying at the outset that
* "hunc virum primum omnium praeter me phaenomenon integrum observasse."
* Büsch adds notes to Gruber's text -- perhaps his dissent from some
* of Gruber's remarks explains Gruber's later hostility toward Büsch.
* Notably, "Non in vaporibus causa est sita." (p. 68) But he thinks
* the air is always denser at the ground than higher up (p.70), and
* argues that that the denser air cannot separate from the lighter to form
* a visible surface, "like two immiscible liquors, such as terebinth oil
* [turpentine] and spirit of wine".
* He ends by offering advice to those who would investigate further:
* make observations in all seasons from a fixed place; use an instrument
* capable of measuring small angles; an achromatic telescope "for avoiding
* all confusion of the image that deceives the naked eye"; a level to
* observe "how much objects are raised and lowered for various conditions
* of the air". And it would also be useful, if convenient, to observe
* from the same place the Moon rising and setting over the sea. (pp.76-77)
* There is a table of Corrigenda on p. 132.
*
* Title page reads:
*
* Ioannis Georgii Büsch
* Math. Prof. Hamburgensis
* Tractatus duo
* optici Argumenti
* cum figuris.
*
* The internal title page of the first essay reads:
*
* I.
* Observata nova
* in
* refractione horizontali
* et inde nata
* mira imaginum reflexione.
*
*
* [Extracts were translated into German by Gilbert in 1800.]
* Special thanks to the ILL people for this one at last!
*
* This is now available at
* https://books.googleusercontent.com/books/content?req=AKW5QafMp1bX3Vg_h8zvgBFeb6uKD2tNk6E1B4k5Urt-Fk-7Tl15AWPzA5YL5Il7CeESrYwKzHj0Rv44UjJAgLTihElDz3hPUr80LxTqdV-mYcz5CltbsDZSmrM6-Nob7bdLDFa9xQl6wfZqB6J-2Ub0NtDCCXVBAuOmPuBThOkqdU1OaYmBJtmebweLhAO0ELIWoVbpA99UL91Sl2WLMhYn5gSrihV0IY33_OM8AD8BCbxUlSqNv4cbIexDe4PfkdJt_HCPaQaLFa2xtzXb111elMg1M5_s7Q
* It contains the figures, placed on the 94th page of the PDF, after
* the title page of the second "argument".
*
* HENRY SWINBURNE's description of the FATA MORGANA
* Our interest is in pp. 263-266 of Vol. 2 of the 1790 Second Edition;
* presumably this first appeared in 1785. Here is what he says:
* . . . "Messina rises out of the waves like a grand amphitheatre; and
* the Faro, lined with villages and towns, seems a noble river, winding
* between two bold shores.
* "Sometimes, but rarely, it exhibits a very curious phænomenon,
* vulgarly called La Fata Morgana *. The philosophical reader will find
* -------------------------------------------------------------------------
* [the footnote on p. 263 says: "The name is probably derived from an
* opinion, that the whole spectacle is produced by a Fairy or a Magician.
* The populace are delighted whenever the vision appears, and run about
* the streets, shouting for joy, -- calling every body out to partake of
* the glorious sight."]
* -------------------------------------------------------------------------
* its causes and operations learnedly accounted for in Kircher, Minasi,
* and other authors. I shall only give a description of its appearance
* from one that was an eye-witness. Father Angelucci is the first that
* mentions it with any degree of accuracy, in the following terms:
* ``On the fifteenth of August, 1643, as I stood at my window, I was
* ``surprised with a most wonderful, delectable vision. The sea that
* ``washes the Sicilian shore swelled up, and became, for ten miles in
* ``length, like a chain of dark mountains; while the waters near our
* ``Calabrian coast grew quite smooth, and in an instant appeared as
* ``one clear polished mirror, reclining against the aforesaid ridge.
* ``On this glass was depicted, in chiaro scuro , a string of several
* ``thousands of pilasters, all equal in altitude, distance, and degree
* ``of light and shade. In a moment they lost half their height, and
* ``bent into arcades, like Roman aqueducts. A long cornice was next
* ``formed on the top, and above it rose castles innumerable, all perfectly
* ``alike. These soon split into towers, which were shortly after lost
* ``in colonnades, then windows, and at last ended in pines, cypresses,
* ``and other trees, even and similar. This is the Fata Morgana , which,
* ``for twenty-six years, I had thought a mere fable.''
* "To produce this pleasing deception, many circumstances must concur,
* which are not known to exist in any other situation. The spectator must
* stand with his back to the east, in some elevated place behind the city,
* that he may command a view of the whole bay; beyond which the mountains
* of Messina rise like a wall, and darken the back-ground of the picture.
* The winds must be hushed; the surface quite smoothed; the tide at its
* height; and the waters pressed up by currents to great elevation in the
* middle of the channel. All these events coinciding, as soon as the sun
* surmounts the eastern hills behind Reggio, and rises high enough to form
* an angle of forty-five degrees on the water before the city, -- every
* object existing or moving at Reggio will be repeated a thousand fold upon
* this marine looking glass; which, by its tremulous motion, is, as it were,
* cut into facets. Each image will pass rapidly off in succession, as the
* day advances, and the stream carries down the wave on which it appeared.
* "Thus the parts of this moving picture will vanish in the twinkling
* of an eye. Sometimes the air is at that moment so impregnated with
* vapours, and undisturbed by winds, as to reflect objects in a kind of
* aërial screen, rising about thirty feet above the level of the sea.
* In cloudy, heavy weather, they are drawn on the surface of the water,
* bordered with fine prismatical colours."
* Evidently, Swinburne's account (largely translated from his mentioned
* sources) was the inspiration for a burst of interest in these mirages
* in the English journals. For the next 20 years, refraction phenomena
* were often compared to Swinburne's account, until Wollaston's (1803)
* introduction of the French term "mirage" (and Nicholson's longer
* translation from Minasi) superseded it.
* Google Books has the Second Edition (1790, 4 vols.) on-line.
* Apparently the passage above is on p. 365 of the first volume of the
* two-volume (first?) edition.
* THOMAS JEFFERSON's observations: notes the importance of DISTANCE
* " Having had occasion to mention the particular situation of Monticello
* for other purposes, I will just take notice that its elevation affords
* an opportunity of seeing a phænomenon which is rare at land, though
* frequent at sea. The seamen call it looming . Philosophy is as yet in
* the rear of the seamen, for so far from having accounted for it, she has
* not given it a name. Its principal effect is to make distant objects
* appear larger, in opposition to the general law of vision, by which they
* are diminished. I knew an instance, at York town, from whence the water
* prospect eastwardly is without termination, wherein a canoe with three
* men, at a great distance, was taken for a ship with its three masts.
* I am little acquainted with the phænomenon as it shews itself at sea;
* but at Monticello it is familiar. There is a solitary mountain about
* 40 miles off, in the South, whose natural shape, as presented to view
* there, is a regular cone; but, by the effect of looming, it sometimes
* subsides almost totally into the horizon; sometimes it rises more
* acute and more elevated; sometimes it is hemispherical; and sometimes
* its sides are perpendicular, its top flat, and as broad as its base.
* In short it assumes at times the most whimsical shapes, and all these
* perhaps successively in the same morning. The Blue ridge of mountains
* comes into view, in the North East, at about 100 miles distance, and,
* approaching in a direct line, passes by within 20 miles, and goes off
* to the South-west. This phænomenon begins to shew itself on these
* mountains, at about 50 miles distance, and continues beyond that as far
* as they are seen. I remark no particular state, either in the weight,
* moisture, or heat of the atmosphere, necessary to produce this. The only
* constant circumstances are, its appearance in the morning only, and on
* objects at least 40 or 50 miles distant. In this latter circumstance,
* if not in both, it differs from the looming on the water. Refraction will
* not account for this metamorphosis. That only changes the proportions of
* length and breadth, base and altitude, preserving the general outlines.
* Thus it may make a circle appear elliptical, raise or depress a cone,
* but by none of its laws, as yet developed, will it make a circle appear
* a square, or a cone a sphere."
* At the word "diminished", there is a note, which is apparently due
* to the editor, William Peden; it says: "MS note by TJ . Dr. Shaw in
* his Physical observations on Syria, speaking of the Easterly winds,
* called by Seamen Levanters, says `we are likewise to observe further
* with regard to these strong Easterly winds, that vessels, or any other
* objects, which are seen at a distance, appear to be vastly magnified,
* or loom , according to the mariners expression.' Shaw's travels, 302.
* Ed. note. Thomas Shaw (1674-1751), English traveller and educator,
* author of Travels or Observations Relating to Several Parts of Barbary
* and the Levant (Oxford, 1738)." [p. 280]
* N.B.: The page (302) that Peden attributes to TJ in this note is
* incorrect. The correct page number is 362. [Cf. Shaw, 1738.]
* This was written in 1781 and revised in 1782. Jefferson had a small
* edition privately printed in 1784 in Paris. A French translation
* appeared in 1786; the original English was published in 1787.
* The passage on "looming" appears on pp. 80-81 of the 1982 Norton
* paperback in our library, at the end of Chapter 7.
* Cited by Talman in his 1932 article in Yachting .
* Early mirages: Claims to have written to Abbe v. Herbert in 1776;
* cites his letter in 1781, published before Büsch's
* "Tractatus duo argumenti optici" of 1783.
*
* N.B.: "Klafter" = "die Länge des Menschens" (approx. 1.9 m)
* according to Grimm; Brockhaus says "6 Fuß; 10 Fuß; 1.7 m im Mittel"
* See also:
*
* Hercule Cavalli
* Tableaux comparatifs des mesures, poids et monnaies, modernes et anciens
* (Dupont, Paris, 1874)
*
* (available at Google Books) for such obsolete units.
*
* First observations published in letters from Krain = Carniola, on the
* bed of seasonally-varying Zirknitzer See = Cirknisko Jezero = Lago
* Periodico near Zirknitz = Cerknica = Cirkonico, south of Laibach =
* Ljubljana. This southern former crownland of Austria, later titular
* duchy, was annexed by the Hapsburgs in 1335. Note the use of Viennese
* measures. This area is currently Slovenia.
*
* Both field measurements and indoor experiments with air heated by an
* iron strip. He repudiates his earlier error (of thinking that the
* surface air was thickened) in the Nachschrift , and now states that the
* heated air is thinned, as shown by the rising air over a candle flame,
* etc. He also notes the wavy appearance of the heated air as it rises.
* Detailed explanations of double images and image elongation at the
* fold line, with good ray diagrams.
*
* Abbé Tobias Gruber, K.K.Kameral-Baudirektor
* note obsolete spelling: "Stralenbrechung"!
* The umlauts are tiny e's printed over the vowels.
* N.B.: Brechmonat = June; Wintermonat = Nov.|Jan.; Christmonat = Dec.
* Pernter gives 1786 for the year, and in the bottom margin at the end
* of every signature my photocopy says "Abh. d. B.Ges. 1786".
* The text (but, of course, NOT the Plates!) is available at Google Books.
* EARLY TREATMENT OF LOOMING & FATA MORGANA, with SUPERIOR MIRAGES
* more "FOG" (p.16)
* ". . . hier wähle ich zum Beyspiele meiner Beschreibung die bekannten
* Gunnilas Felsen, (Gunnilas Oerar) 3/4 schwedische Meilen ostwärts in der
* See von den Svenska Högar.
* "Vermutlich sind diese Gunnilas Felsen auf gewisse Art vor mehr als
* zwei Jahrhunderten bekannt gewesen. . . ."
* GUILLAUME JOSEPH HYACINTHE LE GENTIL's posthumous work on refraction
* Notable not only for an early OMEGA description, but also for the early
* use of the term se mirer and descriptions of mirages (pp. 233 ff.).
* A comment on the RARITY of clear sunsets: ". . . sur quatre mois
* entiers je n'ai vu qu'une seule fois le soleil se coucher complètement
* à l'horizon de la mer . . . ." (p. 227)
* He also notes that Bouguer found a smaller horizontal refraction at
* sea in the tropics (25' to 27') (p. 227)
* His own VARIATIONS in horizontal refraction were 5' at Pondicherry;
* but "il semble . . . que la réfraction à 10'' [sic; he means degrees]
* soit assez bien constatée . . . ." (p. 228)
* The OMEGA descriptions are on pp. 229-232. ". . . c'étoit comme si deux
* soleils se fussent détachés l'un de l'autre, l'un avoit monté pendant
* que l'autre descendoit." (p. 230)
* The etymology is on p. 233: "Les habitans des bords des côtes de
* Basse-Normandie, presque tous marins, appelent ces apparences se mirer .
* Ils disent qu'une isle se mire , qu'un rocher se mire ." He then
* disputes the French translation of a Dutch sailors' dictionary that
* invokes clouds in explaining this term, as "Cela n'arrive que dans un
* très-beau temps, et lorsqu'il n'y a pas la moindre apparence de nuages."
* (p. 234) -- Later on the same page is a classical description: "Je
* vis à la place comme des ruines d'une ancienne ville ou d'une ancienne
* colonnade, qui paroissoit au-dessus de l'horizon, et comme en l'air,
* sans distinguer ni voir de nuages quelconques."
* NOTE: The dictionary was Aubin's 1736 edition; see Aubin (1702) here.
* Finally, he quotes from Maraldi's descriptions of mirages and looming
* of Corsica as seen from Gênes and Provence. (p. 235)
* A footnote says Le Gentil died 22 Oct. 1792, just as the memoir was
* being printed.
* GIUSEPPE MARIA GIOVENE's original account -- very good!
* The mirage observations are on pp. 15-21: "It remains for me to speak
* of a phenomenon seen by me on the evening of 9 February, and of other
* similar phenomena, which are observed in these regions. For greater
* accuracy I shall copy almost literally from my journals for those which
* I have observed, and the reports of my friends, for those I have not
* seen with my eyes. The previous days were fine and clear, with rather
* strong winds from N. to W., and I found myself in a small country house
* which I prefer just because, enjoying a wide horizon there, I have the
* convenience of better observing the meteorological phenomena. It was
* one of those beautiful evenings that can happen in winter, and close
* to half past 5 in the evening I was stopped at a window that had a view
* directly to the SSW. I was enjoying the clear air, which was calm, as
* shown by the smoke from the chimneys of the nearby towns of Terlizzi,
* Ruvo, and Corato, which lay beneath my view; it had not any movement,
* but covered those towns motionlessly like an umbrella. Looking around,
* I thought I saw some clouds rising in the western part just along the
* horizon, which occupied about 20 degrees of the same. I determined to
* try to observe their path, with only the idea of being able to predict
* which way the wind would blow the next day, and consequently what could
* be the state of the air, which, as I found myself in the countryside,
* interested me. In fact, I observed that the supposed clouds rose more
* and more above the horizon until they had ascended about two degrees.
* But suddenly they began to take various shapes, so that finally I
* realized they were quite different from clouds. I therefore invited
* Dr. Andrea Tripaldi, a young man well versed in good physics, and who
* had had the courtesy to join me for some days in tranquil solitude,
* to observe with me. We placed ourselves to observe more attentively.
* The originally supposed clouds were always changing shape. They first
* gave us the impression of a city standing along the horizon. We saw the
* shapes of buildings, of towers, of campaniles. At that moment, we came
* to suspect that the landscape of Cerignola, reflected to be situated in
* the direction of the phenomenon, but thirty-four Italian miles distant
* from the place of observation, was presented to our eyes by a powerful
* refraction of light in the atmosphere. But we saw the scene gradually
* change, and two little hills appeared, one facing the other, and these
* later were raised up, and squared off into magnificent towers with great
* apertures like windows, which let the light of the twilight pass through.
* I would hardly be able to describe the diverse shapes and the varied forms
* that were presented to our eyes. But later on our surprise increased.
* The twilight was very bright, and I noticed that waves of more vivid
* light were rising from time to time from the edge of the horizon up to
* an altitude of six or seven degrees. I first believed it could be an
* illusion of my eyes, and informed Sig. Tripaldi, who affirmed that he too
* saw what I said I saw. To assure ourselves, we agreed to inform each
* other when one of us perceived these waves of light. We always found
* ourselves in agreement. We went to another window, which faced directly
* to the WNW, and the thing appeared the same. The waves of light extended
* as far as the twilight extended, and were more vivid where it was more
* vivid, and less vivid where it ended. Five or six waves would come, and
* then a pause for one or two minutes, then they would recommence again.
* Meanwhile, the most capricious shapes were appearing on the line of the
* horizon. The spectacle lasted, charming and pleasant, near half an hour.
* As the twilight grew darker, so the striking appearance decreased in
* beauty, and ended completely after three quarters of an hour. The calm
* lasted all night. In the morning of the following day, 10 February, some
* mists rose, and cloudlets, from the W. At 10 1/2 in the morning the wind
* came from the W rather strong, but near evening the air clouded up, and
* the wind shifted to the N.W. with strong force; on the following day (the
* 11th), the thermometer suddenly fell by many degrees, there was a shower
* of snow, which even froze in some places more exposed to the cold wind.
* "This phenomenon, although peculiar in its circumstances, is
* nevertheless not new in Puglia, as it is not even new in Iapigia, today
* called the Province of the Land of Otranto, and I shall expand a little
* on this article so much more willingly as this class of phenomena is
* either completely unmentioned by the writers, or reported confusedly,
* or even with changes engendered by the ignorance and superstition of the
* populace. The one who has mentioned them with the greatest vivacity and
* accuracy is the celebrated Antonio Ferrari, called Galateo after his
* birthplace, a writer of the last years of the fifteenth, and the first
* of the sixteenth Century. in his elegant little book, reprinted so many
* times, De Situ Iapygiæ :" -- and here he quotes from Ferrari's Latin
* account (1558) in extenso .
* "The reader will forgive the long quotation. But it is not only in
* the places named by the Galateo that the mutate are seen. I find
* from the reports, it is also seen at Galatone, Soleto, and many other
* towns and villages of the cape of Lecce, that is, Cape Japigio.
* The mutate (as is written to me from there) consist of seeing in a
* great plain, now a sea, now a woods, now a town. These apparitions are
* observed only at the rising and setting of the sun.
* "In Puglia Peucezia, similar phenomena are also seen, and are called
* lavandaja [washerwoman], for what reason, I cannot say. They have
* taken it as a sign of change of weather. In fact, when after the wind
* has blown for a long time from a point on the horizon, the atmosphere
* calms to give place to an opposite flow, then is precisely the time when
* the lavandaja shows itself most beautifully. So too the season in
* which it most frequently appears is the autumn, and the winter too,
* although it is not rare in summer, and not extremely rare in spring.
* Indeed in summer there takes place almost daily a sort of little
* lavandaja , after midday, while the time of the phenomenon is properly
* around sunrise and sunset.
* "The ordinary appearance of the lavandaja from Molfetta is on
* Mt. Gargano. This mountain, about 50 miles distant from that city,
* appears like a cloud of a fairly deep blue color resting upon the
* horizon from the W.N.W. to the N.N.W. Of course, I shall not say
* that this mountain is the barometer of the Puglian sailors, and that
* visible or invisible, high or low, covered either completely by clouds,
* or as if by an umbrella of clouds, lets them predict the wind and the
* state of the Puglian atmosphere; I shall speak only of the lavandaja .
* The first time I saw this meteor, knowing nothing of the thing,
* I confess to have been distressed by it in the first moments. I was
* seeing the whole mountain shake, and undulate, as if an extremely violent
* earthquake shook its foundations, and made it totter. So I was seeing
* one part of the mountain collapse, forming a great valley; and then
* this, little by little, rose to form a new peak superimposed on the
* mountain. Beside this peak rose a second, a third; and these, little
* by little, were squared off into high towers; then they too collapsed
* and became valleys again. In sum, I was seeing that mountain in the
* most terrible convulsions. Afterwards, accustomed to observing such
* phenomena, I have very many times seen with the greatest pleasure the
* varied scenes that the view of this mountain offers. It assumes the
* most varied and the most capricious forms, and a warped or slightly
* heated imagination, comparing these figures to well-known objects,
* believes it sees horses, and armies, castles, ships, towers, and towns.
* "And too, a partial lavandaja is seen from the Town of Molfetta,
* especially when a soft wind blows from the east after sunset. That
* peak, of which Lucan sang,
*
* Apulian Garganus extends into the Adriatic waves
*
* continually takes on new forms and figures, now seeming extremely
* long, now shrinking and then dividing into many pieces, which look like
* islands in the open sea. It also happens that sometimes one portion of
* the sea appears notably higher than another, and some other time the sea
* in the distance looks as if in the greatest storm, when in reality it
* was completely calm. But to finish the little story of these phenomena,
* I shall describe another charming display that presented itself to me
* one morning in October, 1789, at the appearance of the sun on the horizon.
* "I found myself in my customary countryside retreat, and as it was
* a beautiful morning with little, or indeed no wind, I hastened to enjoy
* it at a window that looked directly to the N.E., and to observe the
* thermometer and the hygrometer, which hung there. I was really
* surprised to see the most delightful and certainly moving scene.
* The town of Biseglie, which was in my view, in the N.W. part, although
* it was seven miles away, appeared so near that I would have believed
* it only two miles off. I was seeing the pavement of a wide square,
* which is there before the walls of the town, was almost counting the
* houses, and the vision was made not only with the greatest distinctness,
* but also with a certain vividness, which absolutely touched the soul.
* It was observable that the houses seemed more elongated than widened,
* as it was most observable that the bell towers were in their natural
* state. That is to say that at a certain height of the land, the view
* was the normal one. In the part to the W., all the little hovels and
* the houses scattered through the countryside appeared as high pyramids
* or spacious towers. I enjoyed this display, which later became more
* delightful, for almost an hour, in the company of my inseparable friend,
* the aforesaid Dr. Andrea Tripaldi. The town of Trani, placed a little
* more to the W. at a distance of perhaps more than eleven miles, and
* which, in the ordinary state of the air, cannot be seen, except for
* just one cathedral with its high campanile, began to be seen entirely,
* and with the greatest distinctness, so that it seemed to have approached
* by at least six miles. At the start of the next hour, while Biseglie
* was slowly going away, Barletta began to be seen. It is even more to
* the west than Trani, and about eighteen miles distant, and completely
* invisible in the ordinary state of the atmosphere. And this town seemed
* no more remote than seven or eight miles. My colleague and I distinctly
* saw the coast between Barletta and Trani, and were counting all the little
* boats that were fishing along there. Near nine in the morning, that is,
* after more than three hours since we had begun to observe the phenomenon,
* everything seemed to return to normal. But I wanted to go onto the
* terrace, which was higher than the window by about twenty Paris feet.
* I was more surprised to find that from that height the phenomenon
* could still be seen in all its beauty, and Barletta and Trani seemed a
* few miles away. I informed Sig. Tripaldi of it as he stood at the window
* while I was on the terrace. We assured ourselves that the phenomenon was
* now invisible at the height of about 40 Paris feet, extremely visible from
* about 60 feet from the ground. In the whole duration of the phenomenon
* the thermometer was between 12 and 15 degrees Reaumur, and the hygrometer
* between 21 and 25 degrees absolute, which means in temperate heat,
* and moderate dryness; or at least, certainly not in great humidity.
* "By comparing my observations with the little left written of it by
* Antonio Galateo , it is easy to see that the mutate of Japigia and
* the lavandaja of Peucezia are the very same thing, although I will admit
* that the fuochi fatui [will-o'-the wisps] and the capre saltanti ,
* which are not seen by us at all in Peucezia, are extremely frequent
* in Nardò, and in Copertino. The complex of these meteors, and of
* the phenomena described above, gives credence to the tales of witches
* and magicians among the people of Nardò and Copertino; fables that
* nevertheless have begun to lose credit today even among those low people.
* "Meanwhile, everyone sees that the mutate and the lavandaja
* are nothing but the play of variable refraction of visual rays in the
* atmosphere, as from variable refraction comes the increase and decrease of
* our visual horizon by twenty or thirty miles. But a conversation on the
* phenomenon I had seen on the evening of 9 February with the celebrated
* Sig. Thouvenel (whose coming to Molfetta expressly to visit the famous
* natural nitrate deposit of this City gave me the honor of accomodating
* him in my house, and the pleasure of hearing him, . . . ) made my ideas
* go a little farther, and formed conjectures, which will be appraised
* by the Physicists for what they are. Why does this lavandaja always
* have to appear on the western side and never to the east of Molfetta?
* Why must it always be seen along the line going from the famous Apulian
* [Mt.] Vulture, an extinct volcano, as everyone knows, and entering the sea
* at the farthest promontory Gargano, passing by the island of Pelagosa,
* recognized as volcanic by the celebrated Sig. Ab. Fortis, and going
* directly to the N.E. to join the volcanos of Morlachia? Why are the
* mutate of Lecce seen along the line of Galatona, Nardò, Copertino,
* and adjacent towns, put on land where there is some rising heat, and
* where pyrites and coal are found? Why is the famous fata morgana of
* Reggio in Calabria, which nevertheless is very similar to the lavandaja
* of Puglia, and to the mutate of Salento, is found just on the line
* of coal, which passed directly under the Faro of Sicily in Calabria,
* and is also seen in the open air behind Messina, and at Briatico on the
* opposite side? This phenomenon of the lavandaja , that is, of the
* mutate , is certainly, as I have said, a play of refraction, and to
* make such a play it is necessary that a certain quantity of vapors and of
* exhalations change the state of the atmosphere. Even this is not enough.
* Because the striking appearance, despite the calm, means that the wind is
* in continuous movement, the very air is like an uprising, and agitated.
* Those waves of light that I saw the evening of 9 February must be the
* effect of a shaking given to the air. So it seems that either electrical
* fluid or other emanations of some gas rise from the regions above which
* are seen the described phenomena, and force the incumbent atmosphere to
* be disturbed or to undulate. The violent agitations and convulsions,
* to which the same atmosphere is accustomed, occur after the appearance of
* such meteors, which indicate the same. I have not thought it necessary
* to give a complete history of this kind of phenomenon in our regions in
* this memoir. For me, it is enough to have given a small sample of it.
* Meanwhile, one must confess that meteorology is still, at most, in its
* early adolescence, and that there would never be as many careful observers
* of meteorological instruments as observers in the open countryside,
* and with a free horizon."
*
* This was mostly translated into German by Zimmermann later, and then
* reprinted by Gilbert in 1802. (See the entry for Zimmermann's version.)
* Thanks to Maria Toscano for supplying the citation to this, and
* helping with the translation!
* Available at Google Books:
* https://books.google.com/books?id=BN0WAAAAYAAJ&pg=PA3&f=false#v=onepage&q&f=false
* Early looming and mirage observation (apparently a 3-image mirage)
* "On the thirteenth of last month [i.e., October], while we lay on
* the banks of Lake-Erie, we had an opportunity of viewing that singular
* phenomenon, by Seamen termed looming. . . . the 13th was cloudy; but
* without rain: about ten o'clock in the morning, as I was walking on the
* beach, I discovered something that had the appearance of land, in the
* direction of Presque-Isle; about noon it became more conspicuous and;
* when viewest by a good Achromatic-Telescope, the branches of trees
* could be plainly discovered --- From 3 o'clock in the afternoon, till
* dark, the whole Peninsula was considerably elevated above the horizon,
* and viewed by all our company with admiration. --- There was a singular
* appearance attending this Phenomenon, which I do not remember to have
* seen taken notice of by any writer --- The Peninsula was frequently
* seen double, or rather two similar Peninsula's, one above the other,
* with an appearance of water between:--- the separation, and coincidence
* was very frequent, and not unlike that observed in shifting the index
* of an adjusted Godfrey's quadrant. . . . The next morning Presque-Isle
* was again invisible, and remained so during our stay at that position.
* Presque-Isle was about twenty-five miles distant, its situation very low."
* The marginal note says "Read Nov. 21, 1788".
* EARLY DRAWING of SUPERIOR MIRAGE (FATA MORGANA + SUPERIOR MIRAGE)
* by the Rev. Samuel Dickenson, LL.B. the Chaplain of the Dunkirk
* Man of War. . .
* "The term haze , prefixed to the foregoing account, is adopted from the
* phrase then used by the sailors, perhaps improperly; for, there was not
* the least appearance of mist or fog, or thickness of atmosphere; on the
* contrary, the air seemed uncommonly clear."
* INFERIOR MIRAGE and variable refraction reported by
* Lieut. Col. Edward Williams, and Capt. William Mudge,
* of the Royal Artillery; and Mr. Isaac Dalby.
* Dalby's observation in April, 1793 (pp. 586-588):
* "I observed . . . a very uncommon effect of terrestrial refraction. . . .
* ". . . when the eye was brought to about 2 feet from the ground, the top
* of the hill appeared totally detached, or lifted up from the lower part,
* for the sky was seen under it. This phænomenon I repeatedly observed."
* The discussion continues: ". . . it is more than probable, that moist
* vapours were the principal cause of the very unusual refractions:
* the truth of which conjecture seems to be verified by the following
* circumstance. In measuring the base on Hounslow Heath, we had driven
* into the ground, at the distance of 100 feet from each other, about 30
* pickets, so that their heads appeared through the boning telescope to be
* in a right line; this was done in the afternoon. The following morning
* proved uncommonly dewy, and the Sun shone bright; when having occasion to
* replace the telescope, we remarked that the heads of the pickets exhibited
* a curve, concave upwards, the farther-most pickets rising the highest;
* and we concluded they were not properly driven till in the afternoon,
* when we found that the curve appearance was lost, and the ebullition in
* the air had subsided."
* (available at JSTOR; no paper copy filed)
* Woltman's newsletter announcement (1796)
* This is the lead item in the issue, attributed to "Hr. Dir. Woltmann"
* (with 2 "n"s.) "zu Cuxhaven". There is no title; the general heading
* is "Göttingen". This is an account of a paper sent to "der königl.
* Societät" [i.e., the "Königliche Gesellschaft der Wissenschaften" in
* Göttingen], and presented by "Hr. Hofrath Kästner". (The Göttingische
* Gelehrte Anzeigen was its official organ, published almost daily.)
* This extended abstract begins with Gruber's 1786 paper, and goes
* directly into an account of Woltman's measurements of dip by using two
* stakes driven into the dikes, with the distant house as target. This
* seems to be the first appearance of the phrase "Spiegelung unterwärts" in
* print. The basic data (distances between the sights and the house, and
* some angles) are given, with the Hamburg foot as the unit of length.
* The part of his later complete table that summarizes the results for
* Feb. 1795 is printed, showing that the terrestrial refraction is
* greatest in the morning and least in the evening; the total range is
* 10 min. 16 sec.
* "Diese Bilder können nicht ganz allein aus Reflection entstehen, weil
* keine Spiegelfläche in der Luft vorhanden ist; es muss dabey eine
* Refraction mitwirken, die den Strahl unterwärts krümmt." (p. 812)
* He also describes briefly the effects of superior mirages, and for
* further information refers to his forthcoming paper in the "nächsten
* Bande der kaiserl. königl. Gesellschaft zu Prag". The heat has the
* strongest effect of all meteorological variables: "Ist das Wasser 2 oder
* mehr Fahrenheitische Grade wärmer, als die Luft, so findet sich allemal
* Erniedrigung der Strahlen, die sich über die Wasserfläche erstrecken;
* aber Hebung, wenn die Luft über dem Wasser 2 oder mehr Grade wärmer ist,
* als das Wasser." (p. 815)
* At the end, Woltman describes some inferior mirages he has seen over
* land: "Man muss zu dem Ende eine ganz offene Ebene vor sich haben ,
* oder über Gebüsche und dergl. von einer hohe wegsehen können. Dann
* scheint die ganze Landschaft in einem unbeweglichen Glanzmeere zu stehen ,
* worin alle die erhobenen Gegenstände sich unterwärts spiegeln. So hat
* Hr. W. oft von den Geesthöhen herab die Marschen gesehen , als wären
* sie ganz mit glänzendem Wasser überzogen. Diese Bemerkungen . . . findet
* er Uebereinstimmung der Strahlen über Land und über Wasser, der Strahl
* krümmt sich allemahl nach der wärmsten Seite; die Refraction ist desto
* grösser, je grösser der Unterschied der Wärme zwischen beyden Materien
* ist, . . . ." (p. 817)
* He continues with remarks on distortions of the low Sun: "Sieht man
* die Sonne des Morgens heiter aufgehen , so gibt ihre Gestalt ein
* untrügliches Merkmahl , ob Hebung oder Depression Statt finden wird.
* Nähmlich im letztern Falle ist sie nie rund , sondern ein Theil
* der Sonnenscheibe spiegelt sich unterwärts ; der kann , nachdem die
* Depression schwacher oder stärker ist, wohl ein Achtel oder ein Viertel
* des Sonnendurchmessers betragen, Hr. W. bildet dergleichen
* Erscheinungen ab , als wenn unten an der Sonnenscheibe , auch an den
* aufgegangenen Theil, der Anfang einer andern Scheibe angesetzt wäre ;
* dergleichen hat er auch an dem Vollmonde wahrgenommen. Findet dergleichen
* Depression Morgens und Abends Statt, so ist ihre Dauer auf dem festen
* Lande denselben Tag keinem Zweifel unterworfen , weil sie hier um Mittag
* allemahl zunimmt." (p.818)
* Evidently the editor --- at that time, Christian Gottlob Heyne, the
* head of the University Library, and "perpetual secretary" of the Society
* --- thought highly of this report: "Das viele Merkwürdige und Neue
* aus einer noch ungedruckten Schrift wird die Länge dieses Auszugs
* entschuldigen."
* This journal did not have conventional volume numbers; the Bände were
* given year numbers, starting in 1753. The title page of this volume says
* "Der erste Band, auf das Jahr 1796." There were two volumes in 1796;
* this is the first one. The "piece" number is 82, dated 21. Mai. This
* first volume for 1796 ends on page 1040 of the 104th Stück, dated 10 Jun.
* The second volume of 1796 follows on p.1041 of the 105th St.; at its end
* (at page 2105) come the alphabetical indices (separately paginated) and
* a list of printer's errors.
* This is the 82. St. of 1796.
*
* Available at
* https://www.google.com/books/edition/G%C3%B6ttingische_Anzeigen_von_gelehrten_Sac/ujtKAAAAcAAJ?hl=en&gbpv=1&bsq=809
* or
* https://gdz.sub.uni-goettingen.de/id/PPN31973076X
*
* Eberhard August Wilhelm von Zimmermann's translation of Giovene
* The introduction refers to Swinburne's work, and briefly enumerates
* the various sources, and their translators.
* Giovene's interesting mirage passage is on pp. 171-181. Zimmermann
* does indeed copy "S.S.O." literally from the original, which garbles
* the directions, as "O." is "Ovest" in Italian. So the error is the
* translator's and not Gilbert's.
* Note: the umlauts are tiny e's above their vowels.
* Available at
* https://digitale.bibliothek.uni-halle.de/vd18/content/titleinfo/8125331
* EARLY OBSERVATION & EXPLANATION OF INFERIOR MIRAGES and DIP
* "The variation and uncertainty the dip, in different states of the
* air, taken at the same altitude above the level of the sea,, was the
* occasion of my turning my thoughts to this subject; as it renders the
* latitude observed incorrect, by giving an erroneous zenith distance of
* a celestial object.
* "I have often observed that low lands and the extremity of headlands
* or points, forming an acute angle with the horizon of the sea, and
* viewed from a distance beyond it, appear elevated above it, with an
* open space between the land and the sea. . . . I believe it arises,
* and is proportional to the evaporation going on from the sea; and in
* reflecting upon this phænomenon, I am convinced that those appearances
* must arise from refraction, and that instead of the density of the
* atmosphere increasing to the surface of the sea, it must decrease from
* some space above it; . . . ."
* His observations of the miraged ship, made from a height of 40 feet,
* [=12 m] plainly showed the contraction of the inverted image. (p.32)
* His figures show accurate ray diagrams for the inferior mirage;
* he notes the vanishing line ("a little below the maximum of density,
* where inversion begins; therefore no land lower than this can be seen;
* . . . " (p. 37); and he points out the effects seen at the fold line:
* "There are always confused or ill defined images of the objects at
* the height of the dotted line, fig. 1, above the level of the sea, as
* before mentioned; and instead of the points of d [i.e., the apparent
* land horizon] ending sharp in that line, they appear blunted . . . ."
* Notable for having used measurements of the Sun at noon at both
* northern and southern (i.e., opposite) horizons to infer the actual DIP.
* He says "The effect indicated by the barometer and thermometer is
* insufficient;" but he fails to understand why, being fixed on the idea
* that humidity is the main problem.
* Cites Hamilton (1766) on "Ascent of Vapours". Also cites the paper by
* Williams, Mudge, and Dalby (1795).
* Joseph Huddart read his paper to the Royal Society on November 24.
* 1796. It was published on Jan. 1, 1797.
* Available at JSTOR, and at the Roy. Soc. website.
* The same, reprinted:
* Note: Nicholson's Journal merged with Phil. Mag. in 1813.
* Nicholson's summary of MINASI's Fata Morgana paper
* He begins by quoting James Thomson's lines from "The Castle of Indolence",
* Canto i. Stanza 30: "As when a shepherd of the Hebrid' Isles. . .
* (Whether it be lone fancy him beguiles,
* Or that ae"rial beings sometimes deign
* To stand, embodied, to our sense plain) . . .
* A vast assembly moving to and fro:
* Then all at once in air dissolves the wondrous show."
* -- an interesting reference, considering the reports of mirages from
* the Orkneys and other northern outliers of Britain.
* He then cites Brydone and Swinburne as making "mention of a very
* striking phenomenon . . . known by the name of Fata Morgana, or, as some
* render it, the Castles of the Fairy Morgana. The accounts differ from
* each other . . . . How far the effects themselves may be subject to
* variation, or to what extent the imagination of the narrators, who speak
* of the exhibition as calculated to produce astonishment, may be subject
* to irregularity, would admit of discussion. . . ."
* Nicholson borrowed a copy of Minasi's work from Sir Joseph Banks,
* and says, "In this treatise the facts are related with much simplicity
* and precision, and the philosophical reasoning of the author is kept
* distinct from the narrative." [But see Gilbert's scathing commentary!]
* Now comes Nicholson's loose translation of Minasi's description:
* "When the rising sun shines from that point whence its incident
* ray forms an angle of about forty-five degrees on the sea of Reggio,
* and the bright surface of the water in the bay is not disturbed either
* by the wind or the current, the spectator being placed on an eminence
* of the city, with his back to the sun and his face to the sea; -- on
* a sudden there appear in the water, as in a catoptric theatre, various
* multiplied objects, that is to say, numberless series of pilasters,
* arches, castles well delineated, regular columns, lofty towers, superb
* palaces, with balconies and windows, extended alleys of trees, delightful
* plains with herds and flocks, armies of men on foot and horseback, and
* many other strange images, in their natural colours and proper actions,
* passing rapidly in succession along the surface of the sea during the
* whole of the short period of time while the above-mentioned causes remain.
* "But if, in addition to the circumstances before described, the
* atmosphere be highly impregnated with vapour, and dense exhalations not
* previously dispersed by the action of the wind or waves, or rarefied by
* the sun, it then happens that in this vapour, as in a curtain extended
* along the channel to a height of about thirty palms, and nearly down
* to the sea, the observer will behold the scene of the same objects not
* only reflected from the surface of the sea, but likewise in the air,
* though not so distinct or well defined as the former objects from the sea.
* "Lastly, if the air be slightly hazey and opake, and at the same time
* dewy and adapted to form the iris, then the above-mentioned objects
* will appear only at the surface of the sea, as in the first case,
* but all vividly coloured or fringed with red, green, blue, and other
* prismatic colours." [Minasi actually says "purple" rather than "other
* prismatic colors."]
* Nicholson's translation seems to have become the canonical version
* of Minasi's account in English (though in Brewster's 1830 "Edinburgh
* Encyclopedia" and some later copies, "alleys" became "valleys").
* (Google Books shows dozens of copies, right up to the present day.)
* Minasi just says "very high trees" -- no alleys or valleys.
* Nicholson refers to Minasi's note on "the etymology of Morgana
* . . . which is so foreign to the Roman idiom, . . . considering the great
* exultation and joy this appearance produces in all ranks of people, who
* on its first commencement run hastily to the sea, exclaiming Morgana,
* Morgana!"
* "In the second chapter the author describes the city of Reggio,
* and the neighbouring coast of Calabria; by which he shews that all the
* objects which are exhibited in the Fata Morgana are derived from objects
* on shore." (I take "derived from" in a different sense, though!)
* In dealing with Minasi's observation (in the 3rd chapter) that the
* tides have something to do with it, he takes from Minasi that "It is high
* water, that is to say, the northern current ceases, at full and change,
* at nine o'clock. There is probably a small rise and fall, though the
* annotation to a large chart before me affirms that there is none."
* The various crank ideas following the 4th chapter, in which Minasi
* "collects the opinion and relations of various writers . . . , namely,
* Angelucci, Kircher, Scotus, and others," are elided, "because it seems
* difficult to make any clear or productive statement either from the
* narrative or the reasoning." [Pace , Gilbert!]
* His summary includes: "3. That the Morgana Marina presents inverted
* images below the real objects, which are multiplied laterally as well
* as vertically; and that there are repetitions of the same multiplied
* objects at more considerable vertical intervals. This I gather from
* the appearance of the dome and other objects in the plate." And:
* "8. By attentive reflection upon the facts and reasonings in Mr.
* Huddart's paper, we may form a theory to account for the erect and
* inverted images . . . ; but for the lateral multiplication we must have
* recourse to reflecting or refracting planes in the vapour, which appear
* nearly as difficult to deduce or establish, as those which have been
* supposed on the water."
* Issue dated August 1797
* William LATHAM's observations of LOOMING, seen from Hastings
* "On Wednesday last, July 26, about five o'clock in the afternoon, . . .
* the coast of France was plainly to be distinguished with the naked eye.
* I immediately went down to the shore, and was surprised to find that,
* even without the assistance of a telescope, I could very plainly see the
* cliffs on the opposite coast; which, at the nearest part, are between
* forty and fifty miles distant, and are not to be discerned, from that
* low situation, by the aid of the best glasses. They appeared to be only
* a few miles off, and seemed to extend for some leagues along the coast.
* . . . the cliffs gradually appearing more elevated, and approaching
* nearer, as it were . . . .
* "Having indulged my curiosity upon the shore for near an hour, during
* which the cliffs appeared to be at some times more bright and near,
* at others more faint and at a greater distance, but never out of sight,
* I went upon the eastern cliff or hill, which is of a very considerable
* height, when a most beautiful scene presented itself to my view; for
* I could at once see Dengeness, Dover cliffs, and the French coast,
* all along from Calais, Boulogne, &c. to St. Vallery; and, as some of
* the fishermen affirmed, as far to the westward even as Dieppe. . . . This
* curious phenomenon continued in the highest splendour till past eight
* o'clock, (although a black cloud totally obscured the face of the sun
* for some time,) when it gradually vanished.
* "I should observe, the day was extremely hot, as you will perceive
* by the subjoined rough journal of a small thermometer, . . . and the three
* preceding days were remarkably fine and clear. . . . Not a breath of wind
* was stirring the whole of the day . . . .
* Latham's temperature log shows that at 10 A.M. each of the previous
* 3 days, the temperatures were 65, 66, and 66 (F), and 68 on the day of
* looming; but at 5 P.M. it was 76. The 10 A.M. temperatures on the next
* 4 days were 72, 70, 72, and 70; so it appears the looming accompanied
* the arrival of a warm front.
* Reprinted in Nicholson's Journal 2, 417-419 (1799).
* Cf. the similar observations of Parnell (1869).
* REINHARD WOLTMAN's 1798 paper
* This is the paper partly reprinted by Gilbert in Ann. Phys. 3, 397 (1800)
*
* At this time, Woltman was "Baudirektor im hamburgischen Amte Ritzebüttel"
* A footnote on the first page says that Woltman began this work toward the
* end of the year 1794, continued it in 1795, and finished on 8. Nov., and
* communicated it in part with Abbe Gruber. It was extensively reviewed in
* the "Götting. Anzeigen 82ten Stück, 21ten May 1796."
* There is some background information on Woltman in the prefatory pages.
* On p. III we see that he was not a member of the Bohemian Scientific
* Society, but had submitted his manuscript to it through Abbe Gruber.
* On p. XXIII we learn that he was "Direktor der Ufer und Wasserbauwerke im
* hamburgischen Amte Rützebütl", and a member of several scientific
* societies, some in Harlem and Rotterdam; but here he is in a list of
* foreign members.
* He begins with a classic description of inferior mirages:
* "The phenomenon is that objects, houses, trees etc. near the horizon
* often are separated from the visible ground surface by a bright strip of
* air, and almost seem to stand in the air; or as if a shining empty space
* were present between the visible horizon and the objects; or if the eye is
* considerably raised, and sees several distant objects behind one another,
* as if these houses, mills, churches, trees etc. stood in a calm shining
* sea, in which the entire landscape were immersed and reflected."
* This is followed by an extensive list of "Alle, die davon geschrieben
* haben: Gruber's 1781 "Briefe"; Büsch's 1783 "Tractatus duo"; Gruber's
* 1786 response. "Diese zwey Abhandlungen hat H. Hofrath Kästner in seiner
* Dioptrik 1792 nebst mehreren Beyspielen angeführt; unter andern, dass H.-
* Justizrath Niebuhr einen Araber auf einem Kamele in freyer Luft reiten
* gesehen. Siehe dessen Reisebeschreibung nach Arabien 1. Theil, S. 253."
* "Ich habe selbst mit einem achromatischen Fernrohr sehr deutlich
* wahrgenommen, dass die entfernten Häuser, Bäume, Schiffe in umgekehrter
* Gestalt sich sehr deutlich abbilden, wie eben dieselben Gegenstande
* in de Nähe thun, wenn zwischen ihnen und dem Auge ein ganz ebener
* Wasserspiegel befindlich ist."
* VISIBILITY IN RAIN:
* "Auch sieht man das Phänomen so gut gleich nach einem Regen, als vor
* demselben; und selbst im Regen verschwindet es nicht eher, als bis die
* Undurchsichtigkeit der Luft das Sehen in der Ferne verhindert." (p. 71)
* He then describes the qualitative effects of object distance and eye-
* height. "Woraus folgt, dass nur diejenigen Strahlen von den Objecten
* durch Reflexion ins Auge kommen, die unter sehr kleinen Winkeln auf
* die spiegelnde Fläche fallen." And he describes how the "bright strip"
* shrinks and vanishes as the miraged object approaches the observer;
* and similarly describes the effects of increasing the height of the eye.
* "Therefore the bright strip is no object, like a luminous surface, . . .
* but is itself an image of a reflected bright object." (p. 72)
* On the next page, he tries to explain the phenomena with ray diagrams;
* he knows that the curvature of the Earth is important, but he draws all
* the rays as straight lines, except where they are reflected. Still, this
* allows him to explain why the apparent horizon is lowered by the mirage.
* He also explains that all the miraged objects lie beyond the effective
* distance to the horizon. (p. 74)
* In §.10. (p.75) he points out that "the images are always considerably
* smaller than their objects." He has found the images generally about
* half the size of the object, and shows an example in Fig. 7. Unfortunately,
* he neglects the curvature of the Earth; so he thinks this might be due to
* the rays being reflected under a smaller angle than that of incidence!
* But "maybe the refraction has something to do with it." On the next page,
* we find the real cause: his eye (in his house at Cuxhaven) is 3 toises
* (almost 6 meters) above the high-water level.
* He goes through a very rough argument that neglects the curvatures of
* both the surface and the rays, and then weasels out: "Zu genauern
* Bestimmungen wären genauere Beobachtungen mit einem Mikrometer nöthig;
* auch musste wohl die Refraktion in Betracht gezogen werden; welches zu
* unternehmen ich mir nicht getraue." (p.77)
* In §.13. he begins by discussing the trembling motion of the images,
* and compares it with the appearance of objects seen through the "vapors"
* above a coal fire. But then in the middle of the paragraph he gets into
* a description of superior mirages: "Eben diese Dünste im aufgelösten,
* durchsichtigen Zustande vergrössern zuweilen die horizontale Refraktion
* dermassen, dass die Meeresfläche, entlegene Ufer, Küsten und Sandbänke
* eine ganz ungewöhnliche Gestalt annehmen. Die Meeresfläche wird concav
* gekrümmt, die nähern Schiffe erniedrigen sich, oder vielmehr der entlegne
* Horizont scheint über ihnen fast hervor, entfernte niedrige Ufer erscheinen
* wie hohe Küsten; und diese, wenn sie auch 7 oder 8 Meilen entfernt, und
* weit unterm Horizont sind, erscheinen wie Gewölke über demselben; ganze
* Landschaften, die man sonst wegen der vorliegenden Sandhügel nicht sehen
* kann, erscheinen über dieselben hervor." (p. 78)
* Next, he worries about how to explain the "reflection". "Die Erdfläche
* selbst, so wie auch das Wasser, wenn es vom Winde in Unruhe gesetzt wird,
* sind zu rauh, um Bilder zu machen."
* "Mein würdiger Lehrer, der Hr. Prof. Büsch pflegte in der Optik zu
* bemerken, dass die zurückwerfung nicht unmittelbar an den Flächen,
* sondern in einer kleinere Entfernung von denselben . . . geschehe."
* He then describes a case where the mirage was seen at both high and
* low tide, when the water was 1½ toise lower; "Die Erniedrigung der
* Meeresfläche hat also denselben Effekt, den eine wirkliche Erhöhung
* des Auges oder des Objects haben würde . . . ."
* In the second part (p. 81) he considers whether the reflecting surface
* shares the curvature of the Earth, and whether this can explain the
* reduced size of the images. Unfortunately, because he neglects some
* small quantities, he thinks the reflection at a spherical surface will
* be the same size as the object, just as if the surface were flat.
* On p. 86, he says that mirages were sometimes still visible in late
* January, when the ground and the ice on the river were covered with snow.
* DIP and the inferior MIRAGE:
* His quantitative measurements of terrestrial refraction (given in
* the Table facing p. 86) clearly show a correlation between refraction and
* the inferior mirage: "bey verstärkter Refraktion oder Hebung des Hauses
* niemals Spiegelung gewesen; oder umgekehrt, dass bey der Spiegelung das
* Haus allezeit weniger erhaben gewesen, folglich eine relative Depression
* der Objekte wenigsten bey der Spiegelung statt habe."
* These measurements clearly establish the connection between refraction
* and the air-water temperature difference, and likewise the connections
* between the inferior mirage and depression, and the superior mirage and
* looming. Here is his memorable "2 deg. Fahr." rule; "unter mehr als 150
* Beobachtungen hat diese Regel keine Ausnahme." (p. 95)
* Woltman's final remark is that these phenomena are very well described
* by Martinet in the Verhandelingen der holländ. Gesellsch. zu Harlem XXVII.
* Deel. II. Stück, under the title "Warneemingen omtrent het opdoemen van
* Zee en Land".
*
* Woltman's figures are at the very end of the volume; in Google's scan at
*
* https://www.google.com/books/edition/Neuere_Abhandlungen_der_k%C3%B6niglichen_B%C3%B6/nqpeAAAAcAAJ?hl=en&gbpv=1&dq=Woltman+Bemerkungen+1798+katoptrisches&pg=PA69&printsec=frontcover
*
* they come after Gruber's figures, at image 491.
*
* Notice the correct spelling of his name here.
* Gruber's comments on Woltman's immediately preceding paper
* [partly reprinted by Gilbert in Ann. Phys. 3, 439 (1800).]
* Gruber's ray diagrams are all drawn for a flat Earth, so he has to
* violate symmetry in them in trying to explain the compression of the
* inverted image in the inferior mirage.
* The Tafel showing Gruber's figures is image 475 in the Google Book.
* early report of SUPERIOR MIRAGE, by Jean François Galaup de La Pérouse:
* (filed slightly out of order to stay with the English translations)
* The mirage observation itself is on p. 10 of Tome 3:
* "Les journées du 15 et du 16 furent très brumeuses ; nous nous
* éloignâmes peu de la côte de Tartarie, et nous en avions connaissance
* dans les éclaircis ; mais ce dernier jour sera marqué dans notre
* journal par l'illusion la plus complète dont j'aie été témoin depuis
* que je navigue.
* "Le plus beau ciel succéda, à quatre heures du soir, à la brume la
* plus épaisse ; nous découvrîmes le continent, qui s'étendait de l'Ouest
* un quart Sud-Ouest au Nord un quart Nord-Est, et peu après, dans le
* sud, une grande terre qui allait rejoindre la Tartarie vers l'Ouest,
* ne laissant pas entr'elle et le continent une ouverture de 15d. Nous
* distinguions les montagnes, les ravins, enfin tous les détails du
* terrain ; et nous ne pouvions pas concevoir par où nous étions entrés
* dans ce détroit, qui ne pouvait être que celui de Tessoy, à la recherche
* duquel nous avions renoncé. Dan s cette situation, je crus devoir serrer
* le vent, et gouverner au Sud-Sud-Est ; mais bientôt ces mornes, ces ravins
* disparurent. Le banc de brume le plus extraordinaire que j'eusse jamais vu
* avait occasionné notre erreur : nous le vîmes se dissiper ; ses formes,
* ses teintes s'élevèrent, se perdirent dans la région des nuages, et nous
* eûmes encore assez de jour pour qu'il ne nous restât aucune incertitude
* sur l'inexistence de cette terre fantastique. Je fis route toute la nuit
* sur l'espace de mer qu'elle avait paru occuper, et au jour rien ne se
* montra à nos yeux ; l'horizon était cependant si étendu que nous voyions
* parfaitement la côte de Tartarie, éloignée de plus de quinze lieues."
* This observation was made the 16th of June, 1787 -- just in the middle
* of superior-mirage season, for mid-latitudes (they were about 44° N).
* The location was off the coast of the Sikhote-Alin mountain range, ENE
* of present-day Vladivostok. The introductory remark indicates that
* La Pérouse was familiar with mirages.
* Furthermore, they had directly observed a strong thermal inversion a
* few weeks earlier (May 26), a little farther south in the Sea of Japan:
* "Si les nuages ne nous avaient par annoncé ce changement, nous avions
* eu néanmoins un avertissement que nous n'entemdîmes pas, et qu'il n'est
* peut-être pas facile d'expliquer : les vigies crièrent du haut des mâts
* qu'elles sentaient des vapeurs brûlantes, semblables à celles de la
* bouche d'un four, qui passaient comme des bouffées et se succédaient
* d'une demi-minute à l'autre. Tous les officiers montèrent au haut
* des mâts et éprouvèrent la même chaleur. La température était alors
* de 14d sur le pont ; nous envoyâmes sur les barres des perroquets un
* thermomètre, et il monta à 20d : cependant les bouffées de chaleur
* passaient très-rapidement, et, dans les intervalles, la température de
* l'air de différait pas de celle du niveau de la mer." (T.2, p.389-390)
*
* Title page reads:
*
* V O Y A G E
* D E L A P É R O U S E
* AUTOUR DU MONDE,
* publié
* conformément au décret du 22 avril 1791,
* ET RÉDIGÉ
* par M. L. A. MILET-MUREAU
*
* Thanks to Luc Dettwiller for discovering the mirage report!
* 1st English translation of La Pérouse:
* This edition uses the long-s, and seems to have been the "popular"
* rather than the "official" translation. The mirage story reads:
* "The 15th and 16th of June were very foggy days. We kept within a
* small distance of the coast of Tartary, and got sight of it at intervals;
* but the last of these days will be distinguished in our journal by the
* most complete illusion I have witnessed since I have been a seaman.
* "At four in the afternoon a perfectly clear sky succeeding to the
* thickest fog. we descried the continent extending from W. by S. to N. by
* E. and soon after, an extensive land in the south, running towards Tartary
* in the west, where it left an opening of less than fifteen degrees.
* We distinguished the mountains, hollows, and all the variations of the
* ground, but could not imagine how we had entered this strait, which must
* necessarily be that of Tessoy, of which we had given up the pursuit.
* In this situation I thought it necessary to haul the wind, and steer
* S. S. W.; but these hills and hollows soon disappeared. The most
* extraordinary fog-bank I had ever beheld occasioned this deception,
* and we soon witnessed its dispersion. Its forms and its tints mounted,
* and vanished in the atmosphere among the clouds; and enough of day still
* remained fully to demonstrate that land to be unsubstantial and imaginary.
* I stood on, during the night, over the space it had appeared to occupy,
* and at day-break no object presented itself to our view. The horizon was
* even sufficiently extensive to admit of our distinctly seeing the coast of
* Tartary, although more than fifteen leagues distant. I shaped my course
* towards it, but at eight in the morning the fog again surrounded us."
* [The above passage appears on pp. 27-28 of Vol. II.]
* 2nd English translation of La Pérouse:
* This edition uses the short s, and is written in a more formal style.
* The mirage story is on p. 7 of Vol. II:
* "The 15th and 16th were very foggy. We sailed along the coast of
* Tartary at no great distance, and had sight of it at intervals, when
* the fog dispersed a little; but the 16th will be distinguished in our
* journal by the most complete illusion that I ever witnessed since I have
* been at sea.
* "At four in the evening the most beautifully clear sky succeeded the
* thickest fog. We discovered the continent, which extended from west by
* south to north by east; and very soon after, to the south, an extensive
* land, running west towards Tartary, so as not to leave an opening of
* 15° between it and the continent. We distinguished the mountains,
* the valleys, and all the particulars of the land; and could not conceive
* how we had entered into this strait, which could be no other than that
* of Tessoy, the search after which we had given up. In this situation
* I thought it advisable to haul our wind, and steer south-south-east.
* But soon these hills and valleys disappeared. The most extraordinary
* fog-bank I had ever beheld was the cause of our illusion. We saw it
* disperse; it's shapes, it's colours, ascended, and vanished in the region
* of clouds; and we still had day-light enough left to remove every doubt
* about the existence of this fantastic land. I sailed all night over
* the space of sea it had appeared to occupy, and at day-break nothing of
* it was visible, though our horizon was so extensive, that we distinctly
* saw the coast of Tartary upwards of fifteen leagues distant."
* [NOTE: the abnormally large distance to the horizon shows that inversion
* conditions were still present.]
* The previous inversion observation appears in this edition on p. 537
* of Vol. I:
* "The sky was clear and serene, but it grew very black, and I was
* obliged to stand off the shore, that I might not be embayed by the
* easterly winds. If the clouds did not give us warning of this change,
* we had an indication of it, which we did not understand, and which it
* is not perhaps easy to explain. The men at the mast-head cried out,
* that they felt burning vapours, resembling those of the mouth of an
* oven, coming in puffs every half minute. All the officers went to the
* mast-head, and felt the same heat. The thermometer at that time was
* at 14° upon deck. We sent one up to the cross-trees, and it rose
* to 20°. These puffs of heat, however, passed with great rapidity,
* and in the intervals the temperature of the air did not differ from that
* of the temperature of the level of the sea."
* Note: this edition has the dates in the margins, like the original.
* early report of SUPERIOR MIRAGE, by Vince:
* ``The uncertainty of the refraction of the air near the horizon has long
* been known to astronomers, the mean refraction varying by quantities
* which cannot be accounted for from the variations of the barometer and
* thermometer. . . .''
* ``In fact, the images were visible, when the whole ship was actually below
* the horizon. . . . The discovery of ships in this manner might, in some
* cases, be of great importance. . . .''
* ``As the phenomena are very curious, and extraordinary in their nature, . . .
* They appear to be of considerable importance; as they lead us to a
* knowledge of those changes to which the lower parts of the atmosphere are
* sometimes subject. . . . it might throw further light upon this subject,
* and lead to useful discoveries respecting the state of the atmosphere. . . .''
*
* This was the Bakerian lecture.
* According to the paper's title, Vince was the Plumian Prof. of Astronomy
* & Experimental Philosophy (i.e., physics) at Cambridge.
* The Décade Philosophique meeting abstract of Monge's lecture
* The full title is "La Décade Philosophique, Littéraire et Politique"
* and the publication date is 10 Nivôse = Dec.30, 1798. The article is headed
*
* Institut d'Égypte
*
* and on p. 2 is the sub-head:
*
* Copie des procès-verbaux des séances de l'Institut
* d'Égypte, envoyés à l'Institut national de France
*
* followed by the account of the first meeting, on 6 Fructidor an VI.
*
* The minutes of the second meeting (11 Fructidor) begins on p. 4, with
* Monge's abstract beginning there and continuing to p. 5. The third
* meeting (16 Fructidor) begins near the foot of p. 5. Later meetings
* continue through p. 11.
*
* Available at Gallica:
* https://gallica.bnf.fr/ark:/12148/bpt6k5616321s/f11.item.r=mirage
* The Ann.Chim. lecture abstract of Monge's mirage memoir
*
* "A la mer, il arrive souvent qu'un naivre appercu de loin, paroit
* tout-à-fait dessiné dans le ciel, et n'être point supporté par l'eau. (1)"
* ------------- (the footnote says): -------
* (1) Cette illusion optique nous paroit avoir quelque rapport avec ces
* apparitions dans la mer et dans l'air pres du phare de Messine, connus
* sous le nom de fée Morgan , dont il est fait mention tom.XXV de ces
* Annales, pag. 80. Note des Rédacteurs .
* [This is a brief mention of Nicholson's translation of Minasi.]
* ------------------------------------------
* "Un effet analogue a frappé tous le Francais pendant la marche de l'armée
* à travers le désert. . . .
* "Le cit. Monge attribue cet effet à la diminution de densité de la
* couche inférieure de l'atmosphère. Cette diminution dans le désert est
* produite par l'augmentation de température qui est la résultat de la
* chaleur communiquée par le soleil aux sables avec lesquels cette
* couche est en contact immédiat. A la mer, elle a lieu lorsque, par des
* circonstances particulières, telles que l'action des vents, la couche
* infèrieure de l'atmosphère tient en dissolution une plus grande
* quantité d'eau que les autres couches. Dans cet état de choses, les
* rayons de lumière qui viennent des parties basses du ciel, étant arrivés
* a la surface qui sépare la couche la moins dense de celles qui sont
* au-dessus, ne pénètrent pas dans cette couche; ils sont réfléchis, et
* vont peindre, dans l'œil de l'observateur, l'image du ciel. . . . "
* So here we have water vapor and a fictitious reflecting "surface",
* from the very beginning.
*
* The text is almost identical to that appearing in Décade Philosophique,
* An 7, No. 10, pp. 4-5, where it is part of the report for the second
* meeting of the Institut d'Egypte.
*
*
* Page 207 is headed:
*
* E X T R A I T
*
*Du mémoire lu à la séance de l'institut
* du Caire, du 11fructidor, an 6;
*
* Par le cit. M O N G E
*
* (That date is 28 August 1798.)
*
*
* However, the issue of Ann. Chim. in which this reprint appears is dated
* 30 Nivôse = 19 janvier 1799.
*
* Available at Gallica:
* https://gallica.bnf.fr/ark:/12148/bpt6k65712092/f7.item.r=mirage
* The text of Monge's mirage memoir
* Monge says that the mirage in the desert may be due to heat, but that
* the mirage at sea is different: "En effet, l'air a la faculté de
* dissoudre l'eau, et même d'atteindre le point de saturation, sans perdre
* sa transparence; et Sassure a fait voir due la pesanteur spécifique de
* l'air décroit à mesure qu'il tient une plus grande quantité d'eau en
* dissolution. Lors donc que le vent qui souffle en mer apporte un air
* qui n'est pas saturé d'eau, la couche inférieure de l'athmosphère qui
* est en contact avec la surface de la mer, dissout de l'eau nouvelle, et
* se dilate. Cette cause, jointe à la légère augmentation de température,
* peut enfin amener les circonstances favorables au mirage, et produit en
* effet celui que les marins observent assez fréquemment." (p. 45)
* This differs by many minor changes in spelling and punctuation from
* the final version (below), which has the addendum on rainbows.
* According to Gallica, this was published in 1799. The title page
* says only " An VII ". This first volume was supposedly printed every 10
* days; as Gallica dates the volume at Jan. 1, this second number might
* have been printed on Jan. 11, 1799. The signature footers say "1.er
* Trimestre, AN 7."
* GASPARD MONGE explains the INFERIOR MIRAGE as total internal reflection,
* and reports REFLECTED RAINBOWS
* He leans very heavily on total internal reflection, and attributes
* the inferior mirages seen at sea to the effect of water vapor on the
* refractivity of air, confusing optical "density" with mechanical density.
* ". . . ce phénomene pourroit ne pas être ignoré des habitants du
* département des landes; mais il est très connu des marins, qui
* l'observent fréquemment à la mer, et qui lui ont donné le nom de
* Mirage ." (p. 65) [Cf. Le Gentil (1789) for "se mirer".]
* He takes the internal-reflection picture very literally, repeatedly
* referring to "la surface qui sépare la couche inférieure et dilatée
* de l'atmosphere de la couche plus dense qui est au-dessus d'elle" (p. 71)
* and "la surface réfléchissante, qui sépare les deux couches d'air des
* densités différentes, n'est ni parfaitement plane" (p. 73). This
* mistaken idea was immediately challenged by Reinecke (see below), and
* by Wollaston (1803). Nevertheless, we still see it stated in physics
* textbooks today.
* This volume simply says "An VIII" on the title page, and no more
* precise date is indicated. As most of that year in the Republican
* calendar was in Gregorian year 1800, I adopt "1800" as the date.
* This also is the date in most library catalogs.
* NOTE: the spelling "phénomene" (without a grave accent) is used
* consistently throughout; it is not a typo here in his title.
* Monge's memoir translated into English
* The translator is not named, though there is an Advertisement of the
* Translator -- in which we read that "Some of the Memoirs bear the marks
* of being hastily composed, but . . . no omissions or alterations have been
* made by the English Editor, which might render the translation any thing
* else than an accurate and complete copy of the original Work."
* Brief mention of Monge's memoir in a review of the whole "Memoires"
* We are interested only in the lines on p. 1850:
* "Abhandlung über die unter dem Nahmen Mirage bekannte optische
* Erscheinung, von G. Monge. Mit der Beschreibung dieses Phänomens wird
* man besser zufrieden seyn, als mit der Erklärung, die M. davon zu geben
* versucht."
* This is the 186. St. of 1800.
* Available at Google Books.
* Interesting REVIEW of mirages by Dr. JOHANN CHRISTOPH MATTHIAS REINECKE
* He begins with the Fata Morgana, "or the Castles in the Air of the
* fairy Morgana," immediately naming Angelucci, Kircher and Scotus as
* the older writers who have tried to offer descriptions and explanations.
* Of the newer writers, he mentions only Minasi, whose work he knows only
* from Nicholson's 1797 extract in the Philosophical Journal. Fortunately,
* it includes Minasi's illustration of the whole thing, which is copied
* here as Tafel I. So it's necessary to translate Minasi's description
* from the English. . . . And in doing so, he refers to the details of the
* engraving.
* Among other things, he points out the Sun low in the sky at the
* left edge of the image -- a detail that seems to have escaped all other
* students of the image. Evidently, he thinks Minasi's "45 degrees"
* refers to an azimuthal angle, not a solar altitude. (Note his remark
* on p. 209 about 9 a.m. being the favorable hour.)
* He also points out the impossibility that the city depicted could be
* Reggio, as it is Messina that lies on the opposite shore. The doubling
* of the images must make the city unrecognizable; and the random angles
* at which the "reflected" towers stand, without falling down, make them
* "true fairy-castles" which could "exist on the coast of neither Italy
* nor Sicily". Then comes a salient point: "Only through precise drawings,
* both of the phenomenon and of the view of the city of Reggio from the
* seaside, which, as has happened in the present copper engraving, were
* placed next to each other, could one part of the riddle and the origin of
* these fairy-castles be found." So he understood the need for photographic
* evidence decades before photography was invented, and centuries before
* photographs of Fata Morgana displays were actually obtained. "Here I
* regret that Minasi is not more detailed." But he generally accepts
* Minasi's account of both the phenomena and their cause as correct.
* So he thinks the sides of the waves generally have an inclination to
* the horizontal of 45 degrees, and supposes that the inclination of the
* mean surface can be similarly large, so that the waves could actually
* have vertical surfaces (as shown in Fig.1 of Tafel II) -- thus making
* the vertical mirror that Minasi imagined.
* He then gives a German translation of Nicholson's English translation
* of Minasi's Italian. This is a different German translation of
* Nicholson than the one published by Gilbert two years later (see the 1802
* entries below). Gilbert clearly used parts of Reinecke's discussion in
* making his own, and cites Reinecke -- though not by name.
* In the end, Reinecke tries to explain how Minasi's wave-facet scheme
* might work because of the shape of the Strait. It is all very contrived.
* However, on p. 206, there is the useful idea that Minasi probably meant
* Puglian miles, of 7000 Neapolitan palms each, in specifying distances.
* Apart from the supposed interactions of local causes, Reinecke admits
* that "it would always appear striking that this phenomenon is not also
* visible at other coasts . . . ". (p.210) In searching for examples, the
* best he can find is Wetterling's 1788 discussion of the Erhebung and
* the Seegesicht . [His accouunt of the virtual "cliffs" seen in Sweden
* in August, 1774, seems quite similar to Forel's identification of a
* "striated zone" as the hallmark of the Fata Morgana a century later.]
* Surprisingly, Reinecke knew of accounts by de Ferrariis and others
* of similar mirages in southern Italy, citing Giovene as well.
* Having identified the Seegesicht as being at least related to
* the Fata Morgana, Reinecke turns to looming. (p.219) Unfortunately,
* he says that it is the same thing as Kimmung , which is the appearance
* of floating or suspension produced when a strip of miraged sky is seen
* beneath objects at the apparent horizon -- but in an inferior mirage;
* the inverted image seems to hang down from the fold line. (P&E call
* this effect "Schwebung oder Kimmung" on their p.137). However, Reinecke
* correctly describes Erhebung as making "objects that lie under the
* horizon, or are hidden by other objects, become visible above it."
* He adds that the phenomenon is mostly observed on the Baltic Sea.
* As examples, he offers both Wetterling's discussion and that of
* Prof. Büsch (in his Tractatus .)
* His first impression was that just one kind of phenomenon had been
* called the Erhebung ; but on closer examination, he found that "many of
* them, especially those in which the images of ordinary objects appear cut
* off in the air, are really Morganas ." He cites examples from Wetterling
* that show extreme vertical exaggeration and rapid variations, noting the
* similarity of circumstances (position of the Sun, calm air) and location
* (near the sea), and compares these with Giovene's Lavandaja observations.
* But he is puzzled: if the circumstances and locations are so similar,
* why are the appearances so varied? (pp. 220-221)
* NOTE: as Reinecke was primarily a cartographer, geographer, and
* paleontologist, his ignorance of physics in general and optics in
* particular is to be expected; so his acceptance of Minasi's nonsense
* "theory" is not surprising. Given this ignorance, his connection of
* looming with Fata Morganas is a substantial accomplishment.
* The first page of this number says "V Bds. drittes Stück. März 1800."
* in italics; and then "A B H A N D L U N G E N".
* No author is named in this issue; but his identity is revealed in the
* July issue. This Abhandlung is numbered I. After the title is another
* italic note: "Hierzu gehören die Kupfer --- Tafeln I und II."
* I do not have a copy of these plates. However, they have been
* reprinted in Marcello Séstito's "Fata Morgana" book, which cites these
* papers by Reinecke, Büsch, and Monge, translating them all into Italian.
* Special thanks to Marcella Giulia Pace for bringing these important
* references to my attention!
* Reinecke's discussion of mirages is commented on by Büsch, followed by
* Reinecke's rejoinder and translation of Monge's article, and Reinecke's
* further comments on Monge. I list these components separately here,
* as they are assigned separate numbers in the Abhandlungen. All are
* in the Appendices to Séstito's book, translated into Italian.
* The first page of this number says "VI. Bds. erstes Stück. Julius 1800."
* in italics; and then "A B H A N D L U N G E N".
* Here is Abhandlung I., divided into four numbered sub-sections; they
* are sometimes cited by the collective title of the whole Abhandlung:
*
* "Fernere Beyträge und Bemerkungen über die Fata Morgana, das Seegesicht
* und die Erhebung."
*
* Büsch had himself already read Minasi's Büchlein some years before,
* and thinks it's better to see the original than Nicholson's English
* translation. And he doesn't think much of Minasi's original, either:
* "There is only one place in the book, p. 74, that makes me believe he
* had seen the phenomenon himself. But instead of describing it exactly,
* he immediately turns to the glorification of God. . . . So I almost
* believe that he himself knows no more about it than his father had
* told him. Then, it seems, this marvel appears only rarely, though even
* so M. produces a theory whereby it should appear very often and regularly
* under his defined conditions." (p.4)
* "Such a marvel should, if it's possible, be seen from more than one
* place, and from different viewing points and distances. But that should
* be easy, as it includes such a great space in the atmosphere.
* "It is a phenomenon of the atmosphere, so M. should have guessed to
* observe the state of the atmosphere at the same time, even if only by
* the height of the barometer. A thermometer would have been no trouble
* at all.
* "All this didn't stop him from devising a theory, but which? It
* should 'come from the different currents that meet in the Strait of
* Messina, pressing hard, and working against one another, create a
* mirror-smooth surface.' But that would be remarkable in a strait where
* a Scylla and Charybdis make currents that already the Ancients
* described as dangerous. But M. has surely never attentively observed
* a body of water in which several streams encounter one another. We have
* several such places in the Elbe , where the water is always restless,
* even if it is moved by no wind from the side. . . . " (p.5)
* After describing those examples in detail, he asks: "Should Nature be
* so completely different in the Strait of Messina, and even form a smooth
* concave mirror whose figure would have to be not just spherical, but
* that of a hollow cylinder?" (p.6)
* Büsch then adds a few more comments on "theorifying", and thanks the
* author [Reinecke] for mentioning his own Latin thesis on mirages. Then
* he returns to the Fata Morgana:
* "In regard to the Fata Morgana , one of three [sic] things must be true.
* 1) Either the whole phenomenon has been described falsely until now,
* or magnified through the desire for the miraculous. . . . Minasi is free
* of such monks'-dreams, but he seems to me not to have seen quite clearly
* yet. 2) But if Minasi has seen correctly, even if it were only one
* observation, then the phenomenon is something completely different from
* what I have seen and described a hundred times. Then we could completely
* lay the Fata Morgana aside, and so it will come to the point that
* Teutons will examine the matter more closely with Teutonic diligence,
* and seek to explain the results, which certainly lie in the study of
* the determination of the refraction. For no one but Gruber and me has
* yet thought to give an explanation of how it occurs over dry land ."
* He then relates some of his own mirage observations made while
* traveling on the Baltic coast. These were clearly inferior mirages,
* "which had been so remarkable to the French, but from which they learned
* nothing." [So much for Monge!] "I saw them at all hours of the day,
* and not a single time with different or unfamiliar circumstances. It
* amuses me when I read so many differences in the description. But then
* I think: 'The man did not see what you saw, or his power of imagination
* has added what yours did not, because you yourself know to keep it in
* bounds.'" (p.9)
* He then mentions Humboldt's observations of mirages, and says that he
* has just received the first part of the British Transactions for 1799
* with the observations by Vince; but he was not able to understand
* Vince's figure. [Obviously, because he only is familiar with inferior
* mirages.] (p.11)
* On the next pages is an amusing anecdote about showing the mirage to
* Graf von Czeczeny from Hungary, while traveling in the Harkshaide [sic]
* on the road from Hamburg to Kiel, in July, 1790. This is followed on p.14
* by a brief mention of the 1798 publication of Latham's observation of
* looming at Hastings.
*
* A footnote on the first page explains that the unsigned review in the
* March issue was written by Dr. Reinecke, a frequent contributor.
* Büsch's letter here is cited in a footnote on p. 133 of Pernter & Exner
* (1922), where it is attributed to Bertuch and Gaspari, the publishers of
* Allgem. geogr. Ephemeriden; Reinecke is not mentioned. Likewise, in
* Gilbert's 1802 discussion of Minasi (see his note on p.30 there).
* This must be nearly the last thing Büsch wrote; he died August 5, 1800.
* Reinecke's reply to Büsch
* Reinecke begins by quoting Büsch, and correcting the "3 for 2" error
* on p.7. He declares that the second is obviously the correct choice.
* And he emphasizes that Büsch has a single observation that seems to have
* some similarity with the Fata Morgana in his Tractatus .
* "That Minasi observed superficially may well be true; but where are
* the better observers?" [Note: Minasi was a medicinal botanist, not a
* physicist.]
* The first page of this number says "VI. Bds. erstes Stück. Julius 1800."
* in italics; and then "A B H A N D L U N G E N".
* This is part 2 of Abhandlung I.
* Reinecke's translation of Gaspard Monge's paper in Memoires sur l'Egypte
* There is a footnote to the title word "Kimmung" that says:
* "Gewönlich Erhebung , Franzos. Mirage , in Niederteutschland
* Währkatten , Updracht , Holl. Opduining , Schwäd. Hägring ."
* The first page of this number says "VI. Bds. erstes Stück. Julius 1800."
* in italics; and then "A B H A N D L U N G E N".
* This is part 3 of Abhandlung I.
* Reinecke's additional comments as translator of Monge
* Reinecke does not mince words: "The above theory requires a correction,"
* is his first sentence. ["Die obige Theorie bedarf einiger Berichtigung."]
* (Cf. Büsch's similar remarks in his 1783 "Tractatus".)
* Of Monge's "einzigen bestimmten Fläche", he says:
* "Eine so genau abgeschnittene Fläche findet aber, wie auch schon Hr.
* Prof. Büsch bey Gelegenheit der Gruberschen Erklärung desselben
* Phänomens bemerkt, in der Natur nicht statt; sondern die Dichtigkeit der
* Luft nimmt fortgehend und allmählich ab oder zu, und es ist kein Grund
* vorhanden, warum sie an einer Stelle mehr als an der andern reflectieren
* sollte. Statt einer einfachen Reflexion erleidet vielmehr ein
* Lichtstrahl, wenn er durch ein Medium von abnehmender Dichtigkeit geht,
* auf jedem Puncte seines Weges eine Brechung, und beschreibt daher eine
* krumme Linie, die, je nachdem die Dichtigkeitszunahme schneller oder
* geringer, und der Weg des Lichtstrahls länger oder kürzer ist, von
* verschiedener Art seyn kann." He goes on to explain that the usual
* state of the atmosphere makes the rays concave toward the Earth; but
* if we invert the usual decrease of density upward, the rays will be
* concave upward and turn their convex sides to the Earth -- "obgleich
* keine wirkliche Reflexion erfolgt."
* "Dies ist nun auch das Phänomen, von dem Hr. Prof. Büsch in
* seinem Tractate und in obigem Briefe handelt. Seine Erklärung, die
* Monge nicht gekannt zu haben scheint, weicht von der hier gegebenen
* ganz ab, aber wie? --- Nach Hr. Büsch erklärt sich alles aus der
* gewöhnlichen --- verstärkten horizontalen Strahlenbrechung, statt
* dass wir es eben aus der umgekehrten horizontalen Strahlenbrechung
* erklären." He goes on to explain that either explanation will work; that
* is, he sees that it is the change in the ray curvature that is needed
* to produce the inverted images. Both explanations produce "the same
* phenomenon, a variation of the horizon." Büsch's model should produce
* "eine Erhebung der Gegenstände über den Horizont"; in Reinecke's
* model, "die Gegenstände müssen . . . unter den Horizont hinabsinken."
* He decides that Hebung is the usual case in northern latitudes, and
* thus accounts for Büsch's observations of looming.
* So he notes the problem: "Monge hat keine Winkelmessungen
* angestellt, und überhaupt auf diesen Punct, wie es scheint, nicht
* Rücksicht genommen." So Reinecke recognized that the absolute values of
* the altitudes near the horizon are needed to understand the full details
* of the mirages. The DIP is an essential feature of mirages.
* "Inzwischen ist es sehr zu wünschen, dass Beobachter, die sich in
* Rücksicht ihres Wohnorts in einer dazu günstigen Lage befinden, ---
* denn bey Erscheinungen, die den Beobachter ganz unvorbereitet auf der
* Reise überraschen, ist das nicht zu erwarten, --- ihre Beobachtungen
* mit Winkelmessungen, und was sich ohnehin versteht, mit Thermometer-
* und Barometer-Beobachtungen verbinden mögen, wie schon Hr. Büsch am
* Schlusse seines Tractats empfiehlt, weil ohne diess nothwendig manches
* schwankend bleiben muss."
* Reincke's perceptive remarks here show a much better understanding of
* the mirage problem than his earlier comments would suggest.
*
* The first page of this number says "VI. Bds. erstes Stück. Julius 1800."
* in italics; and then "A B H A N D L U N G E N".
* This is part 4 of Abhandlung I.
* Available from Google Books:
* https://www.google.com/books/edition/Allgemeine_geographische_Ephemeriden/OJgPbBBjqpQC?hl=en&gbpv=1&dq=Monge+Reinecke+mirage&pg=PA15&printsec=frontcover
* and
* https://www.google.com/books/edition/Allgemeine_geographische_Ephemeriden/aRiKHZFw3zUC?hl=en&gbpv=1&dq=Monge+Reinecke+mirage&pg=PA15&printsec=frontcover
* EARLY MIRAGES; DISTORTED MOONRISE
* extracted and translated from:
* Jo. Geo. Büsch tractatus duo optici argumenti, Hamburgi 1783, 132 S. 8.
* "Ich bemerkte dieses Phänomen schon in meiner Jugend bey den
* Ueberfahrten von Hamburg nach dem eine Meile entlegnen Harburg, wo mein
* Grossvater lebte. Wenn der Wind die Wellen mitten im Strome ziemlich
* heftig um das Schiff bewegte, schien das Wasser am Ufer vollkommen ruhig
* zu seyn, gleich einer Spiegelebene. Dieses komme, sagten mir die
* Uferbewohner, von den Untiefen am Strande her; allein, wenn wir eine Höhe
* erstiegen, und von da nach dem entgegengesetzten Ufer sahen, war auch das
* Wasser voll Wellen."
* (cf. Abbott, 1854, who reports the same phenomenon in India!)
* (also, Forel, p. 526 of his 1895 monograph; and Manning, 1912.)
*
* includes a distorted moonrise: "Der Mond, der beynahe voll war, ging
* auf, wie ihn Fig. 6 zeigt. Als ich die anderen Passagiers fragte, ob
* ihnen nicht etwas besonderes am Monde vorkomme, antwortete einer:
* `Meiner Treu, er gleicht einem umgestürzten Nachtgeschirr.'"
* [See Büsch, Tractatus duo (1783) for the original quote in English.]
*
* Prof. Johann Georg Büsch (1728 - 1800) taught at the academic
* Gymnasium in Hamburg. About 1780 he allowed Reinhard Woltman to attend
* his lectures and use his extensive library. Woltman in turn became the
* supervisor of Heinrich Wilhelm Brandes, who was in charge of the water
* works on Neuwerk in 1794-95, and was recommended by Woltman to the post
* of "Deichconducteur" in Eckwarden in 1801, where he continued Woltman's
* observations of refraction phenomena.
* This is Part 3 of Band 3, mostly devoted to refraction and mirages. It
* begins with a German translation of Huddart's paper on dip, followed by
* General Roy and Dalby's work. The issue date is not known, but Gilbert's
* preface to the whole volume is dated "den 2ten Februar 1800".
* HUDDART translated by Gilbert
* With the usual copious comments by Gilbert! Already on p. 259, he
* inserts a footnote referring to Gruber and Büsch, "die der Leser im
* nächsten Bande der Annalen in kurzen Auszügen finden wird".
* This volume of Gilb. Ann. is available at
* https://www.google.com/books/edition/Annalen_der_Physik/_3zqQ4mRhO8C?hl=en&gbpv=1&dq=Gilbert+Annalen+Physik+1800+Huddart&pg=PA265&printsec=frontcover
* EARLY MIRAGES
* summaries of the work of others by Ludwig Wilhelm Gilbert:
* 1801 review of Monge's final paper
* Buried in a long paragraph on a variety of technical publications,
* we find: "One other optical phenomenon has been illustrated by the
* publications of the present year, viz. what is called the Mirage, in the
* Collection of Memoirs published by the Philosophers who followed Bonaparte
* to Egypt. The author is M. Monge, whose account is neither very clear
* nor scientific." (This follows a mention of Wollaston's 1800 paper.)
* As this is mentioned under "Domestic Literature", I suppose it is based
* on the official English translation of the Memoirs published in London.
* Full title: "The New Annual Register or General Repository of History,
* Politics, and Literature, for the Year 1800."
* NOTE: the several sections of this volume are separately paginated.
* This is in the last one, which starts with "Biographical Anecdotes and
* Characters"; its sub-section "Domestic Literature of the Year 1800" runs
* from p. 225 to p. 336. The subsection "Foreign Literature . . . " begins
* on p. 337. No authors' names are given.
* EARLY EXPERIMENTAL DEMONSTRATION OF MIRAGE
* Abbé Tobias Gruber (Grüber?) -- see his 1786 paper.
* Gilbert says this is an extract of Gruber's "Physikalischer Abhandlung
* über die Strahlenbrechung und Abprallung auf erwärmten Flächen" in
* Abhandlungen der böhmischen Gesellschaft der Wissenschaften, B.II, (1787).
* Pernter and I both have 1786 for its date; Gilbert's date might be the
* actual year of publication -- or that of the Dresden offprint.
* Büsch's reference to Gruber in his comments in Vol. 6 of A.G.E.
* [see above], and his contributions to Gilbert's Annalen in the next few
* years suggest that Gilbert reprinted Gruber's work at Büsch's suggestion.
* Gilbert's preface ("Vorredé) to the volume is dated "de 2ten Februar".
* This begins the fourth part of Band 3.
* QUANTITATIVE MEASUREMENTS of MIRAGES and VARIABLE REFRACTION
* Reinhard Woltman (Not "Woltmann", says Pogg.)
* [It seems that Woltman was Brandes's supervisor in 1794-95.]
* Gilbert attributes the term "Spiegelung" to Woltman.
*
* Mirages visible in RAIN and on overcast days (cf. Ashmore, 1955):
* ". . . selbst im Regen verschwindet sie nicht eher, als bis die
* Undurchsichtigkeit der Luft die Aussicht in die Ferne verhindert.
* Ueberhaupt ist die Erscheinung (wenigstens um Cuxhaven) weit häufiger
* als man sie mit blossen Augen gewahr wird, indem an dunkeln Tagen der
* Luftstreifen, welcher die Gegenstände von der Erde zu trennen scheint,
* nicht so als an hellen Tagen ins Auge fällt." (p. 399)
*
* REDUCED SIZE of image attributed to reflection at a convex surface (p.403):
* "Bey unserm Phänomen sind . . . die Bilder allemal beträchtlich
* kleiner , als ihre Objecte." (Cf. Bravais, 1853; Riccò et al., 1888)
*
* VARIATIONS:
* "Auch die astronomische Horizontalrefraction würde daher wenigstens
* um eben so viel, d.i. etwa um 1/6 ihrer ganzen Grösse veränderlich und
* ungewiss seyn." (p. 421)
*
* Gruber's footnote, pp. 429-430, on CORRELATION of DIP & MIRAGEs:
* ". . . so ist bey allen Spieglungen ohne Ausnahme Depression , so wie bey
* Spieglungen aufwärts, Hebung über diese scheinbare Horizontallinie."
* See Gruber's paper on this in the following item.
*
* VERTICAL STRIPES at the fold line of SUPERIOR MIRAGES:
* "Zuweilen trennt ein Luftstreifen das verkehrte Bild von dem darunter
* stehenden Gegenstande; doch stossen häufiger Bild und Gegenstand
* zusammen , und vermischen sich so, dass keins von beiden kenntlich ist,
* und das Ganze wie eine hohe Seeküste, mit vielen senkrechten Strichen,
* erscheint." (p.430)
*
* Relation of "seeing" (TURBULENCE) to inferior mirage (pp. 432-433):
* "Die Bilder der Spieglung unterwärts sind sehr unbeständig und
* wandelbar; sie werden bald grösser, bald kleiner, bald in Stücken
* getrennt, und sind zuweilen eine Zeitlang in steter Bewegung."
*
* TEMPERATURE DIFFERENCE between AIR and WATER:
* ". . . allemal, wenn das Wasser um 2° Fahrenh. oder mehr wärmer als
* die Luft war, eine Erniedrigung der Strahlen, die sich über die
* Wasserfläche erstreckten, und (vorausgesetzt, dass die Gegenstände
* sichtbar waren) eine Spiegelung herabwärts stat find. War dagegen das
* Wasser um 2° F. kälter als die Luft, so fand Hebung der Strahlen
* und nie eine Spiegelung herabwärts statt." (pp. 434-435)
* SEASONAL and DIURNAL variations: p. 435.
* OMEGAs are described, p. 438:
* "Sieht man die Sonne oder den Mond aufgehn oder untergehn , so
* giebt ihre Gestalt ein untrügliches Merkmal, ob Hebung oder Senkung
* statt findet. Im letztern Fall scheint die Sonnen- oder Mond-scheibe
* nicht rund, sondern in die Länge gezogen. Ein Theil derselben spiegelt
* sich unterwärts; das umgekehrte Bild kann 1/8 bis 1/4 des Durchmessers
* betragen, und es ist, als ob an dem auf- oder untergegangnen Theile der
* Anfang einer andern Scheibe angesetzt wäre." (p. 438)
*
* Gilbert's footnote on p. 397 says this is an extract of two works of
* Woltmann's "under the above title, one still unpublished, reported in
* the Götting-gelehrten Anzeigen J. 1796, St. 82; and from Woltmanns
* Bemerkungen über ein (scheinbar) katoptrisches Phänomen , welches
* an den Gegenständen nahe am Horizont nicht selten sichtbar ist , . . . in
* den Neuen Abhandl. der kön. böhmischen Gesellsch. d. Wiss. B. 3.
* Prag 1798. S. 67-97. 4."
* Note that Gilbert prints double-s as a long followed by a short s.
* This continues the fourth part of Band 3.
* EARLY THEORY OF MIRAGE; connection of MIRAGE and DIP
* Abbé Tobias Gruber (Grüber?) comments on Woltman's preceding paper;
* possibly an extract of his 1793 "Theorie . . . Senkung und Hebung" ??
* He uses ray diagrams, assuming a flat Earth, and thereby has some
* difficulties in explaining the reduced size of the inverted images in
* inferior mirages, and the vertical striation associated with superior
* ones.
* There is also extensive editorial discussion of terminology in Gilbert's
* long footnotes; e.g., he criticizes Gruber and Woltman for using the
* words "Abprellung" and "katoptrisches" for inferior mirages: "allein
* da sie das wirklich nicht, sondern ganz und gar eine dioptrische
* Erscheinung ist . . . ". (p. 441)
* This continues the fourth part of Band 3.
* a simple case of LOOMING in the mountains
* Gilbert unaccountably makes more of this than it deserves. His final
* footnote contains: "Auch bei uns, mitten im Deutschland, ist also die
* Fata Morgana zu Hause, obwohl bei weitem seltener als in dem heissen
* Unter - Italien und unfern der See. Denn dass die wundervolle
* Fata Morgana zu dieser Klasse ungewöhnlich starker Refractionen
* gehört, glaube ich in einem der folgenden Stücke der Annalen ziemlich
* ausser Zweifel setzen zu können." But he recognizes that it's similar
* to Latham's observation.
* This may be the earliest MIS-USE of "FATA MORGANA" for a simpler case.
* In the fourth part of Band 5.
* William Hyde WOLLASTON's paper on mirage theory:
* Wollaston re-invents Hooke's (1665) two-liquid demonstration here.
* He distinguishes between "two opposite states of the atmosphere" that
* produce double or triple images; he also notes what we would call
* looming, and explicitly mentions mirages on roads.
* His laboratory experiments on liquids showed the focusing effect:
* ". . . adjacent portions of the converging rays will form a focus, beyond
* which they will diverge again; and the varied medium will produce
* effects similar to those caused by a medium of uniform density having
* a surface similar to the curve of densities . . . ." (p. 242)
* "When an oblique line . . . is viewed through any variable medium . . . ,
* it appears bent into different forms . . . .
* "If it be at the distance of the principal focus, one point of it is
* bent into a vertical line . . . ." (p. 244)
*
* He also discovers the laminar sub-layer, via the third image:
* "To explain why red-hot iron occasions two [additional] images, while
* solar hear produces but one, I imagine that the intense heat in the
* former case rarefies the air for some small distance uniformly, and
* thereby affords the same series of variations as between other fluids
* of uniform density; but that, in the latter, the heat is conveyed off
* as fast as it is generated . . . ." (p. 248)
* On the next page, he mentions that "a level open road" is best for
* observing what we would call inferior mirages. He also uses "a pocket
* telescope magnifying about 16 times".
* Jean André de Luc's inferior-mirage observation, and disbelief
* A curious paper: "Es ist allgemein bekannt, dass am Ufer der Seen und
* der breiten Flüsse und am Strande der Meerbusen eine gewisse optische
* Täuschung oft statt findet, wenn der Zuschauer sich auf einem erhöhten
* Standpunkte befindet; er sieht nemlich alsdann unter gewissen Umständen
* das entgegengesetzte Ufer wie in der Luft schwebend, und man pflegte
* dieses Phänomen auf die Strahlenbrechung zu reduciren: ich glaube aber
* nicht, dass es von dieser Ursache herrühre."
* He nicely describes the effects of eye height; but manages to convince
* himself the apparent "sky" is just a band of haze, "eine Dunstschicht",
* that manages to be indistinguishable from the sky. (This seems incredible
* to anyone living in a dry climate, but is perhaps not so far-fetched
* for someone living in hazy Germany.) At the end of the 10th page
* of the paper (p.177), he lets the cat out of the bag: "Ich zweifle
* kaum dass dies der wahre Grund aller Erscheinungen dieser Art wirklich
* sei, und zwar um so weniger, da ich nie habe begreifen können, wie
* Strahlenbrechung etwas dergleichen hervorbringen könnte."
* The observation was made over a peat-bog; the miraged trees were
* "ohngefahr eine deutsche Meile" away (6 or 7 km).
* The GNF had a number of well-known members, including Adelbert von
* Chamisso, Alexander von Humboldt, Adolf Traugott, and Johann Elert Bode.
* Reuss fails to give the year, but other citations to this volume say
* 1801 [confirmed by e-mail from Hans-Ulrich Raake of the
* Universitätsbibliothek, Humboldt-Universität Berlin (30 July 2002).]
* Prof. De Luc was Swiss.
* Gilbert's translation of Wollaston's 1800 paper, with copious notes:
* Gilbert's version of Giovene's observations, heavily annotated
* Here Giuseppe Maria Giovene is Germanized to "Johannes"; the whole
* thing is taken from Zimmermann's "Allgemeiner Blick auf Italien" (1797).
* A good first-hand account of a Fata Morgana observation from near
* Molfetta, on the Adriatic coast (about 300 km north of Reggio):
* "Die von mir selbst beobachteten Phänomene dieser Art schreibe ich
* wörtlich aus meinen Journalen ab; von den übrigen theile ich die
* Nachricht meiner Correspondenten unverändert mit.
* "Ich befand mich am 9ten Februar 1790 auf einem kleinen Landhause,
* wo ich mich wegen des freien Horizonts vorzüglich gern aufhalte.
* Die Tagen vorher waren heiter gewesen, und es hatte ein mässiger
* Nordwestwind geweht. Der ausnehmend schöne Winterabend lockte mich
* ungefähr eine halbe Stunde nach Sonnenuntergang an ein Fenster, das
* sich gerade nach S.S.O. öffnet. [Giovene's original Italian indeed has
* "S.S.O."; but "O" stands for "ovest"; so the directions are wrong here.]
* Die Luft war so still, dass der Rauch von den Städten Terlizzi , Ruvo
* und Corato , auf die ich die Aussicht hatte, sich gar nicht bewegte,
* sondern über diesen Städten wie ein grosser Sonnenschein hing.
* [Certainly "Sonnenschirm" was intended here; this correction is made
* by P&E on p. 164, without comment.] Indem ich am Horizonte umher sah,
* schienen mir an dem äussersten Ende desselben gegen Westen einige Wolken
* aufzusteigen, die etwa 20 Grad einnahmen. Um daraus auf den Wind und auf
* die Witterung des folgenden Tages urtheilen zu können, wollte ich ihren
* Zug beobachten. Sie stiegen bald auf 2° Höhe, fingen dann aber an
* mannigfaltige Gestalten anzunehmen, und dieses Spiel überzeugte mich,
* dass sie ganz etwas anderes waren, als Wolken.
* "Ich bat daher den Doktor T r i p a l d i , einen sehr unterrichteten
* Mann, der mich gerade auf einige Tage besucht hatte, an der fernern
* Beobachtung Theil zu nehmen, und wir schickten uns beide dazu auf das
* sorgfältigste an. Die vermeinten Wolken nahmen alle Augenblicke eine
* andere Gestalt an. Zuerst sahen wir im Hintergrunde eine Menge Palläste
* und Thürme, die eine grosse Stadt vorstellten, so dass wir glaubten,
* vermittelst einer sehr verstärkten atmosphärischen Refraction den
* Flecken Cerignola zu sehn, der in der Richtung lag, jedoch über 8
* deutsche Meilen, (in gerader Linie nur 6,) enfernt war. Allein gar bald
* veränderte sich das Schauspiel: wir sahen zwei Hügel gegen einander
* über, die immer höher und höher wurden, und sich dann in viereckige
* Thürme mit grossen Fenstern verwandelten, wodurch das Licht von der
* Abenddämmerung einfiel. Doch ich kann unmöglich alle die verschiedenen
* Figuren beschreiben, die mit der grössten Schnelligkeit abwechselten.
* "Unsre Verwunderung wurde indess bald noch sehr vermehrt. Die
* Dämmerung war sehr hell, und ich sah verschiedne Mahl Lichtströme
* vom äussersten Horizonte bis zu einer Höhe von 6 bis 7° aufsteigen.
* Ich hielt dieses anfangs für eine Täuschung, allein D. T r i p a l d i
* sah sie gerade so, und der Zeitpunkt, worin wir einen neuen Lichtstrahl
* wahrnahmen, stimmte jedes Mahl vollkommen überein. Wir stellten uns
* darauf vor das eine Fenster, das gerade nach W.N.W. lag, und sahen das
* Phänomen eben so. Die Lichtwellen gingen gerade bis an die Grenzen
* der Dämmerung; da, wo die Dämmerung stärker war, waren sie lebhafter,
* und gegen die Grenzen der Dämmerung zu schwächer. Fünf oder sechs
* lichte Ströme erschienen unmittelbar nach einander, darauf erfolgte
* eine Pause von 1 oder 2 minuten, worauf sich neue Ströme zeigten, und
* während dieses Spiels wechselte eine unendliche Mannigfaltigkeit der
* seltsamsten Figuren am äussersten Rande des Horizonts ab. Dieses schöne
* Schauspiel währte etwa eine halbe Stunde; es verlor an Schönheit, so
* wie die Dämmerung abnahm, und nach 3/4 Stunden war es gänzlich vorbei."
* Giovene points out that such phenomena are not rare in Apulia and
* Lecce province (Terra d'Otranto, the old Japygia). But writers have
* ignored it, except in folklore, with one exception: he cites Antonius
* de Ferrariis (Galatheus) (De situ Japygiæ , 1558) for reporting the
* name of Mutata . (p. 9)
* A useful common observation: "Nach Versicherung der Einwohner des
* Vorgebirges von Lecce ist die Zeit dieser Erscheinung vor Aufgang
* oder nach Untergang der Sonne, und in der Ebene soll man dabei bald ein
* stürmisches Meer, bald eine Stadt, bald einen Wald sehn." (pp. 10-11)
* He also says: "Die Seeleute von Molfetta nennen sie Lavandaja
* (Wäscherinn,) -- warum, weiss ich nicht -- und halten sie für Vorboten
* einer Veränderung in der Witterung. In der That erscheint die
* Lavandaja in ihrer grössten Schönheit, wenn der Wind lange Zeit geweht
* hat und nun eine Stille erfolt. Im Herbste und Winter ist sie häufiger
* als in den übrigen Jahreszeiten, wiewohl man sie auch oft im Sommer
* und zuweilen im Frühling sieht. Im Sommer haben wir fast alle Tage
* eine Art kleiner Lavandaja des Nachmittags; indess ist sie auch hier
* vor Sonnenaufgang und nach Sonnenuntergang am prächtigsten.
* "In Molfetta sieht man die Lavandaja mehrentheils über dem Monte Gargano ,
* einem Gebirge, welches in die See vorspringt, von Molfetta 60 ital.,
* (15 deutsche,) Meilen entfernt ist, sich von dort am äussersten Horizonte
* zwischen W.N.W. und N.N.W wie eine dunkelblaue Wolke zeigt, und aus dessen
* Ansicht, je nachdem es sichtbar oder unsichtbar ist, und die Wolken den
* Fuss oder den Gipfel desselben bedecken, oder einen grossen Hut darüber
* bilden,) die Schiffer das Wetter mit vieler Zuverlässigkeit vorhersagen.
* Beim ersten Mahle, als ich daran die Lavandaja , ohne noch von ihr
* gehört zu haben, sah, wurde ich wirklich unruhig. Das ganze Gebirge
* war in einer zitternden Bewegung ; ein Theil des Berges versank und
* liess ein grosses Thal zurück; an derselben Stelle erhob sich einige
* Minuten nachher ein neuer Berg, höher als der vorige, und neben diesem
* stiegen mehrere andere kegelförmige empor, nahmen aber sogleich die
* Gestalt grosser viereckiger Thürme an, die sich eben so in einem
* Augenblicke versenkten und grosse Thäler eröffneten. Endlich schien
* mir der ganze Berg fürchterliche Erschütterungen zu leiden. --- Ich
* habe diese Abwechselungen oft mit dem grössten Vergnugen beobachtet.
* Die wunderbarsten Figuren folgen in einem Augenblicke auf einander,
* und eine nur etwas warme Phantasie wird sich sehr leicht überreden,
* Pferde, Menschen, Schiffe, Thürme und Städte zu sehn.
* "Noch eine besondere Lavandaja zeigt sich hier, besonders wenn die
* Sonne gegen Westen steht und ein leichter Ostwind weht. Das Vorgebirge
* Gargano verändert dann mit der grössten Geschwindigkeit seine Gestalt
* auf eine unendlich mannigfaltige Weise. Es verlängert sich, zieht
* sich wieder zusammen, und scheint in viele Theile zerstückt, die das
* Ansehn von Inseln im offenen Meere haben. Zuweilen scheint ein Theil des
* Meeres viel höher zu seyn als das übrige, und das Wasser in der Ferne
* scheint von einem heftigen Sturme bewegt zu seyn, ob es sich gleich in
* vollkommner Ruhe befindet." (pp. 11-14).
* He then goes on to describe a case of looming at sunrise on 15
* Oct. 1789, "in meinem Landsitze eine halbe Meile von Molfetta," which
* brought into view several towns normally hidden. This was also seen by
* Dr. Tripaldi. "Um 9 Uhr, nachdem wir 3 Stunden beobachtet hatten, war
* alles wieder wie gewöhnlich. In Hoffnung, das Phänomen wieder zu sehn,
* wenn ich höher träte, stieg ich auf eine Terasse, die ungefähr 20 par.
* Fuss über dem Fenster liegt, und wirklich sah hier das Schauspiel noch
* in seiner ganzen Schönheit. . . . Da D. T r i p a l d i am Fenster
* geblieben war, so überzeugten wir uns, dass damals das Phänomen 40 Fuss
* über der Erde gar nicht, in 60 Fuss Höhe aber vollkommen sichtbar war."
* (p. 16)
* Giovene recognized that these were all refraction phenomena; but he
* tried to connect them with minerals in the ground. As usual, "Dünste"
* get the blame. Still, he suspects "eine . . . wellenförmige Bewegung" of
* the air is responsible for the motions.
* ANTONIO MINASI's classic (if rather exaggerated) Fata Morgana review
* This is Gilbert's translation into German of Nicholson's translation
* into English from Minasi's original Italian, with commentary by
* both Nicholson and Gilbert. . . .
* Gilbert is very hard on Minasi: "Ich entlehne diesen Aufzug aus Minasi's
* Werke über die Fata Morgana aus Nicholson's Journal of nat. philos.,
* Vol. I, p. 225. Da Minasi's Träumereien selbst bei einem so
* nüchternen und scharfsinnigen Physiker, als Nicholson, Eingang gefunden
* haben, so hielt ich es für nicht unverdienstlich, darzuthun, dass
* Minasi's Nachrichten mit so viel Einbildungen versetzt sind, dass man
* sie im Ganzen kaum für etwas mehr, als für ein Mährchen nehmen darf,
* und sie bei einem Versuche, die Fata Morgana zu erklären, lieber ganz
* bei Seite legt." [footnote attached to the title!]
* Here I credit all three as authors; none is named explicitly. Notice
* that most of pp. 24 - 30 is occupied by a long commentary by Gilbert on
* Minasi's dissertation.
* Furthermore, Gilbert refers to Reinecke's discussion of Minasi in the
* footnote on p. 26 here, as "der Verf. des Aufsatzes in den Allg. ge. Eph.
* 1800, S. 199," and again in the notes on pp.30 ("Verfasser des angeführten
* Aufsates [sic] in den geogr. Ephem. ) and 32.
* The harsh and rather dismissive treatment of Minasi here resembles
* Büsch's scornful comments on Minasi in A.G.E. Vol. 6 (1800).
* William Beauford's perceptive review, just before Wollaston's
* Probably this should be an entry in the FOG file. However, his
* perceptive remarks require its presence here, despite his curious
* explanation: "Of all the phænomena exhibited by nature in her various
* operations, there are none more curious and extraordinary than those
* represented by the reflection and refraction of light from fogs and
* vapours arising from the sea, lakes, and morasses, replete with marine
* and vegetable salts. For such vapours, by means of the said salts,
* form various polished surfaces, which reflect and refract the light of
* the sun, and even the moon, in various directions; thereby not only
* distorting but multiplying the images of objects represented to them in
* a most surprising manner; forming not only images of castles, palaces,
* and other buildings, in various styles of architecture, but the most
* beautiful landscapes, spacious woods, groves, orchards, meadows, with
* companies of men and women, with herds of cattle, walking, standing,
* lying, &c., and all painted with such an admirable mixture of light and
* shade that it is impossible to form an adequate conception of the
* picture without seeing: not any scenery represented by the
* camera obscura can be more beautiful, or more like faithful
* representations of nature."
* Nice discussion of TERMINOLOGY: "The only ones which seem at present
* to have attracted the attention of the curious, are those frequently,
* during the summer season, seen on the southern coasts of Italy, near the
* antient city of Rhegium; and even to this attention they were directed
* by the fishermen and country peasants, who in their native tongue call
* them fata morgana , or dama fata morgana . They are, however,
* frequently noticed by the English, Erse, and Irish peasants, fishermen,
* and mariners; and denominated in the languages of the two latter
* feadhreagh mairethmhe , or sea fairies, and duna feadhreagh , fairy
* castles. . . . On the eastern and western coasts of South America, even
* on the highest summit of the Andes, the fata morgana is met with.
* Also far out at sea, in the midst of the Atlantic and Pacific oceans,
* the adventurous mariner sometimes observes them; and though well known
* under the name of fog banks , yet has their appearance been so imposing
* as to illude the nicest scrutiny, and to promise refreshments to the
* fatigued and sea-worn mariner which he could not obtain. The most
* antient account of these aërial castles and islands which has been
* transmitted to us, is the representation of a beautiful island situated
* nearly in the middle of the Atlantic ocean, between the coasts of
* Ireland and Newfoundland, first observed by Danish and Irish fishermen
* about the year 900, and from that period to the commencement of the 14th
* century frequently by the Anglo-Saxon, English, and French fishermen and
* mariners.
* "But, as this island could never be approached, it was called the
* inchanted island , and supposed by the maritime inhabitants of Scotland,
* Ireland, France, and Spain, to be the country of departed spirits, and
* consequently denominated in Erse Flath Innis , or the Noble Island; in
* Irish Hy Brasil , or the Country of Spirits; by the Anglo Saxons,
* Icockane , or the Country in the Waves; and by the French and Spanish,
* who supposed it to consist of two distinct islands, Brasil and
* Assmanda ; or the Islands of Ghosts."
* He then describes the Irish mirages in agonizing detail: "The country
* seemed laid out in lawns and improvements, in which were situated three
* gentlemen's seats; the houses well defined, the windows and doors
* distinct; some of the windows appeared open, and brass knockers were
* seen on the doors." [etc., etc., at some length.]
* Then we get more factual details: ". . . none of those aërial
* exhibitions continue any length of time, and always in calm weather and
* a clear sky, if the picture is brilliant; for, though those fog banks
* often appear in dark or cloudy weather, the reflection is imperfect, and
* represents only confused images of rocks, mountains, and capes."
* Then the final, fatal admission: "For the vapour, being formed into
* different parts, the light refracted through them causes the confused
* appearance of ruins, houses, woods, lawns, &c. in the same manner as a
* board covered in an irregular manner with black and white spots mixed
* with lines, will at a certain distance resemble a landscape with woods,
* ruins, houses, trees, castles, &c., and under such imposing forms as to
* appear real representations. Of this species of the fata morgana seem
* to be those seen at Youghal in 1801 before spoken of; but in whatever
* manner the representations from vapours and fogs are formed, the weather
* must be calm and serene, otherwise the vapours will be broken and
* dispersed by the wind." (cf. Baur, 1857)
* There is a passing mention of Commodore Byron's Voyage round the World.
* Note that Beauford cites both Swinburne's Travels and Crantz's
* History of Greenland . The long s is used throughout.
* NOTE: In his letter to me of 2 Feb. 2002, Irish folklore expert
* Miceal Ross has some harsh words for Beauford's scholarship here:
* "I do not know where he gets his Irish from. I never heard a word
* called feadhreagh and if it existed the declension would be faulty and
* also the spelling. The 'e ' after dh would be impossible. . . . Duna should
* be Dúnta. It looks like the same William had no Irish and probably
* little access therefore to tradition.
* "Flath Innis [recte Flaith Inis] means the isle of princes; Hy Brasil
* or Brazil is in Irish `Í Bráth-saol' The island of eternal life."
* [Yet the criticized words appear in some 19th-Century books; cf.
* M`Farland, 1853. . . .]
* WOLLASTON picks up Monge's use of "mirage" in his Bakerian Lecture:
* He starts by refuting Monge's density discontinuity:
* "The definite reflecting surface which he [Monge] supposes to take
* place between two strata of air of different density, is by no means
* consistent with that continued ascent of rarefied air which he himself
* admits; and the explanation founded on this hypothesis will not apply
* to other cases, which may all be satisfactorily accounted for, upon the
* supposition of a gradual change of density, and successive curvature of
* the rays of light by refraction." (p.2)
* There is also a fine illustration of the SMOOTH BEND where the erect
* and inverted images meet; the figure on p. 3 is the same one reprinted
* as Tafel VII, Fig. 6 in Gilb. Ann. vol. 23, showing the bent oar. It
* is worth quoting his passage about this (pp. 3 and 4):
* "I was sitting in a boat near Chelsea, in such a position that my eye
* was elevated about half a yard from the surface of the water, and had a
* view over its surface, that probably somewhat exceeded a mile in length,
* when I remarked that the oars of several barges at a distance, that were
* then coming up with the tide, appeared bent in various degrees, according
* to their distance from me. The most distant appeared nearly in the form
* here represented; dd being my visible horizon by apparent curvature
* of the water; ab the oar itself in its inclined position; and bc
* an inverted image of the portion be . By a little attention to other
* boats, and to buildings on shore, I could discern that the appearance
* of all distant objects seen near the surface of the water was affected
* in a similar manner, but that scarcely any of them afforded images so
* perfectly distinct as the oblique line of an oar dipped in the water.
* "A person present at the time (as well as some others to whom I have
* since related the circumstance) was inclined to attribute the appearance
* to reflection from the surface of the water; but, by a moderate share
* of attention, a very evident difference may be discovered between
* the inversion occasioned by reflection, and that which is caused by
* atmospherical refraction. In cases of reflection, the angles between the
* object and image are sharp, the line of contact between them straight and
* well defined, but the lower part of the image indefinite and confused,
* by means of any slight undulation of the water. But, when the images
* are caused by refraction, the confines of the object and its inverted
* image are rounded and indistinct, and the lower edge of the image is
* terminated by a straight line at the surface of the water."
* (Similar advice is given by Bravais, 1853.)
* Brandes's first communication about refraction mentions Woltman
* "Ich hoffe Ihnen nächstens eine Reihe von Beobachtungen über
* die Refraction , denen ähnlich, die Sie von Hrn. W o l t m a n n
* kennen, übersenden zu können."
* This item is under the heading "Auszüge aus Briefen an den Herausgeber"
* Castberg's FATA MORGANA review (translated by Gilbert)
* Several very early references here: Pomponius Mela, Thomas Facellus,
* Athanasius Kircher, Pliny and Haithon. But he is mostly concerned with
* the F.M. classics: Minasi and Angelucci. There are also references to
* then-recent discussions by Gilbert, including looming and mirages.
* Castberg leans heavily on the idea that, if this were a simple mirage,
* the locals would recognize the miraged objects: they don't, so it isn't.
* He makes the good point that the cities are too far apart (6500 toises):
* at this distance, one would be hard pressed to make out individual
* buildings, let alone individual figures, trees, sheep, etc.
* [This matter of DISTANCE is often overlooked in fantastic reports.]
* Furthermore, if it were a mirage of Messina seen from Reggio, then the
* reverse should be true; but (he says) there are no reports of the
* Morgana being seen from Sicily.
* He concludes that it is the shadows of the city cast on mists!
* Brandes comments on atmospheric optics, including FATA MORGANA
* The Fata Morgana is discussed on p. 367, where he comments on Castberg's
* report in Ann. 17, 183. There is an amusing crack: "Die Bilder sind
* gewöhnlich so verzerrt, und der Gegenstand selbst erscheint unter so
* veränderter Gestalt, dass man leicht mit Hülfe einer italiänischen
* Phantasie Säulengänge, Wasserleitungen, u. s. w., in diesen
* Erscheinungen finden kann."
* See also the Brandes papers from vols. 17 & 18 in "Terrestrial Refr."
* [from a letter dated 2ten Febr. 1805]
* Brandes reports his progress to Gilbert
* There is some interesting background here: he explains how he was led
* by Pictet's observations of the diurnal cycle of temperature gradients
* at different heights, which showed the same pattern he had already seen
* in his own observations of variable terrestrial refraction, to make such
* temperature measurements himself.
* [from a letter dated 16ten Mai 1805]
* Biot's astronomy textbook (1805)
* Astronomical refraction is discussed on pp. 36-38; mirages on p. 40
* In §43 (p. 39), he refers to Maraldi's work on terrestrial refraction.
* The description of mirages in lower Egypt is taken almost verbatim from
* Monge's text, though edited down slightly: "Monge a expliqué ce phénomène
* d'apres les lois de l'optique, dans le premier volume de la Décade
* Egyptienne." (p. 41)
* The Plates that follow p. 330 indicate by simple diagrams the effect of
* astronomical refraction; but there are no mirage pictures. [Those appear
* in the 2nd edition (1810).]
* The first volume bears a dedication to Laplace (cf. Biot's anecdote!)
* Often, the two volumes of this work are bound together.
* The 1st volume is available at Google Books:
* https://books.googleusercontent.com/books/content?req=AKW5QaeMiMxzOhQ-yyV3yUE1sfwPMeOJxlGy0n44v6jKTIzjiWVTQN0sgG8bQy_wREdv7JVSaNvq7NZ1oUAq3S4Z2cO1OXn8Le43gtuy6IAdsWATwEFjMv4Oxh6cr0gLh7stxiARR3OipKqTX09mp5R4oCPd_AF9VLLFLlLlx62bXX7KfipBo5kKxM0KJVCwGTMCVKZ15gTEb6jJZ-MOn_2N3rS4RjqY5EPzBDVPxbthL289HJiq3H2hw0-b9LisxfXBMP9-rVUesYPs1gGwBcZB1QWbYJFac5kuAnDsN5iEzF4GlC3XhxQ
* Friedrich Christian Kries points out the lack of explanation in the
* reports of Vince and Wollaston, and tries to explain away Wollaston's
* experimental results as an artifact due to surface tension at the
* edge of the glass. However, his explanation of the 2-image superior
* mirage is exactly the same as Wegener's, apart from using (here) a flat
* Earth. Because of omitting this vital detail, he fails to understand
* how a 3rd, upright, image can be formed. So he introduces the crazy
* notion of a perfect reflection in the sea , which he supposes is
* inverted to form the uppermost, erect, image.
* But there is a prophetic phrase in which he foresees the actual
* complexity of thermal inversions:
* "Und da Luftspiegelung oberwärts mit starken Hebung verbunden zu
* seyn pflegt, so ist es nicht unwahrscheinlich, dass alsdann mehrere
* Luftschichten von verschiedener Dichtigkeit über einander liegen."
* According to Pogg., Kries was born in "Thorn, Westpreuss." -- the
* home town of Copernicus.
* Brandes comments at length on earlier reports, and announces his
* forthcoming ("um Michaelis") monograph (1807) [below].
* Several nice quotes here. On p. 383, good advice for astronomers:
* EARLIEST MENTION of NOCTURNAL INVERSIONS ???
* "Da wohl ohne Ausnahme über einer Erdfläche die Luft Nachts, dicht
* an der Erde kälter ist, als in der Höhe, . . . ." He notes that, with
* strong looming, the sea often appears concave rather than convex (p.385).
* [Note observation of CONCAVE surface.]
* [The concave appearance is also described by Forel (1895), p. 541.]
* Remarking on the stories Busch was told by the dike-workers, he says:
* "Ueberhaupt hat der gemeine Mann selten die Gabe, eine Erscheinung so zu
* beschreiben, dass der Physiker die Erzählung gebrauchen kann." (p. 386)
* On the next page is another suggestion for the origins of strange
* reports: "Ich sah neulich auch früh Morgens von hier aus das weiss
* übertünchte Schloss zu Varel und einige andere Gegenstände mit blossen
* Augen so auffallend hell, dass ich es wohl für näher hätte halten
* können; von besonderer starker Refraction war aber nichts zu bemerken,
* sondern ich konnte keinen anderen Grund finden, als dass diese
* Gegenstände hell von der Sonne beschienen wurden und die übrige Gegend
* im Schatten von Wolken lag. Grösser erschienen die Gegenstände auch
* nicht, aber bei so starker Beleuchtung kann ein scharfes Auge einzelne
* Theile der entfernten Gegenstände erkennen, und dies mochte die
* Täuschung verursachen, dass man sie für grösser hielt."
* The Figures show a distorted sunset, probably with mock mirage.
* He wonders if Heemskerk's observations on Nova Zembla were not this?
* [From letters dated 18ten April & 15ten Mai 1806.]
* Note that his drawing of a mock mirage in Tafel VII, Fig. 3 & 4,
* is probably the EARLIEST such sunset recorded pictorially.
* Wollaston's 1803 article translated by Gilbert.
* His Fig.6 is remarkable for showing the smooth bend in a miraged oar
* extending from a barge to the water. This vertical magnification
* is what makes the inferior-mirage flash visible to the naked eye.
* DANGOS reports his observation of early OMEGA (and looming of Etna)
* "Ayant lu depuis peu, dans la connoissance des temps de l'an 12, une
* observation curieuse sur les réfractions terrestres, faite par un
* savant physicien anglois, j'ai pensé que l'Institut national verroit
* avec plaisir les détails d'un phénomène à peu près semblable, qui se
* montra à Malte en 1784, et dont tous les habitans de l'île furent les
* témoins.
* "Le 20 mars vers 1 heure de l'après-midi, je fus instruit par des
* grands cris qui retentissoient dans les rues, qu'une île venoit de
* s'élever dans le canal de Malte, et j'aperçus bientôt, de dessus les
* terrasses de l'observatoire, une terre très-blanche, entourée d'eau,
* et dont la forme étoit celle à peu près d'un cône droit
* irrégulièrement tronqué. Des marins et des pêcheurs étoient déja
* partis pour aller reconnoître cette île et pour en prendre possession.
* "La figure de cette terre, sa blancheur et surtout sa position, qui
* se trouvoit exactement dans la direction de la mire que j'avois tracée
* depuis long-temps vers le mont Etna, me firent reconnoître bien vîte
* que cette terre n'étoit autre chose que le sommet toujours neigé de ce
* mont élevé de 3326 mètres . . . ." [The modern figure is 3323 m.]
* ". . . cette apparence extraordinaire dura environ 30 minutes depuis
* l'instant où j'en eus connoissance. . . . La mer étoit calme, le vent
* nord-est foible, le thermomètre à 14° 4'; . . . le temps étoit
* humide, et il avoit régné un brouillard épais toute la matinée,
* ainsi que la veille."
* From his further description of a repeat of this performance on 17
* April 1785 at 6:10 a.m., it appears that the island had been hidden by a
* superior mirage that reflected the sea: ". . . l'horizon de la mer qui
* l'entouroit étoit extrêmement net. . . . L'île . . . survint un instant
* de confusion, et lorsque je la cherchois dans les airs, je la vis, avec
* étonnement, assise à sa place. Tout le mont et les côtes de Sicile,
* qui avoient été invisibles, se montrèrent bientôt en entier, et
* furent visibles le reste du jour." On this occasion, he measured the
* "depression" and found it 15' 17'', "ce qui donneroit pour sa distance
* apparente de l'observatoire, à peu près 18000 mètres . . . ."
* [The actual distance is about 130 km.]
* He notes this cannot be a simple reflection, "comme on le prétendit
* dans les journaux d'Italie : car alors l'image auroit dûe être
* renversée, et elle étoit droite . . . ." So I suppose it is the isolated
* 3rd image of a 3-image mirage.
*
* Now comes the OMEGA report:
* "Je finis en rappelant un phénomène assez curieux qui tient à
* l'objet de ce mémoire, phénomène bien connu des marins, des
* astronomes qui ne sont pas fort éloignés de la mer, que j'ai vu assez
* souvent à Malte et surtout à l'observatoire de Rouen.
* "Le soleil prend quelquefois, vers son lever, une forme un peu
* allongée qui se rétrécit tout-à-coup dans sa partie inférieure, et
* qui est terminée par le bas, par une ligne droit, de sorte qu'il
* ressemble à une urne sur son piédestal." (Jules Verne, did you read
* this?)
* "La cause de ce fait est bien simple, d'après la théorie de
* M. Monge sur le mirage . . . ."
*
* ``Lu le 27 prairial an 10'' which works out to June 15, 1803 if my
* arithmetic is correct.
*
* NOTE: I have filed the 1814 German translation in the Colton file.
* It lacks the last paragraph connecting the Omega display with Monge's
* mirage. (Cf. Jacques Cassini's Omega sunrise, nearly a century earlier!)
*
* This is indexed under different titles; I have not seen the actual
* title page of the volume. The Royal Society Catalogue says it was
* ``Mémoires présentés à l'Institut des Sciences, Lettres, et Arts par
* divers Savans, et lus dans ses Assemblées : Sciences Mathématiques et
* Physiques'' for Vols. I and II (1806-1811). The later title, according
* to the same source, was ``Mémoires présentés par divers Savans à
* l'Academie [Royale] des Sciences de l'Institut de France; ou Collection
* des Mémoires des Savans Étrangers'' from 1827 on. However, the
* page headers read ``Mémoires présentés a la classe des sciences
* mathém. et physique'' and the footer has ``Sav. Étrangers. 1. T. 1.''
* The ILL people got a copy by asking the Bibliothèque de l'Institut for
* ``Memoires de l'Institut national de France.'' Take your pick.
* THOMAS YOUNG's remarks on refraction, in his "Lectures" book
* A good source of early references on refraction & mirages.
* EARLY treatment of the RN = const. model: Section 461 (cited in his
* paper below) is pp. 80-81. [Cf. Kummer!]
* On p. 81, he seems to lose the factor of 2 in terrestrial refraction,
* saying ". . . the terrestrial refraction, instead of being 1/7 of the arc
* intervening between two places, is seldom more than 1/10."
* Available at https://archive.org/details/lecturescourseof02younrich
* and http://www3.nd.edu/~powers/ame.20231/young1807.pdf
* THOMAS YOUNG's remarks on mirage theory
* Young comments on the inadequacy of Wollaston's demonstration.
* He proposes a model very similar to that of August Schmidt (1878)!
* "If the variable medium be only thick enough to admit the passage of
* rays below [the height where the conjugate point turns around], there will
* be no direct image, but an inverted one only. . . . the case being nearly
* similar to a very oblique internal reflection." (p. 154) -- cf. Wegener!
* "The points K and ε may be considered as conjugate foci, with
* respect to the refraction of the variable medium."
* He considers DUCTING and CRITICAL REFRACTION: the assumed temperature
* gradient of 1 degree (F?) per foot of height produces a ray curvature of
* 1 second of arc in 16 feet of path length; "The curvature of the earth's
* surface becomes a second in 102 feet; consequently . . . a change of
* temperature of a degree in 6 or 7 feet, would be sufficient to produce
* a refraction equivalent to the apparent depression of a distant object
* arising from this cause, and to elevate the coasts of a wide channel,
* so as to make them visible to each other. This result may also be more
* simply obtained from Simpson's investigations respecting atmospheric
* refraction, the refractive density being inversely proportional to the
* distance from the centre of the earth, when the temperature varies 1°
* in 6 or 7 feet; for, as Dr. Young observes in his extensive system of
* natural philosophy lately published, Vol. II, Art. 461, `If the refractive
* density of a medium vary as a given power of the distance from a certain
* central point, the angular deviation of a ray of light will be, to the
* angle described round the centre, as the exponent of the power to unity.'"
* (p. 155) [cf. Kummer (1860)]
* Then there is a Postscript (pp. 155-156) that continues the discussion,
* finding the image position (cf. Gergonne, Nölke, etc.).
* Note that Plate V faces p. 153, the title-page of the article.
* This is usually known as "Nicholson's Journal"; dated July.
* Heinrich Wilhelm BRANDES uses temperature gradient info
*
* Here is the first paragraph (p. 3):
* "Obgleich es eine lange bekannte Wahrheit ist, daß nur in sehr
* wenigen Fällen die Lichtstralen von einem entfernten Gegenstande auf
* der Erde in gerader Linie zu unserm Auge kommen, und daß wir daher
* selten oder vielleicht niemals die Gegenstände in derjenigen Richtung
* sehen, in welcher wir sie sehen würden, wenn der Lichtstral durch einen
* gänzlich leeren Raum oder durch ein völlig gleichartiges Medium zu uns
* gelangte, so ist doch die Anzahl der Beobachtungen über diese Brechung
* des Lichtstrals in den untern Luftschichten noch immer nicht so groß
* als es bei einem so interessanten Gegenstande zu wünschen wäre, und
* noch immer fehlt es uns an sichern Regeln, um die wahre Höhe eines
* Gegenstandes auf der Erde aus seiner scheinbaren Höhe zu bestimmen."
*
* ". . . die großen Aenderungen, denen die scheinbare Höhe eines
* bestimmten Gegenstandes, den man aus einerlei Standpunkt betrachtet . . . "
* "Schon mehrere Beobachter hatten zwar die ungleiche Erwärmung der Luft
* in verschiedenen Höhen, als einen vorzüglichen Grund mancher hier
* vorkommende Phänomene angegeben; aber so viel mir bekannt ist, hatte
* noch keiner durch Beobachtungen gezeigt, daß die Aenderungen der Refraktion
* ganz genau mit der Aenderung der Unterschiede der in verschiedenen
* Höhen statt findenden Wärme übereinstimmen. Dieses darzuthun,
* waren meine ferneren Beobachtungen bestimmt, und wenn die ersten
* Beobachtungen nur dahin leiten konnten, empirische Regeln für die
* Bestimmung der gleichzeitigen Aenderungen der scheinbaren Höhe
* verschiedener Gegenstände anzugeben, so müssen die leztern,
* wofern sie ihren Zweck erreicht haben, uns in der theoretischen Bestimmung
* der Refraktion einen Schritt weiter bringen." [p. 5]
*
* The INFERIOR MIRAGE discussion begins on p. 111 (section 61). On p. 114
* he mentions the reduced size of the inverted image; if this were due to
* simple reflection, ". . . wo sollte hier die polierte Fläche sein, auf
* welcher sich der Gegenstand abspiegelte? Vielmehr ist das Phänomen aus
* einer Refraction der Lichtstralen zu erklären . . . ." And in §65:
* "Je mehr die Erdfläche erwärmt ist in Vergleichung der höheren
* Luft-Schichten, desto stärker ist die Spiegelung, . . . ." -- and he gives
* several examples from his own measurements. A ray-traced example is
* treated in §66 (p. 115) and Fig. 10. He trips over the horizontal-ray
* paradox, but talks himself out of it by asserting that it is the
* spherical curvature of the refracting surfaces that allows the ray
* to find its way back up from the perigee point!
* §67 (p. 116) discusses the ray vertices: ". . . und deswegen erscheint das
* untere Bild umgekehrt." (p. 117) Then in §68 he has a nice argument to
* determine the point where the erect and inverted images join, by
* interchanging object and observer.
* §68b then discusses the location of the apparent horizon: ". . . die
* scheinbare Tiefe des Horizonts ist also um etwas sehr erhebliches
* grösser, als sie bei gradlinigtem Fortgange der Lichtstralen sein
* sollte. . . . so is offenbar, dass der sichtbare Horizont sich mit der
* Erniedrigung des Auges sehr merklich verkleinern muss, welches auch
* wirklich sehr auffallend der Fall ist, wenn man auch die Höhe des Auges
* nur wenig ändert." (p. 118)
*
* The SUPERIOR MIRAGE discussion begins on p. 121 (section 72).
*
* EARLY MIRAGE OF SUN (cf. the similar publication in Gilberts in 1806.)
* (section 78, p.126): "Eine Erscheinung muß ich noch erwähnen, die
* ebenfalls hier gehört. Am 8. April 1806 nämlich erschien die Sonne beim
* Untergange in einer solchen Gestalt, wie Fig. 18. zeigt. Hier ist offenbar
* a c b das aufrechte, d c e das umgekehrte und d f e das zweite
* aufrechte Bild. Ich hatte damals kein Fernrohr zur Hand, aber am folgenden
* Tage, wo die heitre Witterung mit Ostwind fortdauerte, zeigte sich beim
* Untergange der Sonne etwas ähnliches, obgleich die Spiegelung
* schwächer war, und diese Erscheinung habe ich mit dem Fernrohr beobachtet.
* Die Sonne erschien nämlich wie Fig. 19. und als sie tiefer sank,
* trente sich das Stück oberhalb des Einschnitts ab, schwebte noch
* abgesondert einen Augenblick und verschwand dann. Etwas später trente
* sich noch ein zweiter solcher Streifen. -- Die Sonne erschien zitternd und
* daher schlecht begrenzt, indeß war diese Erscheinung sehr deutlich. --
* Tages vorher waren Nachmittags auch einige südlich liegende
* Gegenstände oberwärts gespiegelt.
* "Diese Spiegelung der Sonne könte, dünkt mich, gar nicht statt
* finden, wenn die Schichte, worin die starke Brechung erfolgte, sich sehr
* weit, z.B. über den ganzen Gesichtskreis, erstreckt hätte.
* Stellt nämlich (fig. 20.) d c die oberfläche der Erde, b die
* Gegend vor, wo der Scheitel des Strals [sic] lag, so würde, wenn in a
* eben so starke Brechung, als in b statt finde, keine Vervielfachung des
* Bildes möglich gewesen sein."
*
* Google Books has the text, but it is made useless by their usual failure
* to open the gatefolds of tables and figures.
* Further observations by Brandes, with an appeal for support by Gilbert
* The letter from Brandes to Gilbert actually begins on p. 135; the
* first 2 pages are Gilbert's comments, citing the earlier works.
* Most of Brandes's letter is a summary of the high points of his book.
* However, he has a few comments at the end about what needs to be done,
* which would be good advice to mirage observers generally (pp. 148 ff.).
* He notes the TRIPLE IMAGE often associated with superior mirages:
* "Eine genaue Betrachtung der Umstände, welche diese Spiegelung fast
* unstreitig bewirken, zeigt, dass man eigentlich dann immer drei
* vollständige Bilder und in dem höchsten alle Mahl die Spitzen der
* Gegenstände sehen sollte . . . ." (p. 146) as well as its association
* with the Fata Morgana.
* There is also a nice comment about the Fata Morgana : "Sie scheint
* mir eine veränderliche Spiegelung zu seyn, die in einem Augenblicke
* vielleicht in demselben Punkte des Horizonts einen Gegenstand zeigt, der
* Meilen weit hinter dem liegt, welchen man im nächst vorhergehenden
* Augenblicke sah. . . . Freilich könnte auch dann noch, wegen der
* Mannigfaltigkeit der Gegenstände, die hinter einander in einerlei
* Richtung liegen, sich mancherlei zeigen; aber gewiss würde man bei
* solchen Beobachtungen doch eher zu einer Erklärung gelangen, als durch
* die Beschreibung von Feenschlössern und andern Herrlichkeiten, die
* gewiss nur die Fantasie sah, und nicht das Auge." [p. 147]
* And (p. 151): "Allem, was ich bis jetzt von Beschreibung dieser
* Phänomene kenne, scheint ganz der philosophische Geist zu fehlen,
* welcher nötig ist, um gerade das Rechte zu treffen, und aus dem Chaos
* von zerstreuenden Nebendingen nur den Hauptpunkt hervor zu heben."
* He also notes the bad seeing that accompanies the inferior mirage:
* ". . . mit dieser Spiegelung . . . fast ohne Ausnahme ein heftiges Zittern
* der Gegenstände verbunden ist . . . ." [p. 150]
* Biot and Arago's expedition recounted
* The "Notice sur les Opérations d'Espagne et de France" (pp. 1-30
* here), "Lue à la séance publique de la classe des Sciences de l'Institut,
* le 2 janvier 1810" is the account quoted in the 1821 book by Biot & Arago;
* see below (at 1821) for excerpts.
* Now available at
* http://www.academie-sciences.fr/membres/in_memoriam/Biot/Biot_pdf/Notice_EsFr_1810.pdf
* but they don't give the exact citation; probably this appeared in one of
* the Academie's serial publications. . . .
* This was reprinted in Biot's Mélanges Scientifiques et Littéraires
* (M. Levy, Paris, 1810), pp. 47 - 68.
* Thanks to Luc Dettwiller for pointing out the availability of this item!
* Abstract of the 8 Aug. talk by J. B. BIOT on refraction phenomena
* A marginal note says:
*
* Instit. Nat.
* 8 Août 1808.
*
* and the signature footers say "Tome I. N°. 15, 2e. Année." The title
* page of the volume is dated 1807, and a few Roman-numeraled pages at
* its front explain the interruption in publication of the Society's
* Bulletin in 1805. On p. vi is the editorial staff of the revived
* Bulletin; Mathematics is handled by Poisson ("P.") The first number
* of this volume is dated Oct. 1807.
* Here, Monge, Wollaston, and Humboldt are mentioned, and their
* explanations are summarized. Poisson says:
* "On ne peut donc pas douter que cette explication ne donne la vraie
* cause du Mirage. Mais, pour ia mettre dans tout son jour, il étoit bon
* de déduire de l'analyse mathématique, les diverses circonstances que
* peut présenter ce phénomène, et qui sont relatives à l'élévation de
* l'observateur au-dessus du sol, à sa distance aux objets mirés, et à
* la rapidité du décroissement de la température. C'est ce que M. Biot
* s'est proposé de faire dans le mémoire que nous annonçons. On trouve
* aussi dans ce mémoire, l'explication de plusieurs phénomènes qui ont
* un rapport plus on moins éloigné avec le Mirage. Le plus remarquable de
* ces phénomènes est la double image du soleil à l'horison, observée par
* Le Gentil à Pondichéri et sur les côtes de Normandie. M. Biot attribue
* cette parélie à la même cause qui produit le Mirage. En général,
* M. Biot a rassemblé dans son mémoire les nombreuses observations de
* Mirage ou de phénomènes analogues, qui ont été faites jusqu'ici,
* afin qu'on puisse en comparer les résultats à ceux du calcul."
* This is available at the BHL website:
* https://www.biodiversitylibrary.org/page/31774998#page/278/mode/1up
* Full title of publication is:
* Nouveau Bulletin des Sciences, par ls Société Philomatique. Paris.
* (A variety of local scientific societies called themselves "Philomathic"
* in this period; so it's necessary to specify which one by location.
* The Roy. Soc. Cat. calls this "Paris, Soc. Philom. Bull." The BHL
* calls it "Nouv. Bull. Sci. Soc. Philom. Paris".
* Note the spelling "horison" with an "s" rather than a "z", in both the
* title and the text.
* The abstract is signed with the initial "P." = Poisson.
* Italian report on Biot's mirage memoir: first use of "miraggio" ?
* The title page of the volume says:
*
* GIORNALE
*
* DI FISICA, CHIMICA
* E STORIA NATURALE
*
* ossia <-- (in small caps)
*
* Raccolta di Memorie sulle Scienze, Arti, <-- (in flowery script)
* e Manufatture ad esse relative
*
* DI L. BRUGNATELLI
*
* [followed by a long paragraph of his degrees, awards, memberships in
* numerous foreign learned societies.]
*
* TOMO II
*
* CON TAVOLE IN RAME
*
*
* PAVIA nella Tipografia Capelli 1809.
*
* -----------------------------------------
* Page 3 is headed "PRIMO BIMESTRE 1809"
* -----------------------------------------
* Successive pages are headed "Giornale" and "di Fisica, Chimica, ec."
*
* This item beginning in p. 63 is headed:
*
* ESTRATTO DI UNA MEMORIA
*
* Sopra le refrazioni straordinarie che si osservano
* vicinissime all'orizzonte; del Sig. Biot
*
* (Instit. Naz. di Francia 8. Agosto 1808. l. c.)
*
* The footnote about Pliny on p.65 is signed "L'Edit." so I think I am
* safe in attributing it to Luigi Valentino Brugnatelli (as does the Royal
* Society Catalogue), Considering the timing and the dates, this must be
* based on the Philom. Soc. Bull. abstract; and in fact this is just a
* translation into Italian of that abstract.
* This is available at:
* https://www.google.com/books/edition/Giornale_di_Fisica_Chimica_e_storia_natu/ObVUAAAAcAAJ?hl=en&gbpv=1&dq=miraggio&pg=PA65&printsec=frontcover
*
* The first full version of Biot's monograph; read 8 Aug. 1808
* The Mémoires are for the year 1809; but the publication date is Aug. 1810,
* and observations made in 1809 are discussed in several places. Clearly,
* lots of material was added after 8 Aug. 1808.
* The first 98 pages of this volume contain the history of the Institute.
* (The "Histoire" and the "Mémoires" are bound together as one volume here,
* each beginning with p. 1, just like those of the Académie des Sciences.)
* After this "Histoire" comes the table of contents for both it and the
* Mémoires that follow.
* The edition scanned by Google has "1809." in its signature footers.
* The Google scan is available at HathiTrust:
* https://babel.hathitrust.org/cgi/pt?id=ucm.532436086x&view=1up&seq=9
* -- but it completely lacks the figures!
* Its table of contents on the unnumbered page after p. 98 gives the
* title as "Recherches sur les réfractions extraordinaires qui s'observent
* très-près de l'horizon", as does p. 1. Notice that the odd-numbered
* pages in both versions have the "très-près" in their headers.
* This seems to be the version that is often cited as 1809.
* Both the Readex and the stand-alone version of the mirage monograph have
* the same page numbers, and seem to be printed from the same type, except
* for some minor changes from the Google version, such as the title,
* and the end of the third line of the body text, which ends in a comma
* in the Google scan but a semicolon in the Readex/monograph version.
* The last line of text on the first page of the monograph appears at the
* top of p.2 of the edition scanned by Google. Yet the two versions must
* be printed from the same type: look at the pale e-acutes in the word
* "détachés" in line 9 of the Google scan (line 8 of the monograph) on
* page 2. (There are other pale é types in the text; evidently this glyph
* was cast separately and shrank a little more on cooling than the main
* font.)
* On p. 11, the bottom line of the monograph version appears at the top
* line of p. 12 in the Google scan. The bottom two lines on p. 12 of the
* monograph are at the top of p. 13 in the Google scan. After this there
* is a steady creep of text, with the monograph generally having one more
* line per page than the Google version. But at p. 15, the monograph
* absorbs the accumulated space by adding a 4-line footnote about Arago.
* The two versions then remain in step until Biot's text ends on p. 266.
* That page says "FIN" in the monograph; but the Mémoires continue with
* several more mathematical papers by Lagrange, Laplace, et al.
* The signatures are all marked "1809" in the footer at the first
* page of each in this Mémoire; but that date was removed from most of
* the signature labels in the monograph (see, e.g., p.201 which begins
* signature 26, or p.193 which begins sig. 25.)
* BIOT's MIRAGE MONOGRAPH
* This is the stand-alone reprint of the monograph.
* It contains BIOT + ARAGO's multiple-image red/green observation:
* "Bientôt nous ne vîmes pas seulement deux lumières, mais trois,
* quatre ou davantage. Elles se formoient et disparoissoient ensuite sans
* que le nombre de celles qui paroissoient ensemble eût rien de
* déterminé. . . . Cette formation successive a beaucoup d'analogie avec un
* autre phénomène que nous avons observé plusiers fois dans l'autres
* stations. On voyoit le point lumineux s'allonger comme une petite colonne
* de feu sous le fil vertical de la lunette, et s'étendre ainsi jusqu'à une
* certaine longueur, après quoi la colonne se rompoit tout à coup et
* formoit deux images dont le plus basse étoit sensiblement rouge, et la
* supérieure sensiblement verte; ou bien elle se concentroit de nouveau sur
* elle-même; et redevendroit un point lumineux unique, de dimension
* insensible, comme auparavant. . . . " (p.15 -- his experiments with Arago)
* See their 1821 report for more details!
* [cf. M.O. 24, 13 (1954)]
*
* This is a remarkable work: it is not only the first theoretical
* monograph on mirages, it explores many important ideas later forgotten
* and rediscovered, such as the effect of uneven ground in truncating the
* inverted image of the inferior mirage (pp. 28-33), based on Wollaston's
* (1800) measurements on a sandy road -- even including a warning about
* radiation-induced errors in air thermometry; the relation between
* the locus of the minima in the ray-paths and the occurrence of erect
* or inverted images (pp. 41 - 63; cf. Tait, 1883); the divergence of
* rays above the horizon, and hence the need for the minimum to occur
* between observer and object if a mirage is to occur (p. 65; cf. Meyer,
* White, Fraser, et al.); an observation of conjugate inferior mirages
* over uneven ground (p.84); the importance of the Earth's curvature, and
* caustic curves (pp. 151 ff.); the role of temperature in determining
* the dip of the horizon; the possibility of ducting (p. 196), and hence
* of negative dip and a false horizon (p. 203); etc. -- and all supported
* by quantitative measurements!
* The circulating ray is on p. 154. Measurements in thermal inversions
* begin on p. 163; negative dip is discussed on pp. 167 ff.
* MULTIPLE HORIZONS are mentioned on p. 265.
* August Schmidt's (1878) comments are appropriate.
* [cf. the German treatment by Brandes, 1814.]
* A "Table des Matières" follows p. 266. It contains a one-paragraph
* abstract of each major section of this long paper. The figures are
* immediately after this Table.
*
* This is occasionally cited as:
* Recherches sur les réfractions extraordinaires qui s'observent
* très-près de l'horizon, avec 9 planches; lu le 8 août 1808
* (Mémoires de l'Institut national des sciences et arts 10, pp.1-266)
* as that title (from "sur" on) appears on the first page of the text.
* That was the original title published in the Mémoires, and is repeated
* here in addition to the slightly changed wording on this volume.
* The title page gives the date of publication as 1810; but a few
* individual signatures bear the date 1809: see pp. 129 and 169.
* P. 169 discusses observations made in Dec., 1808, and p. 168 shows dip
* measurements of 6 Feb. 1809. Data measured on 8 March 1809 are on p. 31
* and 82. The last line in the table on p.32 is a Dunkirk observation on
* 23 March, 1809.
*
* Note that the drawings are by Claude Louis Mathieu (cf. Delambre, 1827)
*
* Google Books has finally made available a PDF of the whole book,
* INCLUDING Mathieu's drawings! Here's the URL:
*
* https://books.googleusercontent.com/books/content?req=AKW5Qaf5mZ7iXOyoE33ib1IUaF5cGMjYL82QdYt45kk1Al3V3dK_QSJg3RrzkyZqakad4i2v6I6zAUALrPoPI0aGCBImDkNAksaI5yfYJA33Z_UTN5aBdH1yoPm3B2eEIp_nilM_SninhFW4mFe0NEVhR5VLkAVJv9eGnDMAbfUraiZ6s1YJ_X-4JiSQKc4nHKX1RdnWzkxG3DI0xC06Ksl_o1nGnbcS57hmgrSAZPkS7bRDnl2fP3zocHpjWIyFS-m4zYpi4OBEK6JGIMKenze0VjYbHHaw3gnM_nzRUSrGeiPK9Y-Kig8
*
* Jean Baptiste Biot
* Some of the same figures appear in Biot's revised (1810) textbook:
* The miraged man is (Fig. 41); the distorted sunsets (42 & 43) are in Pl.9
* ORIGIN of the term "MIRAGE" (cf. Le Gentil, 1789!):
* After describing the ordinary inferior mirage over hot sand, such as was
* seen by the French army in Lower Egypt, he says: "On observe
* à-peu-près la même chose à la mer dans des tems très-calmes. Un
* navire, vu dans le lointain et à l'horison, offre quelquefois deux
* images, l'une directe, l'autre renversée; celle-ci absolument pareille à
* l'autre, souvent égale en intensité, en un mot parfaitement semblable à
* l'effet de la réflexion dans un miroir. De là est venu le nom de
* mirage que les marins ont donné à ce phénomène." (p.229)
* The first volume bears a dedication to Laplace (cf. Biot's anecdote!)
*
* Sergey Kivalov points out that in the second volume of this 3-volume
* work, on pp. 558-560, Biot calculates the flattening of the full Moon
* at the horizon; this establishes a long-standing interest in this topic
* that helps explain his discovery of the magnification theorem in 1836.
* [NOTE: we have this book in our Special Collections; when I went to look
* at those pages, I found them uncut. I was the first person ever to have
* read that passage in our copy, in nearly 200 years!]
* Unfortunately, the treatment here is oversimplified: he supposes the
* Moon so small that its image is symmetrical, and (worse) repeats Kepler's
* error of supposing the difference in refraction of the upper and lower
* limbs to correspond to the difference in altitudes of the true (rather
* than diminished) vertical diameter. Having neglected an appreciable
* second-order effect, he then evaluates the effect of refraction on
* the horizontal diameter, which he finds diminished by about 3 parts
* in ten thousand.
* The publication date of the second volume is 1811.
* A very poor copy is available from Gallica. Google Books also.
* The HathiTrust website has the 3rd edition -- but only the Google scan,
* so no plates. There, the discussion of the Moon's diameter is in Vol. 3,
* pp. 19 ff., published in 1845.
* The German treatment of Biot's monograph, by Brandes
* In the first 2 pages, Brandes explains why and how he has abridged this
* partial translation.
* This is only the first of two installments. As usual in Gilberts Ann.,
* the notes are as valuable as the text.
* On p. 245, commenting on Biot & Arago's observation of red/green
* dispersion of the signal light (p. 15 of Biot's book), Brandes remarks
* on "die prismatischen Farben," and cites Herschel's 1785 double-star
* catalog, p. 52 [an error: really p. 83]. His translated quotation
* attributed to W.H. is very much abbreviated, however.
* On p. 257 [Biot p. 26] appears the "magic number" of 1° 23'.
* On p. 275 [Biot p. 65] is the discussion of the minimum of the
* trajectory. Biot says the rays must be horizontal to give a mirage
* -- this is the later mis-named "Fraser's theorem". Brandes explains
* that the order of inclination of the rays at the eye is also their order
* in any layer, in the branch above the horizontal. And immediately
* afterward is Tait's belated rediscovery about the ordering of the
* minima and the nature of the image (Biot p. 66). This is discussed in
* detail later [p. 279 = Biot p. 72], after the locus of the minima is
* discussed [Brandes p. 278; Biot p. 71].
* NOTE: "Breslau" is now Wrocłow, Poland.
* The German treatment of Biot's monograph, by Brandes -- part 2
* Rev. Edward Polehampton's review of natural phenomena
* There is a fuller summary of Minasi's work than one usually finds.
* Mirages begin on p. 504; see pp. 509-514 for the section covering the
* Fata Morgana.
* "Fellow of King's College, Cambridge" says the title page.
* So this is the Edward P. who was rector of Greenford, Middlesex (1822-30).
* He was born in 1776 and died in 1830.
* This is "Vol. IV" of "six volumes".
* Evidently this is the source for Thomas Milner's similar work (1846+).
* Available on Google Books
* MANY OLD REFERENCES and some current observations (MIRAGE HISTORY)
* Cites Quintus Curtius Rufus, as well as many references to mirages
* ("Sarab") in the Koran and other Arab writings
* (Johann Friedrich von Erdmann, according to Roy.Soc. index)
* Available at:
* http://books.google.com/books?vid=OCLC05854993&id=-QUAAAAAMAAJ
* William Scoresby's "Arctic Regions" book
* The mirages are described in Sect. V, on pp. 383-392:
* "Under certain circumstances, all objects seen on the horizon, seem
* to be lifted above it a distance of 2 to 4, or more minutes of altitude,
* or so far extended in height above their natural dimensions. Ice, land,
* ships, boats, and other objects, when thus enlarged and elevated, are
* said to loom . The lower parts of looming objects, are sometimes
* connected with the sensible horizon, by an apparent fibrous or columnar
* extension of their parts, which columns are always perpendicular to the
* horizon : at other times, they appear to be quite lifted into the air,
* a void space being seen between them and the horizon." (pp. 384-385)
* A typical Fata Morgana display is well described on pp. 385-386, with
* "lofty spires, towers and battlements," converted in a few minutes into
* "a vast arch, or romantic bridge." "A mass of ice on the horizon,
* appeared of the height of a cliff, and the prismatic structure of its
* front, suggested the idea of basaltic columns. It may be remarked,
* that these phenomena took place on a clear evening, after an uncommonly
* warm afternoon." So, a textbook case; July 16, 1814.
* On the next page, another example of "variegated basaltic columns" was
* see on the coast of Spitzbergen, in June. An iceberg became "a
* prodigious cliff of alabaster pillars." Likewise, on May 13, he saw
* "a dense appearance in the atmosphere," which "advanced with the wind
* toward the N.W." The horizon under this apparent density "was
* considerably elevated; . . . a separation of seven minutes extent of the
* altitude, showed the division of the true and refracted horizons." The
* refracted horizon "had the appearance of a line drawn nearly parallel to
* the true horizon, distant from it 7 minutes, with an open space between.
* Two ships lying beset about fourteen miles off, the hulls of which,
* before the density came on, could not be wholly seen, seemed now from the
* mast head, not to be above half the distance, as the horizon was visible
* considerably beyond them. . . . Their hulls were much enlarged and
* elongated, and their masts very much shortened. They had precisely the
* prospective appearance of ships in a heeling position." (pp. 387-388)
* [This description resembles Minasi's tilted ships.]
* On p. 389 is another observation, April 28, 1811: a ship "at such
* a distance, that her hull was not visible ; and when viewed from an
* elevation of ninety feet, with a good telescope, half her lower masts were
* intercepted by the ice on the horizon. Now, at the elevation from which
* this ship was seen, the horizon, under common circumstances, would be nine
* miles distant ; and from the knowledge of the dimensions of her masts,
* I estimated the portion of the hull and masts intercepted by the horizon,
* at about 22 feet ; consequently, her distance beyond the horizon must have
* been at least 4½ miles, and her distance from us not less than 13½."
* [In addition to the quantitative estimates, notice that all these were
* seen during the normal superior-mirage season.] It had been a bright,
* sunny day; at 11 p.m., the officer of the watch reported "that the ship to
* the eastward of us, appeared to he forced by the ice upon her beam ends ,
* or into an heeling posture. I immediately ascended the deck, and having
* cleaned the glasses of a good telescope, I hastened to the mast-head. I
* at once attributed the cause of the deception to unequal refraction. This
* ship, which, two hours before, was 4½ miles beyond the visible horizon,
* now appeared as far within it, and was in every respect deformed like the
* ships above mentioned." The intervening ice was "compact and motionless".
* "The horizon on this occasion, between the east and north, though
* continuous, appeared curiously undulated. There appeared a difference of
* nearly a quarter of a degree, between the elevation of the highest and
* lowest portions of the circumferential boundary." (p.390)
* On p. 391, Scoresby notes that these refractions "have usually
* occurred in the evening or night, after a clear day." He correctly
* infers that "two streams of air of different temperatures" are involved;
* but unfortunately supposes that "an irregular deposition of imperfectly
* condensed vapour" may produce the phenomenon.
*
* Also noteworthy for a brief discussion of halo phenomena on p. 393:
* here Scoresby criticizes Huygens's suggestion of circular cylinders as
* the cause, remarking that "It is, however, probable, that such a form
* of hail does not occur in nature, though snow or hail of a prismatic or
* spicular form is not uncommon in the polar regions."
* There are also remarks on the ice-blink on pp. 299-300; and an
* interesting discussion of sea-ice and icebergs in Chapter IV, where the
* word "effulgence" occurs in connection with seeing icebergs at night.
*
* Available at
* https://archive.org/details/accountofarcticr01scor/page/390/mode/2up
*
* and at the Biodiversity Heritage Library.
*
* On the title page of the original volume, the author's name is
* W. Scoresby Jun. F.R.S.E.
* Cited by Prof. Everett (1874).
* Thanks to Eric Frappa for pointing this out!
* BIOT & ARAGO (details)
* This gives the real story of the expedition: how Delambre and Méchain
* began the project, to determine the length of the meter; how the
* southern part of the arc was lost by Méchain's death; and how the
* completed part was published by Delambre in Base du Système
* métrique . The work reported here was done in 1806-07. The very
* breezy Introduction (it is explained in a somewhat apologetic Note) "est
* tirée d'une notice lue par M. Biot, à la séance publique de
* l'Académie des Sciences, pour l'année 1810." It gives the general
* public the bare outlines of how geodesy is done -- along the way,
* offering one of the earliest comparisons of the smoothness of the Earth
* to the peel of an orange (p. vi) -- and reviews the great
* accomplishments of French geodesists, from Picard (1670) and the
* Cassinis, through "Bouguer, Godin, la Condamine, Clairaut, le Monnier,
* Maupertuis et La Caille, tous nos compatriotes, et membres de
* l'Académie des Sciences".
* "Malgré tant d'efforts, malgré tant d'entreprises, on pouvait
* faire mieux encore; . . . les instrumens d'Astronomie étaient bien
* éloignés alors de la perfection qu'ils ont maintenant acquise,
* perfection telle, qu'on peut régarder comme le dernier terme de la
* précision que l'on atteindre par des évaluations mécaniques, surtout
* depuis qu'un autre français, Borda, aussi membre de l'Académie des
* Sciences, eut trouvé le secret d'atténuer indéfiniment les erreurs
* des observations partielles, en les faisant suivre et succéder les unes
* aux autres sur le limbe circulaire de l'instrument auquel il a donné le
* nom de cercle répétiteur." (p. viii)
* So (p. ix), the Bureau des Longitudes has chosen Arago and Biot to
* finish the job. The big problem (p. xi) is that one of the sides of the
* Yvice triangle must be some 160 km long, "environ quarante et une lieues
* de longueur. [ Assuming, as the footnote says, a league of 2000 toises;
* "je n'ai employé cette dénomination vague que pour rendre sensible à
* l'esprit la grandeur de nos triangles, par des évaluations encore
* habituelles pour beaucoup de personnes, mais que, sans doute, avec le
* temps, on finira par abandonner pour les évaluations métriques qui ont
* sur les autres l'avantage d'avoir toujours, et partout, la même
* signification." -- now, read on: ] A de si grandes distances, des
* signaux de jour auraient été complètement invisibles. On devait y
* suppléer per des lampes à courant d'air, derrière lesquelles on
* plaçait de grands miroirs de métal poli, pour réfléchir la lumière,
* et toutes les observations devaient se faire de nuit."
* Desierto de las Palmas is so called "parce qu'il y croît en
* abondance une petit espèce de palmier à feuilles en éventail, que les
* botanistes nomment le chamærops humilis ." (p. xii)
* Then come all the anecdotes: Biot's ship is driven by a storm to the
* tiny islet of Espalmador, inhabited only by a lighthouse keeper and a
* family of poor fishermen. "Jamais on ne vit de plus profonde misère;
* mais, dans cette misère même, il y avait encore de la vanité: le
* gardien de la tour méprisait beaucoup les pauvres pêcheurs." (p. xiv)
* There are the French consuls who helped the expedition, only to lose
* everything later, having to seek refuge in France. (p. xvi) There is
* the loss of one repeating circle, broken in shipment (p.xvii). He
* describes the wonderful view of the Kingdom of Valencia (p. xviii),
* including the site of Méchain's death and entombment; and "les tours
* de la brillante ville de Valence, heureux séjour du peuple le plus
* insouciant et le plus frivole. Mais ces beautés . . . n'avaient alors
* pour nous aucun attrait. Tout remplis, de la seule idée qui nous
* occupait, nous ne songions, nous ne pouvions songer qu'à nos travaux,
* et aux invincibles obstacles qui . . . ." (Well, you get the idea.)
* Here is the story of the tents blown into the sea by a gust of wind;
* "et nous n'avions pu en préserver notre pauvre cabane qu'en passant
* par-dessus des câbles, et la liant au rocher." (p. xix)
* After 2 months of futile effort, they figured out how to spot the
* signals at Ybice, by pointing the telescope to the summit of Campvey
* just after sunset. "Je ne saurais exprimer l'émotion que nous
* éprouvâmes, lorsqu'après tant de peines et tant de doutes, nous
* eûmes enfin la certitude de réussir." (p.xxi) And then Biot
* dramatically reveals Méchain's letter, to top it off!
* We also have the story of the station in the Favaretta mountains
* where Arago tried to establish a station; "mais nous fûmes obligés d'y
* renoncer, à cause de l'abondance des neiges qui couvraient presque
* tout-à-fait les tentes, et aussi parce que les brigands, maîtres de
* ces montagnes, exigeaient que l'on fît un traité avec eux pour avoir
* le droit d'y séjourner." (p. xxii)
* Then there is the episode where Biot leaves the English safe-conduct
* with Arago and promptly gets himself captured by Ragusan pirates. (p. xxvi)
* The original note of 1810 is now available as a PDF file at
* http://www.academie-sciences.fr/Membres/in_memoriam/Biot/Biot_pdf/Notice_EsFr_1810.pdf
*
* But of course our real interest is in the refraction observations.
* These commence on pp. 84-85: "en observant Iviza un instant auparavant,
* la lumière de cette station nous paraissait partagée en plusieurs
* lumières distinctes et bien séparées . . . ." (25 Dec. 1806) This
* story continues on p. 106: "Tems parfaitement calme depuis plusieurs
* jours. . . . Mais à la quatrième ou à la sixième . . . , l'un de nous
* commenc,a de voir à Campvey deux lumières, exactement dans la même
* verticale et éloignées l'une de l'autre d'une quantité que, sur le
* fil, on estima au moins de trois minutes. La vraie lumière . . . était
* à sa place ordinaire; l'autre . . . était plus élevée dans le ciel
* . . . ; elle était aussi plus grosse, plus dilatée, plus irisée." They
* first took it to be a star. There was a problem caused by the two
* observers requiring different eyepiece settings; but when "l'autre
* observateur dut amèner sa lunette sur ce même point, non-seulement il
* apperçut deux lumières, mais il en vit trois et quatre les unes
* au-dessous des autres. . . . Quelquefois on appercevait plus de quatre
* lumières . . . . Le autres, toujours plus élevées dans le ciel, se
* formaient ensuite successivement . . . ." The regular image brightened as
* the others appeared; sometimes the extra images were still brighter than
* the bottom one. No color reported. Biot's monograph is cited.
* Similar phenomena are reported on pp. 134-135, in observing the signal
* at Desierto from Cullera. Again, the multiplicity of images is
* accompanied by brightening.
* It gets really interesting in the observation from Mongò (p. 144),
* in which DISPERSION is at last reported (though not recognized):
* "Tems parfaitement calme, mais vaporeux; lumière de Cullera bien
* visible; celle du Desierto faible, quelquefois diffuse comme si on la
* voyait à travers une gaze; d'autres fois alongée en un
* parallélogramme vertical; d'autres fois brillante et bien terminée.
* Pendant la 16e observation, on l'a vue double; on l'a vue double aussi
* pendant la 20e. Dans ces deux cas, l'une des deux lumières paraissait
* rouge, l'autre paraissait d'un vert pâle. La première nous a semblé
* à tous deux répondre à la place qu'occupait un instant auparavant la
* lumière véritable; le seconde image, celle qui était verte,
* paraissait, dans le champ de la lunette, au-dessous de la lumière
* rouge, ce qui la mettait au-dessus en réalité, puisque les lunettes de
* nos cercles renversent les objets; en sortant de la cabane, nous
* observâmes qu'il y avait des masses de brouillards moutonnées sur la
* mer, comme lorsque nous observâmes de la station de Desierto plusiers
* lumières à Campvey." (13 Feb. 1807; both B&A again.)
* Another DISPERSION report comes from La Mola de Formentera; "Les
* habitans de cette petite île sont très-peu nombreux, et ceux d'Yviza
* les regardent comme des sauvages, quoiqu'ils ne soient pas eux-mêmes
* très-civilisée." (p. 170) But I digress; the good stuff is on p.
* 175, where we have both Arago and Biot observing again, 27 April 1807.
* The light on Mongò was ordinarily "un petit point rond bien terminé;
* mais quelquefois elle s'alongeait verticalement et occupait plus d'une
* minute décimale. Il nous a semblé remarquer alors que cette image
* n'était point de même couleur dans toute son étendue. le rouge était
* en haut, le verd en bas dans la lunette qui renverse. . . . Tems calme."
* Full title is:
* Recueil d'Observations Géodésiques, Astronomiques et Physiques,
* exécutées par ordre du Bureau des Longitudes de France, en Espagne, en
* France, en Angleterre et en Ecosse, pour déterminer la variation de la
* pesanteur et des degrés terrestres sur le prolongement du Méridien de
* Paris, faisant suite au troisième volume de la Base du Système
* métrique; rédigé par MM. Biot et Arago, Membres de l'Académie des
* Sciences, Astronomes adjoints du Bureau des Longitudes, etc.
* (Umberto Eco mentions this in section 84 of ``Foucault's Pendulum'',
* calling this title ``phantasmagorical''!)
* available at Google Books
* SUPERIOR MIRAGES of SHIPS
* cf. Rees, 1988, and Lehn & Rees (1990) for inversion
* WILLIAM SCORESBY's Journal
* The full title is "Journal of a Voyage to the Northern Whale-Fishery;
* Including Researches and Discoveries on the Eastern Coast of West
* Greenland, Made in the Summer of 1822, in the Ship Baffin of Liverpool"
* The refractions are discussed on pp. 96-97: "Hummocks of ice assumed
* the forms of castles, obelisks, and spires; and the land presented
* extraordinary features. In some places, the distant ice was so
* extremely irregular, and appeared so full of pinnacles, that it
* resembled a forest of naked trees; in others it had the character
* of an extensive city, crowded with churches, castles, and public
* edifices."
* NOTE the footnote on pp. 96-97 (spanning Plate II) warning the reader
* that phenomena that were not contemporaneous are depicted together in
* the Plates!
* Looming of distant land, well over 100 miles away, is described on
* pp. 106-108.
* There is another short account of mirages on pp. 117-119: "The ice
* about the horizon assumed various singular forms: -- hummocks became
* vertical columns, -- floes and fields arose above the horizon, like
* cliffs of prismatic-formed spar, -- and, in many places, the ice was
* reflected in the atmosphere at some minutes elevation above the horizon."
* He then describes mirages of ships. . . . "The most remarkable effect
* produced, was on the most distant objects, the interesting appearances
* of which not being discernable without the use of a telescope, probably
* escaped general observation."
* [Note observation of CONCAVE surface.]
* The main account of mirages is on pp. 163-173; see Plate V, between
* pp. 164 and 165. "Often the hummocky parts of the horizon were reared
* into various architectural figures of extraordinary elevation : and
* occasionally, as observed in a former instance, the whole distant margin
* of ice was deeply serrated, in resemblance of an innumerable collection
* of spires and pinnacles, or in the form of a thick forest of naked trees."
* (p. 164) . . . . ". . . the space in which the ship navigated seemed to
* be one vast circular area, bounded by a mural precipice, of great
* elevation, of basaltic ice. . . . And it should also be observed, that
* these phenomena were principally telescopic, both the ships and images
* being so distant, that, to the naked eye, they only appeared as
* indistinct specks." (p. 165)
* "The general telescopic appearance . . . is frequently that of an
* extensive ancient city, abounding with the ruins of castles, obelisks,
* churches, and monuments, with other large and conspicuous buildings.
* Some of the hills often appear to be surmounted with turrets,
* battlements, spires, and pinnacles; while others, subjected to another
* kind of refraction, exhibit large masses of rock, apparently suspended in
* the air, at a considerable elevation above the actual termination of the
* mountains to which they refer. The whole exhibition is frequently a grand
* and interesting phantasmagoria. Scarcely is the appearance of any object
* fully examined and determined, before it changes into something else.
* It is, perhaps, alternately a castle, a cathedral, or an obelisk: then
* expanding and coalescing with the adjoining mountains, it unites the
* intermediate valleys, though they may be miles in width, by a bridge of
* a single arch of the most magnificent appearance." (pp. 166-167)
* He continues: "The cause of these phenomena, as far as they depend on
* refraction, is, I imagine, the rapid evaporation which takes place in a
* hot sun, from the surface of the sea; and the unequal density occasioned
* by partial condensations, when the moist air becomes chilled, by passing
* over considerable surfaces of ice. The vapour produced by evaporation
* and partial condensation, is sometimes perceptible to the eye, rising
* like transparent steam in all directions, in little curling clouds, and
* passing along with the breeze near the surface of the sea. Its influence
* can sometimes be perceived at the distance of a few fathoms, or, perhaps,
* half a furlong, by the tremulous motion it appears to give to all bodies
* on the water or near it. In this case, it has a tendency to produce a
* serrated or basaltic appearance of the ice on the horizon, similar to
* what occurred on the 10th and 19th of June. But at other times, when
* repeated, well-defined and proportionate images of ships appear in the
* air, the vapour giving rise to the unequal density, obtains more of a
* stratified arrangement. In its distortive effect, it seems to act like
* clear glass, of unequal surface or thickness; consequently it disfigures
* all objects seen through it. In its looming effect, or that property
* of it by which bodies on the horizon, or beyond, appear to be greatly
* elevated, or suspended, as it were, in air, it seems to act by that kind
* of refraction common to other mediums, when the density about the object
* seen is greater than at the eye of the observer. The lesser density of
* the air about the observer, arises from the elevated position he occupies
* when at the mast-head, where the phenomena are always the most striking.
* Hence, while near objects, which are seen through a very rare portion of
* this vapour, are little or nothing elevated: bodies at the distance of the
* horizon, which are seen through a mass of it several miles in thickness,
* are elevated ten, fifteen, twenty, or even thirty minutes of altitude.
* And when ships or ice within a few furlongs distance are disfigured by
* the action of this vapour, so as to present a varying and tremulous
* outline; other similar objects, at the distance of several miles,
* are, perhaps, steadily elevated. In most cases, the refracted portion
* of the distant ice is closely connected with the ice of the horizon,
* from whence it takes its rise; and when it assumes the columnar form,
* it presents the appearance of a vast amphitheatre, which is so disposed,
* that every observer, whatever may be his position, imagines himself to be
* in the centre of it. But in some instances, and these not unfrequent,
* the stratum of refracted ice is completely detached from the horizon,
* and appears to form a white horizontal streak in the lower part of the
* atmosphere. And occasionally, multiplied images of the ice, as well as
* other objects, occur, forming a parallel vertical series." (pp. 167-169)
* [This is followed by a long footnote, referring to Wollaston's paper,
* and Brewster's works, of a similar nature.]
* He then describes the appearance of the highest parts of the land seen
* above the duct, and correctly concludes that "the tops of the mountains
* were above the vapour, . . . so that no influence could be exerted by the
* refractive medium, but on the base of the land, which was concealed by
* the looming of the ice." (pp. 171-172)
* "As the more extraordinary and beautiful effects of unequal
* refraction cannot be fully discovered, without the use of a telescope,
* they escape general observation; and as the looming of the distant ice,
* or distortion of objects, is the most common effect of this state of the
* atmosphere, it becomes a considerable annoyance to persons not interested
* in the phenomena. As in this case, the vapour gives an indefinite and
* tremulous outline to every object beyond a certain distance;— ships, a
* mile or two off, cannot be recognised ;—a wall of ice seems to surround
* the navigator, the openings and leads in which cannot be discerned at
* a distance;—and, of the actions and employment of remote vessels,
* within sight, a knowledge of which is often of great importance to the
* unoccupied fisher, no correct conception can be formed." (pp. 172-173)
* Now comes the incident of seeing his father's ship miraged (July 24):
* "On my return to the ship, about 11 o'clock, the night
* was beautifully fine, and the air quite mild. The atmosphere,
* in consequence of the warmth, being in a highly refractive state, a
* great many curious appearances were presented by the land and icebergs.
* The most extraordinary effect of this state of the atmosphere, however,
* was the distinct inverted image of a ship in the clear sky, over the
* middle of the large bay or inlet before mentioned,---the ship itself
* being entirely beyond the horizon. Appearances of this kind I have
* before noticed, but the peculiarities of this were,--- the perfection
* of the image, and the great distance of the vessel that it represented.
* It was so extremely well defined, that when examined with a telescope by
* Dollond, I could distinguish every sail, the general `rig of the ship,'
* and its particular character; insomuch that I confidently pronounced it to
* be my Father's ship, the Fame, which it afterwards proved to be;---though,
* on comparing notes with my Father, I found that our relative position
* at the time gave our distance from one another very nearly thirty miles,
* being about seventeen miles beyond the horizon, and some leagues beyond
* the limit of direct vision. (Plate V. fig. 2.) I was so struck by the
* peculiarity of the circumstance, that I mentioned it to the officer of
* the watch, stating my full conviction that the Fame was then cruizing
* in the neighbouring inlet. (pp. 189-190; the Plate, between 164/165)
*
* Thanks to Mila Zinkova, for prompting me to include this item!
*
* Available at Google Books:
*
* https://books.google.com/books?id=n-MUAAAAQAAJ&source=gbs_navlinks_s
*
* Info kindly supplied by A.R.Macdonald, librarian at ROE:
* Henry Home Blackadder
* "In adverting to this subject, one can hardly avoid noticing the
* remarkable inattention of not a few to what is passing under their
* immediate view, while they eagerly search after that which is distant,
* and far removed from the sphere of their contemplation. . . . Is nothing
* interesting but what is distant?"
* GIUSEPPE DEL RE's comments on Minasi and the terminology
* (dedicated to the Duke of Calabria)
* The tides and associated flows are discussed on pp. 30-31.
* Then comes the interesting discussion (p. 32):
* "A rare and surprising phenomenon in the Strait of Messina is the
* Iride Mamertina , called the Fata Morgana by the natives." He cites
* Ribaud for information on this as well as the tides.
* "P. Minasi of Silla . . . claims that the beautiful Fata Morgana is
* seen only from Reggio; but it seems undoubted that it is seen also from
* Catona, from Gallico, from Villa s. Giovanni and from Messina, city
* where it has the name of Iride Mamertina ."
* This is the reference mentioned (but not cited) by Bayfield (1835)
* whose quotation is not strict. The original reads:
* "At one moment, the rippled surface of a lake was before my eyes; at
* another time, a thick plantation appeared on either side of me; the
* waving of the branches was to be seen, and this view was only changed
* for that of a distant glimpse of a city; the mosques and minarets were
* distinct, and several times I asked my Bedouins if that were not Suez
* before us; but they laughed and said it was all sand; and what appeared
* to me a city, a forest, or a lake, the nearer I endeavoured to approach
* it the farther it seemed to recede, till at last it vanished altogether,
* `like the baseless fabric of a vision, leaving not a wreck behind.'
* "If I were to speak of the nature of the Mirage from my own
* sensations, I should say, it was more a mental hallucination than a
* deception of the sight; for, although I was aware of the existence of
* the Mirage, I could not prevail on myself to believe that the images
* which were painted on my retina were only reflected, like those in
* a dream, from the imagination, and yet so it was."
* Background on the next two items. Henry Wolsey Bayfield had spent
* several years in mapping the Great Lakes; the Royal Navy was worried
* about naval warfare on the Great Lakes after the War of 1812, and
* needed maps. As the war scare on the border between Canada and the
* United States calmed down, the Navy reduced the mapping effort; but
* Bayfield, who had grown to enjoy his work in Canada, persuaded the
* Admiralty to extend the effort to the largely unmapped St. Lawrence
* estuary. But his exertions under harsh conditions had brought him
* some severe medical problems; so in staffing the new vessel under his
* command, he asked that a medical officer be added to the crew. This
* turned out to be Dr. William Kelly, "an experienced naval surgeon".
* These are volumes 54 and 55 of the Publications of the Champlain
* Society. The index to both volumes is at the end of the second one.
* The first volume contains Bayfield's notes on two mirages later
* published: the first (on pp. 175-176) is the mirage of June 19,
* 1832, published in Bayfield's 1835 note in the Nautical Mag.; the other
* (pp. 380-381) is the mirage of 13 Sept. 1835.
* Dr. William Kelly's first mirage paper
* Here he introduces some half-baked ideas, later retracted. But he has
* already discovered for himself the difference between the inferior and
* superior mirages. In the original text, he cites only Humboldt; in the
* later commentary, he reviews the papers by Latham, Vince, Huddart,
* Wollaston (whom he consistently calls "Woolaston"), Biot, and Parry.
* He says he has seen the mirage in Egypt. Note the FOG in the title;
* also (p.11): "There was generally with the mirage an appearance of a fog
* bank on the horizon . . . . The air within the horizon was at the same time
* perfectly clear."
* Effect of HEIGHT OF EYE mentioned repeatedly: "All these unusual
* appearances were generally lost in ascending the rigging from ten to
* thirty steps, when objects were seen in their natural shapes."
* Effect of DISTANCE noted: "The appearances differ much; owing,
* apparently, to the ships being more or less remote." And, in discussing
* Vince's report on p. 34, he says, "The refracted objects were all without
* the natural line of the horizon; those within it retaining their usual
* appearance." (This point was already made by Vince.)
* HEIGHT and DISTANCE COMBINED: (p. 12): ". . . during the mirage, which
* occurred in a calm with a considerable swell of the sea, the appearances
* presented by two small islands or rocks, at different distances from us,
* was very remarkable; for as the vessel rose on the wave, the more
* distant seemed to sink, and the nearer to be raised up; and again as the
* vessel sank, the first rose, and the near one was lowered. Even the
* different parts of the same island were variously affected, appearing to
* dance as the vessel rose and fell."
* Reflection in an apparently SMOOTH MIRROR (inf. mir.): "The portion of
* reflected sky between the inner islands and the vessel, resembles a
* perfectly smooth lake." (p. 17)
* MIRAGE and DIP: (p.20): he found the large dip of the inferior mirage
* ". . . so remarkable a feature, that I distinguished this in my notes as
* the mirage with shortened or depressed horizon, whilst the other was
* designated the mirage with elevated horizon, on account of the contrast
* between them . . . ", citing Humboldt's earlier work.
* Captain Bayfield's first 3-image report (with Kelly); seen June 19, 1832
* With air 5° F warmer than sea surface, a vessel 7 miles away was seen
* "with her hull occasionally raised, so as to shew it distinctly above
* the horizon, although the height of our eyes was not over eleven feet.
* Her sails appeared elongated laterally, but were perhaps only shortened
* vertically, which made then appear so elongated." (This probably
* explains many other reports of APPARENT HORIZONTAL MAGNIFICATION as well.)
* There was a very light breeze from the west.
*
* This item is followed by two rather ordinary inferior-mirage reports
* from A. Inderwick in Mexico, and R. R. Madden in Egypt, on pp. 93-94, and
* p. 94, respectively. The latter's comment, taken from his "Travels in
* Turkey, Egypt, . . . ", that "I should say it was more a mental hallucination
* than a deception of the sight; for, although I was aware of the existence
* of the mirage, I could not prevail on myself to believe that the images
* which were painted on my retina were only reflected, like those in a
* dream, from the imagination, and yet so it was" -- is apposite.
* (Though to him "the mosques and minarets were distinct," the Bedouins
* "laughed at me, and said it was all sand.")
* FIRST observation of FIVE IMAGES?
* William Kelly, M. D. was an acute observer:
* "When my attention was directed, some years since, to the different
* forms of objects, seen through mirage in the St. Lawrence, one of these,
* which I particularly remarked, was the flower-pot shape assumed by small
* islands, when affected by the mirage, which depends on the contact of warm
* moist air with a surface of water colder than its dew point. Whatever
* the real shape of the island, or rock might be, its top seemed raised and
* flattened; generally extending in a straight horizontal line so far on
* each side, as at least to equal the base in extent; often beyond it;
* whilst, midway between the base and distorted top, the figure was
* contracted, having the appearance of a neck. When two islands lay close
* together, these flattened tops sometimes met, giving the appearance of an
* arch from one to the other. In all cases of mirage, depending on the same
* cause, the tops of objects seemed straight and horizontal in the same way,
* but the sides were like a wall. They frequently presented an appearance
* as if they were horizontally stratified."
* He describes an instance in detail: "A line answering to the horizon,
* was also seen on a level with the upper flat part of the inverted image of
* the island, and extending from it to a sandy point on the main. The true
* horizon was quite distinct, and well marked beneath. The sandy beach
* between us and the point seemed raised like a wall."
* Another case "presented to the naked eye nothing more than the flat top
* and walled sides usually seen in this form of mirage. But on examining it
* carefully with a telescope, in some parts of the flattened top, the
* picture of a beach was seen above the trees; thus shewing that this form
* also depended upon a second inverted image lying above, and confounded
* with, the upright one."
* "All the various forms assumed by objects, under the influence of this
* mirage, seem to be the result of two or more images, alternately erect and
* inverted, either distinct or mingled together in a greater or lesser
* degree."
* In June, 1832, "in passing Point des Monts, where the breadth of the
* river is very considerable, we saw the three images distinctly marked,
* such as they have been described by Vince and Scoresby. . . . We have
* frequently since seen treble images in the estuary and gulf . . . ."
* GOOD ADVICE TO OBSERVERS:
* "A telescope, if at hand, should always be employed in observing mirages
* of any kind, as it enables us to detect particulars, that would escape the
* naked eye. On one occasion, to the naked eye, the hull of a ship seemed
* raised to an enormous height, and the sails very small, the telescope
* shewed three distinct images. . . . By the help of the telescope we were
* afterwards enabled to detect five distinct images, though the whole gave
* to the naked eye the impression of only one almost shapeless mass. . . ."
* Another time, with the air 48° and the water 39°.5, ". . . a vessel
* with all sail set, at one moment looked like an immense black chest, no
* sails or masts being visible. On observing her for a time the black body
* seemed to seperate horizontally into two parts; and two sets of mingled
* sails occupied the intervening spaces, with one set of very small sails
* above. The figures afterwards became more distinct, and three images were
* clearly discerned. Another vessel changed also from the form of a great
* square flat-topped chest, to five distinct images, the upper with sails
* erect, and the two lower double images with their sails rather confusedly
* intermingled. A raised horizon was parrallel to the upper figure of the
* hull. . . . Captain Bayfield and Mr. Bowen observed five distinct images of
* another vessel after I left the deck. When I first noticed extraordinary
* appearances, like those I have endeavored to describe, I was not aware of
* the advantage of employing a telescope for the examination of objects at
* inconsiderable distances." [spelling errors all sic ]
* "It seems probable that the horizontally stratified appearance, which
* the coast often assumes under this species of mirage, may be the effect
* of multiplied images of the horizon, or level sea at its base. The number
* of images may well exceed five, as we find they do three, which I believe
* was the greatest number hitherto noticed by any observer."
* IMPORTANCE OF MIXING in stratified waters:
* "Several rivers empty themselves into the sea at this place [the Mingan
* islands], the waters of which, in calms, float on its surface, which thus
* is sometimes several degrees warmer than the water at a depth of a few
* inches. A moderate current of air, which amongst small islands is often
* partial, sometimes, by agitating the water at one place, renders the
* surface there cold, whilst it continues warm in places sheltered from the
* wind. We have hence occasionally strange combinations of mirage." Thus,
* starting from an ordinary inferior mirage, where "The horizon on this side
* was low and near -- a rock, three miles distant, seemed above it. As the
* breeze sprung up from the S.W. the horizon receded beyond this rock, and
* the islands generally appeared to have flattened tops, shewing the mirage
* of the opposite kind. But the extreme points of the most distant island
* seemed still in the air, notwithstanding, the island generally presented
* the same flat level top as the others -- thus shewing, in its different
* parts, the opposite forms of mirage at the same time."
* ALTERNATION OF ERECT AND INVERTED IMAGES DISCOVERED:
* "Whatever the number of images may be, they appear in every instance to
* be alternately erect, and inverted."
* DISCONTINUOUS HORIZON:
* "But on one occasion near the Labrador coast, the point of junction of
* the two species of mirage was so well marked that it appeared like a step
* in the horizon."
* ASSOCIATION WITH STRAITS:
* "The most remarkable mirages over water have occurred in straits; those
* seen by Mr. Vince at Dover, and the celebrated Fata Morgagna at Measina.
* In the St. Lawrence they are most frequently observed, and present the
* greatest varieties in similar situations: as at Bic, Point des Monts,
* and the strait of Belle-isle." [typos strictly sic .]
* VARIATIONS IN DIP:
* He also cites a case in which the dip, measured with the dip sector,
* increased from 3' 15" to 4' 11" as the water temperature changed from 43.5
* to 46.5 F (both as seen from 12 ft. 6 inches elevation).
* Footer says "ENLARGED SERIES. -- No. 6".
* MICHELE SAFFIOTI's letter
* This is the second edition (1837), placed here to be next to Capozzo's
* disastrous derivative. The author's name is spelled "Saffioti" on the
* title page, and at the end. That spelling (according to Google Books's
* "Ngram viewer") was the more common in written material before 1874.
* Both Boccara (1902) and Costanzo (1903) spell his name "Saffiottï
* (with two t's); since then, the two-t spelling has dominated. The two
* spellings are about equally common on the Web today . . . .
* He hoped to see images vaguely colored with the colors of the rainbow.
* (pp. 9, 10) These colors are mentioned again on pp. 14 and 20 (referring
* to Minasi),
* He quotes Facellus (p. 14), and Angelucci's letter (p. 15).
* Then there are reports of the 26 April 1828 display, beginning with a
* "current of transparent vapor." (p. 17)
* Kircher, Allegranza (!) and Minasi appear on p. 19; he thinks none of
* them were observers, and that only Angelucci saw the Fata Morgana.
* The second part, beginning on p. 21, describes the geography around
* the strait. The tidal currents are treated on pp. 25 - 28. Then comes
* his theory, full of crystals and "vesicular vapors" (!) (p. 33)
* At least he understands that the sea and the air must both be perfectly
* calm to produce the F.M.
* Available on the Web at
* https://archive.org/details/bub_gb_HOxu7xksWzMC
* GUGLIELMO CAPOZZO's review of the Fata Morgana (via Saffiotti)
* The Introduction, and particularly the "Literary Appendix" on pp. 36
* to 38, shows that this is another work devoted to Sicilian patriotism;
* so the uncritical acceptance of Giardina as an authentic F.M. observer
* is hardly surprising.
* Quotes Giardina (1758) and Angelucci/Kircher in extenso on pp. 74-76,
* evidently believing that Giardina actually observed the 1643 display.
* After quoting Angelucci's account in full, the author says:
* "Our Padre Domenico Giardina of the society of Jesus describes more
* fully the same phenomenon seen in Messina on the 14th of August of that
* same year 1643." But, of course, Giardina didn't see that display;
* so the "added" details are all fabricated. (Cf. the growing embroidery
* of the New Haven "ghost ship", or the spurious details added to Minasi's
* account by Nicholson and Brewster.)
* There are many errors. He consistently calls Saffiotti "Salfiotti",
* consistently calls Angelucci "Angellucci", and mentions Allegranza
* (footnote, p. 72). And, as he plainly knows little about physics or
* optics, his attempts to explain the reflections with "vesicular vapors"
* and the like (p. 88) are useless nonsense.
* A final note, at the end (p. 92), says this article is an extract of
* the letter from Saffiotti cited on p. 72, note 1, with some additions.
* Those additions include the notion that Giardina saw the 1643 F.M.
* from Messina!
*
* Unfortunately, this wrong account has been propagated by careless
* readers: Consolo (in his 1993 Italian original, and then again in
* translation in 2006), and the ignorant Marina Warner (also in 2006).
* Then Capozzo's Italian was republished again in 2011 by Séstito.
* This is just as useless as Boccara (1902) says.
* The title page of the volume adds “con aggiunte e note per
* Guglielmo Capozzo” to the title given below; and Capozzo signed the
* dedication, the preface "to the readers", and the Introduction.
* The footers on pp. 17, 33, 49, 65, 82, etc. say "Capozzo Vol. I."
* So he is clearly the editor and effectively the publisher.
* Available at Google Books, and at the HathiTrust site.
* VINCENZO CONSOLO's essay on the Strait of Messina, with Fata Morgana errors
* repeats Capozzo's phony story (hence its placement here).
*
* A beautiful "coffee-table" book (quarto: 9x13 inches = 24x33 cm), with
* 34 color plates and 65 b/w in the text. The body type is large (about
* 12/15); the references and notes are about 11/13; and the photo credits
* on p. 183 are about 8/10.
* The contents exactly fit the title: it's mostly a picture book of
* views of the Strait of Messina, from the Middle Ages to the middle of
* the 19th Century.
* The subtitle "Con un saggio di Gioacchino Barbera" refers to Barbera's
* essay "Per un'iconografia dello Stretto di Messina" on pp. 41-64,
* followed by 3 pages of notes -- considerably longer than Consolo's text
* on pp. 15-37, followed by only 3 column-inches of notes on p. 38.
* The last 5 pages of Consolo's text are enclosed in quotes here, and
* set off by a break, as they are taken from his 1988 publication "Fra
* Contemplazione e Paradiso" with N. Rubino, as indicated by his final
* note on p. 38 here. The transitional paragraph on p. 33 that leads in
* to this story was reduced to a single sentence when this was translated
* by Mark Chu for Bouchard and Lollini's 2006 book.
* Barbera's essay is followed by 6 pages of biographical notes, and
* 18 pages of short notes on some of the works of art that are reproduced,
* prepared by Giovanni Molonia. Five of these are works by Willem Fortuyn,
* including his engraving for Minasi's Fata Morgana review.
* Then comes a 5-page bibliography, which mentions an unpublished letter
* by Gallo on the Fata Morgana of 18 Aug. 1768.
* The emphasis of the book is on art history; but it's garbage history,
* with no regard for factual accuracy in Consolo's text.
*
* Considering Consolo's repetition of Capozzo's false account of the
* 1643 Fata Morgana display, the main value of this for our purposes is
* the re-publication of Minasi's dissertation in full.
* Pages 159-168 contain a verbatim transcript of Minasi's dissertation,
* complete with its notes. Here there are some discrepancies with the
* original, starting with the extract from Pliny's Historia Naturalis:
* the original cites this as book VII, but Consolo's copy says book IV.
* The formal closing of the dedication has also been edited slightly: a
* comma was inserted after "Roma", and the tildes over the m's in the
* signature were omitted.
* Similar edits were made in the Proemio, including the addition of
* typos like "gravissimus" for "gravissimis" and "dibiis" for "dvbiis"
* in the quoted inscription. [As "i" and "u" are adjacent keys on modern
* keyboards, it's obvious how these were produced.] These same copying
* errors appear in the version of Minasi's text reproduced in Séstito's
* book; so that was probably copied from Consolo, rather than from the
* original.
*
* Likewise, there are changes in the reproduction of Minasi's footnotes,
* which have been converted to end-notes here, with re-numbering within
* each Chapter (instead of each page, as in the original.) The change
* in format from Minasi's small single columns to much wider double
* columns with narrow margins has compressed Minasi's 102 pages to just
* 20 pages.
* However, the re-numbering was not extended to the cross-references
* within the Notes. So "Cap. III, § 8, nota 1" that is cited in notes
* 7 and 30 to Cap. V is now note 11; and the "Cap. III, § 8, nota 2"
* cited in note 28 is now note 12. But everything is here, including
* the notes in Cap. IV that discuss the plagiarism of Angelucci's account
* by Giardina.
* Evidently, Consolo was another of those careless writers who cite
* references (and, here, even re-publish them) without reading them.
* VINCENZO CONSOLO (in translation) serving up Capozzo (1840)
* (and so placed here out of chronological order):
* The translator has rendered Angelucci's account in graceful English,
* on pp. 196-197. Then we have:
* "And the Calabrian Jesuit sees that Fata Morgana precisely on
* the feast of the Assumption -- the great feast of the patron saint
* in Messina on the day of 15 August -- creating the suspicion that
* his might be a devout fantasy. This is all the more so for the fact
* [sic!] that another Jesuit, Father Domenico Giardina, has the same,
* identical vision, like the reflection on the second side of a double
* mirror, with only the temporal displacement of barely a day, on 14
* August of that same year of 1643, from the opposite side, from Messina.
* [Here, footnote 21 cites Capozzo as the reference.] The story of the
* Calabrian is identical to that of the Messinese (which we would like to
* reproduce here if we were not afraid of boring the reader); the details
* are identical, except for the number of the pillars: ten thousand for
* Angelucci, one hundred thousand for Giardina."
* "Identical"! So why didn't Consolo suspect that Giardina's account
* was copied from Angelucci's? And why didn't his editors suspect this,
* and investigate? Instead, he wanders off into airy lyricism, and
* reality and truth are abandoned. Shameful.
* The translator of this essay was Mark Chu, another person very
* interested in Sicilian matters; which may have dampened his critical
* sense.
* This essay (pp. 188-) is called "Views of the Strait of Messina".
* On p. 294, we find it comes from "Vedute dello Stretto di Messina"
* in "Di qua del faro" (1999), pp. 67-91; though I also see it listed as
* a separate publication by Sellerio, Palermo, dated 1993.
* The book says copyright 2006; the publisher's website says 2007.
* Sir Charles LYELL's textbook example of LOOMING:
* "June 14, 1842. - From Queenstown we embarked in a fine steamer for
* Toronto, and had scarcely left the mouth of the river, and entered Lake
* Ontario, when we were surprised at seeing Toronto in the horizon, and
* the low wooded plain on which the town is built. By the effect of
* refraction, or `mirage,' so common on this lake, the houses and trees
* were drawn up and lengthened vertically, so that I should have guessed
* them to be from 200 to 400 feet high, while the gently rising ground
* behind the town had the appearance of distant mountains."
* (No photocopy; this is on P-10 microform.)
* THOMAS MILNER's update of Polehampton's 1815 work
* This version went through many editions; the 1855 one is on Google Books.
* It bears the label "A NEW EDITION, CAREFULLY REVISED" on the title page.
* A copy of the 1848 edition from the U.C. libraries is at the HathiTrust
* website. It seems identical to the 1855 one; and the quality is better.
* The 1846 edition is also at the HathiTrust site.
* In all 3 editions, mirages are in Section 5, "Spectral Illusions",
* of Chapter XVI on "Optical Phenomena": pp. 535-540. It then goes on
* to deal with the Brocken spectre and similar images on mists, which are
* attributed to "reflection". The text returns to mirages on p. 542: "In
* northern latitudes the effects of atmospheric reflection and refraction
* are very familiar to the natives. By the term of uphillanger the
* Icelanders denote the elevation of distant objects . . . ." The mirage
* discussion then continues with Scoresby's observations, Wollaston,
* Jurine & Soret, etc. until p. 543. [Cf. Milner's 1850 book.]
* Note: "upphillingar" seems to be the correct spelling.
* Minasi's stuff about the tides is omitted.
* Dr. William Kelly seems to have been as sharp an observer as Willard Fisher
* "On The Dip Of The Horizon, and Mirages of the Gulf and River St.
* Lawrence. By William Kelly, M.D., Surgeon, R.N., attached to the Naval
* Surveying Party on the St, Lawrence.
*
* "Every one conversant with nautical astronomy is aware that some
* uncertainty always attends observations made with the natural horizon,
* from the varying amount of the dip occasioned by terrestrial refraction.
* The cause of these variations is very obscure. The best authorities seem
* to regard differences of temperature in the air and water as the sole
* cause of the irregular density of the lower strata of the atmosphere on
* which the varieties of the dip depend. It is known that, in general, when
* the water is warmer than the air, the dip is greater than that given in
* the tables; and that when the water is colder than the air, the dip is
* less. But cases occur where the deviations from the tables are found to
* bear little relation, at least in amount, to the relative temperatures of
* the air and water. Some other property of the atmosphere must therefore be
* sought after, by the influence of which the effects of temperature are
* modified."
* He recognizes the two main types: "In one (the mirage of Arctic regions)
* the horizon is elevated, the forms of objects distorted, and frequently
* two, three, or even as many as five images of the same object are seen,
* alternately erect and inverted -- the lowest always being erect. This
* kind of mirage is only met when the water is colder than the air. In the
* other kind of mirage, (the mirage of the desert), the horizon is
* depressed, distant points of land seem raised into the air, the form of
* objects is seldom materially changed, there are never more than two images
* of an object, and when a second is seen, the lower is always inverted, the
* upper erect. When this kind of mirage is seen, the water is usually
* warmer than the air."
* "The mirage with depressed horizon was constantly seen if we had an
* opportunity of observing distant points of land when the water was warmer
* than the air."
* Kelly grants that the temperature difference between water and air is
* the main factor, but thinks humidity plays a part as well.
* "The occurrence of either form of mirage, and its intensity, seemed to
* be affected by other circumstances besides the relative temperatures of
* the air and surface water, and the hygrometric states of the air. Thus
* they appeared more frequently, and their phenomena were more intense in
* calms or light winds than in a fresh breeze." -- with a footnote:
* "Still I have seen both forms in fresh breezes, and the mirage with
* depressed horizon during a strong gale."
* He gives a few extreme examples of dip, and notes a DIURNAL VARIATION in
* dip. The variations of dip parallel those of the mirages:
* "The force of the winds had the same effect on the dip as on the
* mirages. Either the elevation or the depression was comparatively greatest
* in a calm, and least in a breeze. This was often very observable when a
* set of observations was commenced in a calm, and a breeze happened to
* spring up before it was finished."
* On the whole, a careful, cautious argument; should be taken seriously.
* NOTE: This and other selections from Nautical Mag. were plagiarized
* in Vol. 2 of The American Merchant (1859) by "Capt. John H. Bell".
* No.8, August, 1846. Title page says "The Nautical Magazine and Naval
* Chronicle". Available at Google Books.
* Commander Bedford thinks it has to do with water vapor, not temperature.
* See detailed discussion below, following the reprint in J. Franklin Inst.
* I have only a very bad copy of this from a scratched microfiche.
* Full title is "The Nautical Magazine and Naval Chronicle".
* Commander Bedford thinks it has to do with water vapor, not temperature.
* But he recognizes that the difference in temperature of sea and air is
* the decisive factor. He has observed carefully:
* "The occurrence of mirage during strong, or even fresh, winds, can be, I
* imagine, but seldom, particularly of that kind with elevated horizon. . . ."
* Despite the title, this is about mirages. This seems to be a verbatim
* reprint of his Nautical Magazine article, in response to Kelly.
* A curious report, including claims of LATERAL MIRAGE
* ". . . the said light became perfectly distinct , and proved to be, (as
* in a former instance communicated to you, Calais Light , and in a
* position 2 3/4 points from its real bearing. . . . right over the middle
* of the North Sand."
* A Classical allusion: "The pilot of Ulysses was deceived, as Ithaca
* melted into mist . . . ."
* Cited by Lt. Raper.
* Capt. Martin is listed as "Harbour-Master, Royal Harbour, Ramsgate."
* Full title is "The Nautical Magazine and Naval Chronicle".
* Sept. issue.
* HEIGHT DEPENDENCE mentioned for BLACK SEA mirages
* In the section headed "Black Sea" (p. 418), Capt. Leighton says:
* ". . . I have found that dark overcast rainy weather occurs frequently,
* . . . and this weather sometimes clears off suddenly to beautiful clear
* weather, but leaves a miraged horizon. This, when it occurs at night is
* very deceptive, as it cannot then be seen, and may mislead you by false
* altitudes of stars. I have seen it several feet high all round the
* horizon during the day, appearing like broken water, or the tops of trees
* upon a low plain just rising above the horizon, that did not disappear
* until the eye was fifty feet above the sea. I have also observed the
* land to be affected by this mirage, particularly near Cape Fontane."
* EARLIEST BLANK STRIP ?? Note references to "DRY FOG" throughout
* Many good descriptions and a DRAWING of black bars across the Sun!
* The "météore" is evidently a DUCT, which he says is known as "qobar"
* in the language of the Ethiopians. "Toutes les langues éthiopiennes
* ont un mot spécial pour le désigner et pour éviter les périphrases."
* (According to the E.B. (9th ed.), d'Abbadie compiled a catalog of
* existing Ethiopian manuscripts; see the article on Ethiopia.)
* "Vu de loin, aux limites de l'horizon, le qobar semble disposé par
* couches, le plus souvent horizontales, à tranches nettes, sans bavures,
* et tellement denses que le soleil s'y éclipse comme derrière l'écran
* le plus opaque. Ainsi, dans Ynarya nous vîmes, le 24 janvier 1844, le
* soleil disparaître complètement derrière un banc de qobar qui devint
* ainsi visible négativement. A mesure qu'il descendait, son disque
* paraissait, au-dessous de la limite inférieure du qobar, aussi net et
* exempt de déchirures que si l'on avait enlevé d'un trait de diamant la
* moitié supérieure d'un disque de verre rouge. Cette couche de vapeurs
* sèches avait une légère réfraction de lumière rouge sur sa surface
* supérieure pendent que l'astre était caché derrière, et nous pûmes
* voir ainsi que cette surface était tant soit peu plus déchiquetée que
* la surface inférieure."
* "Le caractère le plus frappant de notre météore, outre l'énorme
* sécheresse qui l'accompagne toujours, c'est sa faculté d'éteindre
* la lumière." N.B.: Drawing shows a VERTICAL COLUMN -- cf. Livesey, 1985.
* ". . . et toutes ces couches interceptaient totalement et sans
* déchiqueture la lumière du soleil."
* Many nice accounts of phenomena over a small lake (Tana).
* The comments following on pp.303-304 by the Commission of referees say
* that d'Abbadie was from a family of the Midi, and educated in Toulouse;
* he apparently inherited wealth, which he used to support scientific
* expeditions. This connection explains his presenting the paper here, and
* his final paragraph thanking the city fathers for their support of the
* Toulouse Observatory.
* THOMAS MILNER's "Atlas" -- mostly taken from his "Gallery of Nature"
* The "Icelanders" part has changed to: "The most usual effect is an
* increase in the vertical dimensions of the objects affected, so that
* low coasts appear elevated, what seamen call looming , and sites below
* the horizon are brought into view. The Icelanders, who are familiar
* with this effect of atmospherical refraction, call it upphillingar . . . .
* "It is an old tradition, that Hvidsærk, a mountain in Greenland,
* and Sneefields, in Iceland, have both been visible at the same time
* from the middle of the intervening strait, which at the nearest point
* is about 300 miles wide. Though treated as a fable, it may be strictly
* true, owing to the effects of refraction. The last named mountain,
* Sneefields, though it is not seen under ordinary circumstances for
* more than 80 miles, has yet been often visible from the sea beyond
* the Westmanna Isles, a distance of more than 140 miles; and Scoresby
* relates having seen a part of the Greenland coast of inferior height,
* Home's Foreland 3500 feet high, when 160 miles distant." (p. 95).
* Note: "upphillingar" seems to be the correct spelling.
* A very SUCCINCT SUMMARY of all of atmospheric optics
* J. Bradford Cherriman's review article deserves to be better known!
* He covers everything: refraction, mirages, scattering, absorption,
* rainbows halos, glories and coronae. He explains superior and inferior
* mirages, and says: "To this class of phenomena belong the well-known
* Fata Morgana , the appearances seen on the sandy plains of Egypt, and
* called by the French Mirage , and the Looming occasionally seen in
* parts of Great Britain."
* N.B.: The Roy. Soc. Cat. has this under "Bradford".
* See Cherriman's entry in the Dictionary of Canadian Biography at
*
* http://www.biographi.ca/en/bio/cherriman_john_bradford_13E.html
*
* IRISH Fata Morganas, some with COLOR
* The first sentence is: "These singular illusions are termed in the
* Irish language Duna Feadhreagh , or Fairy Castles."
* After citing several rather fantastic reports, the author describes
* his own observation: ". . . in June, 1833, he himself and a party of
* friends, when standing on a rock at Portbalintrea, perceived a small
* roundish island as if in the act of emerging from the deep, at a distance
* of a mile from the shore; at first it appeared but as a green field,
* afterward it became fringed with red, yellow and blue; whilst the forms
* of trees, men and cattle rose from it slowly and successively; and these
* continued for about a quarter of an hour, distinct in their outlines,
* shape and colour; the figures, too, seemed to walk across it, or wandered
* among the trees, the ocean bathed it around, the sun shone upon it from
* above; and all was fresh, fair, and beautiful, till the sward assumed a
* shadowy form, and its various objects, mingling into one confused whole,
* passed away as strangely as they came."
* Further instances are mentioned, but do not seem to be first-person
* accounts. A few references are offered for these later examples.
* There seems to be no standard abbreviation for these Reports; see
*
* http://www.scholarly-societies.org/history/1831baas.html
*
* The full title of the volume is: Report of the twenty-second meeting of
* the British Association for the Advancement of Science; held at Belfast
* in September 1852.
* Note: these "Transactions of the Sections" are paginated separately
* from the rest of the Reports, though both are bound together. They
* are headed "Notices and Abstracts of Miscellaneous Communications to
* the Sections", and follow the first 355 pages of the volume. According
* to the Indexes that appear at the end of this section, the first part
* of the volume is "Reports on the State of Science", while the second
* is "Miscellaneous Communications to the Sections."
* Following p. 144 of this section comes yet a third, separately
* paginated, section of the volume (again starting on p.1) that lists
* "those Members of the British Association . . . to whom Copies of this
* Volume [for 1852] are supplied gratuitously . . . ." -- with separate
* lists of "Honorary Members", "Life Members", and "Annual Subscribers".
* This is followed by several un-numbered pages listing the past volumes.
* Note that the M of M`Farland is followed by a left single quote mark.
* He does not appear in any of the lists of members.
* Adolphe Ganot's famous textbook
* This went through 18 editions under Ganot himself; Hachette continued to
* produce revised editions until 1931. It was distinguished by the
* introduction of numerous woodcuts, from the 2nd (1853) edition on.
* The PALM-TREE diagram appears on p. 366: "Le mirage est une illusion
* d'optique. . . .
* "Ce phénomène a été observé dès la plus haute antiquité; mais c'est
* Monge, le premier, qui en a donné l'explication, lorsqu'il faisait
* partie de l'expédition d’Ègypte."
* The 17th ed. is at Gallica; the figure is slightly more elaborate, and
* appears on p. 473 there.
* BRAVAIS reviews mirages
* (This 53-page article is filed separately.)
*
* EARLY USE of "INFERIOR" and "SUPERIOR" mirage terminology:
* "Description du mirage ordinaire ou mirage inférieur" (p. 234)
* "Mirage inverse ou mirage supérieur" (p. 264)
*
* This is an outstanding review of the early literature, containing many
* results not re-discovered until much later. EXCELLENT INSIGHT into
* the problem, despite being confined to simple analytical cases.
* Very complete REFERENCES to the earlier literature, even mentioning
* Quintus Curtius (p.227). But he relies on secondary sources (like
* Gilbert), consistently calls Minasi "Minazi", and confuses Biot's
* publication date (1809) with the year of his observations at Dunkirk.
*
* He is very impressed with Wollaston's 1800 paper. (pp.231-232)
*
* Much discussion of the fact that the inferior mirage is usually smaller
* than the direct image (pp. 233, 241, etc.), and tentatively attributes
* it to the CURVE of the Earth: "J'ai remarqué que, lorsque l'oeil est
* près de la surface des eaux, à 1 mètre ou 2 mètres au plus de
* hauteur, les objets étant rapprochés, les deux images ne diffèrent
* pas beaucoup de l'égalité; mais que, si l'oeil est beaucoup plus
* élevé, par exemple à 10 ou 12 mètres d'elévation au-dessus du
* niveau de la couche liquide, le rétrécissement de l'image inférieure
* devient extrêmement sensible: d'après cela, il me paraît probable
* que la courbure de la terre joue un rôle assez actif dans ce
* phénomène." (p.241) [cf. Riccò et al., 1888.]
* This idea was proposed earlier by Woltman (1800).
*
* CARE in observing: "Pour bien discerner le mirage, il faut
* non-seulement une vue longue et étendue, mais savoir observer des
* détails, et avoir l'habitude de l'horizon. Aux voyageurs, aux marins,
* aux météorologistes, cet exercice est devenu familier; le reste des
* hommes s'en doute à peine; vous leur montrerez le mirage et ils ne le
* verront pas, ou ils ne verront qu'un peu de brouillard et de fumée
* à l'extrême horizon." (p.235)
*
* EFFECT of INFERIOR MIRAGE on HORIZON (WAVES):
* "L'horizon sensible de l'eau paraîtra presque toujours offrir un
* léger tremblotemont: si le mirage est fort, il sera bordé par une
* crête dentelée dont les sinuosités paraîtront sans cesse monter et
* descendre, s'effacer et reparaître." (p.235)
* How to tell REFLECTION on water from inferior mirage, p.237.
* "En général, dans le cas du mirage, le raccordement d'une ligne
* oblique avec sa symétrique située au-dessous se fait, non par un angle
* à sommet net, mais par un arc de courbe ayant son principal élément
* vertical." (p.238) [cf. Wollaston, 1803; & Gilbert's 1806 transl., Fig.6 !]
*
* OPTIMAL HEIGHT of EYE: "Il est très-probable qu'il existe une certaine
* hauteur de l'oeil pour laquelle l'angle entre l'horizon apparent et la
* ligne de partage des objets situés à une distance donnée est un
* maximum. Ce maximum, dont la hauteur doit varier avec les circonstances
* météorologiques du mirage, paraît avoir lieu pour une élévation
* de l'oeil de 1m.5 à 2m . . . ." (p. 242)
*
* He seems to be the first to see that the whole TEMPERATURE PROFILE must
* be measured, and that the thermometer must be ventilated. (pp. 242-243)
*
* Effect of UNEVEN GROUND: ". . . le mirage des plaines ne pourra jamais
* offrir une régularité aussi parfaite que le mirage des mers ou des
* lacs." (p. 244)
*
* Notices "que le niveau de la caustique ne peut jamais s'élever . . .
* au-dessus de l'horizon apparent." (p. 250) -- a hint of The Theorem.
*
* LOOMING is explained on p. 256: the ray curvature can exceed the Earth's.
* He also finds hints of the CONCAVE SURFACE and the appearance of
* "high cliffs" in Woltmann and Biot (p.257) -- i.e., the Fata Morgana.
*
* An early EXPLANATION of NEGATIVE DIP (cf. Kimmfläche, and Biot):
* the space below the level where ray has constant height "est pour
* l'observateur comme s'il n'existait pas, c'est-à-dire comme si le sol
* ou la mer s'élevaient . . . ." (p. 262)
*
* He notes de Tessan's observations of "terres qui paraissaient bordées
* d'immenses falaises" (p. 263) in the estuary at Rio de Janeiro. And
* in discussing Woltmann's observations, he says: "souvent une strie
* d'air séparait l'image renversée des objets placés au-dessous; mais le
* plus souvent, l'image et l'objet se rencontraient et se pénétraient de
* telle sorte qu'il en résultait l'apparence d'une haute falaise avec des
* stries verticales." (p. 268) [translated from p. 430 of W., (1800).]
*
* His numerical difficulties (bottom of p. 272): ". . . j'ai été arrêté
* par la difficulté de cette analyse, et surtout par la complication
* des calculs numériques."
*
* He also emphasizes the parallels between inferior and superior mirages,
* and deals with the paradox of the missing 3rd image in inferior mirages:
* "le sol interceptera les trajectoires qui la forment et fera disparaître
* l'image directe secondaire qui devrait cette fois se montrer en dessous
* de l'image renversée." (p. 274)
* "Cette non-observation de la troisième image, dans le cas du mirage
* ordinaire, ne forme donc point une objection sérieuse contre la
* théorie que nous venons d'exposer." (p. 275) Yet Wollaston has seen
* it in the lab (p. 276).
*
* ADVICE to observers: ". . . il est très-utile d'être muni d'une longue
* vue, ou à son défaut, d'une lorgnette de spectacle groissant au moins
* deux à trois fois, et que certains détails échapperaient à l'oeil
* nu qui pourront être facilement saisis par une lunette . . . ." (p. 280)
*
* The first 3 volumes of this Annuaire were bound together, with a common
* table of contents. This 4th volume is separate, with its own Introduction
* that mentions Bravais's "Note" on p. VIII. The formation of the new
* Société Météorologique is reported on p. XIII. Bravais is one of the 5
* signers of the Letter announcing this event.
*
* As usual, the Google Books scan is half useless because the plates are
* only shown folded up, and so mostly invisible.
* Gallica tries to show the plates; but the lines are too fine for the
* scanner they used, and so again are nearly useless.
* Note the Erratum on the last page, correcting the error on p. 256.
* No date is assigned to the manuscript; but as it comes toward the end of
* the collections of papers in this volume, I assume it was submitted
* late in 1852.
* Bravais's follow-up comments on his "Notice" (above)
* He begins by explaining his strategy in dealing with the mirage problem.
* Notice that he seems to prefer his "direct/inverse" terminology to the
* "inferior/superior" alternative that won out.
* After briefly summarizing his first mirage "Note", he gets into the
* horizontal-ray problem on p.56:
* "Jusqu‘ici on a fait jouer au phénomène de la réflexion
* totale des objets un grand rôle dans la théorie du mirage. Le
* redressement des trajectoires lumineuses qui, après avoir été
* plongeantes vers le sol, deviennent horizontales pendant une courte
* portion de leur trajet, et vont ensuite en s‘éloignant du sol,
* paraissait à plusieurs physiciens ne pouvoir s’expliquer que par
* un phénomène de réflexion totale. Je montrerai que les conditions
* nécessaires pour produire cette réflexion ne peuvent exister, et que
* le mirage est un simple phénomène de réfraction. M. Biot a fait
* voir que le fait du redressement s‘expliquait très—bien, dans le
* système de l‘émission. On verra qu‘on l‘explique avec la même
* facilité dans le système des ondes lumineuses, en adoptant les idées
* de Fresnel sur la vitesse de la lumière dans les différents milieux.
* 0n arrive alors à cette conséquence remarquable. que lorsqu‘un rayon
* de lumière traverse un système de couches planes et parallèles, et,
* par exemple, horizontales, dont la densité varie suivant la normale
* commune aux couches, la courbure de la trajectoire est partout égale au
* quotient de la variation du logarithme de l‘indice de réfraction, par
* la variation correspondante dans la hauteur de la couche considérée. De
* là se déduisent facilement les équations qui peuvent ensuite servir
* à expliquer les circonstances du problème."
*
* This is in the section called "Bulletin des Séances" -- the
* reports of the meetings. The date is 8 Mars 1853; Bravais presided.
* The report of this meeting begins on p. 34 and ends on p. 64.
* The volume is in two sections, separately paginated. The part with
* the meeting reports ends on p. 241; the Table of Contents is pp.239-241.
* Mostly superior mirages, with DRAWINGS; Fata Morgana mentioned
* "Few have traversed the plains of central India without being struck
* by the appearance of distant cliffs --- sometimes also of towns and
* forests, seen shortly after the rising of the sun, but which they have
* vainly looked for later in the day. I first observed this phenomenon in
* October 1829, when marching with my company from Kurnaul to Mhow in Malwa.
* Several times on reaching camp, I found it pitched in a plain, walled
* apparently to westward by lofty (See Pl. VI.) cliffs which had an inviting
* aspect. Several times I promised myself that in the afternoon I would
* pay those cliffs a visit. But, whenever I would accomplish this design,
* I found that the cliffs had entirely disappeared, and I questioned whether
* I had not been suffering some illusion of the eye or mind: for I was not
* then aware that Mirage is known in India. A residence in Malwa, where
* it is common, made me familiar with some of its phases. . . ." (pp.163-4)
* Major Abbott understands the appearances well, but not the physics
* behind them. He continues:
* "The Mirage most commonly observed in India is the effect produced upon
* distant objects, by means of a mirror, suspended with its surface
* downwards at the distance of from 60 to 230 feet from the earth. . . .
* This mirror is a stratum of dense but transparent and scarcely visible
* vapor, evolved from the dewey earth by the action of the sun's rays,
* generally about an hour or two hours after sunrise. The refractive power
* of this vapor being greater than that of the atmosphere, acts precisely
* as would a mirror of glass . . . ."
* So his "cliffs" are the striated zone of the Fata Morgana; and his
* timing is that of Angelucci's observation from Reggio. He fails to
* understand the atmospheric physics, either optically or dynamically.
* "This reflecting canopy exhibits the images of distant objects alone,
* because its substance is not sufficiently dense to repel those rays
* of light which fall upon it at any sensible angle of incidence. It is
* only when the angle of incidence is extremely small, that the ray will
* rebound from the surface of the vapor. It follows that supposing the
* strength of the illumination sufficient, the image will be distinct in
* proportion to the distance of the object." (So, unlike Monge, he does not
* think this is total reflection.)
* He does give us some further information: "The ordinary Mirage of India
* occurs at distances of from three to eight miles. But . . . the effect may
* be produced at distances so remote, as that the substance is completely
* hidden in the convexity of the earth, and only the reflected image is
* seen suspended in the air. Of such an effect the Fata Morgana are an
* instance. And the pictures of coming vessels, as seen from the Isle of
* France, are another."
* "In India, the most general appearance is that of a long range of
* cliffs standing to westward of the spectator. . . . Trees are the objects
* most commonly pictured by the Mirage. . . . But sometimes the monotonous
* aspect of the cliff is diversified and enlivened by the presence of a
* white town or of moving objects. Every stump of a tree becomes a palm or
* a column. Every little bush becomes a tall mass of foliage." (p. 165)
* "With respect to the Isle of France, the vapor hanging over the sea is
* probably more transparent and of higher elevation than that which
* overhangs the land. . . . the sails of a vessel brightly illuminated by the
* sun, might be seen at the distance of a hundred or more miles. . . . the
* reflecting canopy is not a perfect plane, but is a mirror slightly
* concave answering to the convexity of the earth. The image therefore
* would probably be magnified in the concave mirror . . . ." (p. 166)
* "The effect of mirage is greatly enhanced by the use of a telescope
* which . . . greatly increases the beauty of the exhibition." (p. 167)
* He then briefly describes seeing "another variety" of mirage, "in which
* the reflecting surface lies below the object and the spectator's eye.
* . . . The effect was precisely that produced by water upon objects standing
* beyond it, excepting that the strong undules of the vapour [sic] did not
* much disturb the accuracy of the reflection." (p. 167; cf. Büsch, 1800)
* [So he saw inferior mirages more rarely than superior mirages! And on
* the next page, he says he had not been able to study the mirage of the
* desert, which "is commonest at night in India."]
* "I have also observed upon the Nurbudda and other large rivers that,
* whereas the nearer current is too rapid and turbid to reflect the rocks
* upon its banks, the more distant current, equally rapid and equally
* turbid, presents a perfect reflection of the banks without any waving of
* outline. This may be attributable to the transparent vapour, ever hanging
* over streams, acting as a mirror to reflect surrounding objects." (But
* then he allows that it might be due to the combined reflections from wave
* crests -- cf. Budde (1885) and Venturi (1889).)
* EARLIEST WAVE-CREST THEORY?
* On p. 169, he says he has "referred to Brewster's treatise on mirage,"
* and thinks that Brewster's attribution of superior mirages to "a denser
* stratum of atmosphere" is "a mistake." "It is undoubtedly a stratum
* of vapour which forms the mirror". So he thinks his own crank theory
* explains why "the phenomenon is only or chiefly visible from the 1st to
* the 2nd or 3rd hour after sunrise and when the nights are rather chilly
* and the skies clear."
* So his observations are accurate and useful, but his theory is nonsense.
* Major James Abbott
* Long verbal descriptions of inferior mirages; no drawings
* Remarks on effects of height of eye, etc.
* From 37 m height, "l'image inférieure était moindre de moitié."
* Possible FATA MORGANA with SUPERIOR MIRAGES with a fine fold-out plate.
* A very detailed account of observations from 37 m with 40x telescope.
* DIP VARIATIONS of 4' reported.
* "Abnormal" refraction is in fact normal:
* "Ces divers effets, je les ai observés si fréquemment, qu'on pourrait
* dire que c'est l'état normal de la contrée."
* A reasonable interpretation of "FOG":
* "Ce nuage est venu du côté de la haute mer. Sa largeur est faible, sa
* teinte et sa consistance sont celles d'un nimbus. It est probablement
* l'image du sol vu de profil." (p.248)
* "Il s'annonce par une vapeur générale qui couvre le ciel à l'horizon,
* sur une hauteur d'environ 3'." (p.251)
* A "BREATHING" MIRAGE:
* ". . . montant . . . et . . . redescendant renversées : one dirait qu'il les
* aspire à son passage."
* ". . . it n'eût ondulé, au point qu'il semblait danser , selon
* l'heureuse expression de M. Humboldt."
* At one point the inverted image disappeared, leaving 2 erect ones.
* (cited by Mascart)
* EARLY MURAL MIRAGE
* "Le soubassement sud-ouest de la Bourse de Paris, que pour abréger
* j'appellerai le mur méridional, est formé d’un mur vertical en pierre
* de taille, parfaitement construit, et sans aucune partie saillante dans
* une étendue d’environ 78 mètres. Lorsque, entre midi et 3 ou 4 heures,
* ce mur est frappé parles rayons solaires, il présente le phénomène
* du mirage avec une assez grande intensité. . . .
* "Le mirage se manifeste aussi très-bien sur les murs des
* fortifications de Paris, surtout du côté du sud. . . . si l’on observe
* les images réfléchies avec une lunette, on peut voir jusqu'à des arbres
* entiers avec leurs branches et leurs feuilles. Si le prolongement de
* la muraille rencontre une route fréquentée, on distingue très-bien
* à la lunette les images réfléchies des passants, des chevaux et
* des voitures, lorsqu'ils se présentent près du prolongement du mur.
* A un degré plus ou moins intense, ces phénomènes ont lieu tous les
* jours, ou du moins toutes les fois que le soleil éclaire les murs des
* fortifications, depuis deux ou trois heures.
* "Au reste, comme il résulte des faits consignés dans ce Mémoire,
* le mirage se manifeste à Paris, dans beaucoup d’endroits, d’une
* manière permanente, l’hiver et l'été, la nuit et le jour. Lorsque le
* soleil brille avec un certain éclat, on peut l'observer très-facilement
* sur toutes les surfaces planes d’une certaine étendue exposées au
* soleil, sur les parapets des quais, sur les trottoirs, sur les marches
* des églises, etc.; mais c'est à la Bourse, je le répète, que le
* mirage se développe plus énergiquement et plus régulièrement que
* partout ailleurs."
* This is NOT the well-known astronomer with the same last name.
* The initial "E" is listed in the volume's author index.
* SUNSET MIRAGE
* "Auf einmal bemerkten wir, dass unsere Schatten, die wir vor uns liegen
* hatten, da wir ostwärts gingen, doppelt waren und zwar in der Weise,
* dass über unseren Köpfen im Schatten noch ein zweiter Kopf deutlich
* und scharf hervortrat. Ich sah mich um nach der Sonne, und
* es zeigten sich im Westen . . . zwei klare Sonnen vertikal
* übereinander. Der vertikale Abstand beider Sonnen von einander betrug
* etwas über einen Sonnendurchmesser."
* A good account of mirages seen on the Bodensee ( = Lake Constance)
* with many DRAWINGS and a good description of the DISTANCE EFFECT:
* "Ein in der Richtung nach Constanz fahrender Dampfer bot die bequemste
* Gelegenheit dar, die Erscheinung nach allen Modifikationen, welche die
* zunehmende Entfernung mit sich brachte, zu verfolgen."
* (The description is a whole page long -- too long to quote here.)
* He also notices the slight vertical compression of the inferior image,
* and mentions (but does not cite) a mural mirage "nach den Comptes rendus
* der Pariser Akademie . . . neuerdings an der südlichen sonnenerwärmten
* Aussenwand des Börsengebäudes in Paris . . . ."
* [This seems to refer to Bigourdan's report of 1855.]
*
* There is a good concluding EXPLANATION of the FANTASTIC SCENES often
* reported: "Wie ist es aber möglich, dass die Luftspiegelung Gegenstände
* darbietet, welche in der Wirklichkeit gar nicht vorhanden sind, Gebäude
* mit Kuppeln, Balkonen, Säulen, Palmenhaine, wo der enttäuschte Reisende
* nichts findet als Felsblöcke, Sandhügel und Gestrüpp? Bringen wir in
* Abzug, was auf Rechnung der Phantasie und der Vergrösserung durch die
* Fama beim Übergang der Beschreibung von Mund zu Mund, von Buch zu Buch
* kommen mag, so bleibt vielleicht folgende natürliche Auflösung des
* Zaubers. Ich sah hie und da eine rundliche Masse wie einen Baum,
* Steinhaufen oder dgl. mit ihren verkehrten Spiegelbild zu einem
* Doppelgebild zusammenfliessen, das an beiden Seiten den Anschein von
* senkrechten Wänden darbot. Hie und da zeigte sich am Seenufer ein
* steiler, senkrecht wie von Erdrissen durchstreifter Absturz, wo ich keinen
* solchen vermuthen konnte, und auch bei der nachfolgenden Betrachtung
* Nachmittags oder von einem höheren Standpunkte aus nur den schmalen Saum
* einer Kiesbank oder eines sonstigen unbewachsenen Bodens vorfand. Wie aus
* einem Felsblock dieser Art ein Gebäude, aus einem kurzen senkrechten
* Fleck eine Säule, aus Gestrüpp ein Wald werden kann, wenn der Wunsch und
* die Phantasie das ihrige dazuthun, mag einleuchten." (cf. Beauford, 1802)
* This paper makes no sense until you know that the German "geogr. Meile"
* was 1/15 of a degree, or 4 nautical miles.
* This is the only place outside of America where I have seen ' used for
* feet and " used for inches!
* A more direct account of the inferior and superior mirages than the
* following one. Good descriptions of FOG ("nuage").
* A rather tedious account of inferior mirages seen at Montpellier
* FOG : "La mer la première se couvrait de la vapeur du mirage, vapeur
* blanchâtre qui le signalait toujours."
* TURBULENCE: ". . . un fort miroitement se prononçait dans le région du
* mirage, malgré le calme qui régnait dans toute la contrée; les images
* y flottaient, comme agitées par un vent violent . . . ."
* DEMAGNIFICATION: "Cette précision des images rendait encore un autre
* service: elle permettait de voir que l'image réfléchie était d'un tiers
* au moins plus petit que l'objet." (seen from 37 m height)
* (cited by Mascart)
* Pierre-Adolphe Daguin's textbook
* A pretty thorough treatment, containing an early version of the
* "PALM-TREE" diagram -- complete with an 18th-Century French soldier
* as the observer (p. 372). [Cf. A. Ganot (1853).]
* This is the section on atmos. refr.
* The first volume appeared in 1855. A second edition came out in 1861;
* the third, in 1867; and the 4th, in 1878.
* Title page also lists Dezobry & E. Magdeleine, Paris, as publishers.
* KUMMER's paper on super-critical refraction in dense atmospheres:
* Multiple complete images of the whole sky and the whole surface of the
* planet, even for an outside observer.
* Novel treatment of the problem from a mathematical point of view;
* Kummer has fun with PDE's. Note that he correctly describes the
* multiple horizons and the apparent horizon at the top of the duct,
* when the observer is inside the duct-producing inversion, as well as
* the distorted images:
* ". . . das erste Bild [der Sonne] welches . . . zu einer sehr schmalen
* Ellipse abgeplattet erscheinen müßte . . . ."
* Available at last at
* http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften#A9
* The volume for 1860 was published in 1861. Meeting date: 12. Juli
* [cf. Bouguer (1749), T. Young (1807) and J.de Graaff-Hunter (1913)]
* See also the 1863 reprint and its English translation (below).
* VERDET translates (?) Kummer's paper
* The section is headed "Mémoires sur la physique publiés a l'étranger.
* Extraits par M. Verdet." Verdet's presentation is somewhat more compact
* than Kummer's; it is not just a straight translation. In particular,
* note that Verdet defines the angle i as the local zenith distance of
* the ray, whereas Kummer uses the same symbol for its altitude (see the
* bottom of p. 498). Consequently, Verdet has sin i where Kummer has
* cos i . Similarly, Verdet's "I" is the complement of Kummer's.
* There is a typo on p. 500, where Verdet says "I" when he means Kummer's
* small quantity ε. (He was thinking of the special value of i at the
* top of the duct, which he denotes by I a page or so later on.)
* (available from Gallica)
* An exact reprint of Kummer's original paper:
* (this is the version reprinted in Kummer's collected papers, edited by
* André Weil (Springer-Verlag, Berlin, 1975) pp.337ff.)
* Mila Zinkova has discovered an English translation at
* http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/kummer_-_on_atmospheric_ray_refraction.pdf
* However, this translation is rather awkward, as the translator is not a
* physicist, and adopted peculiar terms instead of conventional terminology:
* thus we see "refraction exponent" instead of "refractive index"; "Kugel"
* is translated as "ball" rather than "sphere" or "globe"; "Luftspiegelung"
* is literally rendered as "air reflection" instead of "mirage"; and the
* niceties of German syntax sometimes become sheer nonsense in English.
* Hunt's observation of an OMEGA MOONRISE in Key West
* "When becalmed in a beautiful evening between the Reef and the Key, the
* water being very tranquil, I saw the moon rise over the sea with some
* interesting appearances. The long reflection of the emergent disc on the
* water was well defined, and seemed to be a part of the moon itself. As
* the under semicircle of the disc began to rise above the water, there was
* an appearance of drawing in at the sides of the combined luminous figure.
* As this seeming contraction progressed, the outline showed a curved
* figure, like that made by water in raising a cohering disc from its
* surface. There was no cusp point between the disc and the
* disc-reflection, but a seemingly distinct curve, concave outwards. As
* the disc rose above the water, this curve opened, and a broad connecting
* column seemed to bind the disc and its reflection, just like a coherent
* water column between the lifted disc and the level water surface.
* Instantly this seeming column parted as if broken, when the moon was seen
* to be distinctly above the water by about a fourth of its diameter, as
* nearly as I could estimate. The sudden shock of rupture appeared
* perfectly distinct, and the semblance of a material connection between the
* disc and reflection was perfect, both before and at the instant of visible
* separation. This observation has interest in its relation to the contact
* phenomena of eclipses." So he mis-interpreted what he saw, in spite of
* very accurately recording the details.
* This is a short numbered section at the end of the longer paper called
* "Key West Physical Notes". Am.J.Sci. was also known as "Silliman's
* Journal".
* A paragraph on the mirages in the Rio de la Plata
* This is a derivative work "compiled by Staff Commander James Penn, R.N."
* and "Published by order of the Lords Commissioners of the Admiralty"
* But the Advertisement that follows the title page is signed by "G.H.R,"
* at the Hydrographic Office, Admiralty, London. It says "The Rio de la
* Plata is from the surveys of Admirals FitzRoy and Suliva, Commander
* Sidney, the French charts of 1833, and the Spanish of 1837, with also
* many additions and corrections by M. Mouchez."
* The actual paragraph, headed "Mirage or Refraction", says:
* "In the Rio de la Plata there is a great deal of refraction, and
* more so in the tributary rivers. It often happens that objects above
* the visible horizon disappear; others under the horizon rise and are
* clearly seen at great distances. At Buenos Ayres the cerros de San
* Juan, under the horizon, on the Oriental coast, a distance of 36 miles,
* are sometimes seen. When this is the case the atmosphere is extremely
* clear, and it is a most certain sign of bad weather."
* [Here a footnote adds: "Colonia lighthouse, and vessels at anchor there,
* were plainly seen by the naked eye, at a distance of 30 miles. ---
* R. Cook, master, H.M.S. Stromboli , July 1862."]
* "This extraordinary refraction not only takes place near the horizon
* but also many degrees above it. E. Mouchez, capitaine de frégate,
* gives an instance of a fog rising during the time he was taking
* observations, which hid the sun but slightly, leaving the limbs clearly
* visible. In calculating the hour angles and comparing the different
* series, it was found that the refraction had regularly increased with
* the fog, and that at the last observation, when the altitude was 31°,
* it was higher by 1'25" than that given by the tables."
* Obviously this is an error in the dip, not the refraction.
* Available at Google Books.
* C. T. Ramage's report of FATA MORGANA in Apulia
* "In travelling over the Japygian peninsula, . . . I heard the natives
* speak of what they called “Mutate,” and on questioning them as to
* what they meant, I found that this was only another name for what is
* known as the “Fata Morgana.” At Nardo and Galateo, and more
* particularly at Manduria, they assured me that at dawn, when the
* atmosphere is perfectly calm, or when a “scirocco” is just beginning
* to blow, the appearances at times are very remarkable, exhibiting,
* if we can believe them, beautiful representations of castles, plains
* with cattle and flocks, men on horseback, and, what must be striking,
* the edges of the figures are often fringed with the prismatic colours."
* The mention of DISPERSION in mirages is unusual; cf. Minasi. But
* as the enumeration of details is close to Minasi's, I wonder if this
* may all be taken from his account. Ramage cites Antonio de Ferrariis
* Galatei De Situ Japygiae (1727). He then adds:
* "I have observed in another part of Italy some approach to the
* “mirage” which is here described. At early dawn, on my way through
* the Caudine Forks towards Benevento, thick mists rested on the lower
* valleys; as the sun rose and the mist began to be dissipated, the villages
* seemed to be raised by the refracted light into the heavens." This
* may be an observation of the concave appearance of the surface.
* Cited by Talman (1912).
* John Parnell's MULTIPLE-IMAGE MIRAGES at Folkestone, 13 April (1869)
* FOG: "During the morning, and up to 2 o'clock P.M., a dense fog had hung
* over the sea; but apparently it was not very deep, as the sun's rays
* penetrated it pretty freely. At the hour above mentioned the fog opened
* towards the S.E., disclosing the cliffs on the French coast; and in the
* course of a few minutes the fog had disappeared, leaving the atmosphere in
* a state of unusual transparency. The French cliffs were apparently so
* lofty and with every indentation so clearly visible, that one might easily
* have imagined that they were but ten miles distant."
* CONCAVE SURFACE: "The French coast could be seen from near Calais
* towards the E. to far away and many miles beyond Boulogne towards the
* S.W., the land in the latter direction being ordinarily invisible, as it
* is situated below the horizon. Immediately under the erect image of the
* coast was an inverted one, of about double the height of the former.
* The lighthouse at Cape Gris Nez gave five images in a vertical line: --
* the lowest erect but somewhat magnified; above that and separated from
* it a pair of images of the centre and highest portion of the building
* only, one erect and the other inverted; and over these another pair, the
* inverted image being like the former one, but the erect image showing the
* whole building."
* These are often supposed to be the first observations of more than 3
* images, though Kelly saw 5. However, Parnell reports seeing both 7 and
* 9 : ". . . some fishing-luggers were observed hull down, so that the
* position of the horizon could be ascertained . . . but over these were pairs
* of images of vessels which ordinarily would have been invisible. In some
* instances three and even four pairs could be observed placed in a vertical
* line, the lower image in each pair being inverted. With the exception of
* the uppermost pair, the images seemed to represent the maintopgallant
* sail only, and that considerably elongated; but the highest erect image
* showed the mizzen- and the fore masts and the jib, but in no instance
* could the hulls be seen. In all cases the inverted images were of about
* twice the height of the erect. Soon after 3 o'clock vessels between the
* observer and the horizon began to be affected. The Varne light-ship,
* which is about 8 1/2 miles from the English coast, had her mast-flagstaff
* and stanchions elongated to some three times their proper length: this
* effect lasted for about ten minutes, when they shrank to less than half
* their usual size, and the hull began to rise till it was nearly as high as
* it was long, and formed a most conspicuous object even to the naked eye.
* I then looked towards Dover: the pier seemed completely disorganized;
* it appeared to be divided in half longitudinally, with the sea in the
* midst, and the stone coping moved as if huge waves were agitating it. A
* steam-boat entering Dover harbour was shrunk to less than half her proper
* vertical dimensions, but elongated horizontally. Captain Paull, of the
* S.E.R. steam-boat 'Napoleon III.,' crossed the Channel between the hours
* of 2 and 4; and he told me that he saw Beachy Head during the passage, a
* circumstance which had never previously occurred during the many years
* that he has been on the Folkestone and Boulogne route."
*
* ". . . wind S.W., very light at 2 o'clock and dropping to a calm . . . ."
* "The place of observation was about 30 feet above high-water mark."
* Observations made "through a small telescope with a 25-power".
*
* Cited by Garbasso (1907). Cf. the similar report of Latham (1798).
* Available at Google Books
* JANSSEN's first mirage report, followed by Silbermann's comment
* Janssen calls it "mirage inverse qu'il a eu occasion d'observer sur
* la mer Rouge, au moment du soleil levant. Ce phénomène est dû à
* l'influence des côtes élevées qui bordent la mer. Il résulte de
* cette situation qu'au moment où se produit le phénomène observé, la
* température maximum se trouve à une assez grande hauteur au-dessus des
* eaux ; c'est seulement à partir de ce niveau qu'elle décroît
* lorsqu'on s'élève. Ce mode de distribution des températures de l'air
* est très-différent de celui qui a lieu dans une plaine unie ; il
* explique nettement et dans tous ses détails la production du mirage
* inverse au lieu du mirage direct."
* Evidently, this is a superior mirage; unfortunately, no detail is given.
* (For more of his Red-Sea sunset observations, see his 1874 paper.)
* Août 1870, No. 8
* Silbermann's comment on Janssen's mirage report
* (This is the dog-like-a-fish report.)
* "M. Silbermann . . . signale certains phénomènes curieux que l'on peut
* observer à Paris même, dans tous les points où les couches d'air
* voisines du sol peuvent être échauffées exceptionnellement sur de
* grandes étendues. Ce cas se présente assez souvent en été sur la
* place de la Concorde pour un observateur qui place ses yeux tout près
* du sol."
* Then follows a direct quote from Silbermann:
* «Si un chien passe sur le trottoir à une centaine de mètres, ses
* pattes plongeant au-dessous de la couche d'air qui produit le mirage,
* les parties supérieurs de l'animal sont réfléchies en dessous de
* cette couche. Elles offrent alors l'aspect d'une espèce de poisson
* fantastique qui semble nager à la surface du sol.»
* Août 1870, No. 8
* FLAMMARION quotes DIODORUS SICULUS (but gives no detailed reference)
* "An extraordinary phenomenon occurs in Africa at certain periods,
* especially in calm weather; the air becomes filled with images of all
* sorts of animals, some motionless, others floating in the air; now they
* seem running away, now pursuing; they are all of enormous proportions, and
* this spectacle fills with terror and awe those who are not accustomed to
* it. . . . Strangers not used to this extraordinary phenomenon are seized
* with fear; but the inhabitants, who are in the habit of seeing it, take no
* particular notice of it." (p.149)
* "Certain physical philosophers attempt to explain the true causes of
* this phenomenon, which seems extraordinary and fabulous. They say that
* there is no wind, or scarcely any, in this country. The masses of
* condensed air produce in Libya what the clouds sometimes produce with us
* on rainy days, viz., images of all shapes rising on every side in the
* air."
* On the next page, he drops a tantalizing hint:
* "This same phenomenon (of which Quintus Curtius has also spoken) has
* long been remarked by the Arabs, and it is often discussed in the
* treatises of Oriental writers."
* Flammarion has found Büsch's work, but not Gruber's; so he thinks
* Monge was the first to explain it. [Thus, the source of that error.]
* Joseph David Everett's review article in Nature
* This appears to be an exact reprint of his Belfast lecture in the
* "MIRAGE THEORY" file.
* "Another class of appearances are known (especially among nautical men)
* under the name of looming . Distant objects are said to loom when they
* appear abnormally elevated above their true positions. This abnormal
* elevation not unfrequently brings into view objects which in ordinary
* circumstances are beyond the horizon. It is also frequently accompanied
* by an appearance of abnormal proximity (though this may perhaps be rather
* a subjective inference from the unusual elevation and clear visibility
* of the objects than a separate optical characteristic), and it is further
* accompanied in many, though not in all cases, by a vertical magnification,
* the heights of objects being many times magnified in comparison with
* their horizontal breadths, so as to produce an appearance resembling
* spires, pinnacles, columns, or basaltic cliffs."
* "In rare instances, two or even three of these images are seen one
* above another, vertically over the real object; but these multiple images
* are usually too small to be seen without the aid of a telescope -- the
* objects whose images they are being so distant as to appear mere specks
* to the naked eye." (p. 49)
* He then recommends Scoresby's accounts in his "Greenland" and
* "Arctic Regions"; and quotes from Latham's (1798) account of looming
* seen at Hastings.
* "The circumstance which it is most important to know . . . in order
* to predict the degree of curvature, is the rate at which the temperature
* changes with height." (p. 50)
* "An increase of temperature upwards, at the rate of about
* one-sixteenth of a degree Fahr. per foot, would make the curvature of
* rays equal to that of the earth, so that a ray might encircle the globe.
* . . . The visible effect is precisely the same as if the convexity of the
* surface of the earth were diminished. And not only will objects which
* were previously beyond the horizon be brought into view, but objects
* which were previously visible near the horizon will become plainer,
* inasmuch as the rays by which they are seen will not pass so close to
* the intervening surface as before, but will traverse a higher portion
* of the air, which is less liable to be obscured by impurities." (p. 51)
* He then considers a parabolic temperature profile, so that "A pencil
* of rays diverging . . . from a point . . . will thus converge accurately
* to another point. . . . Such a pair of points may be called principal
* conjugate foci." (p. 51)
* ALTERNATION of erect/inverted images:
* "As every point on the surface of an object will thus have its
* conjugates, we shall have a succession of images of the object. The first
* image will be upside down, the second erect, and so on alternately.
* They will be what are technically called `real' images . . . ." (p. 52)
* He ends this part by pointing out the astigmatism of the images.
* On p. 69, he quotes (in translation) from Monge, and adds:
* "The only objection which I think can be taken to this explanation
* of Monge, is that it seems to imply not a curvature, but an angle,
* in the course of the rays, just as in the case of what is called
* total internal reflection at the bounding surface of a piece of glass
* when the angle of incidence exceeds the critical angle.
* "Now, the formation of an angle (even a very obtuse angle) in a ray
* would require a perfectly sharp transition from one degree of density to
* another, instead of the gradual transitions which are more in accordance
* with our knowledge of the properties of air."
* "As to the propriety of applying the name reflection to an action
* such as that . . . , it is perhaps just as proper as the application of
* the name refraction to the bending of rays which takes place in the
* atmosphere . . . ." (pp. 69-70)
* On p. 71, he repeats Wollaston's experiment; but "a much finer
* effect is obtained in the arrangement . . . in which three liquids are
* employed, the middle one having the highest index of refraction, while
* its specific gravity is intermediate between those of the other two.
* The three liquids are -- (1) A strong solution of alum at the bottom;
* (2) pure water at the top; (3) Scotch whiskey mixed with enough sugar
* to make its specific gravity intermediate between those of the other
* two liquids. It is introduced last by means of a pipette."
* "The arrangement of three liquids just described, which was suggested
* to me by Prof. Clerk-Maxwell, is extremely effective, but requires much
* delicacy in its preparation to ensure success."
* "With the two-liquid arrangement I have obtained three spectra,
* the middle one inverted, by employing as object a horizontal slit in the
* shutter of a dark room; and very brilliant colour effects were obtained
* by bringing the eye to the conjugate focus of the slit."
*
* "a Paper read by Prof. J. D. Everett, M.A., D.C.L., before the
* Belfast Natural History and Philosophical Society"
* In the Nov. 19 and 26 issues.
* Cited by Humphreys (1919, et seq.) and Wood (1899).
* The English version of Janssen's "mirage at sea" note
* As it is very short, I quote it completely here:
* "Many facts relating to the phenomena of mirages at sea are already
* known; but the author has paid great attention to these appearances in
* all his voyages since 1868, and has made some remarkable observations on
* mirage, especially at sunrise and sunset. He has established: -- 1.
* That the mirage is nearly constant at the surface of the sea. 2. That
* the appearances can be explained by assuming the existence of a plane of
* total reflection, situated at a certain height above the sea. 3. That
* the phenomena are due to the thermic and hygrometric action of the sea
* upon the neighbouring atmospheric strata. 4. That there exist at sea
* direct, inverse, lateral, and other mirages. 5. That these phenomena
* have a very general influence upon the apparent height of the
* sea-horizon, which is sometimes lowered, sometimes raised.
* "This variation of the apparent horizon is very important to take
* into account, if we consider the use made of the horizon in nautical
* astronomy."
*
* Note the considerable differences between this and the French version.
* Here we have "a certain height" instead of a variable distance of the
* reflecting layer above the sea; here we have both thermal and
* hygrometric effects, there just thermal; here we have lateral mirage as
* well as direct and inverse. And here, the 1868 trip is made explicit.
*
* As this was given at the Bristol meeting in August, 1875, it seems to
* pre-date the French abstract -- which may explain the disappearance of
* "lateral mirage" in the latter (below).
* [Thanks to Madame Françoise Launay for information about the date.]
* Jules Janssen's French summary of mirages at sea
* "D'après mes observations, qui embrassent plusieurs années déjà,
* le mirage en mer est très-fréquent, même dans les mers
* septentrionales. Dans le golfe de Siam et dans le mer Rouge
* [-- remember he observed the 1868 eclipse in India --], j'ai observé
* des cas très-remarquables de mirage direct et inverse . Les
* apparences observées, soit sur le Soleil levant et couchant [-- so no
* wonder Fisher was interested in this work! --], soit sur les objets
* situés à l'horizon, conduisent à admettre un plan de réflexion
* totale situé à une distance variable de la mer. La cause de ces
* effets de mirage et de réfractions anomales réside dans l'action
* thermique de la mer sur les couches atmosphériques voisines. Une des
* conséquences les plus importantes de ces études, c'est qu'elles
* conduisent à reconnaître que le niveau apparent de l'horizon de la mer
* est affecté d'une manière très-notable par ces effets optiques et
* qu'il y aura en tenir compte quand on prendra (pour des mesures
* soignées) la hauteur d'un astre par le moyen de l'horizon de la mer.
* Je construis un instrument pour donner la correction."
*
* It is almost inconceivable that Janssen had not also seen numerous
* green flashes on these trips, though he says nothing of them here. And
* it is said that Janssen was consulted by Jules Verne for technical
* information while Verne was writing "From the Earth to the Moon." Could
* Janssen be the source from which Verne learned about green flashes?
*
* I have no volume number for this.
* very brief mention of Janssen's mirage-at-sea observations
* "En outre, . . . études sur le mirage en mer, études qui
* conduisent à l'explication des variations apparentes de la hauteur de
* l'horizon marin, et fourniront des bases plus sûres à l'Astronomie
* nautique." (p. 584)
* [followed by a detailed description of the Revolver photographique ,
* with detailed plates.]
*
* The Annuaire turns out to be a sort of French World Almanac ,
* rather than another Connaissance des Temps . There are tables
* of foreign exchange rates, conversions between decimeters and
* feet/inches/lines, densities and refractive indices of various
* materials, a list of the principal cities of the world, the areas
* and populations of the Arrondissements of France, etc., etc.
*
* Reprinted in Janssen's collected works, Tome I, pp.329-332; see p.332.
* Prof. PRESTEL's mirage review, with many ILLUSTRATIONS
* It includes his own observation of a superior mirage at Borkum.
* Fig. 9 shows superior mirages, and is captioned "Das Seegesicht".
* This is almost surely Michael August Friedrich Prestel (1809-1880),
* who was Prof. of Mathematics and Natural Science at the Gymnasium at
* Emden, and part-time instructor at the Trade- and Navigation School.
* He wrote numerous papers, primarily on meteorology and related
* matters, and many popular articles, according to Pogg.
* A note on the first page indicates that earlier installments were
* in Nr. 1760 and 1761, March, 1877.
* abstract of the later Phil. Trans. paper, with comments by Everett
* O'C #136a
* vicious, nit-picking attack on Vince
* USEFUL REVIEW of HISTORY, including BIOT's book, and WOLLASTON.
* TAIT explains that VINCE's drawings were only schematic;
* "Scoresby . . . has given numerous careful drawings of these most singular
* appearances. The explanatory text is also peculiarly full and clear,
* giving all that a careful observer could have been expected to record. It
* is otherwise with the descriptions and illustrations in Vince's paper . . . .
* In fact the latter are obviously not meant as drawings of what was seen;
* but as diagrams which exhibit merely the general features, . . . -- the
* details being filled in at the option of the engraver. That such was the
* view taken by Brewster, is obvious from the illustrations in his Optics
* . . . ."
* clearer account of his mirage theory than in the Trans.Roy.Soc.Edinburgh
* O'C #137
* TAIT's full paper at last
* ". . . I do not think that Wollaston's square bottle with two
* inter-diffusing liquids presents a fair analogy." [p. 552]
* An implied DEFINITION: ". . . only one image: -- not, of course, in the
* true direction of the object: -- but erect, and therefore not properly
* coming under the designation of `mirage.'" [p. 559]
* He also notes that "although aqueous vapour diminishes the refractive
* index of air, the practical effect is so minute at its utmost that we
* neglect it." [p. 564]
* He observes directly a phenomenon closely related to GREEN FLASHes, but
* fails to make the connection: "The middle image . . . coincides with the
* upper image when the eye, gradually moved downwards, reaches the line DB.
* When they meet, both become blue and then disappear by moving the eye
* farther down." [p. 571]
* "It is much to be regretted that Vince's description, like his drawings,
* is of the very roughest character." [p. 576]
* Tait foresees the multiply-LAYERED STRUCTURE that is so common with
* inversions: ". . . when a trough, in which brine has been diffusing for
* some time into water, is suddenly and roughly stirred for a short period,
* it settles in a few minutes into a large number of strata of different
* densities. Something similar must hold in the case of air irregularly
* heated . . . . In the absence of wind such strata, once formed, would last
* for a long time, in consequence of the very small thermal conductivity of
* air." Then he cites Tissandier's observation of a mirage from a balloon,
* mentioned in Glaisher's Travels in the Air , p.297. "This, of course,
* proves the existence, at a great elevation, of a stratum in which there
* was a comparatively rapid diminution of refractive index with increasing
* height." [pp. 576-577] Cf. Gossard et al. (1985).
* Finally, he points out an essential difference between inferior and
* superior mirages [which an astronomer would call SEEING]. After quoting
* Scoresby's observation of his father's ship beyond the horizon, where the
* miraged image "was so extremely well defined, that when examined with a
* telescope by Dollond, I could distinguish every sail . . . ", Tait adds,
* "It seems hard to reconcile the clearness of definition in this case with
* any other than a stable state of equilibrium of a transition stratum. The
* mirage of the desert, where the equilibrium is essentially unstable, is
* always exceedingly unsteady."
* At the very end, he admits that most of his results were already found
* by Biot, in his mirage monograph.
* O'Connell #136b
* Jules JANSSEN claims to photograph mirages in Algeria
* Possibly EARLIEST PHOTOGRAPH of mirages? (But not published.)
* Mostly about the transit of Venus; but in the last paragraph:
* "Enfin j'ai pu faire quelques études sur le mirage, dont les
* manifestations sont presque permanentes en ces régions. J'ai pu même
* faire photographier plusieurs de ces manifestations, et constater que
* les causes de ces phénomènes, dans les cas les plus nombreux, sont
* tout autres que celles admises généralement."
* EARLIEST demonstration of "Fraser's THEOREM" by Edward Sang; he thought
* Vince had seen "a sloop floating on a calm sea with its shadow in the
* water" and imagined the rest.
* FLAT EARTH:
* FIRST derivation of flat-Earth model: "No sun, moon, or star could have
* been seen at a lower altitude than 1° 22'. All light reaching the
* eye from a lower elevation must have come from some terrestrial
* object. . . ." [But see Biot's 1809 monograph for the magic angle!]
* "Inverted images, then, can only be seen when the air is in an unusual
* condition; there must be unusually light air above. Now, in these, as in
* all investigations on the subject, the air is assumed to be disposed in
* horizontal layers, each of uniform density. . . . The absolute need for
* smoothness of arrangement may easily be illustrated: -- the sun's light is
* certainly reflected from the surface of the sea; yet we do not see an
* image of the sun in the water; we see only a confused brightness."
* Earliest crude OMEGA drawing after Joule's? (cf. Fig. 7)
* An unclassifiable paper, but put here because it deals with the inferior
* mirage at sea. Like Maltézos, Budde discovers the mirage on his own;
* but, unaccountably, he discounts it as mirage because ``wenn über dem
* Meer eine spiegelnde Luftschicht vorhanden wäre, die bis a b Fig. 2
* reichte, so würde der Beobachter unter 5m Höhe unter ihr stehen, könnte
* also, wie leicht zu sehen, nicht das Bild Fig. 2 etc. erhalten." (p.358)
* (I.e., he assumes here that the angular difference between the apparent
* horizon and the vanishing line corresponds to the linear height of the
* mirage reflection above the sea surface.) Nevertheless, he recognizes
* that the inverted image is a "reflection", so he attributes it to the
* sea surface -- much like Venturi's 1889 wave-crest model. This leads
* him to the (correct) conclusion that the apparent horizon is depressed
* and nearer than the geometric one; but he then fails to see that this
* invalidates his reason for rejecting the mirage as the cause.
* I could as well have filed it in the Colton or Ricco files, or under Dip,
* or even with the Floor papers . . . .
* (reprinted in Naturwiss. Rundschau 1, 13 (1886).)
* An implausible "distant city" mirage
* ". . . un curieux mirage qui . . . a rendu visible toute la ville de
* Saint-Pétersbourg, qui est située à 180 kilometres de Merexull."
* Possible Biblical mirages: "AEROMANCIE" and aerial INFANTRY
* In the Hungarian plains, a mirage in which
* ". . . on voyait distinctement de nombreuses divisions d'infanterie . . . ."
* "La tradition nous offre des exemples nombreux de ces visions que les
* anciens appelaient l'aéromancie; le spectacle en devient général
* quand le système nerveux des populations se trouve modifié à la suite
* d'événements de la nature de ceux qui y avaient préparé les Hongrois."
* "On trouve au Livre VII, Chapitre XII, de la Guerre des juifs , par
* Josephe:
* « Pendant tout le cours de cette guerre, des armées qui manoeuvraient
* et formaient des sièges apparurent dans l'air. »
* "Au Livre II des Macchabées , Chapitre VII:
* « Avant que Jérusalem fût pillée une seconde fois par Antiochus,
* tous les habitants de cette ville purent voir dans l'air, pendant
* quarante jours, des chevaliers richement vêtus et des cohortes armées
* de piques; on voyait leurs mouvements, celui de leurs boucliers et une
* grêle de traits lancés de part et d'autre. »"
* [These citations are nonsense. The first may be Book VI, Ch. V, sect. 3;
* there is no Ch. XII in Book VII. See Whiston's translation of
* Flavius Josephus. The second is certainly Ch. V, not Ch. VII. ]
* After citing some more recent examples of aerial infantry seen during
* or just before wars, he says:
* "L'énumération de faits similaires pourrait fournir la matière de
* plusiers volumes. . . .
* "Ajoutons qu'il y faut faire beaucoup la part de l'imagination. Mais
* peut-être, à notre époque surtout, l'imagination n'est-elle pas seule
* en jeu. Le mirage (?) observé cet été in Hongrie est bien bizarre."
* Cf. the final remarks of William Beauford (1802).
* [ Presumably, this is Flammarion. ]
* DARK BANDING, or SKY? DOUBLE SUPERIOR MIRAGE
* "The land seen just above the lines (α) and (β) was paler than
* that seen just below these lines."
* Fringes shown experimentally in mirages -- cf. Raman's papers
* The Eiffel tower reflection (cf. Tissandier's 1890 review)
* Letter from Charles-Henri Martin to Flammarion, referring to his book
* "l'Atmosphere". The engraving is evidently from the description, not
* from observation. Probably not a mirage. In the Feb.,1890, issue.
* Janssen's mirage photography in Algeria (continued); cf. his 1883 note
* "Un autre objet intéressant a été l'obtention, par la Photographie,
* des images des phénomènes si varie's et si curieux du mirage dans les
* régions des grands chotts qui se trouvent entre le Souf et Biskra, le
* chott Melrir, Merouan, etc. La Photographie permettra de discuter, sur
* documents certains et mesurables, les conditions qui président à la
* production de ces singuliers phénomènes dont les apparences et les
* causes sont beaucoup plus multiples qu'on ne le croit."
* (Cf. his 1892 paper for more details.)
* This is reprinted in Janssen's collected works, Tome II, pp.187-188;
* but the initial page is given incorrectly there as 1067.
* It is the same expedition on which the "Janssen bands" were
* investigated.
* Unfortunately, the photographs appear to have been lost; neither
* the Academy of Sciences nor the Institute has them today.
* "The mirage of the reflection of the sun in the sea was, when seen
* through a glass, especially beautiful. It resembled a glorious cataract
* of golden water." (cf. Pekka's photo!)
* W. M. Davis's Harvard mural mirage
* On a NNW-SSE brick wall about 3 pm, Feb.10
* [This is evidently the same William Morris Davis whose paper on
* rainfall appears in the proceedings of the New England Meteorological
* Society on p. 493. He is given as "Prof. W. M. Davis" on p. 481.]
* ". . . the sunshine was strong enough by noon to melt the snow and ice on
* the streets."
* "On looking closely, I found that when my eye approached within about
* an inch of the plane of the wall, the further extension of the wall
* disappeared, and was replaced by a reflection of distant objects a little
* to the west of its line. . . . The reflection repeated all the familiar
* forms seen over the surface of the sea, when cold winds blow from the
* land over its warmer waters. . . . Effects of this kind must be common,
* for on the day in question, all the conditions were such as might easily
* occur again."
* Available at Google Books.
* The volume spans 1891-1892. This is No. 11, dated March, 1892.
* The journal was published in Ann Arbor, Mich.
* Janssen's mirages in some detail! A good OMEGA described
* The first (p. D.9) is a good description of a sunrise of Fisher's type A
* seen in the Gulf of Siam in 1874, en route to Japan for the Venus
* transit. There is no mention of a green flash: "Le lever a débuté par
* un point brillant, lequel, circonstance remarquable, se montrait non pas
* sur la ligne d'horizon de la mer, mais à quelques minutes d'arc
* au-dessus." Then comes the Omega stage: "Puis l'image solaire
* présente, à la hauteur où tout à l'heure le Soleil commençait à
* poindre, un étranglement qui va en ce rétrécissant de plus en plus,
* et l'image ronde ordinaire se dégage enfin.
* "Mais cette image est toujours accompagnée au-dessous d'elle d'une
* portion de disque qui s'en sépare et s'enfonce de plus en plus dans la
* mer pour disparaître enfin, laissant le disque supérieur dans les
* conditions ordinaires." (But he thinks it is due more to water vapor
* than to temperature.)
* This is evidently the observation Fisher (1921) tried to find, but
* without success.
* The mirage photographed in Algeria is also described (p. D.10):
* "En regardant cette photographie, on dirait qu'on a sous les yeux la
* vue d'une plage de la Manche avec ses dunes, ses eaux basses et son
* horizon de mer. Quand j'étais en face du chott, l'illusion était si
* complète que, malgré ma connaissance de la véritable nature du
* phénomène, des doutes traversaient encore mon esprit. Il était alors
* 5h du soir, le Soleil allait se coucher; toute cette plage avait une
* belle couleur bleue et un petit tremblement, qui faisait comme
* frissonner ces eaux, ajoutait encore à l'illusion.
* "Tout à coup, quand le Soleil eut disparu derrière l'horizon, la
* scène changea brusquement, et, à cette scène d'une belle plage
* maritime succéda celle d'une solitude glacée. Le tableau riant d'une
* rive méditerranéenne avait été subitement remplacé par celui d'un
* paysage d'hiver en Sibérie.
* "J'ai analysé les causes de ce curieux phénomène, mais cette
* discussion serait déplacée ici . . . ."
* His contribution is Appendix D of this volume, which also contains a
* report by rear-admiral Mouchez on the progress of the Carte du Ciel.
*
* The passage of interest here appears on pp. 265-266 of Tome II of
* Janssen's collected works. It says there that parts of the paper were
* also reprinted in pp. 92-111 of Janssen's Lectures Académiques (1903)
* but this seems not to include the interesting mirage observations.
* Applications of mirage theory to study interdiffusion of liquids,
* and corresponding laboratory simulations of mirages
* COLTON's street mirage in D.C.
* "On June 25, at about 4 P.M. . . . "
* "I infer that the mirage may not infrequently be seen over pavements
* or other surfaces of sufficient heat-absorbing capacity."
* Useless; but noted because of Colton's 1895 sunset observations.
* Available at Google Books.
* No.5, Sept. 1892; now published in Boston, Mass. -- see Editorial, p. 98
* DELEBECQUE's first Fata Morgana note
* Cited and partly quoted by Forel (1895), p. 557
* The BNF says the date is 15 Mars 1892; I have not seen it yet.
* According to Rev. Sci., this was reprinted by Ciel et Terre in 16 Sept. 1892.
* Their copy, titled "La « fata morgana », is on p. 478 of the 1892 volume.
* GOOD REVIEW of earlier mirage simulations and theory [FILED SEPARATELY]
* "Die Darstellung dieser Sachlage ist in keiner Weise neu,
* doch wohl wenig bekannt."
* Comments on Biot's theory
* EARLY mention of modeling the SETTING SUN
* Metrologist Charles-Edouard Guillaume was the inventor of Invar, and
* received the Nobel Prize in physics in 1920 for his work.
* He says Kummer first predicted a ray encircling a planet.
* [No mention of Bouguer, though.]
* "L'étude de la marche curviligne des rayons, fort intéressant en
* elle-même, devient très importante lorsqu'on l'applique aux phénomènes
* naturels. La reproduction des formes du soleil couchant offre un exemple
* d'une imitation de cette sorte. Nous pouvons, à volonté, imiter le
* phénomène normal que l'on observe chaque soir en plaine ou au bord de la
* mer, ou bien ces apparences exagérées, qui témoignent d'un équilibre
* particulier des couches d'air, ou même produire des déformations plus
* grandes que celles observées."
* This is the last volume of the old BSAF before it merged with
* l'Astronomie.
* A general introductory discussion of atmospheric optics, including
* rainbows, halos, scintillation, blue sky, refraction, (including mirages).
* The figure from Müller's "Kosmische Physik" was recently reproduced in
* *color* by Vollmer & Tammer (Appl.Opt.37,1557 (1998)).
* Note that volumes and years of H&E don't match up.
* Warren Upham's mirages on the Minnesota/North Dakota border
* "In crossing the vast plain of the Red River Valley on clear days the
* higher land at its sides and the groves along its rivers are first seen
* in the distance as if their upper edges were raised a little above the
* horizon, with a very narrow strip of sky below. The first appearance
* of the tree tops thus somewhat resembles that of dense flocks of birds
* flying very low several miles away. By rising a few feet, as from the
* ground to a wagon, or by nearer approach, the outlines become clearly
* defined as a grove, with a mere line of sky beneath it. This mirage is
* more or less observable on the valley plain nearly every sunshiny day of
* the spring, summer, and autumn months, especially during the forenoon,
* when the lowest stratum of the air, touching the surface of the ground,
* becomes heated sooner than the strata above it.
* "A more complex and astonishing effect of mirage is often seen
* from the somewhat higher land that forms the slopes on either side of
* the plain. There, in looking across the flat valley a half hour to two
* hours after sunrise of a hot day following a cool night, the groves and
* houses, villages and grain elevators, loom up to twice or thrice their
* true height, and places ordinarily hidden from sight by the earth's
* curvature are brought into view. Occasionally, too, these objects,
* as trees and houses, are seen double, being repeated in an inverted
* position close above their real places, from which they are separated
* by a very narrow, fog-like belt. In its most perfect development the
* mirage shows the true upper and topsy-turvy portion of the view quite
* as distinctly as the lower and true portion; and the two are separated,
* when seen from land about a hundred feet above the plain, by an apparent
* vertical distance of 75 or 100 feet for objects at a distance of 6
* or 8 miles, and 300 to 500 feet if the view is 15 to 20 miles away.
* Immediately above the inverted images there runs a level false horizon,
* which rises slightly as the view grows less distinct, until, as it fades
* and vanishes, the inverted groves, lone trees, church spires, elevators,
* and houses at last resemble rags and tatters hung along a taut line."
* So, here we have first a nice account of the HEIGHT and DISTANCE
* dependences of the inferior mirage; then a FOG report connected with
* the superior mirage.
* Quoted (but not cited) in Frazer (1929).
* More FATA MORGANA studies, following FOREL
* His telescopic observations indicate that the F.M. is not a simple
* vertical elongation, but a stack of direct and reversed images: "J'en ai
* compté jusqu'à cinq. Comme ces images sont, en général, très
* rapprochées; que parfois même elles empiètent l'une sur l'autre, il est
* très difficile de les séparer à l'œil nu, et elles donnent l'illusion
* d'un objet agrandi." However, there is useful seasonal information:
* "Je ne les ai observées sur le Léman que par des temps calmes, et
* lorsque la température de l'air est notablement plus chaude que celle
* du lac; mars, avril et mai sont les mois où elles sont les plus belles."
* Reprinted, with a faked "mirage photograph," in "La Nature" 25:1 (1897).
* Cited by C.Abbe in the next item.
* Good review article with some references
* Leans heavily on the papers of Charles Dufour and F.-A.Forel;
* follows the latter's classification, and discusses the Fata Morgana.
* He thinks everything is explained in Mascart's Traité d'Optique .
* [Cleveland Abbe edited MWR from 1872 to 1909; later his son, C.A.Jr.
* took over.]
* A novice discovers mirages
* This seems to be the first of Constantin Maltézos's "tunnels" papers
* A disappearing city; Lord Rayleigh invoked in favor of "total reflection"
* quoted from the "Echo" on 9 Sept.
* "I believe that Lord Rayleigh some time since suggested total reflection
* as affording at least a partial solution of some of these phenomena, in
* preference, or, in addition, to the refraction and simple reflection of
* the older theory."
* No. 1747, Sept.16,1898
* ROBERT W. WOOD's excellent EARLY MIRAGE PHOTOGRAPH in San Francisco
* This seems to be the FIRST PUBLISHED MIRAGE PHOTOGRAPH, preceding Alfred
* Wegener's 1907 photograph, published in 1911, by about a decade.
* "The refracting layer is probably only a thin skin of warm air, which
* adheres as it were to the surface of the flagstones, for the mirage is
* unaffected by the strong winds which frequently sweep the top of the
* hill." [cf. McNair, 1920.]
* Oct.20, 1898 issue
* E.M. 68 series started by Query 94348
* No. 1752, Oct.21, 1898
* Reply to Query 94348 -- EARLIEST MIRAGE PHOTOGRAPH CLAIMED
* ". . . I possess a photograph of a church spire in Tenby, halfway up which
* appears an inverted image of what was afterwards identified as the gunboat
* Gadfly , then being launched at Pembroke Dock, 12 miles distant. Though
* it was taken so long ago as May 5, 1879, it is possible that copies can
* still be procured if the photographer, Robert Symons, St. Julian-street,
* Tenby -- is still in business. The editor of the Photographic News , and
* chief of the photographic department at Woolwich, said: -- `Mr. Symons
* must be congratulated: he is the first to photograph that most romantic
* phenomenon, the mirage.'"
* According to Eric Hutton, "Glatton" was the pen-name of Mr. Clement
* Stretton [ref. No. 3105 p327]
* No. 1758, Dec. 2, 1898
* RESTRICTED HEIGHT of visibility; nice BEACH MIRAGE
* (Report of a talk by Major MacMahon to the Camera Club)
* "One very curious thing about mirage is that it depends very much upon
* the position of the eye: a few inches in the height of the eye may make
* all the difference. On one occasion on the plains of India he observed a
* mirage which was only evident when he was at a particular height; there
* was only a vertical space of two or three inches in which the effect could
* be seen, so that these phenomena may easily escape notice. A singular
* effect may sometimes be observed at a particular spot on the south coast,
* and very likely at other places, when the waves come in on to a very hot
* beach; if you place the eye about a foot from the ground and look parallel
* to the wave fronts you can see an image of the wave two or three feet
* above the real wave."
* No. 1767, Feb. 3, 1899
* STREET and LATERAL (MURAL) MIRAGES
* Report of R. W. Wood's mirage photography on San Francisco streets
* (not cited, but obviously refers to the 1898 paper in Nature).
* Also, a reference to mural mirages with both direct and reversed images,
* which certainly predates Hillers's report!
* Nr. 495, 5.April
* R.W.WOOD's mirage demo essentially repeats Gruber's experiment
* Note that he admits Wiener's writeup (1893) is better
* Cites Everett's 1874 paper.
* [I forgot to copy Plate III but it is only moderately interesting.]
* DARK STREAK
* Eastern shore seen from Chicago, Dec. 20, 1900: "The view was elevated
* above the horizon and was enveloped in a pale blue light. It formed
* the lower lining of a maze of darkness that hung over the lake shortly
* after noon and was visible for more than an hour.
* "There was a dark streak between it and the horizon."
* BORCHGREVINK's Antarctic mirages and Novaya Zemlya observation
* "On May 15th we had the last greeting from the departing sun.
* The refraction of it appeared as a large red elliptical glowing
* body to the north-west, changing gradually into a cornered square. . . .
* The promising effect of that evening . . . lasted until the returning sun
* again made the peaks and crevasses shine on the 27th July.
* "Both during the time the sun was low in its descent and when
* it rose again, a strong mirage effect was observed towards the west,
* showing images of icebergs far below our horizon, and Antarctic scenery
* only visible to us through this phenomenon. This strong mirage remained
* after the sun's return late in the summer, and the opening of the ice was
* prophesied to us in the mirage long before the ice-fields near Victoria
* Land broke.
* "It was very interesting to see the picture of far-away broken
* ice-fields, with their dark channels and towering icebergs, in the
* north-western sky; and on several occasions towards the time when the
* vessel was expected back, members of my staff returned to the camp in
* enthusiasm, thinking to have discovered the masts of the Southern Cross
* in the mirage, so strongly did their hopes confirm the impression made
* by the wonderful creations in the air."
* (Nice to see the WISHFUL THINKING factor made explicit.)
* Mentioned but not cited by Frazer (1929).
* This is the reprint edition; the original was published by George
* Newnes, Ltd., London, 1901.
* SUSPENSION of islands; "TUNNELS"
* "FOG": "Parfois, l'île paraît suspendue tout entière, une bande
* laiteuse, brillant, s'interposant entre elle et la surface de l'eau."
* The "tunnels" are the reflected images of dips in the miraged terrain.
* Some data are given on the HEIGHT effect (changes in 40 cm, 2 m).
* He seems a novice at the mirage game, but the observations are good
* and the SKETCHES are accurate.
* Here he quotes Aristotle and Theophrastus.
* cited in Maltézos's 1912 paper
* A useful review of the FATA MORGANA in the Strait of Messina!
* Boccara claims to have read everything published on the subject!
* There is a half-page footnote quoting Minasi's etymology of the term
* "Fata Morgana"; it seems far-fetched.
* Unfortunately, so does his explanation of the phenomenon; the paper is
* most valuable for his own observations, and the references.
* He confines his attention to the Strait of Messina (whose local
* geography, he thinks, is responsible); so Forel, etc. are ignored.
* He dismisses Kircher's explanation, saying: "And with him are put
* together Giardina, [and a host of others], all of whom, not having seen
* the phenomenon, as they say explicitly or make clear by their arguments,
* can only be repetitive, both in the invented descriptions and in the
* puerile explanations." (p. 201)
* But there are some serious errors: he believes the F.M. is not a
* mirage, because "the images are erect". He accepts the idea of multiple
* images displaced sideways (i.e., "lateral mirages").
* A copy of Willem Fortuyn's engraving for Minasi is Fig. 1 (p. 203)
* There is an extensive annotated bibliography at the end.
* For a summary in English, see Nature 67, 393-394 (Feb.26, 1903).
*
* Available from Google Books (with OCR text, but a badly aliased version
* of Fortuyn's engraving), and from ADS (no text, but much better figure):
* http://adsabs.harvard.edu/abs/1902MmSSI..31..199B
* See Talman (1912) for a good summary in English.
* QUANTITATIVE MEASUREMENTS of inferior mirages, showing vertical stretching
* N.B.: Pernter was the publisher of Met.Z.!
* J Fenyi, S.J. (note accent over e: "Fényi")
* Despite the title, this is not an optical illusion, but a fine
* LATERAL MIRAGE at the surface of a hot smokestack.
* The author's attempt to explain differences between naked-eye and
* telescopic views led to his optical-illusion notion.
* [Cf. Nölke (1917) for the image-location problem.]
* A Fata Morgana review in Nature, prompted by Boccara's 1902 paper
* in Mem. Soc. Spett. 31, 10. Reproduces Boccara's drawings (see P&E).
* Is "G.H.B." the "G.H.Baines" who wrote a GF note in 1910?
* Probably not. A more likely choice is George Hartley Bryan, FRS,
* who wrote many items for Nature around this time. Whoever he was,
* "G.H.B." reviewed some more Italian works on mirages in 1908.
* Number 1739
* Early modern observation of road mirage
* FINE REVIEW article on FATA MORGANA in Strait of Messina
* This is a French translation of Boccara's original in Mem.Soc.Spett.
* There is a half-page footnote quoting Minasi's etymology of the term
* "Fata Morgana"; it seems far-fetched.
* Boccara claims to have read everything published on the subject!
* Plate VI, mentioned in the second part, appears in the first one.
* However, some errors have crept into the translation, such as the
* statement in §7 that Capozzo made no additions to Saffiotti's letter.
* Both parts are available at ADS.
* Another great REVIEW ARTICLE on Fata Morganas: GIOVANNI COSTANZO
* Cites everybody (Agrippa, Facellus, Carnevale, Politi, Reina, Kircher,
* Gaspari Schott, Minasi, Pindemonte, Houel, Ribaud, Saffiotti, Boccara).
* He skipped Giovene, and has de Ferrariis only in an addendum. There
* are extensive quotations from unpublished letters, and from newspapers.
* Costanzo cites the Amsterdam reprint of Kircher's Ars Magna , quoting
* Angelucci's letter -- but with the "Salome" typo corrected -- and
* mentions the Roman editions of 1645 and 1647.
* A table (p. 123) compares the various observations.
* The dateline at the end says "Napoli, marzo, 1903".
* Costanzo's revised version
* Here a few more observations are added to both the text and the table.
* The addendum "SULLE MUTATE DI TERRA D'OTRANTO" has been removed.
* The dateline at the end says "Napoli, Maggio, 1903".
* Maltézos discovers the oil slick???
* This starts out with a mirage report, and then refutes Lazzaro's
* criticisms that the mirages reported earlier were only optical illusions.
* Then he goes off on a tangent:
* "Tandis que la surface de la mer présentait une agitation due à une
* multitude d'ondulations différents, coexistant, la surface des plaques ne
* présentait qu'une seule espèce d'ondulations, de plus grande longeur
* d'onde."
* ". . . le phénomène est dû, pour les uns à des souillures de l'eau par
* diverses matières étrangères . . . ."
* "BLACK LINE" (der schwarze Strich) discussed (cf. his distorted-sunrise
* paper in Met.Z. earlier in 1904; this issue is No.10, but dated Feb.15)
* Wilhelm Krebs argues that the horizontal black line seen in the mountain
* sky is due to reflections at an inversion layer, not an aerosol
* boundary. (cf. his distorted-sunrise paper in Met.Z. earlier in 1904;
* this issue is No.10, but dated Feb.15)
* He also argues that multiple features in the rising Sun could be due to
* WAVES on an inversion, thus prefiguring Fraser's 1975 suggestion;
* (cf. Garnier, 1899, for a less definite, but similar, suggestion).
* Citing von Wrangell's observation: "Bei Beginn der Morgendämmerung sah
* er am östlichen Horizont den schwarzen Strich in der scheinbaren Form
* einer grauen Wolkenbank von etwa 1° Höhe." (cf. FOG file)
* Detailed study of mirages and refraction in tunnel
* The importance of FIELD-GLASSES in a first-hand report
* In response to a boy's letter reporting "a ship upside down in the sky",
* the writer (editor?) says:
* "Not long after I received this letter I was riding in a fast
* express-train across the sandy plains of New Mexico, where the only
* vegetation was a few low scattered shrubs and some tufts of coarse
* grass. On the nearer parts of the lake there were beautiful islands
* with trees and shrubs . . . and I remarked to a fellow-passenger: `. . .
* Perhaps there may be interesting water-birds that have nests among those
* tall grasses and shrubs. It seems to be a better home for the pelicans
* than on those muddy banks by that small river a few miles back.'
* "He smiled. He had been over the road half a dozen times, he told
* me, while this was my first trip.
* "`Try your field-glass,' he merely remarked.
* "I did; and, like a beautiful dream that is lost on waking, the lake
* disappeared when viewed only through the glass. Later, as the train
* came nearer, I saw that it was only sand and scattered shrubs and
* grass."
* Edward F. Bigelow's "Nature and Science for Young Folks" column runs
* from p. 1032 to 1039; only the "mirage" section is cited here.
* Two separate reports from different ships
* The first reports "SURF" all around the horizon, after a
* water-temperature drop of 3 C with constant air temp., near 41 N, 54 W.
* The captain changed course from WNW to SW.
* "Ich glaube, daß dieses Phänomen eine Fata Morgana
* (Seeluftspiegelung) gewesen ist. Wahrscheinlich haben wir die Küste
* von Neufundland etwas nördlich von Kap Race gesehen."
* The second reports "land" ahead and on both sides: "Deutlich vermochte
* man Höhenzüge, sogar einzelne Bäume zu unterscheiden, und so
* überzeugend was die Erscheinung, daß Kapitän Bodmann das Schiff über
* den anderen Bug auf östlichen Kurs legte, um vorläufig, der Sicherheit
* halber, von diesem verwirrenden Phänomen wegzuliegen. Da nun aber nach
* der ziemlich gut festgestellten Position des Schiffes wirkliches Land gar
* nicht in Sicht kommen konnte und die Erscheinung nach und nach auch am
* östlichen Horizont auftrat, überzeugte sich der Kapitän von der Bramrah
* aus, daß es sich nur um eine Luftspiegelung handelte. Daraufhin wurde
* der westliche Kurs wieder aufgenommen." (near 56 S, 66 W)
* "v.S." is probably von Schrötter. (Feb. issue)
* "G.H.B." on Italian mirages again
* This time he reviews Garbasso's papers, and Rolla's lab simulation
* of Parnell's observations.
* Number 1998
* Claimed mirage of a rainbow, but impossible at 45° altitude
* (Some halo arc is a more likely explanation.)
* C. Fitzhugh Talman's Fata Morgana article, summarizing Boccara and
* Costanzo, and citing Forel and Ramage as well. A good summary of the
* observations, with a decent copy of Fortuyn's engraving for Minasi.
* (Thanks to Eric Frappa for a good PDF copy!)
* Typical mirages on St. Lawrence River, seen from Alexandria Bay, N.Y.
* ". . . seen during the spring and autumn months . . . when cloudy skies
* prevail, and soon after northerly winds have set in and the weather
* is growing colder . . . several small islands, about 2 miles away, . . .
* appear as though they were situated on a snow-covered ice field with the
* trees standing out in strong relief, giving the appearance of a dead
* calm . . . . in reality the wind is strong and the water quite rough,
* for north winds blow against the river current.
* "The most interesting feature is that if one ascends a nearby bluff
* about 25 feet high, the illusion disappears entirely, and the islands,
* surrounded by the rough, blue waters, and the trees take on their
* natural look."
* (Cf. Büsch, 1800; Abbot, 1854; and Forel, 1895.)
* Nov. issue
* Maltézos summarizes his mirage studies, and quotes Aristotle again
* The quotations from Aristotle turn out to be:
* "Problems" XXVI. 53: "Why, when the east wind blows, do all the things
* seem larger?" and
* "Meteorologica" III. IV (p.253 of the Loeb Library edition):
* "Distant and dense air does of course normally act as a mirror . . . ,
* which is why when there is an east wind promontories on the sea appear to
* be elevated above it and everything appears abnormally large;. . . "
* and unfortunately Aristotle then drags in the Moon illusion.
* VILHJÁLMUR STEFÁNSSON's astute remarks on "suggestion" in the Arctic
* After a brief description of the deceptive-appearing mirages, he says:
* "I think it is David Hanbury who tells of mistaking a lemming for a
* musk-ox, and Lieutenant Gotfred Hansen speaks of being astounded by
* the courage with which his dogs attacked a polar bear, and of being
* dumbfounded not only at seeing them killing the bear but more especially
* at one of the dogs bringing the bear back in his mouth. It turned out,
* of course, that the polar bear had been an Arctic fox. In things of
* this sort there is always a certain amount of suggestion; Hanbury had his
* mind centered on musk-oxen, and Hansen was expecting to see a polar bear."
* He then tells of seeing a grizzly bear that turned out to be a marmot.
* "The main reason for such cases of self-deception is that one sees
* things under circumstances that give one no idea of the distance, and
* consequently one has no scale for comparison. The marmot at twenty
* yards occupies as large a visual angle as a grizzly bear at several
* hundred, and if you suppose the marmot to be several hundred yards away
* you naturally take him for a bear. There is, under certain conditions
* of hazy Arctic light, nothing to give you a measure of the distance,
* nothing to furnish a scale to determine size by comparison."
* (available on Google Books)
* WILHELM HILLERS -- MURAL MIRAGE PHOTOGRAPHED
* Eilhard Wiedemann's additional Arab mirage refs. to supplement Erdmann
* Unfortunately, he uses "Fata Morgana" for inferior mirages here.
* Eilhard was a son of Gustav Heinrich Wiedemann, who assumed the
* editorship of Ann. Phys. after Poggendorff's death.
* Hillers applies his model to Vince's observations
* He shows that an inflection point in the temperature profile is required
* Hillers generalizes his model, removing a restriction to small T changes
* Note that he comes up with the "magic number" of 1° 20'
* Hillers compares theory with observation in nature as well as in his
* laboratory simulation.
* He discovers the interference fringes later seen by Raman (1959).
* [see also J.Macé de Lépinay and A.Perot (1889).]
* This is a fine piece of work!
* This is Hillers's complete, detailed work
* "Wie es scheint, liegt aber noch nirgends ein Vergleich der Theorie
* mit der Erfahrung vor; noch niemals ist es bisher geglückt, die zur
* dreifachen Bildentwickelung notwendige anormale Dichteänderung der
* Atmosphäre gleichzeitig mit der Beobachtung der Luftspiegelung
* durchzumessen." (p. 3)
* "Ferner muß nach theoretischen Erwägungen die Winkelgröße des
* Gesamtbildes stets recht klein bleiben, es wird bei normaler Entwicklung
* niemals über 20 Bogenminuten hinausgehen können. Eine gewöhnliche
* photographische Aufnahme wird deshalb von dem Schauspiel auch kaum
* etwas zeigen. Handzeichnungen, denen man öfter begegnet, sind stets
* nach Fernrohrbeobachtungen ausgeführt und lassen leicht die Größe
* und die »Bildmäßigkeit« überschätzen." (pp. 3 - 4)
* On carrying out the desired comparison, he finds that "der ganze
* Vorgang der Abbildung sich in überraschend dünnen Schichten abspielt."
* He discusses the ASTIGMATISM of the image, pp. 42-44.
* THREE SUNS, one above the other, about 2 degrees apart (cf. Hevelius!)
* This short paragraph precedes his GF report.
* O'C #223
* Pedagogical treatment of street mirage
* Mirages appear DARK:
* ". . . dann findet man bald eine Stelle, die ganz dunkel erscheint."
* ". . . erscheint es einem ganz sonderbar, daß man diese Strasse
* jahrelang zu jeder Tageszeit begangen hat, ohne diese Luftspiegelung zu
* bemerken."
* Hubbard was a participant in the Mesopotamian campaign
* There are two parts here: the eyewitness account on p. 60:
* "Our caravan . . . straggled over two or three miles of country,
* and to anyone riding somewhere near the middle the head and tail of
* the procession seemed always to be marching through a smooth, shallow
* lake; occasionally, for some unfathomable cause, the mules and men would
* execute a bewildering feat of `levitation' and continue their progress
* in the sky. Often we saw a lake spread out on the horizon, stretching
* a long arm towards us to within a few hundred yards; at other times
* a clump of palms or a group of mounted men appeared in the distance,
* only to resolve themselves, as we approached nearer, into bushes of low
* desert scrub or a grazing flock of goats."
* Here there is a footnote on the "curious incident . . . reported to have
* happened . . . at the beginning of the Mesopotamian campaign:
* "Our men, after a particularly courageous attack across the open
* desert (which at the time was such a sea of mud that they had to advance
* at the walk), reached the Turkish trenches and put the Turks to flight.
* The enemy were now in the same predicament as the British had been in
* just before, and provided a splendid target for our artillery as they
* floundered through the mire. A gunboat was lying in the river, and the
* men in the tops were watching the proceedings when they were surprised to
* see our guns suddenly stop firing, although the Turks were still easily
* within range. It transpired later that, to the eyes of the gunners on
* the desert level, the target had disappeared into the mirage ."
* Quoted by Hurd (in the 1937 Pilot Chart article)
* "houses and trees with writing underneath" at sunset
* "People living in the Karroo are accustomed to see mirages in the veldt,
* but not at sunset nor during wet weather, as far as my own experience
* goes."
* might be a cloud miraged?
* This seems to be the original account of the battle stopped by mirage
* "Fighting had temporarily to be suspended owing to the mirage, but
* upon this lifting our offensive continued." [on April 11, 1917.]
* Presumably this is the dispatch from Lt.-Gen. Sir Stanley Maude.
* quotes but does not cite the previous item, mis-dating it the 10th
* (April issue; See p. 294 for the quote.)
* Story of Turkish retreat caused by mirage "in the early days of the
* Mesopotamian campaign."
* Seems to be taken from Mrs. Eleanor Franklin Egan's stories in the
* Saturday Evening Post .
* (Oct. issue; see pp. 295-296.)
* ROAD MIRAGE between Canton and Alliance, Ohio: SMOOTH SURFACE required
* Two letters from a resident of New Castle, Pa., with the Editor's
* explanation between them. The first reports: "On July 24th, while
* traveling in an easterly direction between Canton and Alliance, Ohio, I
* noticed a car about half a mile ahead apparently perfectly reflected in
* the roadbed, as if the latter was flooded with water. . . . the road in
* front was straight almost to the horizon and an exceptionally fine
* cemented brick surface. When I came up to the `given point' I found the
* road perfectly dry and the car ahead again showing a reflection in a
* perfectly mirror-like surface about the level of the bottom of the spare
* tire. I called the attention of the rest of the party to the
* reflection, they seeing it very plainly, then and several times later
* when similar stretches of roadway offered, but each time only above the
* heated brick surface.
* "I have traveled the roads in this section since the high wheel days
* of 1885 but have never been favored with any such phenomena."
* The second letter says, "Since receiving your reply . . . , I have been
* out mirage hunting with some friends and have been successful in bagging
* some beauties as well as establishing a list of requirements . . . .
* "The requirements are a very hot, dry, clear day, and a smooth hard
* road (brick gave the best reflections) . . . ." He adds sketches that
* illustrate the need for the observer's eyes to be "just above the level
* of the level piece ahead." This usually requires the observer to be in a
* slight dip. "The best point of observation I have found is the stretch
* between Canton and Alliance, but any similar road should give equally
* clear reflections."
* [NOTE: When I was a small boy, I remember this part of the Lincoln
* Highway was still paved with bricks.]
* This was when Sci.Am. was "bedsheet" size -- hard to copy!
* Looming and mirage at sea
* "with air at 63° F and sea surface at 53° F, "Strong mirages
* noted all around. Four other ships . . . appeared at times to be steaming
* along at the top of a hugh [sic] wall of ice; at other times the bodies
* of the ships seemed to rise out of the water at least twice their height.
* Horizon had all the appearance of a long, rugged coast line.''
* July issue
* Inferior mirage seen over a road "just after dusk"
* Oct. 3 issue
* A mural mirage reported in Garden St., Cambridge!
* Cf. his 1892 note in Am. Met. J.
* cites Knowlton (above)
* ought to mention R.W.Wood, but doesn't
* Two responses to McNair:
* Platt mistakenly thinks it is a grazing-incidence reflection . . .
* . . . but Burr suggests these mirages "may serve in part to account for
* ideas of temporary disappearance, or dematerialization, of solid
* objects, and for occasional accounts of apparent hallucination."
* A report of large lateral displacement that needs detailed
* investigation: 6 degrees -- probably a misidentification.
* Mercanton's mirage DRAWINGS and HEIGHT EFFECTS in Greenland, in 1912:
* [actually FILED with green flashes]
* The mirage observations are on pp. 196-197.
* 1. On 15 April 1912 in the Davis Strait, "un beau mirage d'«eau chaude»"
* 2. On 27 May, a superior mirage of icebergs; "vent faible"
* 3. On 2 June "nombreux isbergs visibles au loin apparaissaient tous
* étirés verticalement et surmontés de leur image renversée et
* ratatinée. Une fine ligne sombre courait parallèlement à l'horizon
* marin, représentant, sans doute possible, [!] l'image réfléchie de
* la nappe liquide." (So, he's not always reliable.) He took a telephoto
* picture, but it wasn't good enough to reproduce.
* 4. On 10 Sept., "j'ai vue sur quelque trente kilomètres de côte
* se développer une fatamorgana très belle. Elle se présentait sous
* l'aspect d'un ruban horizontal, strié de lignes verticales floues
* correspondant aux linéaments du paysage recouvert par le dit ruban.
* Celui-ci était nettement limité en haut et en bas. Son bord inférieur
* se découpait sur la mer, sa lisière supérieure sur le paysage côtier.
* Devant de Hjortetakken il marquait le 1/6 de la hauteur apparente de
* cette montagne, soit les 200 m inférieurs. . . . Quelques isbergs . . .
* apparaissaient très nets et dans leur position normale mais étirés
* et coiffés dès le tiers supérieur de leur image renversée, limitée
* par ailleurs strictement au bord supérieur de la zône floue.
* "La largeur verticale de la dite zône variait d'ailleurs en sens
* inverse de la hauteur de l'œil au-dessus des flots."
* The title pages are given in both German and French; I give only the
* German here, as de Quervain (despite his name) writes only in German
* and was the expedition's leader; and this was published in Zürich.
* Dated 1. Dezember 1920; abstracted by Brooks in MWR, 1923.
* Account of a meeting of the Roy. Met. Soc.
* "A paper on the Mirage, by Dr. W.H.Steavenson . . . . The visibility
* of the mirage was found to be dependent solely on the distribution of
* temperature near the ground . . . not necessarily associated with hot
* weather, and had, in fact, been well seen when the shade temperature
* was below 50° Fahrenheit. Investigations had shown that the old
* reflection theory was untenable, and that the phenomenon was purely a
* refraction effect. . . . The paper was illustrated by actual photographs
* of the mirage, taken by Dr. Steavenson with a telephoto lens." (p.421)
* [The published paper is the next item (1921).]
* Dated Dec. 1920. Available from ADS.
* HEIGHT EFFECTS + PHOTOS
* Use of mirage for DESERT NAVIGATION (cf. Hassanein Bey, 1925)
* Rosita Forbes (1893-1967) nearly died in the North African desert.
* "On clear mornings, about an hour after dawn, when the desert is
* very flat, a mirage of the country about a day's journey distant
* appears on the horizon. For a few minutes one sees a picture of
* what is some 50 kilometres farther on. The Arabs call it `the
* country turning upside down.'" (p.135)
* Another note by Du Shane, commenting on McNair (1920)
* He mentions but does not cite his earlier observation.
* Fine example of LOOMING
* accompanied by detailed temperature and wind data
* "sea 1 . . . air 43 F, sea 39 F"
* "The ice presented a curious mirage effect, being reflected upwards.
* When first sighted with the sun on it, it looked very like a continuous
* line of chalk cliffs in a slight haze; with the sun behind it, small
* detached pieces appeared as dark blurred objects which might be anything,
* and might be mistaken for land. On closing, it was found to be floating
* not more than a foot or so above water."
* LOOMING and STOOPING of other ships reported as well.
* Fine example of LOOMING and "FOG"
* originally cited as "Bay of Plenty Times" of Dec.6, 1920
* "All this time there was a dark grey-blue band on the horizon . . . .
* Soon after 4:30 this bank appeared to condense from the surface of the
* sea towards its upper margin, till it resembled a thick dark-coloured
* cable stretched from island to island."
* Note the Editor's WRONG explanation of the "black band", which confuses
* radiance and irradiance !!
* More comments on the previous letters to Science
* Arctic "CLIFFS" mirage that sets like a heavenly body
* Vilhjalmur Stefansson is following Storkerson's trail:
* "Beyond Cape Grassy we found that Storkerson had struck away from the
* land in a direction 22 degrees west of north which is the proper course
* for Cape Murray . . . . But four miles from Cape Grassy we found a place
* where the sledges had stopped briefly by the way, to judge by the tracks
* of men and dogs. After this the trail led for eleven miles in a
* direction 20 degrees east of north. . . . But after eleven miles of this
* course the party had turned back to their previous one, heading again
* for Cape Murray. I learned later that the reason had been one of the
* remarkable mirages or `appearances of land' that have deceived so many
* arctic explorers. Storkerson told me later that the fog had suddenly
* lifted, showing a land with bold cliffs apparently only fifteen or
* twenty miles away. This surprised him, but after consulting his
* companions, both Eskimo and white, and studying the land carefully
* through the glasses he made up his mind that they could probably reach
* it that day and that he might as well strike it first at this cape and
* follow it westward. But for two or three hours as they advanced the
* land kept receding and getting lower, until finally without becoming
* obscured by any fog or mist it sank beneath the horizon as if it had
* been some heavenly body setting."
* Met.Mag.'s brief account of the next item
* TRIPLE SUPERIOR MIRAGE
* Several mirages and other phenomena (Kenneth Sinclair, Maughold Head
* Lighthouse, I.O.M.) "ORKNEY WITCH" original report
* ". . . I remember the remark of a Highland fisherman made to his fellow
* boatman after directing his attention by a sweep of his massive hand to
* the northern sky. . . . `there's Margaret, the Orkney witch, going to meet
* the sun.' and there, sure, hung, as if suspended by invisible threads, a
* stretch of the Orkneys mapped in the sky. I remember the sea was smooth
* and the sun glaring."
* PERIODIC MIRAGE and the ORKNEY WITCH
* ". . . in the Pentland Firth the superior mirage is sometimes referred to
* by the name of `Margaret, the Orkney Witch'. . . ."
* ". . . as sure as the timely rise and fall of a fountain ball, so did this
* strange sight rise and fall as if governed by the movement of some sighing
* bosom."
* "Such direct evidence for Helmholtz waves in the transition layer
* between a warm current and the cold air beneath it is valuable."
* NOT a FATA MORGANA (according to Bonnelance, 1929) but an inferior mirage
* decent photograph reproduced
* pretty standard mirage story (stapled with the previous paper)
* "absolutely characteristic" FATA MORGANA (according to Bonnelance, 1929)
* NOT a FATA MORGANA (according to Bonnelance, 1929) but an inferior mirage
* This is a repeat of one published in Mon.Wea.Rev. for June 1923 (above)
* Report in the Times by "P. Neame, Lieutenant-Colonel, Royal Engineers"
* [quoted in full in the QJRMS report, so not copied.]
* "Mr. F. S. Smythe and I were climbing the Finsteraarhorn in the Bernese
* Oberland on May 2. . . . Suddenly at 11.55 a.m. the image of a ship
* appeared in the sky just to the east of the Eiger peak, floating in
* a blue shimmer just beyond the visible horizon. This lasted for a
* minute or so, and then vanished. Very soon after a line of five ships
* appeared farther east, funnels and masts clearly distinguishable. This
* image lasted for some fifteen minutes, and varied in its clearness from
* time to time. The ships appeared of course greatly exaggerated in size,
* and were right way up, not inverted."
* "On reference to an atlas, this brings their position on the nearest sea to
* approximately the eastern exit of the English Channel into the North Sea, a
* distance of some 400 miles."
* ILLUSION of ships in SUPERIOR MIRAGE
* This is hard to classify: first, Neame's report in the Times is quoted;
* then comments on it by Newnham and Whipple. I'll isolate Neame's item
* as a separate entry (above), and attribute just the comments here.
* However, note that in April, 1924, MWR indexed this under "Neame".
* Newnham just gives the synoptic situation. But Whipple says:
* "The illusion of distant ships would seem to be explicable by the
* presence of an inversion of temperature. . . . The illusion of the ship's
* masts is comparable with that of reeds growing by the edge of water in the
* 'inferior' mirage of the desert. A similar drawing out of a small object
* can often be observed through a windowpane of poor glass." (p. 281)
* Saved as "AlpineMirage1923.pdf"
* EXTREME LOOMING
* Hard to believe they saw mountains 750 km away,
* ". . . jedoch ließen sich die mächtigen Schneegipfel und ihre von
* Klüften zerfurchten Abhänge überaus deutlich wahrnehmen."
* The feet of the mountains couldn't be made out, so maybe the long
* path is explicable by the great height (4560 m) of the peaks.
* A garbled footnote refers to Jessen's (1914) mistaken observation.
* Cf. Garner (1933).
* Use of mirage for DESERT NAVIGATION (cf. Rosita Forbes, 1921)
* On p. 124, after mentioning the ordinary (inferior) mirage, he says:
* "Another kind of mirage comes sometimes in the early morning. Then the
* country far ahead of one appears in the sky at the horizon, as the
* Bedouins say, `upside down.' This is not, as the other variety of
* mirage is, entirely an illusion. It is really the reversed reflection
* of the country thirty or forty kilometers ahead of where the observer
* stands." He also says, "Sometimes . . . a small pebble the size of a
* cricket-ball seen from a mile away might assume the appearance of a big
* rock, standing like a landmark. The skeleton or part of the skeleton of
* a camel or a human being may take on the most fantastic shapes on the
* horizon, but the Bedouins know it well."
* and: "The seasoned desert traveler knows a mirage when he sees one. It
* is entirely possible indeed that the `upside down' variety may be a
* positive assistance, since it can suggest what kind of country lies ahead."
* FATA MORGANA with LATERAL MIRAGE (according to Bonnelance, 1929)
* textbook example of MULTIPLE HORIZON due to INVERSION
* Seen at Hampton Beach, Mass., June 17, 1925.
* Sounds like Forel's "FATA MORGANA" displays. 8' HEIGHT.
* "The Isle of Shoals looked like a city of skyscrapers of uniform
* height. . . . The loomed horizon joined with the other farther and farther
* northward in the course of the hour from 10 to 11 a.m. The extending
* upper line of the loomed horizon became visible first in rather regularly
* spaced spots (marking air waves?) which developed columnar connections
* with the lower sea level as the top line became continuous. A rough
* angular measurement indicated the looming to be about eight minutes
* of arc.
* "Over the ocean there was the normal cool cushion of air, represented
* by the moderate sea breeze at 59° F. blowing in from the ocean (shore
* water 54.5° F.), over which was beginning to run a warm southwesterly
* wind, which became strong by mid-afternoon at points a few miles inland."
* [The islands are about 20 km from the beach.]
* A mirage photograph discussed, not very informatively
* WEGENER's statistical support for superior mirage predicting warmer
* weather
* MIRAGE CLASSIFICATION (preliminary version; see his 1929 paper in BSAF)
* This is on the first leaf of No.2; the title says "Tome IX" but that
* must be an error, as the title page of the *volume* says Tome VIII (1926)
* Mirages across Lake Ontario; random reports in discussion
* Available from ADS.
* Ivanov reports miraged sunsets from Anapa (Northern Caucasian coast of
* the Black Sea) and cites Wright's experiments with colored filters.
* He shows crude MIRAGE DRAWINGS of setting Sun (all Omega type)
* Maltézos reports his work as well, in response to Bonnelance's note
* The page numbers overlap with the previous item, as Ivanov's drawing
* is placed on p.219, in the middle of Maltézos's letter.
* PHOTOGRAPHS of SUPERIOR MIRAGES in the Alps, by A. Vaupel
* Commentary by Alfred Wegener (June issue)
* Nice observation of HEIGHT effect, and "SURF"
* "From a rowboat, the low, rocky coast of one of the outlying islands was
* seen to alternate rapidly between its normal shape and that of splendid
* `cliffs.' The alternations synchronized with the rising and falling,
* respectively, of the boat over the slight swells of a glassy sea. So thin
* was the refracting layer of air, that when the boat was on top of a swell,
* the distant coast appeared in its true character to a person sitting in
* the boat. When the boat was in the trough, up popped the `cliffs' to form
* a fine palisade along the whole visible length of the island. From the
* deeper troughs the looming very nearly went over into full mirage, the
* normal form of the island shore then shooting out horizontally bottom up,
* over the true shore. . . . The most spectacular feature of the display was
* the magnificent `surf' made by the very moderate swell when its breaking
* coincided with the dips of the boat into troughs. The spray would at such
* times shoot upward in a brilliant white column as high as the `cliffs'
* produced by the momentary looming."
* Aug.-Sept. issue
* Lengthy but fanciful descriptions of mirages in the manner of James Gordon
* Mentions "FOG" on p.7. Also:
* "A mirage is the reflection of something; sometimes the mixed
* reflection of several things. It appears that an object or a landscape
* is lifted, perhaps by reflection, projected afar, and then set down in
* another place as a mirage. . . . It may be photographically clear, or
* vague and cloudy, or a confused mixture. This confusion may be due to
* several reflections mingling in the same picture . . . ." (pp. 7, 8)
* "The mirage shows many ambiguous images. Desire often insists we are
* seeing the thing we want." (p. 9)
* "The turning of my field glass upon a mirage often changed it into
* nothing -- or formless light and shadow." (p. 12)
* There is a nice description of how a mirage made a couple of stalks
* of grass appear to be distant spruce trees in snow (pp. 16-17): "Before
* me, two slender grass stalks stood above the snow. I circled back to
* where I had first seen the spruces. They were in view again, but this
* time they were upon a snowy rim of a cañon -- the magnified
* overlapping snowshoe tracks that I had made by the grass stalks."
* There is a good description of a "breathing" or waving mirage on
* p. 18: "Up and down they rose and sank, teetering as though upon an
* invisible support laid across the peninsula. Sometimes they balanced or
* swung back and forth slightly as they seesawed."
* Peary's "Crocker Land" is on pp. 21-22.
* "During the Franco-Prussian War a number of scattered and independent
* observers in northern Sweden and Norway saw mirage armies marching
* through the air, equipped like the real ones that were fighting a few
* hundred miles to the south." (p. 23) [but no references!]
* "A vague or confused mirage . . . often reveals something in the mind of
* the onlooker." (p. 25)
* "Generally, the image shown is not moved to one side, but just
* uplifted above the horizon's rim. That these mirages often are directly
* above the real, I have proved with islands in the Pacific by taking a
* compass course and sailing directly to the real island." (p. 27)
* Bonnelance's detailed statistical study of the frequency of different
* forms of refraction during the year and their relations to temperature
* gradients. He finds a rough relation to temperature difference between
* air and water, but not to humidity or barometric pressure. Comments on
* the importance of a trained eye.
* Dubious lateral mirage of mountains
* The explanation proposed by R.Corless does not seem plausible.
* Wimperis calls attention to his 1903 note in Nature:
* "The shapes of these ships are distorted when the temperature of the sea
* is higher than the temperature of the air . . . wind force makes no
* difference . . . ."
* Comments from an unobservant reader:
* "I have not observed any road mirage in my time and am an octogenarian . . . ."
* Report of persistant inferior mirage on a tarred road at airport
* ". . . it was visible both in winter and summer (although less intense in
* the former season) under most conditions of wind, weather and temperature.
* . . . Even with a damp road and drizzle falling one was considerably
* surprised to find that, on approaching what appeared from a distance to
* be a puddle of water, the puddle vanished." (Cf. Ashmore, 1955)
* Describes LABORATORY DEMONSTRATION of mirages (syrup + water; hot-plate)
* Curious terminology: "hot" and "cold" mirages, as the surface layer is
* (compared to those higher up). He also makes a hot-wire refraction,
* with no mirage counterpart: a shadow zone around the wire, with
* "brightly coloured interference bands."
* July 21 issue.
* STANDARD TRIPLE IMAGE with drawing of SUPERIOR MIRAGE
* "The day was hot and clear with a temperature of about 65°."
* Available from ADS.
* Mirages studied on sandy beaches
* Notable for observations in the LAMINAR layer.
* DOUBLE SUN, compared by F.J.W.Whipple in the following comment (p.68)
* to Hevelius's observation in 1682. He points out that it does not
* appear to be 2 images of the Sun separated by a blank strip; I am not so
* sure. This is the observation invoked by Botley (1935).
* "In the path of the pillar there was an image alike in all respects to
* the sun, the distance between the two balls being equal to the diameter of
* either. It was quite impossible at that time to say which was the object
* and which the image but this was decided when, two minutes later, the
* upper `sun' quite suddenly faded."
* cf. Emsmann, 1856, as well as S&T, 1980.
* Calvin Frazer's mirage article
* Despite the title, this is about mirages, not variable dip. Contains
* several interesting references (but not citations) to Bonnefont (1837);
* Warren Upham (1895); Lt. Wilkes; Borchgrevink; Bottineau. Alas, the
* "accompanying illustration" by Arctowski was not published.
* SUPERB treatment of mirages observationally; much improved classification
* scheme compared to his 1926 paper. Schiele's review missed this.
* Many comments on FOREL's work; good FATA MORGANA discussion:
* "La Fata-Morgana . . . atteint et déforme des objets plus ou moins hauts
* et donne continuellement l’impression que l’on regarde le paysage à
* travers la longueur d’uneplaque de verre qui en donnerait une image
* confuse, étirée ou multiple." (p. 497)
* Useful comments about "FOG", which he seems to equate to the Fata-Brumosa.
* Useful comments on earlier reports in BSAF, too; see notes elsewhere here.
* EXCELLENT ADVICE to observers (cf. Nijland's list for GFs)
* He also notes the unexplained nature of "lateral mirage" reports.
* Interesting review of mirages at sea, with many examples
* badly drawn OMEGA sketch
* Claims that mirages in Kansas are less frequent than before farming of
* the plains, due to the effects of more plant cover. Several anecdotal
* accounts of mirages there.
* (cf. Fingado, 1932)
* impossible balloon sounding explained by abnormal refraction at inversion
* LOOMING and cases of LONG VISUAL RANGE due to refraction
* Cites examples of long triangulation baselines: 192 miles [309 km]
* from Mt. Shasta to Mt. St. Helena, and 183 miles [295 km] in Utah.
* Then, on p. 73, there are examples of seeing great distances: the
* Explorer , in 1911, is said to have seen the Fairweather Mountains
* at 330 miles [531 km]. Other examples of looming on land are given.
* Cf. Korzenewsky (1923).
* CHARLES FITZHUGH TALMAN's article in Yachting
* An EXCELLENT popular review! Mentions Justice's note in MWR, 1930; the
* mirages of Mt. Canigou seen from Marseille; mirages near Chicago on Lake
* Michigan; Thomas Jefferson's "canoe" mirage; and many classical examples.
* Very clear on terminology -- a specialty of his, according to the obit.
* Explicitly says: "When abnormal refraction increases the apparent
* elevation of distant objects -- often lifting above the horizon things
* normally below it -- the process is described as `looming.' Because we
* associate a certain apparent altitude with a certain distance, this
* phenomenon generally makes the objects seem nearer than they really are."
* Excellent advice: "The yachtsman who wishes to become better
* acquainted with mirage . . . if he knows enough German, . . . will read the
* appropriate sections of Pernter and Exner's Meteorologische Optik , and
* his best guide in English will be W. J. Humphreys' Physics of the Air .
* . . . A good pair of binoculars or other optical aid will be found necessary
* for making out details, especially in the observation of superior mirage,
* as great distances are usually involved . . . ."
* Much of the wording is borrowed from his earlier works.
* This mag has had a varied history. Founded in 1907 by Yachting
* Publishing Inc., it made its way to Z-D, then to CBS Magazines, who sold
* to Diamandis Communications, bought by Hachette Magazines c. 1987; then
* they sold it to Times Mirror Magazines, Inc.. In 2000, they sold it to
* Time, Inc. In 2008 it was acquired by Bonnier Magazine Group. It is
* still publishing 2 volumes/year in an unbroken series.
* I have a *very* poor photocopy -- can anyone provide a good one?
* Mirage of Isle of Man from Holyhead, with looming
* SKETCHES of mirages, reproduced in Minnaert's book
* The drawings are about as reduced as is tolerable, here; but they were
* reduced still further, to illegibility, in Minnaert's book.
* [For larger versions, see ten Kate (1951).]
* Fig. 6 is a nice superior mirage of a ship beyond the horizon, like
* the drawing with the Sun in M.O. 37, 18 (1967).
* I don't think Pinkhof's argument against the supposed mirage of the
* cliffs of Dover holds water; he forgets that towering can magnify the
* image -- cf. Met. Mag. 56, 40 (1921), where again "chalk cliffs" were
* imagined. But he may well be right that this interpretation was wrong.
* Nice REVIEW of mirages and looming in mistaken claims of polar discoveries
* See some other of his papers in the "Lehn/Novaya Zemlya" file, esp. the
* 1937 paper for an update of this topic.
* GOOD PHOTOGRAPHS of mirages
* Good PHOTOGRAPHS of mirages (Tafel 46)
* Okt. 1934
* DOUBLE HORIZON; DEVELOPMENT of the superior mirage above 3 boats in 5
* minutes, from masts downward.
* GOOD REVIEW of mirage phenomena, with discussion of terminology, and a
* mention of Diodorus Siculus at the end (probably via Flammarion).
* Thesis -- good references
* This is a good guide to the mirage literature. There is a good
* review of the classical treatments -- particularly, a fine appreciation
* of Biot's monograph, Wegener's theory, etc.
* The second part develops the ellipsoidal case in series, using
* perturbation theory. Today, it would be easier to just do the
* numerical integrations, as van der Werf has done.
* Cited by Humphreys (1940) in connection with the mention of Japanese
* Fata Morganas on p. 107; however, the ellipsoidal theory is never really
* applied to that situation.
* Rudolf Meyer FIRST DISCOVERED the Mock Mirage ("intermediate mirage")
* too many good quotes to give here!
* Rudolf Hans Wilhelm Meyer (1880-195x?) was educated in Warsaw and
* Berlin, after being a student at Dorpat Meteorol. Obs. He was born in a
* suburb of Riga, and often contributed to the Korrespondenz-Blatt there.
* O'C #88
* Good DRAWINGS showing a DOUBLED image with one part TILTED
* July issue
* Good DRAWINGS and FOG description
* "The appearance of a fog bank lay on the horizon, the angular height of
* which was 2° 10'." This complex display needs work.
* Jan. issue
* Not a Fata Morgana, but a spectacular case of LOOMING,
* in which a farm appears (and a town is reported to have appeared)
* at "less than 10% of the real distance." Not even a drawing.
* Observed on 20 May.
* Humphreys was probably the inspiration for Fraser's "Theological Optics"
* This note also mentions the incident of April 11, 1917 reported by
* General Maude. [see London Times for April 16.]
* GOOD CASE for a MOCK MIRAGE in MOUNTAINS
* From Donnersberg (835m) mirages described in abstract as "Fata Morgana"
* were seen of Fichtelberg (1214m) and Keilberg (1244m), 71 km away.
* "Fichtelberg und Keilberg sowie sämtliche Bergkuppen bis herüber zum
* Wieselstein (Entfernung = 26 km NW, h = 856 m NN) standen auf sich selbst
* Kopf, nach oben begrenzt durch eine messerscharfe, waagrechte Linie."
* "Sämtliche Berge verloren ihre ursprüngliche Form. Vor allem der
* Oedschloß-Berg im Duppauer Gebirge (Entfernung = 70 km SWzW, h = 925 m
* NN) machte alle Stadien von Klumpen, feinst zugespitztem Kegel bis zu
* einem sonderbar geformten Zylinderhut durch. Auch das Riesengebirge
* (Entfernung 130 km E, h = 1400 bis 1600 m NN) zeigte, wenn auch nicht in
* so deutlich wahrnehmbarer Form, die im Westen so ungewöhnlich stark
* auftretenden Luftspiegelungen."
* Mountains were about 15 C warmer than valleys; "Der Temperatur- und vor
* allem der Feuchtigkeitssprung (Donnersberg nur 3% rel. Feuchte!) lag bei
* rund 750 m NN."
* GOOD REVIEW OF DESERT MIRAGES (ALL KINDS)
* Ives had degrees in geography and geology, but had a minor interest
* in meteorology, which led to a few publications on mirages.
* This paper is particularly interesting in describing some rare mirage
* phenomena, esp. on pp. 468-469. The inversion of 15°F in one inch of
* height reported on p. 468 exceeds the 1°C in 5 cm inversion of Balsley
* et al. (2003) by an order of magnitude.
* Superior mirages are discussed on pp. 469-471, including association
* with inferior mirages. Miraged nocturnal lights are treated on p. 470.
* Fata Morgana mirages are on pp. 471-472. They "not infrequently have
* peripheral color fringes" -- cf. Minasi! -- and are complicated "in many
* instances" by "wisps of steam fog".
* More remarks on mirages by Ives, with climatology
* The brief mirage discussion is just pp. 175-176. After mentioning
* the common inferior mirages (and accompanying turbulence), he says:
* "Less common in this area are superior and multiple mirages, occurring
* when the lower layers of air are thermally stratified. These are
* particularly common over the Gulf of California, and on the west side of
* Baja California, where the California Current (Fig. 17) chills the lowest
* stratum of air, producing great stability, and leading to stratification.
* "Near the sea, particularly in areas where high mountains are quite
* close to shore, Fata Morgana mirages are not unknown, and lead to annoying
* or serious misobservations by navigators and pilots."
* [no hard copy filed.]
* GOOD DRAWINGS showing the change in mirage with DISTANCE of ship
* Ronald L. Ives describes mirages in the Gulf of California
* while working as an engineer at Cornell Aeronautical Laboratory.
* This is a VERY THOROUGH OBSERVATIONAL REVIEW of many kinds of mirage,
* with clear drawings of 3-image and other superior mirages, looming,
* and descriptions of CONCAVE appearance of the sea, truncated images and
* false horizons, etc.; "False sea horizons, due to refraction, are a
* standard midday condition . . . . Fata Morgana is a common occurrence
* when cold air drainages from high mountains reach the warm waters of
* the Gulf of California." (from Abstract!)
* The section on "False Sea Horizons" is on p. 287:
* "On hot clear days, which are frequent near the Gulf of California, the
* sea horizon acquires a peculiar appearance in midmorning, the visible
* horizon being 10' to 15' of arc higher than its sunrise position.
* This condition persists until very late afternoon, at which time the
* "upper horizon" dissolves, not always regularly. Onset of this false sea
* horizon is contemporaneous with the development of a thin warm surface
* stratum of water. Neither the warm surface stratum nor the false sea
* horizon develops when the wind speed is much more than 5 mph.
* ". . . inferior mirages commonly develop over flat land areas 15
* minutes to two hours before formation of the false sea horizon. On very
* hot summer afternoons, the inferior mirages over land may merge with
* the false horizons over water.
* "Although deceptive to the unaided eye, so that its presence
* complicates accurate marine navigation, the false sea horizon can be
* distinguished from the true horizon by use of a deep red viewing filter,
* such as a Wratten "A" or "F."
* "When winds of small areal extent blow over the sea surface, they
* remove the false sea horizon locally and temporarily, in much the same
* manner that dust devils "eat holes" in inferior mirages on land.
* "In a great majority of observed instances, objects at sea
* considerably nearer the observer than the apparent horizon have an
* entirely normal appearance during the middle hours of the day, whether
* or not a false horizon is present. As these objects recede from the
* observer, they will cross the horizon and disappear below it in a normal
* manner if no false horizon is present; but will sail off into the sky,
* undergo great vertical distortion, or partake of more complicated visual
* transfigurations when a false sea horizon is present."
* On the next page: "The shallow northern part of the Gulf of
* California, roughly from Latitude 27° north to the mouth of the Colorado
* River, is noted for its mirages, which, in one form or another, are of
* almost daily occurrence at all seasons." Fig. 2 (p. 288) shows the
* progressive changes in appearance of a ship steaming away from the
* observer as it crosses the horizon. "If . . . mirage conditions exist,
* as is usually evidenced by a false horizon at sea, and by inferior mirages
* over adjacent lands, the appearance of the vessel will not remain normal
* after it reaches the apparent horizon." (p. 289)
* "Never reported from Puerto Peñasco, but common in the narrow
* channels between islands farther south, is the Fata Morgana , a weird
* mélange of diffuse and ever-changing images, perhaps magnified and
* distorted views of objects on the shore. These annoyances to mariners . . .
* are most commonly seen in the early morning, when the air is very cold
* relative to the water, and are usually accompanied by steam fogs."
* "Where study of air conditions has been possible during Fata Morgana
* displays, a thin layer of relatively cold air, in turbulent motion, has
* been present over the surface of relatively warm water. Above the
* thin cold air stratum, which usually results from local air drainage,
* is a layer of much warmer air. Other stratifications aloft are sometimes
* present.
* "Observed colors in the main body of the mirage are always
* degradations of those present in the local environment. Occasionally
* spectral hues are present, as "rainbow glints," adjacent to steam fogs
* associated with the Fata Morgana ." (p. 290) [Cf. Minasi!]
* Next comes a discussion of "looming" of distant mountains:
* "On any ordinary clear day, when air temperatures are substantially
* normal for the season, and wind speed is below about 15 miles per hour,
* dim shapes, that might be distant mountains shrouded in desert haze,
* appear on the western horizon at about noon . . . [A]bout an hour before
* sunset, . . . the images sharpen . . . . A few minutes before sunset, the
* images tower and sharpen still more, . . . This image lasts for about
* half an hour, until very shortly after sunset, at which time it darkens,
* and rapidly falls below the horizon.
* "After an abnormally hot still day, the image towers to a much
* greater height, and the sea appears to have a concave surface from the
* observer to the base of the range, with "embayments" of mirage extending
* up valleys in the distant mountains." (p. 291)
* On p. 292 he describes loomed images of distant islands to the south,
* as seen from a height of 250 ft. (76 m). They appear in midmorning or
* later, "snapping into view" about a minute of arc above the horizon.
* [This means the images appear at the inferior-mirage fold line.] "The
* images slowly rise as the day progresses," -- or, more likely, the dip
* of the apparent sea horizon increases as the mirage grows stronger.
* "Appearance of the upper images changes with each minor change in
* the position of the observer, and the actual changes in appearance
* with changes in the height of the observer's eye above sea level are
* disproportionate to the change of elevation." So, here again,
* we have an inferior mirage at the surface, with inversion (superior)
* mirages above. The similarity to Forel's account is striking.
* Thanks to Eric Frappa for an excellent PDF of this!
* Big reproductions of Pinkhof's (1933) drawings
* GOOD DEFINITION: "What is a mirage? One should be able to define this
* as the phenomenon whereby we see objects at a sufficient distance in the
* open air not singly, but double or sometimes multiple, from which it is
* obvious that the light rays that leave an object come to our eyes along
* different paths. Then the light rays are not all propagated
* rectilinearly but sometimes also along curved paths . . . . The question
* is now more how it is possible that the rays become bent."
* He is one of very few writers who contrasts the astronomical and
* terrestrial refractions; but he supposes that straight rays are possible,
* or even common; and that superior mirages are rarely seen because the
* thermal gradients there tend to be weaker, not because of the restricted
* height from which they are perceptible. However, he does emphasize the
* importance of eye height.
* FATA MORGANA discussed
* Cites his mirage article in the previous volume: "The Fata Morgana are
* also mirages, but of a much more complex form than we have described in
* the cited article."
* He correctly connects the phenomenon with air-water temperature
* differences, and especially those near land; but thinks the F.M. is due to
* CURVATURE of the isopycnic surfaces.
* a nice SKETCH of MURAL MIRAGE
* on the last page of the previous item.
* MOUNTAIN MIRAGES and nocturnal inversion data
* Comments on inadequate resolution of soundings (200 - 300 m)
* Werner Weigel, Met. Station auf dem Fichtelberg i. Erzgebirge
* Gerhard Kohl tries to explain Weigel's observation
* Notable as the FIRST paper to consider the MOCK-MIRAGE geometry
* explicitly: "Einmal handelt es sich um eine Luftspiegelung eines weit
* entfernten Objektes (rund 165 km), zum anderen lag der Beobachtungspunkt
* einwandfrei oberhalb, aber nicht unterhalb der Grenzfläche zwischen
* Bodenkaltluft und der darüberliegenden, bedeutend wärmeren Luftmasse."
* -- though he tries to force Wegener's model onto it, and
* mistakenly asserts that "die Lichtstrahlen [werden] von der totalen
* Reflexion betroffen." But at least the radiosonde profile shows an
* 8-degree inversion close to the peak-to-peak line of sight.
* Many other circumstantial details are given, as well as a tell-tale
* drawing of the mirage (Abb. 4) supplied by Weigel.
* a series of M.O. mirage reports -- NOT ALL indexed here!
* HOT, DRY GUSTS -- cf. M.O.24,13(1954).
* "In one of these gusts (at 0820) the dry bulb rose to 89 F and the wet
* bulb fell to 71 . . . ." "Sea temperature remained 76 throughout . . . ."
* Fine DRAWINGS of 3-image mirages
* NOVAYA ZEMLYA (leaky-duct) display of great duration
* Surface-based DUCT phenomena (cf. ATY's April 23, 1995 ducted sunset)
* "The upper limb of the sun appeared elongated and remained above the
* horizon for approximately two minutes." [This is the flattened image
* above the duct.] "Three minutes later a bright red light appeared,
* intermittently, in the sea about two-thirds of the distance to the
* horizon. The light was rectangular in shape, 40' of arc in length and 3'
* wide, and lasted for eight minutes." [This is the Sun seen through the
* duct. Note the long visibility -- a fine Novaya Zemlya display!]
* Evidently the observer mistook the top of the duct for the horizon
* (cf. Le Gentil's "whale" remark). The Editors were completely baffled
* by this report: "It is not possible to give any simple explanation of it. . . "
* MULTIPLE IMAGES OF VENUS and "VERTICAL WHITE STREAK" --> GF
* "Before finally setting the planet appeared elongated to a vertical
* white streak which immediately turned a bright green. All these changes
* were visible to the naked eye."
* [cf. Biot's "petite colonne de feu", and M.O.24,13(1954)]
* DRAWINGS of distorted sunrise
* (belongs in "DISTORTED" file but on same page as above)
* Seems to be a CREPUSCULAR RAY from VENUS
* ". . . gusts of hot, dry breezes were encountered, readings of the dry and
* wet bulbs then noted were 88 and 64 F . . . " [cf. M.O.23,77(1953).]
* "During the phenomena Venus was observed setting. Just before setting
* a column as of fire shot up from it to a height of a few degrees and
* remained visible for 30 sec while the planet set."
* [cf. Biot's "petite colonne de feü!]
* MOUNTAIN MIRAGES - identified as superior mirages
* Strong inversions (15 C in 540m)
* Werner Weigel, Brocken
* ASHMORE's road-mirage observations: almost unaffected by clouds
* Ashmore's by-line reads "Hon. Meteorologist to Wrexham Borough".
* Observations made by an observer sitting on the "kerb" at Wrexham,
* and using binoculars. No info on the road surface!
* Visibility in RAIN:
* "It became evident that the mirage can be formed during favourable
* conditions at any time the sun's altitude exceeds 24½° and that it is
* almost always present, whatever the conditions, with a solar altitude
* of 29° or more. . . . cloudiness may have a slight effect, but in
* general, the only conditions which prevent it are snow lying, rain heavy
* enough to produce considerable splash, or visibility less than about
* 150 yards . . . ." (p. 338) [cf. Woltman 1796, 1798, 1800, and Bigg, 1928.]
* By measuring the ray curvature (using Vedy's method), ". . . it
* appears that the temperature gradient lies mainly in a layer of air
* about ¾ in. thick, and since even the strongest winds do not upset the
* gradient, it is probable that most of it is confined to a portion much
* shallower even than that." (p. 341)
* At the end, he comments: "This work was not always easy ; the road is
* often busy, chiefly with pedestrian traffic. Naturally the activities of
* the observers, involving prone lying in the roadway, aroused curiosity;
* occasionally expressions of commiseration were overheard as passers-by
* receded from the scene."
* Cites Vedy's 1928 paper, and Miss Botley's in Weather (1952).
* (kept only as a PDF)
* SUPERIOR MIRAGE of cumulus cloudtop from airplane
* "Such phenomena as described in this paper do not appear to have been
* previously reported from aircraft in flight, unless some of the reports
* of 'flying saucers' may have been due to this effect."
* MOUNTAIN MIRAGE - identified as superior mirage; but the stretched zone
* looks like Wegener's Nachspiegelung (viewed from above).
* The mirror image is drawn equal in size to the erect one.
* Milleschauer (835m) seen from Fichtelberg (1214m) above "Nebelmeer" at 750m.
* A 1958 Dutch newspaper clipping found by R. H. van Gent in a copy of
* Flammarion's "l'Atmosphère":
* Besides giving the wrong date ("1708" !) for Monge's observations, and
* exaggerating the French army's reactions to the desert mirages ("the
* men thought the end of the world had come"), there are a couple of
* tantalizing hints of mirages seen from AIRPLANES:
* "The pilot Martin flew into a mountain peak 30 years ago [this is dated
* 1958] when he tried to evade a mirage. Lindbergh himself said that he
* had seen strange shores in the middle of the Atlantic Ocean."
* James H. Gordon's mirage summary
* Useful remarks on the difference between ASPHALT and DIRT surfaces,
* despite his ignorance of the literature and optics. Cf. his 1923 paper.
* Good line: "Mirages are definitely not photogenic."
* Penny Porter tells me James Gordon was Janet Gordon's father.
* Trautmann's attempt to interpret mirages of the Alps
* This is a useful but problematic report. The mirages are merely
* described (no drawings). But the observations are accompanied by
* balloon soundings from Munich, roughly on a line between the observers
* on Gr. Falkenstein and the miraged mountains. Unfortunately, only
* Wegener's simplified theory is used, so the comparison of theory with
* experiment is not exact (although he does demonstrate that ducting
* conditions existed in 2 of 3 superior mirages). Worse, he supposes that
* "reflections" can occur at the inversion layers seen below eye level;
* so the attempts to interpret these supposedly "inferior" mirages are
* nonsense. The resulting disagreements are "explained" by some
* hand-waving arguments of little merit.
* Obviously, this needs to be re-done properly.
* [Cited by Löw in his "Luftspiegelungen" book.]
* DISTORTED MOONRISE with INFERIOR MIRAGE (textbook example)
* good drawings
* DISTORTED MOONRISE with multiple MOCK MIRAGES (Filed in GF file!)
* good drawings
* BOTLEY mixes up mirages and other phenomena
* James H. Gordon's short note
* "These road mirages are a comparatively modern development, almost
* unknown on the old dirt roads, and rarely seen today over dirt surfaces."
* Ford Times was a travel mag put out by Ford Motor Co.
* Thanks to Penny Porter for providing a copy!
* REGULAR MIRAGES IN BAJA
* Visual and radar looming compared; "FOG" observed
* During the "fog" episode, the air was 2.5 deg. warmer than the water;
* apparently the inversion then lifted and became inaccessible.
* "A star fix taken by two officers from seven stars came out with useless
* results, although stars and horizon appeared good visually. While
* searching for the error that might have caused the useless results, it
* was found that if 10 min were added to the height of each observation,
* the results would have been correct." [Cf. Koss's footnote, 1901]
* [Note observation of CONCAVE surface:]
* A lighthouse with normal range 15 miles was seen at 75 miles.
* This appears to be a clear case of NEGATIVE DIP (cf. Hasse's
* "Kimmfläche") caused by a strong inversion overhead. The editor's
* comments are mostly wrong and should be disregarded.
* N.B.: There is no apostrophe in the title of this publication.
* TRIPLE-IMAGE mirage within "yellow band . . . thought to be dust or haze.
* The yellow colour was very distinct and it may have been significant
* that the sun was setting over mountains around the coast at the time."
* A miraged ship was seen at 12 n. mile radar range; "the effects
* persisted until each observed target came within seven nautical miles . . .
* On two occasions the inverted image was observed before the true
* object." Air temp. 17.1 C, water 15.2, wind force 2.
* Fraser's parabolic profile
* He mentions the more correct logarithmic profile, but does not use it.
* Interesting DRAWINGS of superior mirages, with ships towering
* Radar distances of targets given.
* Inferior (?) mirage effects on HORIZON, 4 April 1979
* A vessel "was observed fine on the port bow. At a range of 8 n. mile it
* was seen to be in a normal position on the visible horizon, but when at a
* range of 12 n. mile it appeared in very clear detail to be in a position
* above the visible horizon.
* "At the same time a small fishing vessel, at a range of 9 n. mile and
* approximately 4 points on the port bow, was producing a wake on the
* horizon which appeared to the observer as a mountainous sea, see . . .
* sketch. This phenomenon persisted until the range had decreased to 7 n.
* mile." Air 5.5° C, sea 6.3; wind calm.
* LOOMING of trees on shore, despite inf.-mir. temps.
* ". . . there appeared to be a layer of shimmering haze above the land
* . . . the trees were estimated to be 7 n. mile distant from the vessel."
* The DRAWING shows 2 separate layers at least.
* "HAZE" is drawn dark, despite Sun's altitude of 30-40°.
* Air 11.7° C, sea 14.1. A complex and puzzling observation!
* Interesting DRAWINGS of superior mirages, with SMOKE MIRAGED
* The measured altitude of the boundary at 51' is unusually large.
* WAVY HORIZON DRAWING
* An otherwise undistinguished inferior-mirage observation, which calls
* attention to the irregular waves on the apparent horizon. At 11.5 n.
* mile range, a vessel appeared miraged (usual drawing). "As the vessel
* drew closer the fo'c'sle, masts and accommodation appeared to hover above
* the horizon, seemingly separated from the rest of the vessel, which could
* not be observed at the time. Although the sea was calm with only small
* ripples, the waves at the horizon appeared magnified." Air 10.8 C, sea
* 13.2; wind, light airs. Position 39 20 N, 73 18 W (i.e., probably in
* Gulf Stream).
* DRAWING of multiple beach images
* "Initially an apparent line of haze or mist was observed, extending from
* the horizon to an altitude of 0° 10' - 0° 13' and presenting a false
* horizon. The ship's funnel smoke was then observed trapped on a level
* with this, indicating an inversion . . . . As the vessel closed with the
* coast the land was noticed to be apparently sitting on top of the
* inversion level, with the line of beach repeated two or three times in the
* shimmering air below (Figure 2). Sometimes water could be seen between
* the layers of the beach . . . . The top layer did not remain solid-looking.
* At intervals sections would dissolve into narrow vertical blocks that
* resembled single trees before disappearing altogether (see Figure 3); this
* resembled a wave-like motion, with the top layer gradually dissolving from
* right to left, then re-forming from left to right with waves of varying
* thickness forming in the top layer, and ripples moving along the top."
* Air temp 21.0° C; sea 19.5; wind force 2.
* DRAWINGS of superior mirages and miraged ship
* "Shortly after departure from Cape Town a superior mirage was observed
* to extend around two-thirds of the visible horizon. Throughout the
* following 2 1/2 hours very vivid inverted images could be seen. It
* was noted at 1300 GMT and again at 1630 that there were quite marked
* discontinuities of the reflected horizon. The two most distant images
* were observed at 1300 and 1400 GMT, the first being Dassen Island, which
* at the time of observation lay 13 n. mile to the north (the visible
* horizon being 7.85 n. mile distant); the height of Dassen Island is 19
* metres." Air temp. 22.9° C, sea 18.1, wind force 3 increasing to 4.
* Many interesting DRAWINGS of superior mirages, with radar ranges
* "As the Strait of Belle Isle was approached a thick, low band of
* refraction was observed to stretch across the entrance to the Strait."
* Air, 5.9; sea, 4.1 C.
* Drawings of looming of a ship.
* Enlargement of image claimed with no distortion.
* Nice photos. This guy had a whole series of interesting papers for
* several years in Z.Met., all nicely illustrated, on halos, subsuns, the
* shapes of icicles, etc.
* This paper has beautiful illustrations of inferior mirages over lakes.
* The author doesn't understand Fraser & Mach's paper in Scientific
* American, though; he insists on "reflection" without refraction.
* NICE SUPERIOR MIRAGE PHOTO (triple image)
* This really belongs in BLM file, but is in my mirage file because of photo
* ". . . conditions such as these are common in southern California, as
* evidenced by the well-known distortions of the solar limb as the sun sets."
* [Cf. O'Connell's book.]
* Interesting DRAWINGS of towering and superior mirages of icebergs
* at 38 - 43 nautical mile range
* ". . . all the bergs observed at a distance of 18 n. mile and over were
* seen to be abnormally refracted."
* Strong SUPERIOR MIRAGE produces "A SOLID WALL OF WATER" (see DRAWING)
* ". . . what appeared to be land features were observed on the horizon; at
* the same time the horizon ahead of the vessel became distorted and gave
* the impression that the vessel was approaching a solid wall of water. . . .
* The nearest land at this time was 85 n. mile away."
* Air varied from 25.6 to 21.6 C, sea temp. 18.8 C; wind force 2, sea
* slight. "Exceptional radar detection" to 45 n. miles.
* Many SUPERIOR and TRIPLE-IMAGE MIRAGE DRAWINGS in "mist"
* radar ranges from 8.0 to 17.5 n.miles; dry bulb 22.0 C, sea 15.8,
* wind force 1
* Mirage of coasts described, but the sketch "cannot be reproduced"!
* Many interesting details; a puzzling report.
* GOOD DRAWINGS of superior mirages with vertically stretched zone
* Air temp. 30 C, water 26; wind force 3.
* Strong inferior-mirage near Grand Bahama Island, with DRAWING
* Ship at 16 n. miles ahead seen miraged. "Slowly, this effect diminished
* until . . . at a range of 12 n. mile, the ship's hull touched the horizon."
* Air 21.2 C, sea 27.0; wind force 3. "The sea state was slight, with no
* swell." The background land was also miraged.
* SUPERIOR MIRAGE PHOTOS
* Adelbert von Chamisso's 1816 mirages in translation
* A very clear explanation of both the appearances and their causes:
* "I saw a surface of water before me in which a low hill was reflected
* that extended along the opposite shore. I went toward this water. It
* disappeared before me, and I reached the hill with dry feet. When I had
* covered about half the distance, I seemed to Eschscholtz, who had remained
* behind, to have been submerged up to my neck in the reflecting layer of
* air, and, shortened the way I was, he said I looked more like a dog than a
* human being. As I strode onward, toward the hill, I emerged more and more
* from the layer of air, and I appeared to him, lengthened by my reflection,
* to get taller and taller, gigantic, slender."
* "When land rises above the horizon, as seamen are wont to express it,
* the line that is taken to be the horizon is the edge of a reflecting
* surface formed by the lower layer of air and closer to the eye; a line
* that really lies below the visible horizon. I believe that this illusion
* in some cases can have an influence on astronomical observations and can
* cause an error in these of five and perhaps more minutes."
* He also mentions Flinders, Ross, and Scoresby.
*
* NOTE: Johann Friedrich Eschscholtz was the physician and naturalist who
* accompanied Kotzebue's expedition, along with writer/botanist Chamisso
* and the artist L. A. Choris. Chamisso produced the first scientific
* description of California's golden poppy (now the state flower) on this
* expedition, and named it in honor of his friend Eschscholtz.
* The best biography of Chamisso I have seen is in the DSB.
* Good DRAWINGS of towering of ship; another "yellow band" within 1 hr.
* of sunset; cf. Marine Observer 49, 23 (1979).
* ". . . a low, yellow-coloured sand layer was observed, originally thought
* to be haze or fog." Air temp. 25.5 C; sea decreased from 20 to 15,
* then increased to 18 C.
* drawing of triple-image mirage
* with standard commentary by Ken Bignell
* Adrienne Mayor's fair popular review: Tape, Greenler & Fraser are cited
* Besides the standard examples, several less-common ones are mentioned:
* accounts from Giraldus Cambrensis's Topography of Ireland (1187),
* literary passages supposedly inspired by mirages (Wordsworth;
* Coleridge); Wilkes and J.C.Ross; Borchgrevink.
* Jan.-Feb. issue
* SUPERIOR MIRAGE DRAWINGS and descriptions, including land seen
* inverted beyond horizon (25 n. mile range). The mirage of land at 18
* miles was slightly magnified. Wind: force 4.
* INVERSION of SCORESBY's drawings
* See Lehn & Rees (1990) for correction.
* REALLY GOOD piece on inferior mirages by CRAIG BOHREN!
* (with 3 fine color photographs of hot-road mirages.)
* First sub-head is: A Mirage Is Not an Illusion (Thanks, Craig!)
* "I shudder when I see or hear mirages referred to as optical illusions.
* . . . these optical phenomena are no more illusions than are images
* in a mirror." (He offers the Moon Illusion as a real example: "An
* enlarged moon is a creation of the mind; a mirage is a creation of the
* atmosphere.")
* "When images formed by the refracting atmosphere depart markedly from
* what they would be in its absence, they are called mirages."
* "Before considering the consequences of atmospheric refractive
* gradients, I must dispose of the notion that water vapor plays an
* essential role in the formation of mirages. This misconception dates to
* antiquity and persists today, evidence that no misconception ever dies."
* But, alas, he equates inferior mirages with images below the geometric
* position. Despite this single flaw, a fine article.
* Nice Wollaston-style demo using HEAT LAMPS and water
* "When the lamps are switched on, the beam immediately begins to deflect
* . . . . After 30 s a deflection of 6 cm is observed on the screen. . . .
* The deflection rapidly returns to zero when the lamps are switched off."
* Unfortunately they define inferior and superior mirages in terms of
* image displacement, blaming this on Greenler's 1986 OSA abstract. But
* at least they say mirages "are caused by gradients in the temperature"
* and not temperature differences -- still, no second derivatives.
* Rees never read Biot's book, though it is his first reference!
* ". . . inverted mirages . . . are not included in Biot's analysis . . . ."
* Lehn corrects the old Rees (1988) inversion
* This deals with the UNIQUENESS problem, in part.
* Rees et al. introduce the Runga-Kutta forward model
* A worse-than-average account by ignorant physicists
* "Monge . . . was the first to give an explanation . . . . The coordinates at
* which zero slope is reached can be approximated . . . ." A crude empirical
* approximation for the temperature profile over a hot surface is used (with
* no physical basis); the index of refraction "must approach a constant" (!)
* at heights "greater than about 2 m"; and of course the Earth is flat.
* They touch on the horizontal-ray paradox. Pretty dismal.
* 5 papers, all in Am. J. Phys., are cited from 1974 to 1982.
* A glorified version of Wollaston's demo
* The use of a pinch of Coffee-Mate to make the beam visible is a nice
* contemporary touch. And as "alcohol is not benign to most transparent
* plastic containers," he recommends a strong (0.5g/ml) sugar solution.
* our MOCK MIRAGE paper (Paper I)
* Mirages, polarization, and insect vision
* Shows a photograph of a Tunisian mirage
* Thanks to Gábor Horváth for supplying a PDF copy!
* Mirages, polarization, and insect vision (erratum)
* This shows a corrected version of Fig.1
* Thanks to Gábor Horváth for supplying a PDF copy!
* All qualitative, but good photographs
* MURAL MIRAGE well photographed
* But much of the discussion is confused: the erect image is described as
* "real"; Hillers is wrongly credited as being the "first" to study "the
* wall mirage"; the ray trajectory is assumed to be parabolic, or circular;
* the refractive-index and temperature profiles are arbitrarily assumed,
* with no reference to the relevant boundary-layer literature; etc.
* Dec. issue
* Penny Porter's Fata Morgana Arizona observation, plus quotes from Gordon
* The observation was made at 7 am in April 1981
* "A city afloat on a vast blue ocean . . . . doorways on dwellings framed
* in timber and ladders stretching from the ground up to occasional arched
* windows of the upper levels -- suggesting the architecture of the
* pueblo-builders of Arizona or Mexico. Garden plots on upper terraces
* blazed with fiery flowers. Chickens scuttled around courtyards. Two
* heavily laden burros tied to hitching posts were clearly visible, and
* people strolled down quiet, peaceful streets. . . .
* "Finally it broke into sections. Huge fragments collapsed, and in
* slow motion they sank one by one into the sea."
* distant lights seen at night via inversions -- fine MIRAGE PHOTOS in color
* Notable for a good section ("Animation and human factors") that
* discusses the perceptual issues. The colors reported remind me of
* the Biot-Arago observations. Cites my mirage page.
* Formerly available on the Web at
* http://www.optometrists.asn.au/ceo/backissues/vol86/no2/2043
* Presently available on the Web at
* http://onlinelibrary.wiley.com/doi/10.1111/j.1444-0938.2003.tb03069.x/pdf
* Ed Darack's article on MARFA LIGHTS featured on cover
* Nice COLOR PHOTOS of inferior and superior mirages of lights, including
* Fata Morganas. Cites my mirage page.
* Mila Zinkova's good Fata Morgana picture of glitter (see cover!)
* Contains comments by ATY. Nice mock-mirage GF shown, too.
* No. 11 (Nov. issue)
* Siebren's 2011 paper on inferior-mirage wiggles
* He understands the cause of the alternation, but uses a bad temperature
* profile.
* Nice COLLECTION of MIRAGE PHOTOGRAPHS from Spain
* Good examples of the main types, including FM; shows effects of height.
* But: "Although there are descriptions of mirages since the Classical
* Antiquity, the first scientific explanation was given by Gaspard
* Monge, who accompanied Napoleon Bonaparte in the Egypt campaign . . . ."
* doi:10.1088/1742-6596/274/1/012001
* Nice COLLECTION of MIRAGE PHOTOGRAPHS from Spain
* Good examples of the main types, including FM; shows effects of height.
* ISBN 978-989-95095-7-3
* DAVID FARMER's excellent mirage of Mt. Rainier, with my ray-traces
* Siebren van der Werf's nice paper on "sea fences", with waves and animations
* This is a close match to the next item; read both together with the
* Lehn & Schroeder papers (1981 and 2003).
* https://doi.org/10.1364/AO.56.000G51
* my paper with Eric Frappa
* Explains the FM with valley-circulation model (thick inversion)
* many photographs, and a real-time video
* Should be read together with Siebren's paper, just above.
* [Note observation of CONCAVE surface.]
* https://doi.org/10.1364/AO.56.000G59
* Mila ZINKOVA's "Sunset mirages" paper in "Weather"
* http://dx.doi.org/10.1002/wea.3056
* VISIBILITY in RAIN; temperature and humidity data; no profiles
* "It was observed that mirage has shown up from morning to afternoon,
* from 07.00 AMuntil 18.00 PM, even until sunset. Mirage is also still
* visible when the weather is cloudy or drizzling, but disappeared when
* heavy rain." [Cf. Ashmore (1955), above]
* "When the air temperature is high and the humidity is low, the mirage
* appears with high visibility (very thick), so that it can be observed
* clearly visually. Conversely, when the temperature of air is low and
* the humidity is high, mirage appears with low visibility (very thin)
* or almost non-existent or completely gone. [Abstract]
* "Mirage is an optical illusion. . . ." [first sentence!] "The light
* undergoes refraction and total internal reflection . . . ." [first para.]
* "Mercury thermometers are installed at an altitude of 1.5 km from
* ground level." These seem to be naked-eye observations. The broken
* English does not help: ". . . no mirage can be seen on the second morning
* of the day" seems to mean the second observation of the day. They were
* surprised to see no mirage at daybreak on a hot day, and attribute this
* to the effect of humidity. Not useful.
* Nasrullah Idris, Maswati, T. N. Usmawanda,Arlin Maya Sari
*
* This also has the title:
* Voyage de Humboldt et Bonpland. Première partie. Relation Historique.
* The various editions and many translations divide the "books" into
* volumes in various different ways.
* MIRAGES and TERRESTRIAL REFRACTION are mentioned occasionally; one needs
* an edition with an index to find them.
* Note the flowery dedication: "A L'Illustre Auteur de la Mécanique
* céleste, P. S. De La Place, comme un faible hommage d'admiration et de
* reconnoissance."
* Helen Maria Williams's translation, often reprinted. Lacks an index.
* This is a rather crude, literal translation, but at least it is
* unabridged. I have found mirages mentioned in Vol. 1, p.187;
* Vol. 2, p.189 (the footnote citing Hooke); Vol. 3, pp. 542-554
* (the famous Note D); Vol. 4, p. 292; Vol. 4, pp. 299, 325, 327-329.
* The last of these is the passage referring to the Sanskrit phrase, and
* to "the Indian, Persian, and Arabic poets".
* On p. 542 is a reference to "Gruber, (Ueber Stralenbrechung und
* Abprallung des Lichts, 1793)." This may be a later offprint of his
* 1786 work?
* The translator has the quirk of invariably writing "it's" for "its".
* Humboldt's detailed mirage report (see Note D, p. 625)
* This is the original, now available from Gallica.bnf.fr
* This is the republication sponsored by the Humboldt Foundation:
* "Neudruck des 1814-1825 in Paris erschienenen vollständigen Originals,
* besorgt, eingeleitet un um ein Register vermehrt von Hanno Beck"
*
* By far the most interesting passage is Note D on pp.625-631 of Band I.
* It contains quantitative measurements of zenith distance (though
* mostly on the scale of his quadrant, which contained 96 degrees, each of
* which corresponds to 56' 15") of several fixed points on islands, and of
* the sea horizon. He thus was able to observe the VARIABLE DIP and its
* relation to air and water temperatures, and to the color of the sea (p.
* 628). He cites Aristotle, Theophrastus, Büsch, Gruber, Monge, Brandes,
* Wollaston, Tralles, Woltmann, Biot. He mentions the Sanskrit phrase
* "mriga-trichná". He cites his own demonstration that, in the tropics,
* the water is nearly always 1 to 1.5 degrees warmer than the air, as the
* cause of the miraging. Most impressive!
* The Hooke citation is on p. 296 here.
*
* Glaisher's 1865 Oct. 2 ascent, confirming NOCTURNAL INVERSIONS
* [Cf. Brandes (1806), who may have been the first to notice them.]
* ". . . an accidental descent just at the time of sunset showed very
* little or no difference of temperature for a height of nearly half a mile.
* The question then arose as to whether it was possible that at night the
* temperature might increase with elevation, and not decrease as always
* heretofore had been considered . . . ." (pp. 367-368)
* "The results of this first night experiment are very valuable; and,
* so far as one experiment can give, indicate that, on a clear night,
* the temperature, up to a certain elevation, increases with increase
* of elevation." (p. 370)
* Comment on REFRACTION:
* "Certain it is, from the very remarkable results obtained from the
* night ascents, which might, with sufficient number of observations,
* have important bearing both on the theory of astronomic refraction and
* on the theory of heat, that nocturnal observations deserve repetition
* and extension." (p. 373)
*
* These remarks are repeated, without the tabular data, in his part of
* "Travels in the Air"
* Google Books has several scans of this, but only the Harvard one
* is complete.
* Tissandier's part of this 19th-Century ``coffee-table'' book contains
* his brother's woodcut of the mirage over the English Channel, facing
* p.408, in "Troisième Partie: Voyages de MM. de Fonvielle et Tissandier":
* "Nous cherchons les falaises de Douvres et nous nous étonnone bientôt
* de ne pas voir les côtes de l'Angleterre qui ne sont pas bien distantes
* de notre aérostat; elles sont cachées par un immense rideau de vapeurs
* plombées, qui s'étend vers ce côté de l'horizon. Je lève la tête
* pour chercher la limite de cette muraille de nuages, et quelle n'est pas
* ma stupéfaction quand j'aperçois dans le ciel une nappe verdâtre qui
* ressemble à l'image de l'océan; bientôt un petit point semble se
* mouvoir dans cette plage céleste, c'est un bateau, gros comme une
* coquille de noix, et en y fixant avec soin mes regards, je ne tarde pas à
* constater qu'il navigue à l'envers sur cet océan retourné; ses mâts
* sont en bas et sa quille en haut. Un moment après je vois l'image du
* bateau à vapeur qui vient de partir de Calais pour l'Angleterre, et, avec
* ma lunette, je distingue la fumée qui s'échappe de son tuyau. Voici
* bientôt deux ou trois autres barques qui apparaissent au milieu de cette
* mer magique, tableau vraiment saisissant, d'une éblouissante
* fantasmagorie du mirage."
* The popular summary of Gaston Tissandier's 24 balloon flights
* The first chapter (pp.119-127) contains a textbook example of the
* SEA-BREEZE circulation (see diagram, p.125) with a capping inversion at
* 600 m. It alludes to the mirage over the English Channel, but says the
* first 7 flights were described more fully in Hachette's "Voyages
* aériens" (1870).
* Drawings of distorted Sun- and Moon-rises are on pp. 260 & 261.
* There is a 2-page bibliography of aeronautics at the end.
* Tissandier's review of "mirages" -- some may be snowflake reflections?
* (The Eiffel-tower reflection is from l'Astronomie 9, 41-42 (1890), q.v.)
* Here is where he quotes extensively from his earlier work, but
* mis-attributes it to "Histoire de mes ascensions". The illustration by
* his brother Albert, showing the inverted images of ships on the North Sea,
* accompanies this article. As this illustration was based on his
* "crude sketch" made after the flight, it can hardly be regarded as an
* accurate observation.
* NOTE: Gaston Tissandier was the founder, in 1873, of "La Nature".
* Eric Frappa tells me this is "Semestre 1".
*
* (mostly minor references to mirage phenomena)
* N.B.: Admiral Smyth was the father of Charles Piazzi Smyth, q.v.
*
* "The deceitful phenomenon so well known in Barbary by the name of
* `sarab ,' is very frequent in the lower grounds of Sardinia; and while
* at Villa-Cidro, I one morning saw the whole Campidano appearing like a
* vast lake, with the hills of Cagliari in the distance resembling islands."
* Discussion of mirages, pp. 288-291
* The Fata Morgana "is said to occur in sultry, calm weather, when the
* tides, or streamed-up waters, are at their highest, and when the sun
* shines from that point whence its incident rays form an angle of about
* 45° on the water. At such times, they tell us, multiplied images of
* all the objects existing on the two lines of coast -- as castles, arches,
* towers, houses, trees, animals, and mountains -- are presented in the air
* with wonderful precision and magnificence. Padre Minasi assures us that,
* in addition to obvious appearances, numberless series of pilasters,
* superb palaces with balconies, armies of men on foot and horseback, and
* many other strange figures, are seen in their natural colours and proper
* action, as in a catoptric theatre; and there exist paintings and
* engravings of the wonderful phenomenon. Still, on the whole, I cannot but
* repeat the conviction to which inquiry led me, and which I published as
* far back as 1824 ( Sicily and its Islands, page 109): -- `I much doubt,
* however, the accuracy of the descriptions I have heard and read, as I
* cannot help thinking that the imagination strongly assists these dioptric
* appearances, having never met with a Sicilian who had actually seen
* anything more than the loom or mirage, consequent on a peculiar state of
* the atmosphere; but which, I must say, I have here observed many times to
* be unusually strong.'"
* Here is his famous "What's in a word?" discussion
*
* See also Kritzinger (1914), Vogel (1940) in Green Flash file.
*
* Johann Jacob Scheuchzer is sometimes regarded as the "father of
* paleobotany" because of his early work on plant fossils.
* Sulzer edited Scheuchzer's works and translated them from the Latin
* edition published at Leyden by Peter van der Aa in 1723, adding later
* material from Scheuchzer's contributions to Breßlauer Sammlung as well
* as some of his own speculations on the origins of the Alps (he thought
* they were produced by the Earth's center of gravity having shifted!) and
* the fossils in their sedimentary rocks (which he explained by Noah's
* Flood). He attempts to combine the physical evidence with a literal
* interpretation of Scripture.
*
* There are many amusing bits in this work, from the editor's railing
* against people who only buy books for the pictures ["Viele Leute lieben
* die Kupferstiche weit mehr, als eine Beschreibung der Sachen; ja einige
* kauffen die Bücher nur deßwegen. Diesen verständigen Liebhabern zu
* gefallen, hat der dienstfertige Verleger der Holländischen Ausgabe eine
* Menge Kupfer beygelegt, welche aus Merians Topographie genommen sind.
* Stücke, davon oft in dem Texte kein einiges Wort stehet. Diese hat man
* hier weggelassen, und vielleicht in eben der Absicht, in welcher sie Hr.
* van der Aa dazu gethan hat. Wer diesen Abgang nicht vertragen kan, der
* hat die Freyheit, die Holländische Ausgabe oder Merians Werck zu
* kauffen."] to the description on p. 238 (the wrong page number happily
* supplied by "M" in Gilberts Annalen) on how to tell real dragons from mere
* snakes: "Bochart . . . unterscheidet . . . die Drachen von den Schlangen durch
* nachfolgende Kennzeichnen: 1) Die Grösse. 2) Den Bart unter dem Kinn.
* 3) Eine dreyfache Ordnung der Zähnen. 4) Eine schwarze, feuer-rothe oder
* aschenfarbe. 5) Eine sehr grosse Oeffnung des Mundes. 6) Daß sie durch
* das Anziehen der Luft nicht diese allein, sondern auch vorbey fliegende
* Vögel an sich ziehen. 7) Ein erschreckliches und auf gewisse Weise
* trauriges Zischen, daher sie im Hebraischen Tannin genennt werden."
* (Some 20 pages are devoted to these supposedly real creatures.)
*
* Of more interest here is his observation (p. 42) of a "Phænomenon an
* der Sonne": ". . . da sie einen gantz neuen Habit angezogen, (zum wenigsten
* habe ich sie in solchem noch niemal gesehen). Abends um 5. Uhr ist bey
* neblichtem Himmel dieses sonst so hellglänzende Gestirn, zum wenigsten
* einige Augenblicke, in Mitten dem Nebel, in einer angenehmen purpur-blauen
* Farbe erschienen." As this is seen through "fog", I take it to be a
* "BLUE SUN" and not a bluish sunset flash, despite the "few moments"; as
* the date was July 29, 1703, this would be several hours before sunset.
*
* The solar after-images are nicely described under the heading "Von
* ungewöhnlichen in der Schweiz A. 1719. im Heumonat aus der Luft
* gefallenen Bläßgen oder Bullis " with a footnote: "Sihe gedachte
* Breßl. Sam~lung im Julio 1719, Class.IV. Art.IV." The classical
* particulars are there: a hazy sky, in which people could look at the Sun
* without discomfort; a series of images drifting across the sky; a variety
* of colors seen; the "bubbles" vanish into insubstantiality on falling to
* the ground; etc. "Es ist dieses völlig die gleiche Luft-Geschicht von
* Bläßgens oder Bullis , die A. 1553 den 21. Brachm. zu Sculs im
* Engadin ist angemerckt, und in unsrer Meteorol. Helv. p.96 beschrieben
* worden . . . ." Pfarrer Judas Uttiger in Lichtensteig sends him a detailed
* account, of which he writes that "er seye um dieser sehr seltsamen
* Luft-Geschichte willen zum drittenmal spazieren gegangen, und habe sich
* nicht genug verwundern können, daß die bey ihme stehende ihme gleichsam
* mit dem Finger die fliegenden und fallenden Luft-Kugeln gezeiget, deren
* er doch keine mit seinen eignen Augen sehen können." But those who lived
* on higher hills above the fog had seen nothing; "daraus sich schliessen
* läßt, die unterste Gegend der Athmosphaer seye sonderheitlich mit
* dicken Dünsten angefüllet gewesen, da hingegen die obere hell geblieben.
* Diese ganze Luft-Geschicht endlich scheinet es, könne als ein optisches
* Gesichtspiel, oder als ein Betrug unserer Augen, angesehen, und mit
* demjenigen verglichen werden, da einer, der die Sonne mit starren Augen
* anschauet, hernach, ob er die Augen gleich zuschliesset, das Bild der
* annoch scheinenden Sonne siehet oder zu sehen vermeynt, und sie zwaren
* siehet durch verschiedne Farben als roth, blau und so ferner, untergehen,
* bis sie völlig verschwindet."
* This is followed by two more very similar reports, in the last of which
* Scheuchzer himself finally gets to see the "Bläßgen" and confirms his
* opinion: ". . . so wie nemlich das dem Aug eingedruckte Bild der Sonne,
* welches eine Zeitlang, wann man auch gleich die Augen von der Sonne
* abwendete, bliebe, eine mehr oder minder stärckere Bewegung in den
* Augen-Nerven verursachte."
*
* The whole book is printed in old-style Fraktur, with little e's over
* the letters for umlauts. The Courier-like Roman type used is a poor
* match to the Fraktur. A much wider, different face is used for display
* type (still a Fraktur face). It's amazing that anyone would actually
* send this treasure out to another library; perhaps the dowdy 19th-Century
* re-binding deceived them into thinking it worthless.
* A collection of 17th-Century oddities, collected by "Landmesser Weise"
* taken from the Theatro Europaeo .
* Pp. 106-107 relate a double-Moon crescent of 15 July 1633.
* The SOLAR AFTERIMAGES are on pp. 107-108 and 109-110.
* Erik Acharius's second-hand solar afterimage reports
* As Gilbert's German translation appears to be complete and satisfactory,
* see the next item for it.
* An early SOLAR AFTERIMAGE report (see next item for explanation)
* Also a good example of "mass hysteria" or mutual brainwashing by
* the inhabitants of a village: everybody came to believe "eine Menge
* Kugeln oder sphärische Körper nach einander mit Geschwindigkeit
* aufsteigen, die dem blossen Auge von der Grösse eines Hutkopfes
* erschienen, und eine dunkelbraune Farbe hatten." The mysterious
* "balls" vanished soon after falling to earth. One person saw them
* first, "und als es so lange dauerte, wurden nach und nach alle
* Dorfbewohner darauf aufmerksam, so dass es keine Täuschung seyn konnte,
* die bloss bei einem und dem andern Individuum hätte möglich seyn
* können." The Sun had been dimmed by a haze so "dass man ohne
* Unbequemlichkeit mit blossen Augen in sie hinein sehen konnte."
* The above phenomenon explained: ". . . der Grund der Erscheinung in einer
* Blendung der Augen durch die Sonne liege." The anonymous correspondent
* in Göttingen points out some earlier examples: "Dasselbe Phänomen
* erwähnen frühere Schriftsteller beinahe mit denselben Worten."
* Certainly true; but he gives the wrong page number (238 for 338) in
* Scheuchzer's Natur-Geschichte.
* Admiral K. P. Jessen's odd account: afterimage or bleached areas?
* After establishing himself as an experienced observer of phenomena at
* sea in "my numerous navigations, carried out in all nearly 40 years,"
* with a brief account of mirages and looming seen in the Baltic in June,
* 1895, he gets to his main theme: an observation made at sunrise on 25
* Feb., 1902, 12 miles off "Cape Boltin, on the eastern coast of Korea."
* "Standing on the command bridge together with the senior and junior
* navigating officers and the officer of the watch, I observed the rising
* sun: the horizon was perfectly clean, free of clouds and the rising
* sun appeared to us, as always, in the form of a continually increasing
* bright segment. Suddenly I, and behind me also the aforesaid officers,
* noticed on the perfectly clean disk of the sun a dark spot, continually
* increasing just like the rising sun above the horizon and little by
* little taking on the obvious form of a high mountain. In a few seconds
* a new spot appeared on the left beside this peak, gradually changing into
* another such summit, but lower, separated from the first by a deep pass.
* Finally, the entire disk of the sun was covered from limb to limb by
* a whole mountain massif, reaching to the very lowest limb of the sun as
* it rose. Just as the whole solar sphere separated from the water horizon,
* the whole phenomenon instantly vanished."
* The accompanying drawings, based on sketches made as soon as he
* returned to his cabin, show two steep mountains appearing to rise together
* with the Sun, so that their image remains fixed with respect to its disk.
* (Considering the latitude of over 40°, this is impossible.) The
* Sun's disk is shown round, with no distortions.
* "Obviously, those mountains which we saw so clearly on the solar
* disk had to be on a line between us and the rising sun. And, indeed,
* by constructing on a chart the aforementioned azimuth of the sun at the
* moment of its rising, it turned out that this line passed just through
* the high mountain Tonvumi-yama , located on the north-western part of the
* Japanese island of Nippon [sic -- he means Honshu], at north latitude
* 39° 5' and east longitude 140° 10', not far from the city of Akita.
* The distance from the cruiser to that mountain was 480 sea miles."
* An accurate calculation gives 897 km or 490 nautical miles.
* He later gives the height of the mountain as 7130 feet. The only
* mountain of this height near this location is Chokai-San; I cannot find
* any place in Japan with the peculiar name of "Tonvumi-yama" (which he
* repeats later); it might be a mistake for the lower peak Tokami-Yama.
* Photographs of Chokai-San show it has shallow slopes, like Mt. Fuji,
* quite unlike the "mountain" in the drawings. (As the Sun appears
* undistorted, the mountain should, too -- if it were real.)
* His sunrise azimuth of 77° 40' E from S (or 102.3° by the usual
* astronomical convention) agrees well with calculation for the stated
* date and coordinates. He gives the time of sunrise as 6h 4m but fails
* to state whether this was LCT or zone time; predicted sunrise for the
* ship's position is indeed 6:04 zone time, however. As "The state of
* the weather was most ordinary: a light breeze and calm sea" and the
* accompanying table of meteorological data shows the water and air to
* have the same temperature within a few tenths of a degree, the most
* reasonable conclusion is that there was no mirage at all, and that the
* "mountain" was illusory. His drawings show the *lower* limb of the Sun,
* even where it should be occulted by the "mountain" if it were real!
* I conclude that the "dark spots" were either afterimages or bleached
* areas on the observers' retinas. We have no direct accounts from the
* other officers present; they would be unlikely to contradict their
* commanding officer, I suspect.
* Note that Korzenewsky (1923) says the distance claimed here was 1177 km
* but the actual value is just under 900 km.
*
* The title translates as:
*
* "Unusual phenomena of refraction observed in the Japanese Sea."
* "Read at the I.R.G.O. session for the sections of mathematical and
* physical geography, March 11, 1914"
* Reports of the Imperial Russian Geographical Society
*
* Of course the pre-Revolutionary alphabet and spelling are used:
*
* К. П. Іессенъ
* Необыкновенное явления рефракціи, наблюденное въ Японскомъ морѣ
* Известія Императорскаго Русскаго Географическаго Общества
*
*
* Early mention of "Crocker Land" in the London Times
* "Crocker Land" appears 5 times, in passing.
* Dateline is "from our correspondent", New York, July 7 (1908)
* Plans for the "Crocker Land Expedition"
* "It is estimated that not less than fifty thousand dollars ($50,000)
* must be provided for the absolute needs of the expedition, in order to
* enable it to accomplish the valuable results that have been outlined
* above . . . . Subscriptions to the fund are invited."
* At this point, the expedition was to have been led by George Borup,
* then only 5 years out of Yale, with Donald B. MacMillan.
* The start: it is now "George Borup Memorial" with MacMillan leader
* "The original program of work for the expedition contemplated two
* years or three summer seasons in the Arctic, but supplies have been
* taken north which will enable the party to remain three years or even
* longer . . . ."
* The New York Tribune announcement that "Crocker Land" was a mirage
* "The news that the land was not seen . . . where Peary sighted it eight
* years ago, was received yesterday by the American Museum of Natural
* History. The news was relayed . . . through the courtesy of Knud
* Rasmussen" who is quoted from an interview. The word was received
* second-hand from Ekblaw, who met Rasmussen's men while hunting.
* MacMillan's full report "will wait until spring at Upernavik for the
* first Danish boat to convey it to Copenhagen. The report will then be
* cabled to the Tribune . . . probably in April or May. . . ."
* Scientific American reports that the N.Y.Tribune is the "mouthpiece"
* of the Expedition, and reports that the news that "Crocker Land does
* not exist" was in the Nov. 25 issue of the Tribune .
* Donald B. MacMillan's report on the expedition, in HARPER'S
* Contains the first-hand MIRAGE reports.
*
* There's not much of interest in the first installment, except for a
* discussion on p. 654 in which he mentions that he made a point of
* getting rid of "the older and more influential Eskimos, who seemed to
* be very much afraid of walking home in case their dogs should die. In
* a discussion of this kind as to what they should do, the younger men of
* the party listen respectfully to the opinion of their elders and do as
* they advise. Young Eskimos on a long and dangerous trip are much to be
* preferred, for they are fond of adventure and willing to take a chance,
* while the older men wish to make certain of getting home." He then
* says, "From the sixteen Eskimos I picked out seven who appeared to me
* to be of the right stuff and who, I thought, would go the limit."
*
* The second installment tells of reaching "Crocker Land" and contains
* the various well-known (but usually uncited) quotations. Page 924:
* "April 21st was a beautiful day; all mist was gone, the clear blue of
* the sky extending down to the very horizon. Green was no sooner out of
* the igloo than he came running back, calling in the door, `We have it!'
* Following Green, we ran to the top of the highest mound. There could be
* no doubt about it. Great heavens, what a land! Hills, valleys,
* snow-capped peaks extending through at least 120 degrees of the horizon.
* Anxiously I turned to Pee-ah-wah-to, asking him toward which point we
* had better lay our course. After critically examining it for a few
* minutes, he astounded me by replying that he thought it was `poo-jok'
* (mist). Ee-took-ah-shoo offered no encouragement, saying, `Perhaps it
* is.' Green was still convinced that it must be land. At any rate, it
* was worth watching. As we proceeded it gradually changed its appearance
* and varied in extent with the swinging around of the sun, finally at
* night disappearing altogether. As we drank our hot tea and gnawed the
* pemmican we did a good deal of thinking. Could Peary with all his
* experience have been mistaken? Was this mirage which had deceived us
* the very thing which deceived him eight years ago? If he did see
* Crocker Land, then it was considerably more than one hundred and twenty
* miles away . . . ." On the next page he mentions "our almost constant
* traveling companion, the mirage. We were convinced that we were in
* pursuit of a will-o'-the-wisp, ever receding, ever changing, ever
* beckoning." He then quotes from Peary's "Nearest the Pole" book (but
* gives no page reference.)
*
* On the return trip (p. 927): "Throughout the day the mirage of the sea
* ice, resembling in every particular an immense land, seemed to be
* mocking us. It seemed so near and so easily attainable if we would
* only turn back." On p. 928, he is standing on "the very spot" where
* Peary "saw what resembled land. The day was exceptionally clear, not a
* trace of a cloud or mist; if land could ever be seen, it could be now.
* Yes, there it was! It could even be seen without a glass extending
* from southwest true to north-northeast. Our powerful glasses, however,
* brought out more clearly the dark background in contrast with the
* white, the whole resembling hills, valleys, and snow-capped peaks to
* such a degree that, had we not been out there for one hundred and fifty
* miles, we would have staked our lives upon it. Our judgment then as
* now is that this was a mirage or loom of the sea ice."
* Oct. & Nov. issues
* a MIRAGE review article
* A popular and not very critical review, prompted by the article in
* Harper's Magazine debunking Peary's "Crocker Land". The images are
* drawn in both inferior and superior mirages at exactly the same
* distance from the observer as the object. He thinks the intermediate
* images in multiple mirages are all inverted, with only the top and
* bottom ones erect. (p. 519)
* The striations of the Fata Morgana are supposedly "parallel with the
* axes of cylindrical air fields." [sic!] (p. 520)
* The rescue (3rd attempt!)
* Dr. Hunt has made it back, but MacMillan et al. are still isolated in
* northern Greenland. "Direct news" from MacMillan said "that he and
* his companions had only enough supplies to last them until August of
* this year" and that "both relief vessels sent to his aid, the
* George B. Cluett and the Danmark , have failed to reach him and urges
* that a third be sent . . . . This third effort to reach the party will
* cost at least $40,000, provided that the Neptune is able to reach the
* base at Etah . . . . The Committee hopes that in view of the extraordinary
* expenses it will receive substantial financial aid from the public."
* June 15 issue
* Further reports from Dr. Hunt
* The Danmark is stuck in 6 feet of ice and low on coal.
* June 29 issue
* Donald B. MacMillan's book
* This is the full text of the manuscript excerpted by Harper's in 1915.
* Some editor has now tidied up the prose a bit, restraining the somewhat
* breathless pace of the magazine version.
* Dr. Harrison Hunt's story, assembled by his daughter, Ruth Hunt Thompson
* Apparently, the Expedition came near mutiny because MacMillan traded
* necessary supplies to the Eskimos for furs; see p. 71.
* According to Dr. Hunt, MacMillan was irresponsible and had
* "hoodwinked" the Museum. His view was shared by Captain Comer [of the
* Neptune ], who told Hunt's wife that "The whole expedition was founded
* on selfishness. Peary reached a little too far, wished to see land,
* thought he did, and claimed it, resulting in the Crocker Land fiasco . . .
* MacMillan used the expedition as his plaything . . . Dr. Hovey was
* penny-wise and pound-foolish . . . The Cluett was a sailing vessel, not
* fit for a relief ship, and not properly prepared . . . The last two years
* were the hardest, and they were unnecessary." (p.107)
*
* See also p. 207 of T.Forster (1824) for a double lunar crescent
*
* Probably an early BLEACHING observation
* "La journée avait été superbe, le ciel était sans nuages et
* la mer tranquille comme un lac. Le soleil, fort près de l'horizon,
* était rougeâtre comme dans les couchers ordinaires, et son disque
* paraissait à l'oeil nu parfaitement bien terminé. Le bord inférieur
* toucha d'abord l'horizon de la mer, puis le disque s'y enfonc,a peu à
* peu sans se déformer et en conservant sa netteté. Au moment où le
* centre de l'astre atteignait la ligne parfaitement définie qui limitait
* l'horizon de la mer, la partie supérieure du disque, la seule qui fût
* encore visible, se teinta subitement en bleu. Cette teinte nous sembla
* uniforme; elle rappelait exactement le bleu des liquides renferme's dans
* les bocaux que l'on voit ordinairement sur les devantures des pharmacies.
* Ce phénomène persista tout le temps qu'on vit la partie supérieure
* du soleil. Aussitòt après le coucher, l'horizon présenta son aspect
* ordinaire. On distinguait encore, à quatre ou cinq degrés au-dessus
* du point où le soleil avait disparu, trois petits nuages sous-tendant
* chacun un angle d'un ou deux degrés : encore éclairés par le soleil,
* leur lumière était, comme avant le coucher, d'un rouge cuivre très-vif.
* Je n'était pas seul à observer ce curieux spectacle . . . . A quelques
* détails près, nous avons tous été d'accord quand nous avons rassemblé
* nos souvenirs."
* Thanks to Luc Dettwiller for finding this!
* This is the MULTIPLE LUNAR CRESCENT mirage reproduced by Minnaert!
* cf. Clark et al., M.O.1964, and Fultz, 1951.
* Iridescent corona? Or what?
* A curious observation -- not exactly a mirage, though.
* MULTIPLE IMAGE SPLITTING
* Probably not "abnormal refraction" at all, but an AFTERIMAGE report
* "The sun was setting, and about one minute after the sun's upper limb
* had completely disappeared below the horizon five completely circular
* images of the sun were seen to shoot up into the sky at about five
* second intervals."
* The Editor's comment that "it is obviously due to some peculiar form of
* abnormal refraction" is obviously wrong.
* MULTIPLE IMAGES OF THE SUN
* ?? Off-base comment on the preceding report
* Would be an ordinary inf.-mir. sunrise, but 1st drawing makes no sense.
* N.B.: later drawings use circles; so drawings may not be accurate.
* ANOMALOUS COLOR CHANGES of MOON
* "The moon also appeared to be changing colour from the normal yellow to
* green and deep red, and then back again, with a frequency of about 5 sec
* for the complete cycle."
* Otherwise, this would simply be a distorted moonrise.
* DOUBLE IMAGE of MOON
* The colors seen here suggest a grating image. There had been heavy
* rain; could this be a wet grating on a window?
* DOUBLE (??) IMAGE OF SUN
* Surely this can't be right! Because it was taken with a short (45mm)
* lens, and the photo shows cloud strips, I suspect this is simply an
* overexposed image divided by a strip of cloud. It seems impossible to be
* a refraction effect as claimed, at 7 deg. 20 min. above the horizon!
* another fishy-sounding report:
* ". . . disappeared when viewed through a telescope . . . "
* DOUBLE SUN
* "The image was to the right of the true sun, there being no distortion
* of either. This phenomenon persisted for 2 min, after which the image
* gradually elongated in the direction of the true sun, eventually merging
* with it within 1/2 min."
* I think the editor's remarks are off the mark ("lateral mirage").
* Certainly NOT a GF report; the colors sound like mother-of-pearl clouds,
* but the sharp outline is a puzzle.
* The editor's comments, which continue on p.278, are certainly off the mark.
* MULTIPLE LUNAR CRESCENTS
* MULTIPLE LUNAR CRESCENTS
* MULTIPLE LUNAR CRESCENTS
* The drawing is impossible -- something fishy here.
* (A crescent Moon cannot be seen when line of cusps is vertical.)
* Minnaert's review in JOSA
* Minnaert accepts the multiple images as real, largely because of
* Richard's photograph.
* PHONY MULTIPLE LUNAR CRESCENTS
* These multiple images appear to be caused by reflections between glasses
* and eyeball? They are CERTAINLY SPURIOUS, as "This phenomenon could not
* be observed through binoculars or a telescope, it was, however, seen
* through `Polaroid' sunglasses. The phenomenon was also observed, though
* to a lesser degree, on the next five nights."
* The appearance also changed with position of the head, etc.
* MULTIPLE MOONS
* Several disparate phenomena are reported, but treated as if they
* were identical. The original report sounds like a reflection, but too
* few details are provided to identify it. The "answer" provided by John
* Richfield "explains" the report as a mirage, which it cannot be (because
* of the duration of over an hour). Richfield also seems to confuse
* inferior and superior mirages, and understands neither. The second
* "answer", supplied by Hector McDonnell, is clearly a sundog report;
* but he attributes it to "reflection of the Moon and Sun at particular
* angles off the water droplets", which is bizarre nonsense.
* Thanks to Storm Dunlop for the reference!
* MULTIPLE MOONS
* A photograph that most likely shows a ghost image in the camera;
* certainly *not* an atmospheric phenomenon.
* Thanks to Storm Dunlop for a scan of the image!
* cf. photo in Gossard & Strauch book
* For early mentions of "fog", see Marra (1775?), Dickenson (1793),
* Mureau (1798, 1799), Beauford (1802). Kelly (1832), Parnell (1869),
* and Upham (1895).
* also: Schnippel; Bonnelance 1929; P&E pp.184-186 give a bad discussion.
*
* Many lights seen (looming?) from Staten Island at 8 pm, Aug.16
* "All this was seen right side up, and you can imagine how keenly we
* enjoyed it all and longed to reproduce it with a camera. After ten
* minutes during which time we went down to the beach (fourteen feet to
* sea-level), the vision passed suddenly away. At that moment the mirage
* cloud, which was before invisible, was seen. Then we saw in the usual
* place the real lights of Coney Island. This cloud was entirely
* horizontal, very narrow, black, and stationary."
* "The objects of this note are two: the first is to inquire whether there
* is any popular name for the phenomenon, which is, I am told, well known to
* sailors; the second is to ask for references to any measurements of sea
* and air temperatures in conjunction with observations of this character."
* "At about mid-day peculiar cloud effects were noticed on the horizon,
* giving the appearance of a well-wooded tropical coast line. This became
* somewhat indistinct until 16 h. 30 m., when a faint darkness appeared on
* the horizon, increasing in density and in its liquid appearance until
* objects were noticed in an inverted position at an altitude of about two
* degrees [!] above the horizon."
* "FOG" and STRIPES and mirages; TEMPERATURE of air about 4 deg. above water
* ". . . über dem ganzen Horizont ein mehr oder weniger starker
* Dunstschleier,. . . " followed by mirages of ships and looming of lights.
* "Gegen Abend bildeten sich in geringer Höhe über der Kimm die bei
* Luftspiegelungen gewöhnlich auftretenden Streifen, besonders am
* westlichen Horizont, also gegen die Sonne . . . ."
* N.B.: The Gulf of Chihli is the NW arm of the Yellow Sea, usually
* denoted as Bo Hai today, where the Yellow River has its mouth.
* November issue
* Might be REAL FOG in the Straits of Belle Isle?
* "At 8h. on August 17th, . . . although it was perfectly clear and
* sunny where I stood on the shore, there was an extensive layer of fog
* at the scene of operations, about three miles out, and only the smoke
* of the Empress was visible above the layer. . . . I was startled to
* see the Empress above the fog completely upside down with her hull
* pointing skywards and her masts apparently resting on the layer of fog.
* The illusion lasted for about one minute and was perfectly clear in
* every detail when it finally disappeared and the ship came out of the
* fog in its normal position.
* "On a previous occasion I saw three mountains on the Newfoundland
* coast, fifteen miles distant; their summits appeared to be resting on
* the water while the bases were pointing skywards."
* Dec. issue; cited in Hurd's review
* Willis Edwin Hurd's mirage review speaks of "MOCK FOG"
* [Filed separately, because of bulk]
* A review of observations, mostly from the later 1920s and a few from
* the early 1930s; most taken from Marine Observer, but a few "from the
* Hydrographic Bulletin, published by the U.S. Hydrographic Office."
* There is a clear explanation of the terminology, but the observations
* are sometimes misinterpreted, and he seems to count looming in with
* mirages. He unfortunately also says the visibility of objects above
* the horizon when they are geometrically below "is of course an optical
* illusion." [middle of 4th paragraph]
* In the middle of col. 3, he first says ". . . along the line of
* sharpest density change . . . " and then later ". . . a further line of
* density discontinuity." Could this be where O'Connell got the notion
* of "surfaces of discontinuity"?
* The lower part of Col.4 discusses the effects of height of eye, and
* distance to the miraged objects.
* The end of col. 5 discusses "mock fog and haze bands". The "fog"
* aspect is emphasized throughout the paper. He also uses the phrases
* "simulation of fog" and "optical haze".
* The bottom of col. 6 mentions "waterfalls" that are apparently
* either discontinuities in the "horizon", or Lehn's "sea fences".
*
* Cites Barlow (1935, in "Mirage File"), as well as several other
* sources. Because of the large size, this is printed in 8 columns.
* This is known to have appeared on the backs of many Pilot Charts;
* I have seen references to ". . . of the Central American Waters" as
* late as 1944.
*
* THANKS to many people for finding this elusive item! Brenda Corbin
* was instrumental in getting in touch with the NIMA people, who
* eventually came up with it. I had references in the 1930s and '40s;
* but the last paragraph is a post-script saying that Barlow's article
* had appeared "Since preparation of the present . . . article". So the
* writing was evidently done by early 1935. According to Howard J. Cohen
* at NIMA, this was actually published in 1937. Finally, the chart was
* found in a *bound* volume by Albert E. "Skip" Theberge, Jr., at NOAA!
* But, as the format was about 3 ft by 4 ft (that's 75 x 100 cm for the
* metric part of the world), it was too big to photocopy. . . .
* He finally managed to get it photographed and scanned (as a 214 MB
* TIFF file!) Thanks to all these people for their Herculean efforts!
* "When a gray, rather smoky and unnatural-appearing cloud lies along the
* horizon in the early morning, it is generally mirage material. Such a
* cloud will usually form into a clear cut mirage before the morning passes."
* "One fresh morning last autumn . . . a smoky, unnatural cloud graced the
* horizon to the southwest."
* "In the atmosphere at each end of the display the scenery feathered out
* into a misty cloud, which in turn extended ever dimmer into the clear
* sky."
* "The apparent bank of fog was probably an effect of mirage of the horizon."
* Air was 4 F warmer than sea.
* Note: this is shortly after M.O. resumed publication after WW II.
* "From afar, it appeared as if the whole coastline was engulfed in a belt
* of fog with the higher land showing clear."
* "Air temperature 60 F, wet bulb 57, sea 55. The wind was light and
* variable."
* "Approaching Cape St. Francis, a white mist appeared to creep under the
* land and apparently divided it from the sea." See Plate 2, facing p.128
* Here the band is described as a "DUST STORM"
* DOUBLE IMAGES appear in the "dust" band (with its "sharp top outline"!)
* EXCELLENT detailed account of "FOG"
* flanked by rather ordinary mirage reports.
* ". . . what at first appeared to be a fog bank proved to be a mirage.
* With the coastline on the starboard side, distant 15 miles, a dark-blue
* mass, having every appearance of land with undulations as of hills, was
* seen on the port bow from about 4 points to 1 point off the bow where it
* faded into a white band above the horizon."
* ". . . the smoke from these whalers and from our own ship did not rise
* above mast height, but flattened out and hung in the atmosphere in a great
* band about 100 ft above sea level."
* Many nice details of observation, including the effect of eye height.
* ". . . a greenish fog or smoke bank . . . "
* ". . . a heavy whitish mist . . . "
* RED LINE MOONRISE (filed in wrong file here; on same page as previous)
* Seems to be also an example with a dark strip of sky at horizon (false hor.)
* ". . . was obviously in, not on, the water. . . . The moon then rose and the
* red, flame-like light disappeared, to be replaced by two half-moon shaped
* glows in the water."
* Probably belongs in "distorted" file?
* NICE SKETCH
* ". . . the lower ridges were obscured by a grey haze in which appeared
* many inverted icebergs. . . ."
* "All round on the seaward side, there was what looked like a high thick
* bank of fog, which at times resembled a mountainous coastline. This was
* found to have no real existence as it continued to recede as the ship
* advanced."
* NICE DRAWINGS
* ". . . towards sunset, when the sun's upper limb was still well above the
* horizon, an inverted image of this limb, but smaller in area, appeared
* beneath a narrow band of Sc lying very low on the western horizon."
* (Dwg. says "layer of stratocumulus not formed by the spreading of cumulus"
* and it is drawn absolutely flat -- blank strip?)
* NICE DRAWINGS
* "The presence of a heavy grey-brown mist for much of the day gave rise
* to the impression that there was a double horizon. . . . Cliffy Island
* and other small islands appeared very clearly on the `upper' horizon while,
* projecting downwards from them, was a mass of wavy-looking grey-green mist
* and haze." (triple images, a pair between the horizons)
* "Air temp. 81 F, sea 69."
* NICE DRAWINGS of DISTORTED MOONRISE
* (belongs elsewhere, but is filed here because of the next item)
* NEGATIVE DIP
* "During the afternoon the horizon was elevated by between 7 and 10
* minutes of arc above what appeared to be the normal sea horizon.
* All round the horizon there was a band of what looked like fog or mist
* but, on approaching the land, this mistiness disappeared."
* [Note observation of CONCAVE surface.]
* DOUBLE DARK BAND sketched -- just sup. mirages of the ocean?
* ??? This seems to call for a weak duct inside a stronger one.
* "Around the horizon there appeared to be a large bank of fog, topped by
* two thin layers of low stratus. Beneath each layer of cloud there was an
* inverted image of the tanker. . . ."
* ENLARGED DRAWING OF STRUCTURE
* ". . . the horizon appeared to become raised above the sea and separated
* from it by an indistinct misty band. . . . (opposite to the sun) the
* appearance was that of a bank of fog."
* ". . . a layer of haze, dark grey in colour and with a clearly defined
* upper surface, was seen all round the horizon. One ship appeared to be
* completely inverted and an iceberg which was not visible to the naked eye,
* seemed to be hanging upside down from the top of the layer."
* DOUBLED CRESCENT MOON like the one shown in Minnaert (Reimann, 1887)
* (same page as above; belongs in STRANGE PHENOMENA file)
*
* JEAN JACQUES D'ORTOUS DE MAIRAN's first paper on extinction
* He supposes the temperature difference between summer and winter is
* partly due to absorption of the Sun's heat in the atmosphere.
* Curiously, he invokes what is essentially Lambert's [1760] cosine law,
* by introducing the sines of the angles of "incidence" [by which he
* clearly means the altitudes, not the usual angle]; but then decides
* the factor of 3 between the noontime illuminances ought to be squared
* to allow for shadowing by irregularities (pp. 106-107).
* Then he worries about the reflection loss at the upper surface of the
* atmosphere, which he argues might increase with obliquity, as does the
* reflection from water into air as the angle of total internal reflection
* is approached (p. 110). [There is an interesting quote from an earlier
* author about this surface.] But he decides that this is not what happens;
* on p. 111 he argues that the disappearance of the refracted light is
* abrupt. So he thinks the winter attenuation is due to the longer path.
* "Chaque rayon prêt à entrer dans l'Atmosphere, peut être consideré
* comme une balle de Mousquet tirée contre la surface de l'eau d'un
* Bassin, laquelle aura d'autant plus de chemin à faire dans l'eau,
* avant que d'en toucher le fond, qu'elle y fera tirée plus obliquement."
* So he argues that the path is inversely proportional to the sine of
* the angle of incidence, and that the intensity should therefore (!) be
* reduced by this factor yet again. (p. 112)
* But then he has doubts, and wonders about an atmosphere "chargée
* de vapeurs & d'exhalations, telle qu'elle est ordinairement dans toute
* sa partie inferieure, lorsque le Soleil est proche de l'Horison, &
* sur-tout en Hiver." (p. 113).
* He then makes the interesting observation that, at solar eclipses,
* one hardly notices the diminution of the light until the Sun is almost
* completely covered: ". . . j'aurois cru qu'au moins le tiers ou le quart
* de son disque venoit de se découvrir, & ce n'en étoit pas peut-etre
* la milliéme partie." (p. 115)
* On p. 118 he considers the length of the day as a factor. On pp.
* 127-128, he notes that refraction lengthens the day a little; but this
* "est de peu de consequence." [But he thinks it might be important
* near the Poles; and adduces (p. 129) the observations of Bilberg, and
* the Dutch "dans la Nouvelle Zemble."]
* The rest of the paper is an attempt to square his numbers with
* actual temperature measurements. Really, a rather muddle-headed
* attempt all around.
* DE MAIRAN's "Clarification"
* Here he realizes that the extra-atmospheric light of the Sun
* can be extrapolated from two measurements inside the atmosphere.
* Unfortunately, he assumes the light lost is proportional to the
* path length in the atmosphere -- wrong, but not bad near the zenith.
* [But at the horizon, the setting Sun disappears in his model!]
* He assumes a plane-parallel atmosphere (p. 10). He neglects refraction.
* The path lengths are, of course, inversely proportional to the sines of
* the altitudes.
* In section II (p. 12) he considers the curvature of the atmosphere.
* However, he takes the height of the atmosphere to be 15 leagues of
* 2000 toises each, which is much too large; and consequently finds the
* horizontal path to be only 15 times the vertical one. (p. 13)
* "J'ai supposé AT de 20000 toises ou de 15 lieuës, qui est la
* hauteur qu'on donne aujourd'hui le plus communément à l'Atmosphere.
* . . . en faisant AT de 20000 toises ou de 10 lieuës, on trouve AH plus
* de 18 fois aussi grande que AT , . . . & en ne donnant que 1000 toises,
* ou environ demi-lieuë à AT , AH devient environ 74 fois aussi grande
* que AT . D'où il resulte . . . Que lorsque le Soleil est à l'horison,
* les vapeurs doivent nous intercepter une beaucoup plus grande partie de
* la lumiere que ne fait l'Atmosphere, non seulement parce qu'elles sont
* composées de parties plus denses, & peut-être moins transparentes que
* l'air, mais encore que se trouvant d'ordinaire fort près de la surface
* de la Terre, la ligne horisontale qui les travers a un beaucoup plus
* grand rapport avec leur hauteur. . . . Donc des vapeurs qui ne sont point
* du tout sensibles à la vûë, dans le cas des rayons perpendiculaires
* ou peu obliques, doivent affoiblir sensiblement la lumiere du Soleil
* cans le ca de la grande obliquité, & lorsqu'il approche de l'horison:
* ce qui s'accorde parfaitement avec l'experience . . . ." (p. 16)
* On p. 17, he suggests that this obliquity to the vapors might explain
* the variations in the refraction near the horizon as well: "D'où il
* suite que des vapeurs de même nature & de même densité doivent
* donner une refraction horisontale d'autant plus grande, qu'elles sont
* moins élevées, ou que la couche qu'elles forment sur la surface de la
* Terre est moins épaisse."
* PIERRE BOUGUER's first photometric measurements, inspired by de Mairan
* Evidently written by the secretary, rather than Bouguer himself:
* "M. Bouguer, . . . dont nous avons déja parlé en 1721, ayant lû les
* Mémoires donne's par M. de Mairan en 1719 & 1721 . . . , chercha les moyens
* de découvrir par expérience le rapport des diférens degrés de lumiere
* du soleil à différentes élevations . . . ."
* Bouguer's measurements of extinction, and of the ratio of Sun and Moon,
* are reported here. The first date reported is 23 Nov. 1725.
* The copy on Gallica shows 1753 as the publication date on the title
* page; that must be a reprint, as Bouguer corrects a typo on p. 12
* of it in his 1729 "Essai" (below). There are other typos here, too:
* e.g., "lamiere" on p. 11.
* PIERRE BOUGUER's "Essai" (1729)
* Bouguer corrects de Mairan's faulty assumptions, and publishes his own
* airmass table. Only 164 pages are numbered.
* In the Preface, one reads that "C'est Snellius qui a le premier
* découvert la loi de ces réfractions; mais M. Descartes la considérant
* de plus près, en a poussé l'application extrêmement loin." He cites
* de Mairan's 1721 memoir, which inspired his own investigation.
* He also corrects a typo from his 1726 entry in the Histoire .
* de Mairan is cited again on p. 21. He then describes his observations
* of the Moon, and its attenuation at the horizon, "sujet à de très-grande
* varietez;" -- ascribed to "vapeurs", of course. He then endorses de
* Mairan's notion that this is connected with the variations of refraction
* at low altitudes. (p. 25)
* In paragraph VII, p. 28, he compares the Sun with the full Moon, finding
* a ratio of about 300 000.
* His detailed discussion of atmospheric transmission begins on p. 146.
* Here is the origin of the term "air mass". The "Table des masses d'air"
* appears on p. 160. See Bemporad's criticism of Bouguer's derivation.
* The curious remarks about refraction (see next entry) are on p. 151
* here. Most of this atmospheric discussion is reprinted unchanged in the
* 1760 Traité (below).
* PIERRE BOUGUER's "Prize Essay" (1729)
* The first part discusses instruments and their use; the second, the
* necessary corrections to the observations, for both refraction and dip.
* Our concern here is in the corrections, which begin on p.35 [image 46
* of the PDF cited below.]
* Bouguer immediately points out that the angles made by the rays with
* the spherical surfaces of the atmospheric layers are changing with
* distance, and that "cette diversité d'angles d'incidence . . . vient
* principalement de la courbure des couches . . . ." This is why one can
* not apply the famous theorem promoted by Newton in his Opticks to
* the atmosphere. However, on pp. 41-42 a similar invariant for
* the curved atmosphere appears: ". . . les perpendiculaires tirées
* du centre de la terre sur les tangentes de cette courbe, seront
* continuellement proportionelles aux . . . des dilatations . . . ." (This is
* all done in geometric terms, using proportions; but basically he has
* the refractive invariant here.) In the process, he has developed the
* differentials of refraction at each level in the atmosphere.
* Bouguer calls the curved path of the ray "le Solaire", and is
* concerned to find its shape. By taking account of the curvature of the
* Earth and its atmosphere, he assumes that the ray makes the same angle
* at each spherical surface, so that the ray paths are logarithmic spirals
* [p. 43].
* On p. 44, he does the inverse problem, and introduces the sine of the
* apparent zenith distance at the observer, calling it c . This angle is
* the complement of the apparent altitude of the star. [Two decades later,
* he develops this theory more clearly, in his "Second Memoir" published
* in 1753.]
* On p. 47 he writes down an integral for the astronomical refraction.
* His ignorance of the gas laws leads him to believe that the refractions
* are caused by a "refractive material" different from air. [p. 48].
* (His problem is that he expects the refractive index to be the same
* thing as the "refractive power " -- i.e., the refractivity.) So he
* assumes that the sines of the angles are some power of the dilations
* of the air, and that these are proportional to some power of the
* distance from the center of the Earth. But these "dilations" are (in
* modern terms) just inversely proportional to the refractive indices.
* So in fact, this amounts to an assumption that the refractivity is a
* power of the radius, which is equivalent [we now know] to assuming the
* density to be a power of the pressure: he has accidentally adopted a
* polytropic model! So, luckily, he finds his model gives a refraction
* that is a constant fraction of the horizontal arc traversed by the ray
* -- "which is very remarkable!" [p. 49]
* As his Fig. 11 is already too cluttered with about 30 labelled points,
* he removes some of them to make room for more labels, in Fig. 12. Here
* again (p. 50) we have the complement of the apparent altitude of a star.
* So [p. 52] he can construct his refraction table geometrically from
* his logarithmic spiral, given the exponent in the power law. In §.L.
* [p. 53] he explains the details of this process, which requires finding
* the exponent m and the height of the atmosphere. "But nothing is
* easier than to discover these two quantities," says Bouguer [p. 54]
* (though Cassini had a much harder time to do so in a simpler model).
* He has only to fit his model to exact observations of the refraction at
* two different apparent altitudes. He assumes the horizontal refraction
* is one of the known values, and derives an expression for the refraction
* at some other altitude. He then develops an iterative solution for the
* two parameters; this involves the ratio of the sine and cosine of the
* apparent altitude.
* In fact, he calls the sine of the apparent altitude q and the sine of
* its complement (i.e., the zenith distance at the observer) p . (P.54)
* In §.LII. [p. 56] he then shows how to calculate refraction for any
* given altitude -- i.e., how to build a refraction table. He adopts
* 33' for the horizontal refraction, and 2' 12" for 26° altitude.
* These values allow him to compute a new refraction table; he does the
* calculation using 7-place log tables. His new table of astronomical
* refractions is on p. 59 [PDF image 66]. The values are about 10% too
* high, but they do increase steadily near the horizon.
* In §.LVI. [p. 61] he compares his results with the works of Tycho and
* Cassini II.
* On the next page (and Chapter), he discusses the dip of the horizon.
* His dip table [p. 65] is for heights in feet and inches, as the metric
* system had not yet been invented. But on the next page, he points out
* that the ray curvature should decrease the dip slightly. And on the
* next page, he begins the investigation of this correction. And on
* p. 70, he gives a revised dip table.
* Unfortunately, on p. 72 he blames the irregularities of refraction on
* the "vapeurs qui se soutiennent dans la partie basse de l'Atmosphere,"
* and so excuses any discrepancies between his tables and observations.
* Available at https://www.e-rara.ch/zut/content/titleinfo/746433
* NOTE: the text is often obscured by wrinkles in the paper.
* DOI: http://dx.doi.org/10.3931/e-rara-2231
* A MUCH better scan is available at
* https://bvpb.mcu.es/es/consulta/registro.do?id=576360
* Thanks to Luc Dettwiller for this link!
* PIERRE BOUGUER's posthumous "Traité" (1760)
* There is an interesting Preface ("Avertissement") by the Abbé de la
* Caille, who edited Bouguer's work and saw it through the press.
* Bouguer has some curious remarks about refraction (pp. 326-327):
* "Il faut remarquer, que nous négligeons ici la courbure que
* la réfraction fait souffrir aux rayons de lumiere, quoique cette
* courbure les rende un peu plus longs. Il est certain que la réfraction
* astronomique est trop petite , pour que le rapport des sinus d'incidence
* & de réfraction soit conforme à celui des densités de l'air.
* La réfraction suit certainement un autre rapport ; & peut-être
* aussi qu'elle est causée par une matiere particuliere répandue dans
* l'Atmosphere, comme l'ont déja soupçonné quelques Auteurs."
* He then shows how the problem is more complicated if refraction is
* included, so "qu'il est très-difficile de découvrir la relation que
* suivent entr'elles les condensations u de la matiere réfractive; &
* d'ailleurs comme la plus grande réfraction astronomique n'est pas même
* de deux tiers d'un dégré, nous ne rendrions pas notre calcul beaucoup
* plus exact. C'est pourquoi nous négligerons la réfraction . . . ."
* The airmass table is on p. 332. This is available at Gallica!
* Note the English translation by W. E. Knowles Middleton (Toronto, 1961).
* LAPLACE
* Ch. I begins the treatment of refraction; Ch. III is the extinction theorem
* See fuller treatment under "General refraction references".
* FORBES EFFECT -- Forbes's Bakerian Lecture
* See the interesting discussion of Laplace's theorem, and airmass
* generally, in section III, pp. 233-241.
* Forbes says (p.234) that Lambert derived the sec z formula as an
* approximation to the path length in the uniform model, citing p. 393
* of Lambert's Photometria . He has some criticism of L. on p.235.
* Note his treatment of the refraction law on p.237:
* after stating the ratio of sines, he says, "This optical principle
* is derived from experience." [So much for Descartes!]
* Maximil. Julius Maurer's feeble effort
* The historical part is weak, depending mostly on Bruhns for the
* refraction. He shows how little had been done in extinction; this makes
* Bemporad's later remarks about neglect more comprehensible.
* See pp. 21-22 for some snide remarks about Lambert, who thought sec z
* was adequate to 80°. Maurer denotes the airmass function as \Sigma.
* On p.22, he introduces Laplace's theorem, though without understanding
* well the importance of the isothermal assumption.
* On p. 34, there is a curious digression into the arguments of Cheseaux
* and Olbers, and then W. Struve (p. 35) for the absorption of light by
* dust ("fein zertheilter ponderabler Materie im Weltraume") in space. (p.1)
* The more interesting attempt to calculate airmass begins on p. 41;
* but, alas! he adopts an effective height of the atmosphere of 65 km
* (p. 51) and so greatly overestimates the curvature effects. So his
* airmass table (p. 53) gives only 14.961 at the horizon!
* Interestingly, he already (p. 55) points out that the use of
* time and spherical astronomy to calculate ZD gives "die w a h r e n
* Zenithdistanzen der beobachteten Sterne" in Seidel's work.
* This is Maurer's 58-page Inaugural-Dissertation, done under Rudolf Wolf.
* FELIX HAUSDORFF's Habilitationsschrift
* Yes, this is the famous topologist; he started out as a student of
* Heinrich Bruns, writing a thesis on refraction in 1891.
* The style (and notation) is similar to Bruns's: clear, explicit, and
* original. Following Bruns (1891), he immediately notices the important
* product r⋅μ, which he denotes by ν (p.402). He notes (p. 403)
* (cf. Bruns's p.169 footnote) that the refractivity can be proportional
* to [(almost any power of the refractive index) - 1], so that we can
* choose the power to make the integrals easy --- noting that T. Young had
* already made the choice (as he does here) of the first power, in his
* Nautical Almanac tables.
* P.407: he notes there is a formal relationship between the power
* series for refraction and extinction (in terms of powers of tan Z); but
* "Es wäre zwecklos, diese sehr complicirten Ausdrücke aufzustellen,
* da eine Ermittlung . . . aus den Beobachtungen direct . . . wegen der
* Unsicherheit der Messungen im Horizont ganz illusorisch wäre."
* P.408: He describes the airmass "als reducirte Weglänge des
* Strahles" and shows how the extinction can be expressed in magnitudes.
* P.412: He notes that Laplace's approximations have neglected an
* appreciable term, so that the ratio of extinction to refraction contains
* a factor of 1/10 in the zenith, but 1/7 at the horizon. ". . . die
* Laplace'sche Formel . . . die hier dem Gliede erster Ordnung entspricht,
* ist also entschieden unvollständig. Dass sie trotzdem . . . nahezu
* dieselben Resultate ergiebt wie die strengere Formel . . . , liegt daran,
* dass die . . . Coefficienten . . . bis zu hohen Zenithdistanzen einander
* nahezu proportional laufen . . . ."
* P. 417: he recommends a ZD near 87° as a fitting point, in fitting
* 3 parameters (the other two being at Zenith and Horizon).
* P. 420: He notes that twice the path, where the ray is horizontal,
* gives values needed for the theory of lunar eclipses.
* P. 421: note remark on semiconvergent series for Kramp's function.
*
* In Section II (p. 422), he takes a more general approach to resolving
* the discrepancy between theory and observation, by abandoning Laplace's
* proportionality between density (i.e., refractivity) and extinction.
* He notes (p. 423) that this assumption leads neither to closed-form
* expressions nor to a good agreement of theory and observation; while
* taking the absorption as an arbitrary function of height allows a test
* of assumptions about the atmosphere, while operating with closed-form
* expressions instead of series expansions. Here he takes the (nR)
* product as the independent variable!
* This leads (p. 427) to a more general relationship between refraction
* and extinction than Laplace's formula, and one which has "den viel
* weiteren Sinn einer Functionalbeziehung, eines »heuristischen Princips«
* . . . ." (There is still the form of Laplace's relation, though.)
* Semiconvergent series again appear on pp. 431 and 433, as ways to
* evaluate Kramp's (and related) function(s).
* On p. 439, he derives a generalized form of Lambert's extinction
* formula, attributing the simple sec Z form to Pouillet.
* With his decomposition of the extinction into component terms, he
* can represent the observations tolerably exactly -- indeed, I must say
* this is greatly over-analyzing the (rather shaky) data (pp. 440-441).
* On p. 442, he admits as much, pointing out that the result is not
* physically possible: ". . . also die Darstellung der Müller'schen Zahlen
* auf diesem Wege illusorisch ist." (The absorptions become negative.)
* Consequently, in section III (pp. 445 ff.) he investigates what is
* physically possible (i.e., sets limits on the possible extinction
* corrections to the zenith, assuming a positive absorption coefficient
* throughout the atmosphere.) This is done very elegantly by investigating
* the mathematical properties of the extinction integral. The result
* (p.451) is that Müller's values up to 70° ZD cannot represent a
* physically possible run of the absorption coefficient in the atmosphere:
* ". . . die Potsdamer Zahlen wären also in den mittleren Zenithdistanzen
* erheblich zu gross." [So here we see that rara avis , a theoretician
* who actually can detect bad observations!] He tries a more complicated
* (2-term) fit, with similar results: "Diese Zahlen lehren, dass der
* Müller'sche Werth für θ = 75° um mindestens 8 Einheiten der
* letzten Stelle zu gross ist; wollte man ihn beibehalten, so käme man auf
* enorme Widersprüche in den nächsthöheren Zenithdistanzen, z. B. für
* θ = 85° auf eine Mindestabweichung von 0.160."
* Adding more terms to fit more points makes matters worse (p. 452); so
* "Wir schliessen . . . dass eine absolute Darstellung der Müller'sche
* Zahlen durch einen zulässigen Werthverlauf . . . unmöglich ist. . . .
* Auf eine Fehleranhäufung zwischen 60° und 80° liess auch der Gang
* der Widersprüche zwischen M und Laplace schliessen." [ M = Müller ]
* On p. 454, he shows that a fair fit to Müller's data can be obtained
* with a simple rational formula; however, it allows no significant
* improvement. On the next few pages (455-457), he shows that a
* considerably better fit can be obtained by adding a thin absorbing layer
* to the normal atmosphere. This layer turns out to have a height between
* 50 and 170 km; he suggests it could be meteoric dust. [Perhaps it's
* an alias of the ozone layer?] In the subsequent discussion (p. 458),
* he remarks that two acceptable formulae can give quite different zenith
* transmissions; "dies errinnert uns daran, dass Beobachtungen einer
* Station in verschiedenen Zenithdistanzen noch nicht genügen, einen
* Schluss auf die Constitution der Atmosphäre zu begründen, sondern durch
* Beobachtungen auf Stationen verschiedender Meereshöhe zu ergänzen sind."
* He even considers formulae that allow absorption in space, wherein the
* excess of the horizontal over the vertical extinction would be due to the
* one-Earth-Radius longer path length at the horizon! "Derartige Curiosa
* sind bei Formeln mit unendlicher Atmosphäre, die sich der Beobachtung
* einigermassen anschliessen, zwar nicht zu befürchten, wohl aber, dass
* sie den Transmissionscoefficienten zu klein ergeben." (Variants on this
* theme, in which the infinitely thin absorbing layer is replaced by some
* formula with a maximum high in the atmosphere, are also explored.)
* In comparing a number of these variants with observation, he finds
* (p. 463) that there is a tradeoff between the deviations between 60 and
* 80°, and those between 85 and 87.5°: one increases while the other
* decreases. So all these models are so similar that one can only
* conclude "dass die absorbirende Kraft der Atmosphäre zwar zuerst
* mit wachsender Höhe abnimmt, in grösseren Höhen aber (50 bis 200 km)
* wieder merkliche Werthe besitzt."
* In the next section (pp. 464 ff.) he considers additional data, which
* help limit the possibilities. One is the run of the data near the
* horizon: "Für die Horizontalabsorption finden sich aus unseren Formeln
* alle möglichen Werthe bis zu ∞ . . . ." But more important is the
* comparison of data from different heights above sea level. For this,
* he uses Müller's observations from Säntis. These allow some of the
* worst models to be rejected.
* Note: on p. 469, he points out that both Müller's tables and Seidel's
* use true rather than refracted zenith distances as arguments.
* P. 472: at last he comes to Langley's objections (i.e., the Forbes
* effect). He develops this theory in general terms, introducing a
* function s that is the base-10 equivalent of sinh(x)/x. He then
* finds (p. 478) that introducing this effect greatly improves the
* agreement with observation, but without greatly changing the zenithal
* transmission value for integrated light. (Unfortunately, he does not
* cite Forbes's paper.)
* P. 480: "Diese Rechnungen mögen genügen, um zu zeigen, dass man
* mit der Langley'schen Bemerkung in der That einen weit besseren Anschluss
* an die Beobachtungen erzielen kann als durch die Laplace'sche Formel."
* But (p. 481) the zenith transmission for integrated light is always
* close to 0.8, not Langley's 0.6.
* The conclusions of the paper are summarized on p. 481.
* NOTE: This volume is available at Google Books.
* AZEGLIO BEMPORAD's AIRMASS TABLE
* ``Ein mit der astronomischen Strahlenbrechung sehr verwandtes Problem
* ist das der Extinktion des Lichtes in der Erdatmosphäre. Während wir
* aber von Kepler bis Radau eine grosse Zahl von Theorien der Refraktion
* verzeichnen können, fehlt es bis jetzt überhaupt an einer Theorie der
* Extinktion des Fixsternlichtes, welche mit ähnlicher Strenge und
* Vollständigkeit wie die ersteren entwickelt ist. Dies kann Überraschen,
* wenn man die Wichtigkeit und das immer mehr sich steigernde Interesse
* bedenkt, welches die photometrischen Beobachtungen seit Jahrzehnten
* geniessen, und noch mehr, wenn wir die bis jetzt entwickelten Theorien der
* Extinktion mit den umfangreichen Beobachtungsarbeiten auf demselben
* Gebiete vergleichen.'' [1st para. of Intro.!]
* Bemporad, like Forbes, criticizes Lambert (p.8) for his empiricism.
* The historical review is mostly devoted to the isothermal model and
* Laplace's theorem. However, B. shows that the homogeneous model has
* a series expansion in which the second term already has half the size
* of that for the isothermal model (p. 11); thus there is no equivalent
* of Oriani's theorem for extinction.
*
* B. adopts gradient of 6.22 deg/km to at least 9 km (maybe all the way?)
* (n-1)2 = 1.0005864 for 0 C and 760 mmHg
* R = 6377.36 km; g=9.8052m/sec2; p=1013.168 = 760 mm
* finds M(87)=15.364; 88: 19.787; 89: 26.959; 89.5: 32.332; 90: 39.651
* adopts gradient of 6.21 deg/km in summary table (?).
* finds M(87)=15.365; 88: 19.787; 89: 26.959 in F(z) table.
* Published by "W. Valentiner" (Karl Wilhelm Valentiner, says Wikipedia.)
* ROHLFS mentions Bemp. and Schoenberg, calling airmass X(z)
* He gives the airmass integral, and then: "Bemporad [no citation] and
* Schönberg (see Schönberg (1929)) have done extensive investigations
* of X(z), and a Chebyshev-fit to these data up to X = 5.2 with an error
* of less than 6.4 ⋅ 10-4 is given by" a cubic polynomial in sec z.
* "Such a formula should indeed be used in radio astronomy because
* measurements are often made at zenith distances up to 80° (or even
* more!)" [p. 166]
* On p. 168, he gives an expression for the radio refractivity,
* and suggests that an error of 15% would be acceptable, so that "mean
* refraction can be used and this closely resembles the optical refraction.
* Therefore for z < 80°
*
* Δ z = β tan z , β = 1.'50 .
*
* The ratio of radio to optical refraction is . . . 1.56; thus for larger
* zenith distances, optical refraction tables can be used, provided the
* result is correspondingly multiplied." Tsk, tsk.
* My Airmass approximations for geometric ZD
* Eq.(6) is faulty, and should be ignored. And I misspelled Abalakin's
* name.
* L. Kahl Kristensen rediscovers Laplace's theorem and the rational approx.
* with comments on Wittmann's refraction paper. He shows the constancy of
* the ratio r(z)/(M(z)*sin z) for the std. and isothermal models.
* He cites Newcomb's unreliable text for the refractive invariant, and
* uses the old ICAO atmosphere -- which he apparently does not realize is
* different from Bemporad's model.
* Unfortunately, he only fits the Pulkovo table for mean refraction, so
* the claimed high accuracy of the fit is of little practical use.
* Thanks to ADS for making this available! Their scan is better than
* the Wiley one; but Wiley's has OCR'd text, and ADS does not.
* Chambers knows about Laplace's theorem, but . . .
* . . . proposes to use it to calculate airmass for photometric reductions,
* via the Saastamoinen method for calculating the refraction! (pp.142-143)
* There are also some other scary bits, like giving a CO2 refractivity to
* 3 sig. figs. without a dispersion term, and the use of a scale height
* that assumes a fixed water-vapor mixing ratio, and "the local radius of
* the reference ellipsoid" for the radius in calculating h/R . . . .
* [This group's use of square-sided passbands also does not increase
* confidence that they know what they are getting into.]
* Sergey Kivalov's new method of calculating airmass
* Siebren's comment on Sergey's paper
* "Ray tracing by path length is shown to avoid singularities both at
* the horizon and in the zenith. A fourth-order Runge-Kutta numerical
* integration scheme is presented, which treats refraction and air mass
* as path integrals."
* Interesting comparison of choices of independent variables.
* These guys took up my suggestion to show that the "mapping function"
* of the radio scientists is essentially the airmass function.
* Available at: https://doi.org/10.1029/2008JD010176
* Fine REVIEW of 26 airmass approximation formulae
* Jeffrey G. Mangum and Patrick Wallace review refraction and airmass
* for radio astronomers. There is much emphasis on water-vapor effects
* at microwave frequencies.
* They cite my 2004 AJ paper but not the 2006 tutorial paper in Obsy.,
* or the 2008 and 2011 papers by Ígor Rapp-Arrarás and Juan M. Domingo-Santos
* cited above.
* Don't overlook their 2-page Erratum on pp. 500-501, which corrects some
* serious errors in the original paper.
* Cong Qiu and many co-authors compare "mapping functions"
* Here the tilt effect appears as "atmospheric gradients" or "atmospheric
* azimuthal asymmetry" in "gradient models". (See references 49-51 and 61.)
*
* Full list of authors:
* Cong Qiu, Xiaoming Wang, Zishen Li, Shaotian Zhang, Haobo Li, Jinglei Zhang,
* and Hong Yuan
* Available at www.mdpi.com/journal/remotesensing
* DOI: doi:10.3390/rs12010130
*
*
* Logically belongs with the AIRMASS file because of Link's work on both.
*
* Link's thesis on lunar-eclipse photometry: he invents a Biot-like scheme
* He shows very clearly the relation between REFRACTION and AIRMASS:
* refraction is proportional to the integral of a function with respect
* to ρ , but airmass is the same function integrated with ρ dh.
* He shows a graph of his refraction integrand at the horizon.
* The part about refraction is on pp. 89-92. He does the integrals
* graphically!
* Link's "new airmass table" denotes airmass as M
* He uses his graphical method to do the numerical quadratures. The
* atmospheric data are from Humphreys's book.
* Remarkably, there is no mention of Bemporad!
* Available from ADS.
* Link repeats his exposition here, and clearly explains the refr./airmass
* relationship. Fig. 1 shows his airmass integrand for 90 and 84° ZD.
* "La forme générale des courbes . . . montre que la valeur
* des intégrales correspondantes dépend surtout des conditions
* météorologiques dans la basse atmosphère. L'importance des couches
* élevées décroit assez vite pour qu'on puisse les négliger ou mieux
* les remplacer par leurs valeurs moyennes." (p. 166)
* He also suggests that, as a complete atmospheric sounding is needed
* to determine the refraction and airmass near the horizon, "Le procédé
* inverse ne paraît pas impossible à première vue . . . ."
* Cites Tikhov (1936) for large (2°) refractions in winter.
* Again, no mention of Bemporad!
* Available from ADS.
*
* NEWTON
* Book Two, Part III, Prop. X contains the result that in plane-parallel
* media, "the Sum of all the Refractions will be equal to the single
* Refraction which it would have suffer'd in passing immediately out of the
* first Medium into the last." He uses this to derive the "Refraction
* of the Air" from "that of the Atmosphere observed by Astronomers."
* "Based on the Fourth Edition London 1730"; the same passages occur on
* pp. 73-74 of the first edition (1704), which is available at
*
* https://www.google.com/books/edition/Opticks/Oqd3OUaKY0UC?hl=en&gbpv=1
*
* The 1704 edition ends with Query 16 of Book 3, Part I, which is on p.347
* of the Dover edition, and p. 137 of the 1704 edition. After that, the
* first edition contains two mathematical treatises in Latin on third
* order curves, and the quadrature of curves.
* DELAMBRE/Mathieu "Histoire"
* Mathieu edited Delambre's manuscipt for publication, adding extensive
* footnotes and comments of his own, and analysing many old observations
* in the light of current understanding c. 1825.
* Of importance here are the extensive discussions of astronomical
* refraction (indexed on p. xlvi = image 54 of the Gallica PDF); the
* discussion of mirage observations by both Le Gentil and by Mathieu and
* Biot in Mathieu's long footnote on pp. 695-697 (Gallica images 756-758);
* and Mathieu's special "Note" on pp. 774- 796 (images 835-857) discussing
* refraction. The main text ends with Ivory's 1823 work, which was very
* fresh when this was published. The Note refers to Plana's 1823 paper;
* unfortunately, the "Histoire" was published just a year before Plana's
* even more thorough 1828 paper.
* In the mirage discussion (p. 696), Mathieu says: "Ces apparences
* singulières ne sont pas rares dans nos climats, car, pendant
* l'hiver de 1808. je me trouvais à Dunkerque avec M. Biot, et nous
* avons eu ocoasion de voir des effets très variés de réfraction
* extraordinaire. Nous étions presque sûrs de les retrouver quand nous
* nous rendions au bord de la mer, après un abaissement brusque dans la
* température de l'air." On the next page he adds: ". . . et il parait
* bien constant que, quand il a lieu, l'air est toujours plus froid que le
* sol. Les doubles images qui produisent les phénomènes du mirage et de
* la simple suspension peuvent même se former quand les rayons visuels
* rasent de la glace ou de la neige, pourvu que ces corps soient à une
* température plus élevée que celle de l'air."
* Mathieu accepts Arago's spurious "disproof" of Bouguer's observation
* of solar limb-darkening.
* The title page says "Publiée par M. Mathieu", which should technically
* make him the publisher; but in fact he was the editor (as well as a
* co-author!).
* Available from Gallica; the PDF image numbers are larger than the page
* numbers by 61. Gallica's PDF contains the Figures at the end.
* David BREWSTER's "Treatise on Optics"
* Widely cited by later authors; but not entirely reliable. Mirages are
* treated in Chapter XXXI, "On Unusual Refraction", pp. 255-264. He mixes
* in some optical illusions and the Brocken specter; mentions the classic
* examples (Latham, Vince, Monge, Scoresby, Wollaston) without actually
* citing them, and accepts the phony Jurine & Soret "lateral mirage". The
* fata morgana gets a brief summary of Nicholson's translation of Minasi,
* but no citation. He thinks horizontal magnification is "quite possible"
* in mirages, and accepts Monge's "reflecting surface". On p. 263 he says:
* "That some of the phenomena ascribed to unusual refraction are owing to
* unusual reflexion arising from difference of density, cannot, we think,
* admit of a doubt."
* Article in TEATRO UNIVERSALE on mirages, etc.
* Notable for attempts to explain these terms.
* This weekly publication was written for educated general readers,
* bringing them up to date on diverse matters; see the Prefazione
* on p. VII. As the subtitle "RACCOLTA ENCICLOPEDICA E SCENOGRAFICÄ
* indicates, it was profusely illustrated. It ran from 1834-48. The
* printing equipment is described in the Prefazione to Vol. 1, which is
* available at Wikimedia.
* Its publisher was Giuseppe Pomba, who set up the first rotary press
* in Italy. He produced several weekly journals, with the common theme
* of educating the general public.
* The title page says it was published by "una societá di librai
* italiani" (association of Italian booksellers). The Prefazione in
* vol. 5, dated 31 Dec. 1838, is signed by Davide Bertolotti. But Vol. 5
* also shows that Pomba had turned this publication over to Baglione
* in 1838. Bertolotti also signed poems in the Dec.1, 1838 issue,
* and in some 1839 issues. But by 1840, another publisher had taken
* over, and Bertolotti had disappeared from its pages.
* Bertolotti mentioned (in his Preface to vol. 5) that "the illustrious
* Prof. Brugnatelli" had contributed many articles on "physical geography"
* to the Teatro ; so perhaps this item is one of them?
* Google Books has vols. 5 (1838) and 6 (1839) bound as one volume.
* This is the 27 Luglio issue. This article is illustrated with a large
* wood engraving of "Fenomeno del Miraglio nelle pianure del Messico."
* Thanks to Marcella Pace for pointing out this article!
* GRUNERT/CLAUSIUS review
* Good explanation of German terms (Kimmung = looming; Seegesicht =
* inferior mirage) and sloppy usage.
* In the third number, a few pages earlier, Grunert himself comments on
* Gergonne's theory of mirages (p. 308), which he extends; and on
* Biot's monograph. In particular, in section 24 (pp. 348-357), he
* discusses the elliptical locus of the vertices of the rays, and the
* relations [later rediscovered by Tait!] between them and the nature
* of the images. This 3rd number is dated 1849; it begins on p. 267.
* The 4th number (1850) is by Rudolf Clausius. He begins with the
* apparent shape of the sky; evidently this was the model for Pernter &
* Exner's discussion. Then comes extinction, and the light of the sky,
* followed by a long discussion of twilight.
* Refraction begins on p. 399. He discusses the horizontal refraction,
* and the flattening of the Sun and Moon there. The interesting part
* begins on p. 401, with "Ungewöhnliche Senkung und Hebung des
* Horizontes." He mentions "sinking" observed in the Gulf Stream, and
* cites Latham's observations in the English Channel. "Man hat für das
* ungewöhnliche Sichtbarwerden ferner Gegenstände auch im Volke eigene
* Ausdrücke. Bei den englischen Schiffern heisst es looming , und bei
* uns K i m m u n g , welche Namen freilich auch oft für andere
* verwandte Erscheinungen gebraucht werden." (p. 404)
* Then come mirages. Of Minasi's account of the Fata Morgana, he says:
* ". . . hat seiner Beschreibung, die aus mehrfacher eigener Anschauung
* geschöpft sein soll, offenbar Manches aus seiner Phantasie beigemischt."
* Then he brings in Monge. He notes that inferior mirages were long known
* to sailors as "Seegesicht". He cites Büsch's "Tractatus duo". (p. 407)
* and Woltmann's observations, too. "Aber vollständig entwickelt ist sie
* erst von Biot".
* Then comes the passage referred to by Möbius (1925): ". . . dem
* beschriebenen Vorgange eine gewisse Aehnlichkeit mit der
* R e f l e x i o n des Lichtes giebt, obwohl er von dieser seinem
* Wesen nach ganz verschieden ist, und nur auf Brechung beruht." Here,
* he adds a footnote that mentions total reflection. (p. 409)
* Vince and Scoresby then appear. The mirage discussion ends on p. 419,
* where he goes on to discuss the twinkling of the stars.
* This is "Erster Theil, Viertes Heft" of "Beiträge zur meteorologischen
* Optik und zu verwandten Wissenschaften. In zwanglosen Heften
* herausgegeben von Johann August Grunert"
* = Beiträge z. meteorol. Optik. I. 4.
* available at https://archive.org/details/beitrgezurmeteo00claugoog
* (but of course the plates are suppressed).
* CLARKE's important "Geodesy" text (1880)
* Colonel Alexander Ross Clarke, C.B.
* The first page of the Preface says:
* "The Essay entitled 'Figure of the Earth,' by Sir G. B. Airy,
* in the Encyclopedia Metropolitana, is the only adequate treatise on
* Geodetic Surveys which has been published in the English language, and
* though now scarce, it will ever remain valuable both on account of the
* historic research it contains, and the simple and lucid exposition of the
* mechanical theory there given. Since the date of its publication however
* have appeared many important volumes, --- scientific, descriptive,
* official, --- such as Bessel's Gradmessung in Ostpreussen; Colonel
* Everest's Account (1847) of his Great Arc; Struve's two splendid volumes
* descriptive of the trigonometrical chain connecting the Black Sea with
* the North Cape; the Account of the Triangulation of the British Isles;
* the Publications of the International Geodetic Association; recent vo1umes
* of the Mémorial du Dépôt Général de la Guerre; the Yearly Reports
* of the United States Coast and Geodetic Survey; the current volumes by
* General Ibañez, descriptive of the Spanish Triangulation, so remarkable
* for precision; and last, though not least, the five volumes recently
* published by General Walker, containing the details of Indian Geodesy."
* The first chapter is a fine HISTORICAL REVIEW, starting with Snellius
* and Picard. Ch. II is Spherical Trigonometry; III is Least Squares.
* The radius of the (assumed) spherical Earth appears first; dip is in
* the fourth sentence, and the Mount Edgecombe observation is cited as an
* early attempt to measure it. [According to Airy's article "Figure of
* the Earth" in vol. 5, pp. 175-240 of "Encyclopedia Metropolitana" (1845),
* this was measured by Edward Wright, and published by Richard Norwood in
* "The Seaman's Practice, contayning a fundamentall Probleme in Navigation
* experimentally verified, namely touching the Compasse of the Earth and
* Sea, and the Quantity of a Degree in our English Measures, &c." (1637).
* Airy gives the location as "Mount Edgecumbe".]
* A nice feature of the historical introductory chapter is that it
* provides the geodetical connection among the works of the Cassinis,
* the French surveys in Peru and Lapland, and later workers, and thus
* puts into context the works of people like Bouguer, de La Condamine,
* Maupertuis, General Roy, Von Zach, Delambre, Mechain, Legendre, and
* later workers like Tobias Mayer, Struve, Biot and Arago, and Bessel,
* and instrument makers like Ramsden. Finally, on p.27, Colonel Everest
* appears. So, all the scattered studies that seem like isolated details
* in this bibliography are brought together in a grand historical narrative.
* Talcott's Method is discussed on pp. 186-187.
* Refraction is mentioned on p. 2, as "a phenomenon of variable and
* uncertain amount", but is not examined until Ch. XI, "Heights of Stations"
* (p. 280), where Bauernfeind's 1866 papers are cited. Here we find:
* "The amount of terrestrial refraction is very variable and not to be
* expressed by any simple law: the path of a ray of light, inasmuch as it
* depends on the refractive power of the atmosphere at every point through
* which it passes, is necessarily very irregular. This irregularity is
* very marked when the stations are low and the ray grazes the surface of
* the ground. In the plains of India it has been observed that the ground
* intervening between the observer and the distant signal, from being
* apparently convex in the early part of the day, changes gradually its
* appearance as the day advances, to a concavity --- so that at sunset
* the ground seems to slope up to the base of the signal tower which in
* the early morning was entirely below the horizon."
* Here (p. 281) are cited the "Great Trigonometrical Survey of India"
* and Hossard's paper in Mém. du Dépôt Gén. de la Guerre, vol. ix, p. 451
* (1853). Unfortunately this seems to be where the mistaken notion that
* the refraction is least in the afternoon came from. Note that his
* "coefficient of refraction" is about 1/14. not 1/7.
* On the next page are some British measurements, of which the most
* discrepant was made at Ben Nevis, where "for a fortnight --- when
* the greater part of the observations were made --- the state of the
* atmosphere at the top of the hill was most unusually calm, so much so,
* that a lighted candle could often be carried from the tents of the men
* to the observatory, whilst at the foot of the hill the weather was wild
* and stormy."
* On p. 283 a distinction is drawn "between rays which cross the sea and
* those which do not." (A larger coefficient of refraction is found across
* water.)
* HELMERT's "Geodesy" text
* The refraction details are all in Part 2 here; Part I was called
* "Einleitung und I. Teil: Die mathematischen Theorieen". (Notice the
* curious change in spelling; the body of the text wavers between keeping
* and dropping the "h" in both volumes.)
* In the Vorwort, Helmert says: "Bei der Theorie der Refraktion
* im achten Kapitel habe ich mich darauf beschränkt, solche Formeln
* abzuleiten, welche voraussetzen, daß das Gesetz für die Änderung der
* Temperatur mit der Höhe durch eine stark konvergente Reihe nach Taylor
* darstellbar ist. Für diesen Fall sind die Formeln allgemein gültig,
* so daß man die Konstanten aus zweckmäßig angeordneten Beobachtungen
* bestimmen kann. Ein Zahlenbeispiel ist den von v. Bauernfeind
* publizierten Messungen entnommen." (p. VIII)
* The refraction discussion really begins about p.502; but is sparse
* until after p. 550, where "Lateralrefraktion" is mentioned. (This is the
* skewness effect due to the polar flattening of the ellipsoid.) And
* refraction in altitude begins on p. 553, where the familiar expression
* (dn/n) tan z appears. The invariant is on p. 554. But this good start
* is derailed by replacing cot z with sqrt(1 - sin2 z). "Von dieser
* Gleichung, welche schon Laplace kannte, ausgehend, . . . " (But of course
* Newton and several others had it before Laplace.) Then comes the
* Reihenentwicklung. . . .
* P.555: here, kappa is the symbol for -(r/n)(dn/dr), and I hoped he
* would go on to pre-empt Auer & Standish; but no. On the next pages we
* find the surveyors' refraction coefficient k derived. But this all
* assumes that the expansion of κ in terms of its height-derivatives
* converges sufficiently rapidly. On p.556, he says: "Selbstredend ist
* zur praktischen Brauchbarkeit der Formel (7) eine so rasche Konvergenz
* erforderlich, daß zum mindesten die nicht angesetzten Glieder unerheblich
* sind. Inwieweit dieses für einen thatsächlichen Luftzustand der Fall
* ist, kann aber nur die Erfahrung zeigen." [Modern high-resolution
* observations of boundary-layer fine structure do not support this.]
* TILT discussion:
* The skewness effects are discussed on pp. 564 ff.; see references
* cited on p. 565. Of more interest is the discussion of deviations of the
* surfaces of constant density from the "Normalform" due to irregularities
* in the distribution of heat and pressure in the air (p. 566), especially
* those due to sloping ground. If the isopycnic surfaces are inclined, the
* differential of refraction must have the angle between the ray and the
* local normal to these surfaces instead of the zenith distance. (p. 567)
* He denotes the tilt angle as ν, which he imagines might be as big as
* several degrees. (p. 568) But he notes (p. 569) that abnormal lateral
* refractions rarely exceed a few arc seconds, so the actual tilts must
* be small.
* WILLIAM CHAUVENET's treatment
* This used to be the standard textbook of astronomical refraction; it's
* now completely obsolete. Likewise, the treatment of Least Squares in
* Vol. II (especially "Chauvenet's criterion" for the rejection of data)
* is frowned on today, now that we have better methods of "robust
* estimation". However, he does provide an early description of Talcott's
* Method for measuring latitude; cf. Clarke (1880).
* VALENTINER/OPPOLZER
* Oppolzer appreciates the height distribution; see p. 562, where he cites
* Fabritius. There is a good section on TILT of layers, pp. 577-580.
* He also discusses nocturnal inversions (pp. 588-589) and dispersion, and
* has a section on pavilion refraction. Very good!
* The series is "Encyklopædie der Naturwissenschaften"; this is
* "III. Abtheilung. II. Theil: Handwörterbuch der Astronomie".
* Google Books has a good scan of this volume.
* NEWCOMB
* Surprisingly full of errors. The numerical error I found here in my
* 2004 AJ paper is on pp. 217-219. In any case, his treatment, based on
* Radau's series expansions, is completely obsolete today.
* The clarity is not helped by the typography. The publisher chose to
* use a printer in Glasgow (!) -- presumably to save cost in printing.
* That printer used fonts in which the Greek α is very similar to the
* Italic a . In addition, Newcomb used a local constant factor denoted
* by a Roman "a" in some of the equations for refraction.
* The start of each signature is marked by "N.S.A." at the foot of the
* page, which presumably meant "Newcomb's Spherical Astronomy" to the
* binder. It's a bit distracting, as this footer is not separated from
* the body type by leading, but is just the last line printed.
* The scan of this volume in Google Books duplicates some of the later
* pages: pp.356-391 appear twice; next come pp. 392-395, which are then
* followed by an additional copy of pp. 326-444 (the end of the book).
* So pp.356-391 appear three times altogether, and 326-355, twice.
* W.W.Campbell's 20-page biography of Newcomb is in Mem.N.A.S. 17 (1924)
* BEMPORAD's Encyclopädie der Mathematischen Wissenschaften article
* This review begins with a table of contents, followed by the bibliography.
* Bemp. explicitly refers to Bruhns, saying that his list extends and
* continues that of Bruhns. The references are blessedly complete!
* Unfortunately, because of the reliance on Bruhns, Ivory's warnings
* about convergence are ignored here. So the development uses the old
* expansions in odd powers of tan Z.
* The super-adiabatic lapse rate of Laplace's model is mentioned in note
* 24 on pp. 305/6. The paragraph suggesting plain mechanical quadrature
* would be better is in the middle of p. 313; cf. n.4, p.294.
* The publication date is uncertain; the title page of this volume says
* "1905-1923". Bemporad's contribution is dated December 1907, so
* the actual publication date might have been 1908.
* [See the review article about the Enzyklopädie by W. van Dyck
* in Jahresbericht der Deutschen Mathematiker-Vereinigung 17, 213-227
* (1908) for an overview -- available from Digizeitschriften, at
* http://digizeitschriften.de/home/zeitschriften/ ]
* A digital version is available at SUB Göttingen. Its Inhaltsverzeichnis
* shows that in section A (Sphärische Astronomie), chapter 3 (Geographische
* Ortsbestimmung, nautische Astronomie) by C.W.Wirtz has a section V.,
* Nautische Astronomie, with subsection 38. "Die Kimm und ihr Verhalten"
* (p. 139) that might also be of interest. These PDFs have high-quality
* page images, but are not searchable; but tesseract handles them well.
* Bemporad's chapter is number 6.
* BEMPORAD's German Encyclopedia article translated into French
* The sub-title says "Exposé, d'après l'article allemand de A. Bemporad
* (Catane) par P. Puiseux (Paris)"; I give both, but it's mostly Bemporad.
* The very first footnote gives 5 references on atmospheric dispersion.
* And (pp. 15-16): "A nos yeux il est beaucoup moins important d'insister
* sur les artifices de développement que de bien caractériser les
* différentes hypothèses. Il y a en effet une méthode (la quadrature
* mécanique), qui, dans toutes les hypothèses, conduit également vite
* au but, c'est-à-dire à la connaissance de la réfraction théorique."
* There is a succinct discussion (pp. 16-17) of the different formulae
* linking the density to the refractivity, pointing out who has used which
* ones, and concluding that the simple Gladstone-Dale formula is as good
* as any. "On devra donc, dans les théories de la réfraction et de
* l'extinction, choisir la formule la plus avantageuse au point de vue
* analytique . . . ."
* Pp. 23-37 have a nice historical summary of the models of Cassini,
* Tobias Mayer, etc. On p. 28 is pointed out that Laplace's formula gives
* a slightly super-adiabatic lapse rate at the surface. This is a much
* clearer review of the various theories than Bruhns's, with the further
* advantage that the works of Bessel and Radau are included. Bauernfeind,
* Schmidt, Gyldén, Oppolzer, and Bruns are given rather short shrift.
* At the end of this review section (p. 37) is the punch line:
* "Quand on réfléchit à la peine qu'ont demandée les developpements
* analytiques des théories de la réfraction, et notamment les plus
* complets de ces développements élaborées par H.Gyldén et R. Radau ,
* on a le droit de penser que la réfraction astronomique s'obtiendra plus
* aisément par un simple calcul numérique (quadrature mécanique), qui
* tiendra compte directement des donées de la physique de l'atmosphère."
* On pp. 37-50 the refraction integral is developed according to the
* more important theories. The extinction is treated on pp. 58-67.
* The title page says "Publiée sous les auspices des académies
* des sciences de Göttigue, de Leipzig, de Munich et de Vienne avec
* la collaboration de nombreux savants. Édition française rédigée
* et publiée d'après l'édition allemande sous la direction de Jules
* Molk, Professeur à l'Université de Nancy. Et pour ce qui concerne
* l'astronomie sous la direction scientifique de H. Andoyer Professeur à
* l'Université de Paris. Tome VII (premier volume), Astronomie Sphérique.
* Rédigé dans l'Édition allemande sous la direction de K. Schwarzschild
* à Potsdam." The original German edition appears to be:
* Besondere Behandlung des Einflusses der Atmosphäre (Refraktion und
* Extinktion), Enz. der math. Wiss. 6, part 2, (Teubner, Leipzig, 1907)
* My photocopy lacks pp. 21, 51-57.
* Sir ROBERT BALL
* Very readable treatment; derives the usual approx. from Cassini's model
* on pp. 125-128. Unfortunately, an excessive number of approximations
* is used, so the result is not very accurate. However, there is a neat
* proof of Oriani's theorem on pp. 123-124 (though Oriani is not mentioned).
* Theoretical treatment of atmospheric optics; no GF coverage
* There are some useful remarks on mirages:
* "Da plötzliche Übergänge von n , wie zu festen order flüssigen
* Mitteln, hier nicht anzunehmen sind, dürfte man wohl, streng genommen,
* nicht, wie es oft geschieht, von Totalreflexion und Luftspiegelungen
* sprechen, wenn auch eine Analogie zweifellos besteht." (p. 500)
* (Here he cites Claudius [sic; he means Rudolf Clausius, in Grunerts
* Beiträge zur Met. Optik ], 1850, for similar remarks.)
* This is the only work to cite Brandes's article in Gehlers
* Physikalisches Wörterbuch , so far as I know.
* THANKS to Shaun Hardy for supplying a copy of this!
* After much searching, I found that this author is Alfred Willy Möbius
* = Wilfried Möbius (1879 - 1964). See
*
* https://de.wikipedia.org/wiki/Willy_M%C3%B6bius
*
* He published a few papers on the theory of the rainbow, some of which are
* cited in his Encyclopedia article, which seems to be his last publication.
* Most were published by Teubner, beginning with "Einführung in die Optik
* der Atmosphäre" (1907).
* Review article in 1944 "International Hydrographic Review"
* This covers both REFRACTION and DIP, and cites many obscure tables.
* It is available at the University of New Brunswick library website:
*
* https://journals.lib.unb.ca/index.php/ihr/issue/archive/2
*
* The coverage is much more complete (up to 1944) than the recent
* review article by François Mignard in C.R.-Physique (2022). On the
* other hand, this review contains some typos, such as "Bompard" for
* Bemporad, and "Delamare" for Delambre, so that one wonders about the
* accuracy of the discussion.
* On the title page of this article, the author is "Ingénieur Hydrographe
* Général P. de VANSSAY de BLAVOUS, Director". He is just "P. de Vanssay"
* in the IHR archives. On the front matter, he is listed as one of the
* two Directors of the International Hydrographic Bureau (which is now
* the International Hydrographic Organization, whose website is at
*
* https://ihr.iho.int/ .
*
* This issue is No. 39 in the series published by the IHB in Monte-Carlo,
* Monaco, and dated August, 1944. The title page simply says "Hydrographic
* Review".
* GENERAL REFERENCES before 1951
* DANJON
* Chapitre IX is devoted to refraction, including DIP and MIRAGES.
* Dispersion and chromatic scintillation are mentioned, but not green flashes.
* Thanks to Fred Talbert for reminding me of this!
* VASSY
* Étienne Vassy was primarily interested in the upper atmosphere, which
* explains the chapters here on the ionosphere and sound propagation.
* He is mostly remembered today for his work on ozone in the 1930s.
* Section 4 of Ch. I is "Influence de la dispersion; le rayon vert."
* Even at this late date, he says Julius's anomalous-dispersion theory is
* one of two possible explanations; though he points out that Danjon &
* Rougier's work refutes it.
* Having seen the phenomenon repeatedly at a single location during one
* week(!), he thinks it is a result of thermal inversions. He also has
* the Byrd story wrong ("le premier jour de l'apparition du Soleil après
* la nuit polaire. . . "). (p. 15)
* On p. 16, he worries about the variable (and overly long) duration.
* But he thinks this can be explained by the effects of "fluctuations
* notables d'indice le long des rayons . . . si l'obstacle derrière lequel
* disparaît le Soleil est surmonté d'une couche d'air dont l'indice
* commence par croître avec l'altitude."
* He also worries about the sudden change of color, which he attributes
* to the rain-band of water vapor.
* On p. 40, he attributes the distortions of the low Sun to variations
* of index along the trajectory. Much of his mirage discussion is based
* on Flammarion.
* Hardly half a dozen references are cited in the whole book!
* [Tome I was on emission phenomena.]
* SMART
* The classical textbook on traditional spherical astronomy.
* Robert G. FLEAGLE and Joost A. BUSINGER
* Shows a simplified PALM-TREE diagram, with the usual error (p. 296)
* (Ironic, in view of Businger's later importance for inferior mirages!)
* Mirages get only a page here; GF gets one sentence (p. 358, 2nd ed.).
* The Second (1980) edition is on a Ukrainian Website or Scribd; see p. 356
* WOOLARD & CLEMENCE
* General: Chapter 5; DIP, SUNSET in Chapter 10,
* "Determinations of position in the local reference system"
* Specific: a very superficial mention of refraction near the horizon on
* p. 88, listed in the index; but citing few references, and neglecting
* the works of Fletcher, Sugawa, and many others.
* KOLCHINSKII emphasizes issues omitted from the regular texts
* After pointing out the need for refraction of objects within and near
* the limits of the atmosphere, he briefly reviews the literature.
* There are several interesting items in his bibliography, especially
* dealing with refraction near the horizon, in the polar regions, etc.
* Pp. 11-12 have a clear summary of Emden's polytropic model, and give
* his series-expansion terms.
* Pp. 13-14: after describing the tables of Link & Neuzil in BAC (1958),
* he notices that their extreme values at the horizon strongly violate
* the usual refractivity scaling (from T and p values). Then (p. 14):
* "Thus, the dispersion between the refraction at the horizon, calculated
* by [refractivity scaling] and obtained by numerical integration, proves
* to be highly significant. It indicates that in this case the upper layers
* of the Earth's atmosphere influence the value of the refraction integral."
* Pp. 14-15 describe Fuss's observations at Pulkovo, which he attributed
* to a low-lying inversion; but K. says that Bauschinger, and also
* Banakhevich, showed this was insufficient. The discussion of large
* refraction near the horizon continues on pp. 16-17; he seems to consider
* this normal phenomenon "anomalous" simply because it is not in the
* standard tables.
* On pp. 18-19, he discusses TILT of the layers, with several references.
* At the end of the Conclusion, p. 40, he raises the issue of using
* terrestrial refraction to estimate temperature gradients, as suggested
* by Fesenkov -- cf. Faye!
* Martin Hotine's "Mathematical Geodesy" reference (1969)
*
* This work introduces the use of tensor calculus to geodesy; see the
* Preface, starting on p. x. TERMINOLOGY and notation are discussed on
* p. xiii. He does not clearly explain his use of ambiguous terms; it
* appears from context that he uses "altitude" to mean height above sea
* level most of the time, but does refer to "altitude and azimuth" on
* p. 251. He uses "height" to mean "height above the reference surface"
* (which is usually the geoid); see p. 233 for "geodetic heights", and
* also the discussion of sign conventions on p. 70.
* Users of GPS will be amused at the remark on p. 147: ". . . relativistic
* effects . . . are unlikely ever to be significant in the case of near-Earth
* satellites."
* Chapter 24 (pp.209-) is "Atmospheric Refraction". Here the refractive
* index is µ. The refractive invariant for the spherical case is derived
* on p. 211. The discussion is basically in terms of geometrical optics:
* he assumes rays, point sources, and the like.
* A notable comment on p. 214 says: "One possible assumption is that the
* model atmosphere is in static equilibrium , which might be approximately
* so in settled weather conditions during the afternoon. This would mean
* that the isopycnics --- or surfaces of equal density --- which are nearly
* the same as the surfaces of equal refractive index, are gravitational
* equipotentials; the gradient of (In µ) is accordingly in the direction
* of the astronomical nadir." But he then assumes the isopycnics are
* all surfaces of constant gravitational potential, "so that the zenith
* distances are all unrefracted." So tilt is neglected. Then the gradient
* of refractivity "will not usually differ from an exact gravitational model
* by more than a few minutes of arc."
* On p.215 we see that geodesists call vertical angles "elevation"
* (corresponding to the astronomer's "altitude".) Footnote 4 there
* discusses the surveyors' "coefficient of refraction". We also have the
* circular-ray approximation. Then the elegant mathematical formalism is
* wasted, and we are back to Helmert.
* Fortunately, this oversimplification is relaxed on the next page, where
* the equation of state is modified to include the water-vapor partial
* pressure. Here the old "3/8" becomes 0.37803. The refractivity of air
* is taken from Edlén's 1966 formula and Barrell & Sears. The group
* velocity finally appears on p. 217. The radio refractivity is the old
* Essen & Froome value with no dispersion.
* The discussion of lapse rates is quite primitive. On p. 221 he does
* find that the rays are straight in dry air for a lapse rate of 0.0334 °C.
* per meter. On the next page, he says the adiabatic lapse rate is "almost
* double what is usually found during the period of minimum refraction from
* reciprocal vertical angle measurements." [Monin and Obukhov published
* their paper in 1954, 15 years before this was published.]
* Astronomical refraction begins on p.223. "A good historical summary
* is given by Newcomb." [ouch!] Garfinkel's works are cited, too. The
* refraction integral is given with d(ln µ) as the variable of integration;
* but no details are offered. Parallactic refraction is treated crudely
* in section 69. Early attempts to measure terrestrial refraction with the
* two-wavelength method conclude the chapter.
* This is ESSA Monograph 2. Its analyses (but not its obsolete numbers)
* are still widely cited by geodesists.
* for DISTORTED SUN, see Fig. 1.2.23, p.49
* AIRMASS & REFRACTION TABLES for std.atmospheres
* ``Temperature inversions . . . occasionally give rise to abnormal effects of
* refraction. . . . The effects are transient and variable, and there is little
* point in attempting to work out an exact theory for them. . . .'' (p.19)
* NORTON'S STAR ATLAS
* The 17th edition (1986) is the same as here.
* A longer but less accurate account is on p. 38 of the 15th ed. (1966).
* Cassini's "formula" given
* AIRMASS & REFRACTION in Chapter 7, "Astrometry through the atmosphere"
* GREEN -- Ch. 4, esp. pp. 87-93
* Table 4.1 (p. 91) "gives approximately the amount of refraction taking
* place above the level in question, for a source at zenith distance
* 45°."
* 2nd EXPLANATORY SUPPLEMENT
* Recommends the Auer-Standish method to calculate refraction, using the
* Hohenkerk-Sinclair (1985) computational scheme.
* not a book, but a textbook-style tutorial article; so placed here
* Caution: fails to mention the tilt effect, so is incomplete.
* Craig F. Bohren and Eugene E. Clothiaux's textbook on RT
* Chapter 4 on Radiometry and Photometry is a nice review of these
* quantities and their units, with an introduction to color science as
* well. But Ch. 8 on Meteorological Optics (p. 397) is our main interest
* here. especially §8.3 on atmospheric refraction (pp.418-426), which
* touches on mirages and GFs.
* The treatment is quite limited: only the flat-Earth mirage model is
* treated, and only Cassini's uniform model is used for astronomical
* refraction. Because dip is ignored, "Fraser's Theorem" is taken to
* imply that the serrated Sun at the horizon must be due to "horizontal
* variations of the refractive index" (p. 425).
* Unfortunately, the uniform model leads to large errors in the
* flattening of objects at the horizon and the width of the green rim.
* No mention of Biot, who did better.
* §8.3.3 (pp.425-426) treats green flashes, pointing out that the
* atmosphere can magnify the green rim. But the various forms are not
* mentioned. Overall, good on the fundamentals, but lacking in depth.
* The Special Issue of C.R.-Physique on atmospheric refraction
*
* Published online at
*
* https://comptes-rendus.academie-sciences.fr/physique/item/CRPHYS_2022__23_S1/
*
* That link shows the Contents of the whole issue. Its Foreword is at
*
* https://comptes-rendus.academie-sciences.fr/physique/item/10.5802/crphys.132.pdf
*
* or https://doi.org/10.5802/crphys.132
*
* This Foreword briefly enumerates the articles in the Special Issue.
* The emphasis is mainly pedagogical and historical, so the articles are
* reviews rather than technical advances. The Foreward is in both French
* and English; most of the articles are in French, with English abstracts.
* I list here some of the more general articles. The more technical ones
* are distributed in this bibliography to their most relevant positions.
* Also, I omit several contributions that deal primarily with "seeing" and
* other effects of turbulence.
* Although the date of the issue is 2022, most of the papers were not
* actually published until 2023.
* François Mignard's review of refraction tables (and how to compute them)
* This starts out looking like a more expanded version of my own paper
* (see below); but it has considerably more numerical detail. There are
* some interesting variations on Cassini's model.
* However, there is also much emphasis on the tangent series; and some
* peculiar omissions: no mention of Flamsteed's connection to Newton's
* table; considerable discussion of how to evaluate integrals, but no
* mention of S.Y. van der Werf's papers; considerable use of polytropic
* layers, but no mention of Emden; etc. In discussing Newcomb's book, he
* notices that the numbers don't agree with the analysis, but fails to
* identify the exact error in Newcomb's numerical work -- which is pointed
* out in my AJ paper, which he cites. He also has the title of Newcomb's
* "Compendium" wrong in the text (but right in the Références).
* On the other hand, he uses Ciddor's dispersion formula, and points out
* the unrealistic nature of the Standard Atmosphere. And Fig. 22 shows an
* actual sunrise sequence (affected visibly by the nocturnal inversion).
* So, a mixed bag. Read with caution; refraction is not his specialty.
* Published online: 25 May 2023 at: https://doi.org/10.5802/crphys.123
* DOI: doi:10.5802/crphys.123
* Luc Dettwiller's classification of refraction phenomena in CR-Phys.
* Largely a descriptive summary of terrestrial refraction phenomena,
* like a shortened French version of Humphreys (1940) brought up to date
* with recent references.
* There is a nice discussion of the virtual images percieved by the eye,
* and their apparent positions (even when the physical position of the
* real astigmatic image lies behind the eye).
* Luc makes good use of several ray-trace diagrams taken from my website.
* [The discussion is mostly in terms of Lambert's model, which is
* appropriate for beginners; but its unreality tends to mislead them, as
* mirages are due to changes in lapse rate.]
* Published online: 21 February 2023 at: https://doi.org/10.5802/crphys.114
* DOI: doi : 10.5802/crphys.114
* Part of the special issue: Astronomy, Atmospheres and Refraction
* Also avaliable at
* https://comptes-rendus.academie-sciences.fr/physique/item/10.5802/crphys.114.pdf
*
* Review of inf.-mir. history, Monge's error, and reactions to it.
* The origin of the word "mirage" is examined in detail.
* I should also have cited Möbius (1925), and perhaps Garbasso's second
* (1907) paper.
* Published online at: https://doi.org/10.5802/crphys.106
* on 20 Dec. 2022
* DOI: doi : 10.5802/crphys.106
* Part of the special issue: Astronomy, Atmospheres and Refraction
* Review of astronomical refraction and extinction (airmass), and their
* relation to atmospheric structure. Shows that the Standard Atmosphere
* is unsuitable; that Cassini's model is adequate, except near the horizon;
* and that the Auer-Standish recipe fails near the top of a duct.
* Largely historical.
* Published online at: https://doi.org/10.5802/crphys.125
* on 21 Feb. 2023
* DOI: doi : 10.5802/crphys.125
* Part of the special issue: Astronomy, Atmospheres and Refraction
*
* ELLISON HAWKS's book
* ". . . you must watch carefully, for, as the minutes go by, the sun
* will get lower and lower until there is only a tiny tip left. Then,
* just before it finally disappears, you will perhaps see a little green
* flame shoot up, and the tip of the sun itself will turn green. I do not
* say that you will always be able to see this Flash, but only on certain
* occasions. I have known people only see it once out of a dozen times,
* but it is very interesting to watch the sun disappear over the horizon,
* and to look for the green Flash." (p. 60)
* So far, so good. But then, the sun ". . . will also seem a great deal
* larger than it does when seen high in the sky. This is because of the
* extra thickness of atmosphere near the horizon, which acts as a sort of
* magnifying glass and enlarges the sun, when it is low down. The moon may
* also be seen enlarged in the same way, as it rises in the east, when it is
* full." Ouch! (Well, you can't win them all.)
*
* Thanks to Charles Campbell, of Cranleigh, Surrey (UK) for the reference!
* He says it was published in 1912, but the copy I borrowed from Case,
* while undated, has "October 1910" at the end of the preface; and the
* last page of the index has a footer naming the printer (Ballantyne,
* Hanson & Co.) and the notation "5/11"; so I believe it was printed in
* 1911. This is the ninth volume in the "Shown to the Children" series.
* According to the L.C. catalog, Hawks wrote other books in that series.
* The British Library catalog credits 120 popular books to him, and dates
* this one 1910.
* Case's copy showed up with the frayed black register bookmark ribbon
* lying between pages 60 and 61 -- right at the GF entry!
* Note the GF observation by Hawks in 1909, shortly before this was written.
* TURPAIN's book on light, illustrated with photos by Rudaux
* A nice chapter on atmospheric optics, including twilight phenomena,
* zodiacal light, aurorae as well as the usual halos, rainbows, and
* mirages. Mirages and distorted sunsets are illustrated with photos from
* Rudaux; GF is illustrated with his drawings of the 1904 flash.
* Libert's "green Sun" observations are also mentioned.
* Thanks to Luc Dettwiller for a copy of this!
* CHARLES FITZHUGH TALMAN's books
* Talman is listed on the title page as "Chairman Committee on Public
* Information, American Meteorological Society"
* Crepuscular rays are treated on p. 169, ending with mountain shadows.
* Pp. 170-171 describe textbook green flashes, and red flashes. He
* seems to give a little credence to the "after image" explanation.
* Pp. 171-174 treat mirages, described as "some of the most bizarre of
* optical illusions." General Maude is mentioned on p. 173, as is
* Scoresby, and "Crocker Land".
* TALMAN's later book
* In "The Author's Apology", Talman says he "has enjoyed for a number
* of years the exceptional privilege of being the custodian of a nearly
* exhaustive collection of literature on the subject . . . ." [The obit
* on NOAA's Web pages, taken from Weather Bureau Topics and Personnel,
* July 1936, says he had been in charge of the Weather Bureau Library at
* the Central Office since 1908.]
* Facing p. 21 is a picture of "the most famous cloud in the world":
* the "tablecloth" on Table Mountain, near Cape Town.
* The treatment of mirage (pp. 114-118) is much fuller and better
* here than in the 1925 book. Looming and "lateral mirage" are briefly
* mentioned. He suggests the Flying Dutchman probably arose from
* mirages at sea. On p. 116 appears a garbled account of the New Haven
* ghost ship, here transferred to New York, and mistaken for a mirage of
* a real ship. Wilkes Land and Crocker Land are mentioned; Hubbard's book
* is named, and quoted, but without a page reference (p. 117).
* Pp. 136-137 mention sunset distortions; GF on 137-138. The Lick
* sunset photographs are mentioned (p. 137). There is now no mention of
* after images.
*
* The author says these are edited articles from Nature Magazine, Popular
* Mechanics, NY Times, etc.
* No copyright date is given for the book, only for its sources;
* L.C. says "c1931".
* W.E.Harper's Canadian radio talks -- not a book, but belongs here anyway
* This is the lead article in the Feb. 1933 issue, beginning on p.49.
* Available from ADS.
* BOTLEY -- a popularization of meteorology
* The Manx GF legends mentioned on pp. 152 and 206 are both taken from
* the same letter to The Times (M.Douglas, 1929). Botley exaggerates:
* Manx folklore does not "contain much" about it; it was barely known in
* 1929, and nobody there seems to have heard of it today. The reference
* to Rex Clements's story is also overblown. And the purported "superior
* mirage" in Plate XI (facing p.210) is almost certainly a fake.
* Yet the Italian translation of this book is O'Connell's ref. #10.
* Dr. Charles D. Neal's book for juveniles
* "When there is, near the earth, a layer of air that is warmer and
* denser [sic!] than the air above it . . . ."
* [Well, it isn't the *air* that's denser here . . . .]
* Franklyn M. Branley's treatment for juveniles
* ". . . the green flash, a bright green strip of light that appears just
* above the setting sun. Usually it is seen close to the horizon an
* instant after the sun itself has disappeared . . . . Because of its longer
* wavelength red is bent the least." (The diagram is equally poor.)
* Branley wrote many books on astronomy for children; he died in 2002.
* Compendium of reports, as in Mulder's book: this put me on to
* Starr's (1930) paper, so Corliss is accomplishing his aim here.
* Like Mulder, he quotes items and adds short comments:
* "The green flash and the crepuscular rays . . . have long been considered
* as fully explained. The stock explanations, however, seem simplistic
* when the full ranges of these phenomena are considered."
* Of "the appearance . . . of multiple green rays of light ascending from
* the point of the sun's disappearance", he astutely says, "This phenomenon
* may be related to the crepuscular rays."
* Corliss's list of 42 references contains no errors, which speaks well
* for the care he has exercised -- especially considering that the
* ``standard'' references typically have 10% to 20% errors!
* Corliss's book reviewed in JBAA
* GF is mentioned. Available from ADS.
* A juvenile book illustrated in b/w, with the usual mistakes
* Mirages are treated on pp. 14-22. Looming is treated as a mirage:
* "Looming mirages are the only mirages that appear to be nearby. They
* may also greatly magnify the real object."
* "Our first glimpse of the Sun at sunrise is a mirage."
* An interesting variation is the suggestion to observe variations in dip.
* Another juvenile book, full of strange stuff
* ". . . at sea . . . the air layer closest to the water is usually colder
* than the air layer above it. As a result, sea mirages . . . are right
* side up and above the object . . . ." (even worse about Fata Morgana)
* Acknowledgment thanks "William A. Selby, Professor of Geography/Earth
* Sciences, Santa Monica City College . . . for his critical reading of the
* manuscript."
* much misinformation, but some great photographs
* The second edition, published in 2001, is greatly improved, and RECOMMENDED.
* [Although they propagate the "fata bromosa" error.]
* This is a beautiful book, similar to the Lynch/Livingston book;
* it contains the best mirage photos I have seen. The GF pictures are
* poor, but the advice on how to obtain them is good. Unfortunately,
* the multiple inferior mirage (due to uneven ground) on p.60 is
* mis-identified as a Fata Morgana; and the price is a bit high (FF 240).
* See pp. 49-56 for the GF, and 56-60 for mirages.
* Clear presentation of the textbook story, with one of Pekka's GFs.
* Note that the wrong colors were printed on Abb.1.6 on p.24.
* Thanks to Dr. Kristian Schlegel for a copy of his book! It turns out
* to contain many fine pictures of natural phenomena, including one of
* ball lightning. The author tells me a revised edition is in the works.
* All sorts of pretty pictures, not just atmospheric optics
* Pekka's multiple-mock-mirage flash sequence is on pp. 131-133, with
* the final stage on a double-page spread. "The conditions for seeing
* the green flash, or green ray, with an unaided human eye occur only a
* few times out of every ten sunsets over a distant unobstructed horizon."
* a journalist's attempt to cover science?
* Paul Simons's book is full of errors, but has some decent coverage --
* it seems to fall somewhere between Corliss and the National Enquirer .
* The author has believed everything he's read, and has sorted out the
* most sensational accounts. So he asserts, in the introduction, that
* "The Föhn wind in Germany sends people mad," and other nonsense.
* Speculation is presented as fact; there is no index; and the "Select
* Bibliography" at the end is already secondary and tertiary sources, some
* not too reliable themselves. The book is clearly pitched at an English
* readership (British spellings throughout).
* The photographs (some by Pekka Parviainen, some by Alistair Fraser;
* some strangely reproduced with moiré stripes through them) are mixed
* with engravings from Flammarion (!)
* One of Pekka's pile-of-plates clouds is captioned ". . . lenticular
* clouds created on waves of turbulent air." And the adjacent text says
* ". . . called rotor clouds or lenticular clouds." [p. 60]
* The story of Ross mentions his "Croker Mountains" on p. 58.
* "Green Flash" is on pp.85-86: ". . . it sometimes hurls a shaft of vivid
* green light across the sky . . . ." The usual "prism" is invoked.
* While there are hints of interesting reports to pursue, the lack of
* detailed references makes most of them useless. The unwary should
* steer well clear of this confused and unreliable book.
* John Naylor's mixed bag: great photographs, some good (and some misleading)
* diagrams, some good (and some wrong) information. Many of the topics
* of interest here are covered: refraction & mirages (Ch.3, pp. 50-63);
* flattened sunsets (pp. 64-67); crepuscular rays (pp. 77-79); distorted
* sunsets (pp. 80-84); Green Flashes (pp. 84-86). All non-mathematical.
* Pekka's pictures are great. But there are some howlers: Naylor claims
* Monge made up the word "mirage" (p. 51), though he gives the correct
* etymology. He thinks mirages are due to temperature gradient, not the
* curvature of the temperature profile (p. 55). "If your eye is too high,
* it will not intercept the rays that produce the inverted image, and you
* will not see a mirage." (p. 57) [Pekka's over-sized Omega is on p. 56.]
* Ch. 4 (pp. 64-87) deals with low-Sun and twilight phenomena; GFs are
* on pp. 84-86; ". . . blue flashes have been seen . . . only from altitudes
* of several kilometres." The pictured mock-mirage flash (Fig. 4.15,
* p. 85) is mis-identified as "Green segment." Many minor errors.
* There are a number of wrong-word errors that show the manuscript was
* spell-checked but not carefully proof-read.
* The selection of references is also haphazard, including minor works
* while omitting more important ones. He has the date wrong (as 1968!)
* for O'Connell's book.
* MICHAEL VOLLMER's new book on atmospheric optics for beginners
* SUPERB photographs in the color-plates section. This is a more
* technical book than most of the ones in this section -- it's almost a
* textbook rather than a popular work. (He's not afraid to use calculus
* occasionally.) Section 11.2 (pp. 315-322) covers green flashes; there
* are also good sections on refraction in general, and mirages. Each
* chapter has a good list of references.
* Springer issued a slightly revised second edition in paperback (2019).
* MICHAEL MAUNDER's book
* GF treatments are on pp. 72-74 for morning, and 115-118 (evening).
* But he starts off with "The scientific basis for the green flash had
* to wait until 1960 [sic] when D.K.J. [sic] O'Connell of the Vatican
* Observatory produced the first [sic] authenticated color photographs
* of the phenomenon, but he [sic] took those at sunset . . . ."
* Well, it isn't all that bad, but it isn't good. "The green flash
* occurs when light is refracted through an atmospheric layer and thereby
* seems to come from this higher layer." (All this from the top third
* of the first page! He does manage to connect flashes with mirages,
* but clearly doesn't understand either one.)
* On p. 74, we get: "Blues should never be possible and it is difficult
* to give an explanation." [Especially if you don't understand GFs.]
* The mirage discussions on pp. 101 ff. aren't much better; he confuses
* inferior mirages with looming and normal refraction: "The interface
* acts very much as a mirror with light reflected back from the much
* denser air above. . . . this mirage is described as an 'Inferior' mirage,
* from the reflection back from above." (p. 101)
* Like O'Connell, he takes the gaps between multiple mock mirages as
* "blind strips": "These multiple mirages often lead to a whole series of
* green flashes, often seen underneath as well as above, as each layer pass
* through the boundary layers in the atmosphere." (p. 103, strictly sic .)
* Pretty awful. Too bad Patrick Moore's name is on this series.
* MARCELLO SÉSTITO's peculiar "Fata Morgana" book
* A beautifully produced "coffee-table" book, which plays with the
* idea of reflections in its design and illustrations. The author is an
* architect who seems enchanted with the idea of mirror images and symmetry,
* and the architectural theme in the historical accounts of these mirages.
* The first 31 pages provide a brief sketch of the myth of Morgana and
* the literature of the mirages, followed by two pages of more detailed
* references to some sources of information. I was glad to see Boccara's
* paper cited; but Costanzo's is not. And the author has unfortunately
* ignored Boccara's advice about the unreliability of many old works.
* Then come several sections: "Quaderni" ["Exercises"], of colored
* sketches and art studies inspired by the stories connected with Morgana;
* and then other, more formal paintings devoted to Morgana herself, the
* Strait, and Kircher's "Catoptic Theater". Many of these echo motifs
* seen in Fortuyn's engraving, which is well reproduced on p. 128, just
* before the beginning of the second half of the book.
* This second half is a series of Appendices that reproduce several
* well-known works devoted to the mirages, beginning with Minasi's classic
* Dissertation of 1773. Unfortunately, it is followed by some of the most
* unreliable essays ever published on this subject: those of Capozzo
* (1840), Saffiotti (1837), Giardina (1758), etc. Minasi's text and
* Capozzo's are printed in two-column format, with a vertical rule that
* separates the columns; but Saffiotti's and Giardina's are reproduced
* in a peculiar 4-up format that retains the 2-column arrangement, so that
* each photocopied page image at bottom of a book page follows the image
* immediately above it; the reader must envision an invisible 2-column
* format, instead of reading pairs of page images side by side.
* Fortunately, the page images bear the original page numbers. As in
* Consolo (1993), Minasi's notes are re-numbered by section instead of
* by pages, and some copying errors in Consolo's version, including his
* errors in re-numbering Minasi's footnotes, are exactly reproduced
* here; so it seems that this is a third-hand copy of Minasi.
* Minasi's text and Capozzo's are separated by a double-page spread
* that reproduces a widely-reprinted wood engraving from 1865 that falsely
* depicts some imaginary superior mirages, with the upper images shown
* impossibly enlarged in azimuth as well as unrealistically elevated
* in altitude. The misleading text of Giardina, with Gallo's notes and
* Allegranza's garbled commentary, are followed by another pair of phony
* "mirage" images from the 19th Century, including the frequently reproduced
* fantastic image "Mirage in the Desert" from Hartwig's 1875 "The Aerial
* World"; here, Hartwig is mis-identified as "Hartwing". Caveat lector!
* However, the photocopied texts are followed by the little-known but
* influential discussions led by Johann Reinecke in the pages of Allgemeine
* Geographische Ephemeriden in 1800, which have been capably translated
* from German to Italian by Mario Izzi. The copperplate engravings
* (Tafeln I & II) from Reinecke's initial discussion, which are hard to
* obtain, are usefully reproduced on (unnumbered) pages 206 and 208.
* Incredibly, this Italian translation of Reinecke's comments actually
* includes an Italian translation of Reinecke's German translation of
* Nicholson's English translation of Minasi's original Italian description,
* even though this book has already reprinted Minasi's original Italian
* text a few dozen pages earlier. So we get to read the third-generation
* version: "Quando il Sole al mattino raggiunge un'altezza tale che i suoi
* raggi formano col mare di Reggio un angolo di incidenza di circa 45
* gradi, . . . " instead of the original "Quando il nascente Sole splende
* in punto, onde l'incidente suo raggio formar possa sul mare di Reggio
* l'angolo di gradi 45 circa, . . . ". Well, maybe it's useful to show the
* modern Italian reader what the 19th-Century German reader read about
* what the 18th-Century Italian writer really wrote; but maybe not.
* Then come more than four pages of annotated bibliography, containing
* many other little-known and obscure references on Fata Morganas. They
* contain some valuable citations to the recondite literature; but they
* also contain many obvious errors. For example, Humphreys' middle
* initial is given as "L" rather than "J", and the title of his textbook is
* printed as "Phisics" of the Air instead of "Physics"; furthermore, only
* its 1929 edition is mentioned, although the 1940 revision contains
* additional information about mirages. Only the abridged 1671 edition
* of Kircher's Ars Magna (the one with the typo that fooled Marina
* Warner) is cited for Angelucci's letter, rather than the more correct
* text of the original 1646 edition; and the heading of the section is
* cited with "sine" in place of "siue". Similarly, only Pernter's 1902
* edition of Meteorologische Optik is cited, rather than the expanded
* 1910 revision by Exner, let alone the 1922 second revision. Another
* example of carelessness is the misspelling of Marina Warner's last name
* as "Worner", which caused her unreliable book "Phantasmagoria" to be
* placed after Elizabeth Werner's 1896 work. This shows the error to be
* the author's, not that of the printer or proofreader.
* Strangely, the references cited in the bibliography section do not
* include several other useful references that appear in the Notes on
* pp. 32-33, such as Boccara's fine review of the literature before 1900;
* so it is necessary to consult the Notes as well as the Bibliography
* to discover all of Séstito's sources. His omission of important works
* like Costanzo's review and the later editions of both Humphreys and
* Pernter & Exner reveal his unfamiliarity with the mirage literature.
* As is usual with the Fata Morgana literature, one needs considerable
* experience with the field to separate the wheat from the chaff; this
* book contains an abundance of both.
* I was pleased to see the woodcut, or wood engraving, on the
* penultimate page of the book, which illustrates the classical
* demonstration of refraction described by Euclid and Cleomedes.
* It would be nice to know what 19th-Century textbook was its source.
* Special thanks to Marcella Giulia Pace for bringing this attractive
* and useful work to my attention, and for providing a copy!
*
* original edition of Part I of Minnaert's book;
* note that there are three parts to this monograph.
* They are now available on the Web at:
*
* http://www.dbnl.org/tekst/minn004natu01_01/minn004natu01_01.pdf
*
* He introduces verdwijnlijn and grenslijn on p. 47.
* The "Groene Straal" is introduced with a quote from Verne, and a
* reference to Mulder's book; then comes "Volgens een oude Schotse
* legende . . . ." (p. 58)
* first English translation of Part I:
* The term "vanishing line" appears for the first time here, on p. 48
* REVIEW of the 1940 edition; mentions "the green ray".
* I suppose the reviewer is Thackeray.
* REVIEW of the 1940 edition; mentions "the green ray"; and calls
* Hillers's mural-mirage photo "one of the oddest" in the book.
* This should be the same as the 1940 edition
* "According to an old Scotch legend, . . . "
* He has "Continho" for Coutinho
* Note that he endorses Forel's explanation for the Fata Morgana (p.53)
* The Dover edition brought Minnaert's work to a much wider public.
* Even so, his term "vanishing line" does not appear in the technical
* literature until 1960.
* O'C #91
* new translation of Minnaert
* and refraction terminology
*
* NOTE: This file is mainly the "mirage" articles from a number of
* encyclopedias, dictionaries, and similar reference works.
*
* "MIRAGE; an optical phenomenon, produced by refraction. The unusual
* elevation or apparent approximation of coasts, mountains, ships, and other
* objects, has long been known under the name of looming ; and, if the same
* phenomenon is accompanied by inverted images, it is called a mirage ."
* N.B.: "A popular dictionary of arts, sciences, literature, history,
* politics and biography, . . . on the basis of the seventh edition of the
* German Conversations-Lexicon." [see below for a later edition of that]
* "Under it are classed the appearance of distant objects as double,
* or as if suspended in the air, erect or inverted, etc."
* But there are some errors: "In particular states of the atmosphere,
* reflection of a portion only of the rays takes place at the surface of
* the dense medium, and thus double images are formed, one by reflection,
* and the other by refraction -- the first inverted, and the second erect."
* And: "The Spectre of the Brocken , in Hanover, is another celebrated
* instance of mirage."
* "Mirage is the appearance in the air of an erect or inverted image of
* some distant object which is itself invisible." (Garbage.)
* "Luftspiegelung . . . bewirkt, daß Gegenstände, die sich u n t e r
* dem Horizont befinden, deutlich sichtbar, also gewissermaßen gehoben
* werden . . . , oder daß ü b e r dem Horizont befindliche Gegenstände
* doppelt, vergrößert oder umgekehrt in der Luft schwebend erscheinen."
* There is a fine laundry list of TERMINOLOGY here: "Die deutschen
* Seeleute nennen diese Erscheinung K i m m u n g , die englischen
* L o o m i n g , die holländischen U p p d r a c h t , die
* französischen M i r a g e . In Indien nennt man die L.
* C h i l t r a m , » Bild « , oder S i k o t a , » Schlösser der
* kalten Zeit « ; bei den Arabern heißt sie S e h r a b ,
* » geheimnisvolles Wasser « , auch Bacher el Alfrid, » Sohn des
* Teufels « , oder Bacher el Gazal."
* Albright's treatment of the green flash is straightforward and accurate.
* But his section 6 on "Mirages" in Chapter XX leaves much to be desired:
* "The mirage is an optical illusion due to the refraction of light as
* it passes through nonhomogeneous layers of the atmosphere. Distant
* objects are seen in an unnatural position, sometimes elevated, sometimes
* depressed, and often inverted." (p. 355)
* He also seems to think that any images in excess of 2 must be due to
* reflection on water; in discussing the superior mirage, he says (p.357):
* "If the mirage occurs at sea, the image of a distant ship and of its
* reflection in the water also may appear in the sky, the image of the ship
* inverted and the image of the reflection erect, as shown in Fig. 231."
* [N.B.: This spurious suggestion was already made in 1806 by Kries.]
* His description of looming confuses it with ordinary terrestrial
* refraction; his illustration on p. 358 shows a flat Earth!
* Thiessen's Glossary cites Albright's text (above), but omits its
* worst errors. Here looming is succinctly described as "An optical
* phenomenon in which objects below and beyond the horizon appear to
* the view of the observer, and even the horizon itself is extended."
* (I think he is saved by also referring to Humphreys.) Unfortunately,
* for "mirage", he simply quotes the first passage from Albright (see
* above). Here again, he cites Humphreys as well. (p. 188)
* Note that this is "W. B. No. 1445 Issued August 1, 1946" and "Reprinted
* May 1949".
* Hans Neuberger (Penn. State) cites 59 references.
* He gives the standard textbook explanation of the green flash, but adds:
* ". . . most observations seem to be associated with refractions in excess
* of the normal," citing Meyer (1939) and Visser & Verstelle (1934).
* He correctly describes looming, sinking, towering and stooping, and
* attributes the mathematical theory of these to Exner (in P&E II).
* His description of mirages as "one or more images of the object"
* clearly means extra images; he seems to fall into the error of
* assuming that one image is "the object" itself.
* A definition that tries to be all things; or at least to cover all
* mirages -- to its detriment:
* "MIRAGE: An optical phenomenon consisting mainly of steady or wavering,
* single or multiple, upright or inverted, vertically enlarged or reduced,
* images of distant objects."
* About all that is useful here is "distant objects"; though "mainly"
* is a nice touch, in light of the rest of the arm-waving! Furthermore:
* "Objects seen in a mirage sometimes appear appreciably higher or lower
* above the horizon than they really are; the difference may amount to as
* much as 10 degrees." So this is all nonsense.
* In addition, they use the curious non-standard terms "lower mirage"
* and "upper mirage" (in place of "inferior" and "superior", respectively.)
* Another completely wrong-headed attempt:
* "mirage -- A refraction phenomenon wherein an image of some object is
* made to appear displaced from its true position."
* On the other hand, looming, towering, etc. are described correctly
* on p. 349, though described as a "mirage effect".
* The WMO is still confused:
* "Mirage: Optical phenomenon consisting essentially of steady or
* wavering, single or multiple, upright or inverted, vertically enlarged
* or reduced, images of distant objects." (p. 117) [Note that "mainly"
* has now become "essentially"; otherwise, their folly goes on unchanged.]
* Worse yet, they now think there is a distinction between an "image"
* and "the actual object":
* "Superior mirage: Special case of mirage , . . . in which the virtual
* image is above the actual object." And:
* "Inferior mirage: Particular case of mirage , . . . in which the virtual
* image is found below the actual object." (both on p. 118)
* (Note that what they call a "virtual image" is in fact a real image, not
* a virtual one.)
* Fairbridge has the same problem:
* "MIRAGE, FATA MORGANA: The mirage is a general category of atmospheric
* optical phenomena involving refraction of light rays bent by differential
* heating of a land or water surface, which results in the distortion or
* displacement of some object viewed, sometimes leading to a misleading
* optical illusion. . . .
* "Three major types of mirage are recognized:
* "The inferior mirage , where the false image is seen below the true
* position of the object viewed."
* Note that the diagram on p. 606 is reproduced from Hutchinson's book
* on limnology. Fairbridge cites all the right references, but seems to
* have misunderstood them. This article is signed by Fairbridge himself.
* . . . and so does McIntosh:
* "Two main classes of mirage occur, (i) `inferior' and (ii) `superior',
* in which the virtual image is below and above the object, respectively."
* (Of course all this nonsense about "virtual images" is quite wrong:
* it is the erect images that are virtual and the inverted ones that
* are real!) Worse yet, after discussing the superior mirage:
* "In such physical conditions multiple reflections may give rise to
* various images, some displaced laterally with respect to the object,
* as in FATA MORGANA."
* Fortunately, the Second Edition is far better -- both more complete
* and more accurate -- than the First. Green flashes are connected with
* mirages; mirages are explicitly stated to be all images, not an "object"
* plus (supposedly spurious) "images". "Lateral mirages" in the
* wrong-headed sense are refuted: "the rare reports of such sightings
* undoubtedly arose from misinterpretations of observations." The lifted
* inversions responsible for superior mirages "are common over, but hardly
* confined to, enclosed bodies of water on warm afternoons when the warmer
* air from the surrounding land flows over the colder water." And the
* initial definition of "mirage" as "An image formed when the atmosphere
* behaves as a lens" is succinct and accurate.
* On the other hand, there are still a few points I'd quibble with.
* Looming and sinking, stooping and towering are all called "mirages".
* Multiple images are attributed to periodic thermal inhomogeneities.
* Inferior and superior mirages are distinguished according to the
* direction of "displacement" of the image. And the Fata Brumosa is
* mistakenly called "Fata Bromosa". Alas, no references are cited.
* Still, this must be regarded as about the best modern summary of
* refraction phenomena available.
*
* Pernter's original 1902 edition, before Exner got involved
* This edition treats only mirages; there is no mention of green flashes.
* It contains only 212 pages, and does not reach halos and rainbows.
* However, there is much material on the Moon Illusion and its possible
* explanations (pp. 42 ff.) that was removed by Exner in later editions;
* notably the references to Ptolemy's "Optics", and the reference (note 1
* on p.42) to Ptolemy's belief in the Almagest that the "vapors at the
* horizon" are involved.
* Dr. Svante August Arrhenius may have the first textbook account
* The "textbook" story appears here: "Da die roten Strahlen die geringste
* Brechung erleiden, verschwindet zuerst das rote Bild der Sonne unter dem
* Horizont, zuletzt das blaue."
* There is also good coverage of mirages, including a reference to Budde
* (but no citation) on pp.832-835.
* Refraction begins on p.827; dispersion appears on p. 829.
* As the organization and title of the chapter on "Meteorologische Optik"
* are exactly the same as in Pernter's book, that was evidently the model
* for this.
* (Cited by Mulder)
* Here Exner adds a great deal of material, including GF on pp.798-799
* at the very end of the volume. He accepts Julius's 1/10 second and so
* must reject Henry's 1 sec., but can't swallow the anomalous dispersion;
* so "Einfacher scheint es, . . . die selective Absorption des Wasserdampfes
* zu berücksichtigen." Though there is no mention of either Abbe or
* Tyndall, I suspect this notion came from Abbe's 1905 editorial in MWR.
* Thanks to Günter Können for a copy of this!
* Sir John William Moore's curious book on meteorology
* The author was a professional physician, and an amateur meteorologist.
* His book is full of speculations about the effects of the weather and
* climate on disease. This 2nd edition contains a two-page Appendix on
* green flashes (listed in the Contents as "The Green Flash at Sunrise
* and Sunset", and on p. 459 both as just "GREEN FLASH" (below the word
* "Appendix") and "The Green Flash on the Horizon at Sunset" (in italics).
* It contains a brief review of the subject, concentrating on the 1906
* discussions in Symons's Met. Mag., and especially on Rambaut's refutation
* of Lippincott. No further mention of refraction phenomena.
* A very brief exposition of the textbook model
* Börnstein mentions only Julius's anomalous-dispersion explanation
* -- which I hardly think qualifies as "Gemeinverständlich"!
* (Full title is "Leitfaden der Wetterkunde -- gemeinverständlich
* bearbeitet von Dr. R. Börnstein, Geh.Regierungsrat" etc.)
* Dritte umgearbeitete und vermehrte Auflage
* ". . . der `grüne Strahl' . . . nennt man das ganz kurz dauernde
* Aufleuchten eines smaragdgrünen Flämmchens an derjenigen Stelle des
* Horizontes, wo die untergehende Sonne gerade verschwunden ist. . . ."
* Thanks to Steve Williams for getting this. (cited by Mulder)
* Author at least reports a couple of GFs he saw himself, as well as both
* inferior and superior mirages (p.82). Good clear presentation of the
* standard model at an elementary level, with clear diagrams.
* A standard textbook account, often cited
* Wegener's mirage theory is reproduced on pp. 151-155.
* Unfortunately, the French literature is shortchanged here: though
* Biot's mirage monograph is cited, and we have a few mentions of standard
* reference works like Mascart's "Traité", Bouguer and Bravais are cited
* only in connection with Halos, and astronomical refraction is mentioned
* mostly in vague gestures toward "astronomical textbooks."
* Green flashes are mentioned only in the last 3 pages (901-903). The
* colored plate at the end of the book shows Wegener's Nachspiegelung.
* Available at the HathiTrust.
* O'C #101
* Alphonse Berget's interesting book, illustrated by Lucien Rudaux
* Chapt. 3 (pp. 20-27) covers refraction phenomena, and contains many of
* Rudaux's monochrome photographs of low-sun phenomena. Fig. 14 on
* p. 24 is noteworthy. P. 25 shows a mirage photograph and drawings.
* There is a nice COLOR PLATE facing p. 24 that shows some of Rudaux's
* drawings of sunsets and green flashes.
* Thanks to Eric Frappa for pointing this out!
* R.W.WOOD
* "It has frequently been contended that the phenomenon is an illusion due
* to contrast, the green spot being an `after-image.' This however is sheer
* nonsense, as any trained observer can testify."
* BUT: ". . . the case of mirage . . . would be unfavorable for the occurrence
* of the green flash" (assuming super-refraction is the cause).
* N.B.: Reprinted by Dover, 1967.
* HUMPHREYS's book
* Pp. 466-467 give the "textbook" GF description; no numbers or diagrams.
* The section on atmospheric optics is a slightly updated version of
* his 1919 J. Franklin Inst. paper; the 2nd ed. (1920), on Google Books,
* says "Pub. for the Franklin Institute . . . by J.B. Lippincott Company".
* The Fata Morgana section is the last 2 pages (pp. 474-475) of the
* mirage discussion. In the 3rd ed., he adds a reference to Schiele's
* thesis, calling it "an elaborate mathematical treatment of" the F.M.,
* and including the Japanese (Geophys. J.) refs. from Schiele.
* Although this is a standard textbook, I have found that some people
* with no background in physics or optics have difficulty in following it.
* In particular, the brief description of "looming" is too terse -- and
* confusing, because of his mentioning the older broad use of that term
* for all sorts of refraction effects at the horizon.
* probably O'C #54 is a garbled version of this book.
* Standard textbook story
* [Newton Lacy Pierce has a prize named after him, awarded by the AAS.]
* BOWDITCH
* Apparently Bowditch acquired the GF paragraph 3821 in 1958;
* the 1943 edition of H.O. 9 lacks it, but it's there in the 1958 one.
* The Decennial Indices to U.S.Govt. pubs. list no edition between.
* Gives the standard Rambaut-Rayleigh story, but with a nice simile:
* "The effect is similar to that of imperfect color printing in which the
* various colors are slightly out of register."
* ". . . the greatest difference, which occurs between violet at one end of
* the spectrum and red at the other, is about ten seconds of arc."
* ". . . under suitable conditions is far more common than generally
* supposed. . . . With a sharp sea horizon and clear atmosphere, an
* attentive observer may see the green flash at as many as 50 percent of
* sunsets and sunrises, although a telescope may be needed for some of
* the observations."
* "Usually it lasts for a period of about half a second to two and
* one-half seconds with about one and a quarter seconds being average."
* ??? WHERE DID THESE NUMBERS COME FROM ???
* This same treatment occurs on p. 500 of the 1995 edition, available
* on-line at
*
* http://www.irbs.com/bowditch/
*
* Full title is:
* The American Practical Navigator, an Epitome of Navigation
* originally by Nathaniel Bowditch, LL.D. [honorary degree from Harvard]
* published by the U.S.Navy Hydrographic Office . . . .
* S.W.VISSER
* Gives the std. textbook story, but then admits it isn't adequate, and
* that "irregular refraction" is certainly necessary for a good display.
* Fairly good short account; cites only O'Connell
* BUT: "It occurs when refraction in the atmosphere close to the Earth's
* surface is abnormally great . . . ."
* Good "Handbuch" treatment of optical subjects
* "Grüner Strahl", pp.352-353, cites only Meyer's article in Hb.d.Geophys.
* and shows a sketch of Lagaaij's green ray (without attribution). The
* explanation of the phenomenon is a bit muddled, but mostly follows the
* textbook story; however, following Meyer's lead, "Treten nun infolge
* außergewöhnlicher Temperaturschichtung -- insbesondere wahrscheinlich
* durch das Vorhandensein tiefliegenden kräftigen Inversion -- zusätzlich
* Luftspiegelungen und damit in Verbindung wohl auch anormale Verhältnisse
* der atmosphärischen Dispersion in diesen Schichten auf, dann können
* Zerrbilde des oberen Sonnenteiles als Erklärung für den grünen Strahl
* angenommen werden. Es wird auch vermutet, daß die Absorptionsbanden des
* Ozons und des Wasserdampfes im sichtbaren Spektralbereich hierbei mit eine
* Rolle spielen. Eine befriedigende Theorie für den ganzen
* Erscheinungskomplex des grünen Strahls gibt es jedoch noch nicht."
* So this is one of the BEST and MOST TRUTHFUL accounts to be found!
* The "Luftspiegelung" article (pp.498-500) also cites P&E, and redraws
* several of Wegener's diagrams. Both articles are credited to Foitzik.
* Thanks to Siebren van der Werf for this reference!
* Maybe this is the source of Fraser's and McIntosh's error:
* "It is related to the greater Rayleigh scattering and refraction in the
* short wavelengths (violet, blue, green) than in the long (red) waves of
* sunlight. Under hazy conditions it may appear blue or violet."
* (sure sounds as if one copied from the other.)
* (Fairbridge buries "Green Flash" under "Twilight")
* Standard textbook story, well presented
* a JUVENILE book
* Unaccountably quotes from Mostyn's 1891 Nature paper, but confuses
* him with Nijland's similar obsn. & says they were together!
* All the photos are in b/w, alas. Ch.2 is "Green and Blue Flashes".
* SUNSET PHOTOS and refraction in final chapter
* Ch.7 and Plates 7-10 and 7-11 show distorted sunsets
* p.177: "All are variations of the same effect and all, in my judgment,
* may appropriately be given the same name." (green flash)
* He even has a section called "The green flash legend" (pp.172-173), and
* quotes from Verne!
* Note his good (though brief) treatment of the Fata Morgana on pp.
* 165-167 and Plates 7-4 to 7-7.
* Alan H. Batten reviews Greenler's book, citing Hogg's JRASC mirage paper
* No mention of GF. Available from ADS.
* MEINELS' BOOK
* probably the best GF treatment available in hard covers, though the
* references are spotty
* Replete with errors from Botley, etc.;
* but they recognize that ADAPTATION plays a part.
* Kurt Nassau's "Fifteen Causes of Color" book
* A good explanation of the "textbook" flash, with "prism" analogy.
* Thanks to Dave Fenner for pointing this out!
* DUTTON
* The same passage appears on p.620 of the 12th edition, edited by
* G.D.Dunlap and H.H.Shufeldt (1969 - 1972), except that Maloney has
* changed "The" to "A" at the start of the final sentence.
* ". . . the longer waves of red being least refracted, the shorter blue
* and violet waves being more refracted. The red, orange and yellow light
* is cut off by the horizon when the blue and violet is still momentarily
* visible. These blue and violet rays cause the green flash." [SIC!]
* [This nonsense seems to have appeared in the 12th edition, in 1969.]
* [It is not in the 4th (1961) printing of the 1957/58 edition.]
* "It is estimated that at sea in the tropics, the green flash may be seen
* as often as 50 percent of the time; it is, of course, easier to observe at
* sunset. The green flash usually lasts for a period of between one-half
* and one second." Again -- cf. Bowditch! -- mysterious numbers.
* This can't be what Cotter (1968) was objecting to:
* "Using the time of the green flash to obtain a line of position is
* merely a variation of the horizon sight described in the previous article.
* It is somewhat easier to determine the time of the flash than to determine
* the instant the sun's upper limb disappears below the horizon, when there
* is no green flash." [because this appeared after Cotter's book]
* 1972 edition of the glossary originally published in 1916 by the Met.Office
* Looks as if the GF entry was not updated since Mulder's book:
* ". . . greater degree of RAYLEIGH SCATTERING experienced by the violet and
* blue rays. In a hazy atmosphere such differential scattering may not be
* appreciable and the flash may then appear blue or violet."
* This is the same error made by Fraser (1972) and it is likely he got it
* from an earlier edition of this, or from Fairbridge (above).
* ". . . the analogous very rare phenomenon of the `red flash' . . . ."
* Vincent J. Schaefer never saw a GF, I'll wager!
* "Plate 9. . . . The green flash is never seen under the conditions that
* produced the sun's image in this photograph." (Actually, it looks like a
* very good opportunity for a mock-mirage flash; the reddening is
* appreciable, but not excessive.)
* "Quite rarely . . . only occurs when the atmosphere is extremely clean . . . ."
* Caption to Fig. C.Pl.9 says "The atmosphere develops small density
* differences that create the spreading [sic] of the image."
* BLUE-SKY CONFUSION error: (quoted by Hechler, 1994)
* ". . . der noch etwas später verschwindende blaue Oberrand der Sonne
* wegen des mangelnden Farbkontrastes zur bläulichen Himmelsfarbe dem
* Auge nicht sichtbar wird."
* NOT YET IN HAND
* Craig Bohren wisely confines his attention to the Green Rim.
* But he brashly states that "there is a Scottish legend . . . ."
* (Thanks a lot, Jules Verne!)
* "It is indeed true that the green flash is rarely observed, but not
* because it is rarely observable. The sad truth is that most people are
* only dimly aware of their surroundings." You said it, Craig!
* Chet Raymo describes his fruitless search for green flashes
* The reason is not hard to find: "I have sat on the high rocky spine of
* the Dingle Peninsula and watched the sun sag into the North Atlantic."
* Much of the peninsula is over 500 m above the sea; the highest point is
* some 950m high -- all much too high for a inferior-mirage flash to be
* seen without aid; and in a region not much subject to strong inversions.
* He depends mainly on O'Connell's 1960 Scientific American article,
* which he mistakenly thinks had the first color photographs. Much of the
* wording here is identical to his 1990s columns in the Boston Globe .
* [Placed here as it is a tutorial account.]
* Review of the paperback edition of Greenler's book in JBAA
* GF is mentioned. Available from ADS.
* not exactly a textbook, but compiled by and for amateur astronomers
* This is one of the few places where one reads that ". . . it can be safely
* observed with binoculars or a telescope." The description applies to the
* inferior-mirage flash; the advice is sound.
* This popular textbook seems to be the source of the canard about the
* Byrd expedition: "Members of Admiral Byrd's expedition in the south
* polar region reported seeing the green flash for 35 minutes in September
* as the sun slowly rose above the horizon, marking the end of the long
* winter." The actual date was Oct. 16, and the observation was made at
* sunset, not sunrise -- see Owen (1929), Davies (1931) and Haines (1931).
* (Note that Little America was some 11 degrees from the Pole.)
* Also, there is a curious statement about "purple light".
* However, there is also the correct statement, "Usually, the green light
* is too faint to see with the human eye. However, under certain
* atmospheric conditions, such as when the surface air is very hot or when
* an upper-level inversion exists, the green light is magnified by the
* atmosphere."
* MARINE OBSERVER'S HANDBOOK
* The 7th Edition (June, 1950) cited by Hilder (1951) bears the cover
* title: "Manual of Meteorological Observing. Part II. Marine Observer's
* Handbook". That edition gives GF on p.74, and very little on mirage.
* Final paragraph mentions 3 forms of GREEN RAY or fog
* CRAIG BOHREN's encyclopedia article
* The GF treatment is on pp. 423-424.
* "Compared to the rainbow, the green flash is not a rare phenomenon."
* It is preceded by a section on the distortion of the setting Sun, which
* follows Fraser in forgetting about dip, so that the miraged multiple
* images are attributed to gravity waves.
* COLLIER'S ENCYCLOPEDIA
* The whole "Atmosphere" article is pp.161-172; the GF is only a
* two-sentence paragraph. The description is vague and incorrect.
* A popular book on meteorology devotes 2 full pages to "the green flash"
* (including "the Scottish saying" and the textbook explanation.)
* Mirages get the same uneven treatment, and the Novaya Zemlya effect
* is made to appear a normal concomitant of green flashes, "after the Sun
* sets". The bogus term "fata bromosa" appears on p. 51. But the authors
* have tried hard to bring meteorology to the public, despite such lapses.
* A curious feature of this book is that all of the numerous photographs
* are in black-and-white -- no color work, even in the rainbow picture.
* [The authors tell me their publisher cheaped them out here.]
* Another odd thing is the confusion over the publisher. The title page
* says "A Touchstone Book . . . Published by Simon & Schuster"; the reverse
* says "A Fireside book" but also "Touchstone and colophon are registered
* trademarks of Simon & Schuster Inc." The authors retain the copyright.
* Amazon.com says "Fireside". The authors' Web page says "Simon &
* Schuster". The review in Kirkus Reviews says "Touchstone".
* [The Svarneys say the publisher should be given as S&S.]
*
* [see also Hoppe (1941) in GF file, and Bessel (1823) in REFR. OBS. file.]
*
* DISCOVERY of RED and BLUE RIMS by Delisle
* Observing at Luxembourg, 25 Jul. 1715, Delisle says:
* "J'ai été fort attentif à examiner si Jupiter & ses Satellites ne
* prenderoient pas à l'approche de la Lune des couleurs semblables à
* celles que j'avois vû dans l'Eclipse de Venus le mois passé ; mais
* je n'en ai pu remarquer aucune qui se puisse attribuer à l'approche
* de la Lune." (He was accompanied by Chardeloup, from the Roy. Soc. in
* London; Delisle used a 20-foot telescope, and Chardeloup an 8-ft.)
* "Pour nous mieux préparer à observer ces couleurs, nous avions examiné
* avant l'Eclipse les couleurs que la Lunette causoit à Jupiter, & nous
* avons trouvé ces couleurs toûjours dirigées au centre de la Lunette,
* le rouge étant en dedans, comme cela devoit arriver. J'ai aussi aussi
* [sic] fait remarquer à M. Chardeloup que Jupiter prenoit vers l'horizon
* les mêmes couleurs, mais qu'elles provenoient d'une autre cause, car
* elles étoient dirigées autrement, le rouge paroissant toûjours le
* plus près de l'horizon, & le bleu le plus éloigné, & cela dans quelque
* situation de la Lunette que l'on place Jupiter. Ainsi les couleurs que
* nous avons remarqué dans cette Observation, provenoient ou des Lunettes
* ou de l'approche de l'horizon, & nullement de l'approche de la Lune,
* Jupiter nous ayant paru très-blanc pendant son Immersion & son Emersion."
* Thus, he was not sure whether the effect near the horizon was real or
* a telescopic artifact. (Cited by Bouguer, 1748.)
* RED and BLUE RIMS DISCOVERED on Sun by BOUGUER
* This is the ``meeting abstract'' -- evidently written by the Secretary,
* as Bouguer is referred to in the 3rd person.
* The paper is mostly about Bouguer's invention of the heliometer;
* but, in the early observations, ". . . il a toûjours trouvé les bords
* supérieur & inférieur plus ondoyans que les bords latéraux, & de
* plus, toûjours affectés de couleurs qui y forment un iris incommode;
* cette apparence peu sensible, lorsqu'on se sert de lunettes de sept à
* huit pieds, telles qu'on les a jusqu'ici employées à la recherche du
* diamètre di Soleil, devient très-marquée dans l'heliomètre; & les
* couleurs même qu'on observe dans les deux bords, lui en ont indiqué
* la cause: on sait qu'un rayon qui nous vient du Soleil n'est pas un
* rayon simple, mais un composé de sept faisceaux de rayons de couleurs
* différentes, & tous différemment refrangibles. Le plus haut point du
* diamètre vertical sera donc vû par le faisceau de rayons bleus qui
* souffrira une plus grande réfraction, & qui par conséquent le fera
* paroître plus haut, & son extrémité la plus basse par le faisceau
* de rayons qui aura souffert la moindre réfraction, c'est-à-dire le
* faisceau de rayons rouges . . . ." (p. 93)
* So Bouguer understood that the effect is due to ATMOSPHERIC DISPERSION.
* No doubt SIMULTANEOUS CONTRAST helped him detect the color difference.
* ". . . on observera toûjours le bord supérieur terminé par un trait
* bleu, & l'inférieur par un trait rouge, au lieu qu'on n'observera rien
* de pareil dans les bords latéraux, parce que la réfraction de leurs
* rayons se fait dans un plan vertical, & sans les déranger en aucune
* façon dans le sens du diamètre horizontal, dont elle ne peut par
* conséquent altérer ni la couleur, ni la netté, ni la mesure." (p. 94)
* (mentioned, but not cited, by Arago in 1836.)
* Cf. St. Chevalier (1913)!
* Actually printed in 1752.
* The details of Bouguer's HELIOMETER and COLORED RIMS on the Sun
* The first 2/3 or so of this paper are devoted to explaining why the
* horizontal diameter of the Sun could not be measured accurately:
* before equatorial telescopes with good clock drives were available,
* the image moved too fast to check the opposite limbs simultaneously
* with a filar micrometer, and the diurnal motion was too fast to allow
* accurate determinations of the east and west limbs by timings with a fixed
* telescope: "Tout la difficulté qu'on trouve dans cette observation,
* consiste à estimer les fractions de secondes . . . on se trompera
* aisément d'un tiers ou d'une moitié de seconde de temps, ce qui en
* produire jusqu'à cinq ou six, ou même sept de degré sur le diamètre."
* There is also the problem that the clock escapement is not exactly
* symmetrical, so that long and short intervals alternate (pp. 20-21).
* Furthermore, the Moon usually (because of its phase) shows only a full
* diameter in an oblique direction, and so cannot be well measured at all.
* Bouguer seems to have been inspired by the binocular: "On sait
* que le binocle avoit été imaginé pour procurer aux observateurs la
* prétendue commodité de regarder le même objet avec les deux yeux.
* Le nouvel instrument, l'héliomètre ou l'astromètre dont nous
* voulons introduire l'usage, fera voir au contraire avec un seul oeil deux
* objets à la fois, ou deux parties du même, quoique considérablement
* éloignées l'une de l'autre . . . ." [p. 23]
* He diminishes both the brightness and the chromatic aberration by
* reducing the apertures to 6 or 8 mm: ". . . on peut diminuer extrêmement
* les ouvertures des objectifs; % ce sera toûjours le mieux, lorsqu'on ne
* se proposera de mesurer que les diamètres du Soleil. Il sera avantageux
* de réduire alors par des diaphragmes, les deux verres à une simple
* partie de pouce, ou à trois ou quatre lignes de largeur; car on évitera,
* par ce rétrécissement, presque tout le mauvais effet de la séparation
* des rayons colorés qui ternissent les bords de l'astre." [p. 25]
* The state of technical optics in 1748 was dismal: "Un Artiste adroit
* a taillé dans le même bassin huit objectifs de 18 pieds de foyer; &
* c'est entre ces huit verres que j'en ai choisi deux : la précaution
* d'en faire tailler plusieurs s'est trouvée utile; deux ou trois de ces
* objectifs, soit que cela vînt de leur figure ou de ls diverse densité
* de leur matière, avoient leurs foyers différens de 7 à 8 pouces,
* quoiqu'on eût tachéde les rendre parfaitement égaux." [p. 27]
* Finally, he reports his preliminary attempts to verify the sphericity
* of the Sun: "On sait que c'est un des effets de notre atmosphère de
* diminuer un peu les diamètres verticaux apparens du Soleil & de la
* Lune; ce qui vient de ce que la réfraction élève un peu plus le bord
* inférieur de leur disque que le supérieur. Il n'y a personne qui n'ait
* vû ces deux astres sous une forme sensiblement elliptique, lorsqu'ils
* étoient très-voisins de l'horizon & sujets à des réfractions
* plus fortes. Il doit arriver encore quelque chose de semblable dans
* les grandes hauteurs, quoique la différence des deux axes soit alors
* moins considérable, & cesse d'être aperc,ûe à la vûe simple.
* Cette petite quantité devoit être de deux secondes sur le Soleil,
* aux environs de midi, pendant le mois d'Octobre dernier, qui est le
* temps où j'ai commencé à observer : cependant, bien loin de trouver
* cette différence, j'ai toûjours remarqué que le diamètre vertical
* étoit plus grand que l'horizontal ; c'est ce dont je me suis assuré
* en appliquant tantôt l'oeil immédiatement à l'héliomètre, & tantôt
* en recevant l'image des deux portions de disque sur une tablette que je
* plaçois en dehors perpendiculairement à l'axe de l'instrument. . . .
* Qu'on mette à une seconde, ou seulement une demi-seconde, le petit excès
* que j'ai aperc,û, ce sera une demi-seconde à joindre aux deux dont les
* réfractions raccourcissent le diamètre vertical. Il suivroit de là
* que ce diamètre seroit plus grand que l'autre de deux secondes & demie
* ou de trois secondes : le Soleil auroit la forme d'un sphéroïde oblong,
* & la différence des deux axes seroit au moins d'une 750e partie." [p.30]
* He decided to suspend judgment until having made observations at
* different altitudes and with heliometers of different focal lengths.
* In examining the limbs more closely, he noticed that the upper and lower
* limbs were less well defined than the lateral ones, and more subject to
* "ondulations importunes". Then: "Lorsque cet inconvénient n'a pas
* lieu, le haut & le bas de l'image sone encore toûjours sujets à une
* gradation de couleurs qui nuit à sa distinction ; à peu près de la
* même manière que la pénombre empêche de distinguer les limites de
* l'ombre avec laquelle elle confine." [p. 31]
* "Si le défaut continuel de netteté des bords supérieur & inférieur
* du Soleil, est très-capable d'embarraser les Observateurs scrupuleux, it
* offre aussi un sujet de problème pour les Physiciens, qui ne manqueront
* pas d'en demander la solution : elle n'est pas difficile à trouver, &
* je crois pouvoir l'indiquer d'une manière sûre. Cette apparence ne peut
* venir que de la décomposition que souffre la lumière en traversant notre
* atmosphère ; les rayons bleus ou violets qui partent en même temps que
* les rayons des autres couleurs, du haut du disque, sont sujets à un peu
* plus de réfraction que ces derniers, ils se courbent un peu davantage;
* ils nous paroissent donc venir d'un peu plus haut, en portant plus loin
* l'illusion ordinaire des réfractions. C'est tout le contraire si nous
* jetons la vûe sur le bord inférieur, nous devons le voir principalement
* par des rayons rouges qui souffrent un peu moins de courbure dans leur
* trajet ; ces rayons, en se courbant moins, doivent frapper nos yeux comme
* s'ils partoient d'un point plus bas, & par conséquent faire paroître
* un peu en dessous la partie inférieure du disque qu'ils étendent,
* pendant que les rayons bleus & violets contribuent à étendre ce même
* disque par sa partie supérieure.
* "Tout ce que nous avançons ici deviendra incontestable, si l'on
* considère plus attentivement l'image du Soleil fournie par une longue
* lunette, & rec,ûe sur une tablette. On verra que la partie de l'image
* qui répond au bord supérieur, est terminée par un trait bleu, pendent
* que le rouge domine sur le bord opposé." [p. 32] -- and he cites
* Delisle's 1715 observation of Jupiter.
* Then he introduces the analogy of the PRISM: "l'explication que nous
* en donnons, est outre cela tout à fait conforme à ce qu'on sait de
* la nature des couleurs, dont la lumière primitive ou celle du Soleil
* est formée. Lorsque les rayons de cet astre pénètrent obliquement
* les différentes couches de la masse d'air qui nous environne, & qui
* sont successivement plus denses, ils doivent être sujets aux mêmes
* accidens que s'ils traversoient obliquement les faces d'un prisme,
* puisqu'ils coupent les couches de l'atmosphère dans des endroits qui
* ne sont pas réciproquement parallèles les uns aux autres . . . ." [p. 33]
* Dated 24 Avril 1748; actually printed in 1752.
* RED RIM on Sun; EARLY MOCK MIRAGES
* "A little before sun-setting, I have often seen the edge of the Sun with
* such protuberances and indentures, as have rendered him, in appearance, a
* very odd figure; the protuberances shooting out far beyond, and the
* indentures pressing into, the disk of the Sun, and always through a
* telescope magnifying fifty-five times, the lower limb has appeared with a
* red glowing arch beneath it, and close to the edge of the Sun, whilst the
* other parts have been clear.
* "At sun-setting, such protuberances and indentures have appeared to
* slide or move along the vertical limbs, from the lower limb to the higher,
* and there vanishing, so as often to form a segment of the Sun's upper limb
* apparently separated from the disk, for a small space of time.
* "At sun-rising, I have often seen the like protuberances, indentures,
* and slices, above described; but with this difference of motion, that at
* sun-rising they first appear to rise in the Sun's upper limb, and slide or
* move downward to the lower limb; or, which is the same thing, they always
* appear at the rising and setting of the Sun, to keep in the same parallels
* of altitude, by the telescope. This property has been many times so
* easily discernable, even by the naked eye, that I have observed the Sun's
* upper limb to shoot out towards right and left, and move downward, forming
* the upper part of the disk an apparent portion of a lesser spheroid than
* the lower part at rising, and the contrary at setting."
* "These protuberances and indentures . . . enabled me to conclude, that
* certain strata of the atmosphere, having different refractive powers, and
* lying horizontally across the conical or cycloidal space traced out by the
* rays, between the eye and that part of the atmosphere first touched by the
* rays, must have been the cause of such apparent protuberances and
* indentures, in an horizontal direction, across the Sun's limbs . . . ."
* Jim Mosher points out that Mr. Samuel Dunn was a prominent cartographer
* and mathematics teacher in this period. He died in 1794.
* PETER DOLLOND's remark about dispersion
* This is mostly about the use of 2 glasses with a common spherical
* surface, placed before the objective (!) of a telescope to correct
* refraction by sliding the concave glass over the convex one.
* But near the end, on p. 335 (mis-numbered 535), he says:
* "It must be observed, that when a star or planet is but a few degrees
* above the horizon, the refraction of the atmosphere occasions it to be
* considerably coloured. The refraction of the lens acting in a contrary
* direction would exactly correct that colour, if the dissipation of the
* rays of light were the same in glass as in air; but as it is greater in
* glass than in air, the colours occasioned by the refraction of the
* atmosphere will be rather more than corrected by those occasioned by the
* refraction of the lens."
* (mentioned, but not cited, by Arago, 1836.)
* WILLIAM HERSCHEL's remarks on atmospheric dispersion
* The remark appears as a footnote to the catalogue of double stars.
* On p.83, Herschel lists entry #107 as "Congerie Stellularum Sagittarii
* borealior" and gives his approximate measurement, with the remark:
* "As accurate as the prismatic power of the atmosphere, which lengthens
* the stars, will permit." At the end of the entry he has the footnote:
* "What I call the prismatic power of the atmosphere, of which little
* notice has been taken by astronomers, is that part of its refractive
* quality whereby it disperses the rays of light, and gives a lengthened
* and coloured image of a lucid point. It is very visible in low stars;
* FOMALHAND, for instance, affords a beautiful prismatic spectrum. That
* this power ought not to be overlooked in delicate and low observations,
* is evident from some measures I have taken to ascertain its quantity.
* Thus I found, May 4, 1783, that the perpendicular diameter of ε,
* FLAMSTEED's 20th Sagittarii, measured 16'' 9''', while the horizontal was
* 8'' 35'''; which gives 7'' 34''' for the prismatic effect: the measures
* were taken with 460, near the meridian, and the air remarkably clear.
* And though this power, which depends on the obliquity of the incident ray,
* diminishes very fast in greater altitudes, yet I have found its effects
* perceivable as high, not only as α or γ Corvi in the meridian,
* but up to Spica Virginis, and even to Regulus. Experiments on these two
* latter stars I made November 20, 1782; when Regulus, at the altitude of
* 49°, shewed the purple rather fuller at the bottom of the field of
* view than when it was at the upper edge; which shews that the prismatic
* powers of the edges of the eye lens were assisted in one situation
* by the power of the atmosphere, but counteracted by it in the other.
* I turned the lens in all situations, to convince myself that it was not
* in fault. This experiment explains also, why a star is not always best
* in the center of the field of view; a fact I have often noticed before
* I knew the cause."
* [Most of the footnote spills onto p. 84.]
* RED and BLUE RIMS ON MARS
* "With a power of 170 and upwards, the disk of the planet appeared much
* elongated, especially when near the horizon; the upper limb was of a fine
* blue, the lower of a deep red." (p.378)
* [reprinted in German in Bode's Astron. Jahrbuch (1819) pp.113-120]
* [and in French, in vol. 5 of Bibliotheque Universelle (at BHL)]
* Stephen Lee, Clerk and Librarian to the Royal Society
* O'C #79
* Wide-ranging discussion of refraction, dispersion, scintillation,
* chromatic scintillation, spectroscopy, etc., with Greek and Latin quotes
* refers to Lee's 1815 paper.
* "Read before the Meteorological Society of London in February and March
* 1824, and published by permission."
* ARAGO's fight with CAUCHY
*
* The trouble began when Cauchy donated to the Academie a copy of his
* work on the theory of light, which contained the claim that gases did
* not show dispersion. Arago noticed this lapse, and tried to correct it
* with a letter, printed under ``Correspondance'' at the end of the 29
* Aug. 1836 meeting:
* "A l'occasion d'un nouveau mémoire de M. Cauchy sur la théorie
* de la lumière, présenté aujourd'hui à l'Academie, M. Arago croit
* devoir signaler une erreur de fait dans laquelle l'auteur est tombé au
* sujet de la dispersion des substances gazeuses. M. Cauchy suppose cette
* dispersion nulle. M. Arago dit, au contraire, qu'elle est sensible et
* qu'il l'a mesurée pour un bon nombre de gaz simples et composés.
* Dans une prochaine séance, M. Arago fera connaître tous ses
* résultats."
* CAUCHY refuses to take his medicine:
* "Il serait assez singulier que l'erreur de fait se trouvât, non dans
* le mémoire lithographié, mais dans l'assertion qu'on vient de lire,
* appliquée, comme elle semble l'être, à ce nouveau mémoire; . . . .
* Ce que M. Arago aura dit, c'est que jusqu'à ce jour les physiciens
* n'avaient point observé la dispersion dans les gaz. C'est là ce que
* j'ai dit moi-même dans la 9e livraison d'un mémoire plus ancien, où,
* après avoir établi et vérifié les lois de la dispersion dans les
* corps solides, après avoir expliqué comment on s'assure que ce
* phénomène disparaît dans le vide, j'ajoute que jusqu'à ce jour on
* n'a pu découvrir dans les gaz aucune trace de la dispersion des
* couleurs . . . . La note insérée dans le Compte rendu prouve
* elle-même l'exactitude de cette proposition à l'époque où
* j'écrivais ces lignes, et c'est parce que les physiciens n'avaient
* jusqu'ici rien découvert à cet égard, que les observations promises
* par M. Arago contribueront notablement au progrès de la science. Mais
* personne ne s'étonnera que je n'aie point parlé de ces observations
* plusiers mois avant qu'elles fussent publiées et peut-être même
* entreprises."
* [printed under ``Correspondance'' for the 3 Octobre 1836 séance.]
* ARAGO lambastes Cauchy for his obstinacy:
* He calls Cauchy's blunder "une erreur de fait capitale," and goes on:
* "En essayant ainsi de détourner M. Cauchy de persister dans la peine
* qu'il se donnait pour déduire de sa savante théorie une conséquence
* que l'observation démentait de tout point, M. Arago croyait avoir droit
* à des remercîments. Loin de là, M. Cauchy s'est montré offensé.
* Son confrère se voit donc obligé d'examiner ses griefs.
* He then documents in detail Cauchy's wrong statements, and quotes
* Cauchy's claim that Arago should have said that the physicists had
* never observed dispersion in gases "to this day". Then: "M. Arago
* déclare ne pouvoir accepter cette rectification ; il montre en effet,
* que la dispersion de l'atmosphère terrestre avait été aperçue
*
* En 1748 par Bouguer
* En 1761 par Lemonnier
* En 1779 par Dollond
* En 1783, en 1785 et en 1805, par Herschel"
*
* and tops this list with his own measurements from 1812, adding:
* "Enfin, en 1815, M. Stephen Lee lut à la Société royale de
* Londres, et publia dans les Transactions philosophiques , un mémoire
* intitulé : Sur la force DISPERSIVE de l'atmosphère et ses effets
* sur les observations astronomiques .
* « Personne, dit M. Cauchy, ne s'étonnera, que je n'aie pas parlé
* des observations de M. Arago, plusiers mois avant qu'elles fussent
* publiées ET PEUT-ÊTRE MÊME ENTREPRISES. »
* A l'insinuation peu bienveillante que ce passage renferme, M. Arago
* répond par deux faits : Ses mesures de la force dispersive de
* l'atmosphère datent de 1812; elles furent citées, quelque temps après
* cette époque, par M. de Lindenau dans le Journal astronomique de
* Gotha . Quant aux mesures de la DISPERSION des gaz et des vapeurs
* que M. Arago avait faites avec M. Petit, son beau-frère, elles
* remontent à 1815 ; on en trouve une analyse détaillée dans le
* premier article du premier cahier du premier volume des Annales
* de physique et de chimie PUBLIÉ en février 1816! M. Arago
* aurait donc, peut-être le droit de remplacer le dernier paragraphe
* guillemetté de M. Cauchy, par le suivant, où quelques expressions
* seulement sont changées :
* « Tout le monde s'étonnera que M. Cauchy n'ait pas connu les
* observations de M. Arago, vingt ans après qu'elles avaient été
* publiées! »
* ARAGO says the effect is well known
* "Les astronomes qui ont essayé, même une seule fois dans leur vie,
* de déterminer la valeur des réfractions horizontales, savent combien
* peu il est permis de compter sur les résultats. C'est ordinairement le
* bord du soleil qui sert de point de mire; mais près de l'horizon, ce
* bord paraît si fortement dentelé, si vivement irisé, si déchiqueté;
* ces diverses irrégularités sone d'ailleurs tellement changeantes que
* l'observateur ne sait où diriger le fil du réticule, à quel point, à
* quel hauteur arrêter sa lunette sur le limbe gradué de l'instrument
* qu'il emploie." (p. 211)
* BESSEL on DISPERSION
* ". . . la loi de la chaleur . . . est évidemment très-variable . . . ."
* "Jusqu'à ce qu'on ait réussi à exprimer cette loi en fonction du
* temps, il sera impossible de former une table qui représente parfaitement
* la réfraction pour chaque distance au zénith et pour chaque temps."
* ". . . quoique l'air parût être parfaitement clair, le rouge et le bleu
* du spectre étaient seuls visibles, de manière que l'étoile resemblait
* en quelque sorte à une étoile double, composée d'une étoile rouge et
* d'une bleu."
* "Il paraît donc que des observations faites dans des distances au zénith
* plus grandes que 85° ne seraient que d'un très-petit poids pour
* l'astronomie, même si l'on pouvait exactement calculer les réfractions
* nécessaires pour les réduire."
* ". . . l'influence des variations de la loi de la chaleur des couches de
* l'air ne commence à être sensible qu'au delà du 85e degré."
* "Au delà de cette limite, c'est-à-dire entre le 85e degré de distance
* au zénith et l'horizon, l'influence des variations de la loi de la
* chaleur des couches de l'air croît rapidement, ce que la théorie
* indique."
* Day-night variations in refraction residuals amount to 30" at 1/2 deg.
* altitude; "Il est évidemment impossible d'expliquer de telles
* différences sans connaître les variations de la loi de la chaleur des
* couches de l'air dépendantes du temps. . . . Mais cela serait un problème
* dont la solution, supposée possible, aurait plus de prix pour la
* météorologie que pour l'astronomie."
* (Many of these remarks are prefigured in his 1823 A.N. paper.)
* ARAGO indulges his penchant for priority disputes and reminds Bessel
* and others that he saw atmospheric dispersion first!
* "M. Arago a rédigé une Note historique où toutes ces recherches sont
* analysées et appréciées." [Was it ever published? Montigny (1855,
* p.55) thinks not; and in Arago's Œuvres Complètes, T. XI, p. 737, we
* read: "Le Mémoire annoncé par M. Arago n'a pas été rédigé. It then
* records his observations of atmospheric dispersion going back to 1811.]
* RED AND VIOLET RIMS PREDICTED (but thought unobservable)
* "Da nun die Strahlen bei ihren Durchgange durch die Atmosphäre
* gebrochen und somit ohne Zweifel auch zerstreut werden, so muss das Bild
* der Sonne ein in verticaler Richtung liegendes S p e c t r u m bilden.
* Unmittelbar ist freilich dieses Erscheinung nicht bemerkbar, dazu ist der
* Zerstreuungswinkel viel zu klein, dem ungeachtet können wir uns das
* Sonnenbild als eine Reihe farbiger Bilder denken, die einander zwar nahe
* aber nicht vollkommen decken, indem das rothe Bild die kleinste, das
* violette hingegen die grösste Höhe über dem Horizonte haben muss,
* woraus sogleich folgt, dass Blendgläser von verschiedener Farbe auch eine
* Verschiedenheit in der beobachteten Sonnenhöhe zur Folge haben werden."
* (He observed only through such colored glasses, so failed to discover
* the green rim.)
* REFRACTION DEPENDS ON STAR COLOR:
* "Wegen der Farbenzerstreuung der Atmosphäre muss bei den
* verschiedenfarbigen Sternen die Refraction etwas Verschieden sein, bei den
* rothen Sternen geringer, als bei den weissen oder grünen."
* ATMOSPHERIC REDDENING AFFECTS APPARENT REFRACTION:
* "Gewöhnlich ist das Sonnenlicht mehr oder weniger roth, wo dann die
* blauen Strahlen grossentheils absorbiert sind. Hieran knüpft sich von
* selbst die Bemerkung, dass die Refraction der weissen Sterne nahe am
* Horizont sich jener des rothen Strahles nähert, vorausgesetzt, dass die
* scheinbare Mitte des vorzugsweise roth erscheinenden Sternes pointiert
* wird." (p.107)
* (Here the double-s is spelled with two small s's.)
* MONTIGNY:
* OBSERVATION OF --> SOLAR <-- COLORED RIMS (over a century after Bouguer!)
* "On sait sans doute, que, si l'on examine au télescope le soleil près
* de l'horizon, une partie des arcs inférieur et supérieur de son disque
* sont colorés, le premier en rouge et orangé, et le second en bleu.
* "Les arcs rouge et orangé qui bordent la partie inférieure du disque
* solaire en s'amincissant à leurs extrémités, près du diametre
* horizontal, sont très-distinctes; le jaune l'est parfois aussi. Le 27
* septembre, le matin, alors que le bord infèrieure s'elevait sur
* l'horizon, l'épaisseur des trois teintes était de 19''.
* "Quand le ciel est pur, on distingue aisément le teinte violette
* indigo au-dessus de l'arc bleu supérieure; elle est parfois
* très-prononcée. Le vert se voit aussi au-dessus du bleu, mais il se
* distingue moins fréquemment." (p.46)
* Also mentions colors in SUNSPOTS.
* NOTE: Read at the meeting of 5 Nov. 1853, but apparently published in 1855.
* An extended German abstract of this paper appeared in
* "Fortschritte der Physik im Jahre 1855", 11, pp. 575-580 (1858).
* (A shorter version appeared the previous year, in FdP 1854, pp. 633-634.)
* O'C #92
* Casual mention of blue and red rims seen at a low-altitude solar eclipse
* The passage is on p. 41; the observation was not understood.
* ARAGO's collected works: unpublished material from his observing logs
* This volume has two title pages, one for the "collected works", and
* one for the "scientific memoirs". So this is Vol. 11 of the "Œuvres
* Complètes" but only Vol. 2 of the "Mémoires Scientifiques".
* Arago's papers were edited by J. A. Barral, and amount to some 20
* volumes in all.
* The discussion of atmospheric dispersion arose from a dispute with
* Cauchy, who incautiously said in 1836 that gases showed no dispersion.
* Arago, who knew better, had to protest; but never published his promised
* review of the subject, nor the details of his own early observations
* that are recorded here. The section on pp. 733-748 is entitled ``Sur
* les pouvoirs dispersifs'' and the section on air beginning on p. 737 is
* called ``Dispersion de l'atmosphère''.
* Most curiously of all, nothing appears here about his observations
* with Biot. Perhaps those were recorded only in Biot's observing logs;
* perhaps Arago felt their publication on the meridian survey was enough;
* or perhaps the later disputes between Arago and Biot were the reason.
* Anyhow, this is useful supplemental material.
* The discussion begins with the dispute with Cauchy (p. 736; see above)
* and he then mentions his own observations of 1812, which he says were
* cited by Lindenau in Journal Astronomique de Gotha.
* The details of these observations appear on pp. 737 ff.:
* "9 mai 1811. -- A 12h 50m de temps sidéral la bordure rouge du
* bord inférieur réel de la Lune était encore bien visible avec le
* groissement de 200 fois (1ee lunette de Lerebours). Le bord supérieur
* réel (inférieur apparent) ne présentait alors que de très-légères
* traces de bleu verdâtre. Avec le groissement de 90 fois la bordure
* rouge était presque invisible; quant au bord inférieure on ne voyait
* pas la moindre nuance de couleurs." He also notices the colored rims on
* Mars, where (I suppose by contrast) the upper limb appeared blue-violet.
* There is then reported an interesting series of experiments to null
* out the dispersion with a prism placed before the eyepiece, while
* looking at the colored rims of the Sun a little before sunset. The
* upper limb appeared "rouge jaunâtre" while the lower (apparent) limb
* was "bleu violacé" -- so I suppose the Sun was still several degrees
* high, though he says nothing about eye discomfort.
* After describing in detail the prisms' deviations and dispersions in
* the laboratory, he concludes that the "dispersive power" of air was to
* that of crown-glass as 10 : 13.04.
* The discussion of the dispersion of air is followed by those of
* various other gases and vapors.
* A half-size scan of this is available at Gallica.
* MONTIGNY's first follow-up note, on dispersion of air
* He uses Cauchy's dispersion formula to calculate refractivity for 2
* additional wavelengths. He mentions the Sun's colored upper and lower
* rims. On p. 534, he gives the difference in refraction of red and blue
* at the horizon as 28''. He assumes the refraction is proportional to
* the refractivity, even near the horizon.
* MONTIGNY's second follow-up note, on solar colored rims
* Here he wants the occasional appearance of red in the blue rim to be due
* to the chromosphere!
* RAMBAUT's DISPERSION paper
* Good historical coverage, going back to Bouguer (1729) and explicitly
* mentioning Stephen Lee (1815) and Montigny (1867).
* This is a lengthy discussion of observations, a few his, mostly others'.
* Not exactly an "early" paper; but it somehow seems to fit in here:
* He compares the Sun's vertical and horizontal diameters on photographs,
* finding the difference to be about 0.17 arcsec times tan Z.
* (The purpose of the original study was to look for polar flattening.)
* Note that this is a side-effect of the colored rims.
* Cf. Bouguer (1748)!
* and the Popular Books file;
* also Biot (1810) in Mirage file
* Biot & Arago (1821) in Mirage file
* Tait (1883) in Mirage file
* Musgrave (1990) in Fake Mirage file
*
* Looks like a false alarm. When I first saw the German version in
* Kiessling's ``Dämmerungserscheinungen'' I thought it might be a
* genuine very early GF report; the phrase "green, such as I had never
* seen before, except in a prism, and surpassing every effect of paint, or
* glass, or gem" sounded promising. But the actual assertion that "there
* were in the immediate neighbourhood of the sinking sun, and for some
* time after his disc had disappeared, large tracts of a pale translucent
* green" makes it sound much more like the green of nacreous clouds.
* Reginald Heber was the Bishop of Calcutta.
* EARLIEST SUNSET GREEN FLASH (pre-1829)?
* The author is identified only as "W.H., R.N. Yeovil, April 22, 1829."
* "I remember once to have noticed the last ray of the setting sun,
* on a fine calm evening at sea, which was of a bright emerald green.
* I believe the fact is noticed by Lord Byron, in some of his works.
* Does not this prove the blue colour of the sea, in the same way that the
* green appearance sometimes observable on each side of the setting sun
* may be accounted for by knowing that his golden rays intervene between
* us and the colour of the blue sky beyond?"
* (The reference may be to Commodore John Byron's 1764 Circumnavigation.)
* In the "Queries and Answers" section.
* Thanks to Google Books for making this discovery possible!
* EARLIEST SUNRISE GREEN FLASH (Jan. 17, 1837)
* (Note that Meinels have both author & title wrong, in "Sunsets. . . " !)
*
* (after mentioning a daylight green meteor he had missed):
* "In the morning however, at a quarter before ten o'clock, while standing
* on a hummock about seventeen feet high, I had observed the upper limb of
* the sun, as it filled a triangular cleft on the ridge of the headland,
* of the most brilliant emerald colour, a phenomenon which I had not
* witnessed before in these regions." (p.191) -- Sir George Back
* EARLIEST SCIENTIFIC ACCOUNT?
* PIETRO GIUSEPPE MAGGI
* This is a long meeting abstract. "The Author had often observed how,
* when the Sun sets behind distant mountains, the last disappearing edge
* is dyed a vivid blue. Because of its long duration, this coloration
* can not be caused by diffraction" but must be due to "the dispersive
* power of the middle air." "The telescope allowed him to know how the
* image of the Sun always appears (besides the well-known flattening)
* fringed with a blue rim in its upper half, and a red one below . . . ."
* "But neither of them has enough width for the naked eye to grasp,
* when, with the solar rays traversing a uniform atmosphere, the image
* suffers no greater alteration than the ordinary flattening mentioned.
* When the equality of temperature and humidity of the air are disturbed,
* new and very visible changes deform the solar disk, and the colored
* borders and then expand, so that the blue becomes clear and distinctly
* seen even by the naked eye . . . ." He mentions Biot's "treatise on
* physical Astronomy" in which "no mention is made of any colored light
* effect," though the distortions of the disk involved are similar.
* "The more notable conditions" involve "separated pieces . . . above and
* below the image of the Sun." So it seems he noticed mock mirages.
* He supposes there are "lenticular masses" of warmer air that are
* responsible, and thinks they are related to the formation of "the clouds
* called cumuli." So he thinks the "appearance of the blue light which
* dyes the last rays of the Sun" is a precursor of "the change of weather
* from clear to rainy."
* According to Pogg., Maggi was born April 30, 1809 and died March 17, 1854,
* not quite 45 years old. He became Professor of Mathematics at Padua in
* 1853.
* Former earliest scientific account. Nice OMEGA drawing
* DISCOVERY attributed to Joseph Baxendell (Pogson's brother-in-law!)
* who had been a sailor -- see obits in Nature 36, 585 (1887) and
* M.N. 48, 157-160 (1888), and (especially) James Bottomley in
* Mem. Proc. Manch. Lit. Phil. Soc. (4) 1, 28-58 (1888).
* N.B.: Title appears only in Index, not on article page.
* "Mr. Baxendell noticed the fact that at the moment of
* the departure of the sun below the horizon, the last glimpse is coloured
* bluish green. On two or three occasions I have noticed this, and also
* near sunset an appearance like what I have rudely depicted.
* Just at the upper edge, where bands of the sun's
* disk are separated one after the other by refraction, each band becomes
* coloured blue just before it vanishes."
* (The referent of "what I have rudely depicted" is an Omega-shaped sunset.)
* A completely garbled abstract appears in Fortschritte der Physik
* im Jahre 1874, 30, 1377-1378 (1879): "Am unteren Rande der wenig vom
* Horizonte entfernten Sonne befand sich eine streifige Wolkenschicht,
* unter der nach dem Horizonte zu die oberen Theile eines Sonnenbildes
* erschienen." [signed Sch. (= Schwalbe), who noticed only the woodcut]
* Fisher #60; not read by him
* O'C #63
* reprint of Joule's letter
* GENUINE AFTERIMAGE REPORT
* Afterimage moves, is smaller than Sun, and "greenish" in color;
* timescale: 10 sec (4 such, gradually fading out)
* EARLY ACCOUNT by David Winstanley (RED and GREEN RIMS isolated)
* "During the past eighteen months the writer, from his residence
* in Blackpool, . . . has noticed the phenomenon of the final coloured ray
* certainly more than fifty times."
* FIRST MENTION of VARIABLE DURATION:
* "The period of its duration too is likewise variable. Sometimes it
* lasts but half a second, ordinarily perhaps a second and a quarter, and
* occasionally as much as two seconds and a half."
* TERMINOLOGY:
* ". . . the phenomenon of the final coloured ray . . . . To the naked eye its
* appearance has generally been that of a green spark of large size and
* great intensity . . . ."
* ". . . the green ray . . . ."
* FIRST USE of term SEGMENT (but not "green segment"):
* ". . . it begins at the points or cusps of the visible segment of the sun . . . "
* EVIDENCE for (but not recognition of) inferior mirage:
* "From the fact of the green cusps being rounded I apprehend that
* irradiation contributes to the apparent magnitude of what is seen."
* FIRST MENTION of (telescopic) CLOUD-TOP flash:
* "That the waters of the ocean have nothing to do with the production of
* the colour is made manifest by its visibility when the sun `sets' behind
* the edge of a well defined cloud. On the 14th and 15th of June, for
* instance, it was seen at upper contact of the solar limb with clouds.
* . . . And on several other occasions the writer has observed the effect
* when the disappearance of the sun has taken place at an elevation of
* six or eight degrees behind a heavy bank of clouds."
*
* "Of the objective nature of the phenomenon it is needless to offer
* evidence; for it needs to be but seldom seen to preclude the idea of an
* optical illusion."
* "The different colours seen, together with the order of their
* appearance, are suggestive of the prismatic action of the atmosphere as
* the cause of their production."
* (verified telescopically by using an artificial occulter)
* "I apprehend that the results here given sufficiently prove that
* atmospheric refraction is the cause of the coloured rays seen at the
* moment of the sun's departure below the horizon."
* O'C #160
* Joule and Winstanley quoted in Nature -- but without Joule's figure!
* Fisher #161, O'C #161
* Nature's reprint of Winstanley's paper, abstracted
* JULES VERNE's FIRST mention of the "green ray" (1877)
* This novel is set mostly in a coal mine -- in Scotland! The heroine
* has spent her whole life underground, and is about to see her first
* sunrise, in Edinburgh:
* "Enfin, un premier rayon atteignit l'oeil de la jeune fille. C'était
* ce rayon vert, qui, soir ou matin, se dégage de la mer, lorsque
* l'horizon est pur." [This is in Chapter XVII, "Un Lever de Soleil".]
* I have seen only the 1967 Hachette edition, where this passage occurs
* on p. 186. Interestingly, the biographical note at the end (on
* unnumbered pages) claims that "Le physicien et astronom Jules Janssen,
* le mathématicien Joseph Bertrand refont les calculs de Jules Verne --
* et vérifient, dit-on (il serait sans doute imprudent de ne pas placer
* ici un point d'interrogation), l'exactitude des courbes, paraboles et
* hyperboles qui définissent le trajet du boulet-wagon de De la Terre
* à la Lune ."
* As Verne went to Scotland in 1859, and was much taken with the place,
* it seems likely that he may have seen green flashes there: both his
* mentions of the flash are set in Scotland. Also, this book is full of
* talk about how superstitious and full of folklore the Scots are; so the
* invention of the ``legend'' later on seems more natural.
* Thanks to Hezi Yizhaq for pointing this out!
* James Anthony Froude's flash of Aug. 28, 1874
* FIRST USE of "FLASH" ??
* Froude was a controversial historian and excellent writer. This is
* from the section of his book called ``Leaves from a South African
* Journal.'' While sailing to South Africa, he says:
* "The sea calm as Torbay in stillest summer. . . . Last night we had a
* remarkable sunset. The disk, as it touched the horizon, was deep
* crimson. As the last edge of the rim disappeared there came a flash,
* lasting for a second, of dazzling green -- the creation I suppose of my
* own eyes."
* He also tells many poignant stories of South Africa, and saw Kimberly
* in the early days, when the mine was only 120 feet deep.
* An older brother, William Froude, was an engineer and naval architecht
* who devised the Froude Number of hydrodynamics. The family name rhymes
* with "food"; many supposedly authoritative websites get this wrong.
* Many thanks to Agnes McLean for finding this!
* The "BLUE SPARK" quote traced to its source!
* Lt. Claude Reignier Conder of the Royal Engineers was in charge of the
* survey of Palestine in 1872-1875, when he turned the work over to Lt.
* H. H. Kitchener (later to become an Earl, and controversial for his
* use of concentration camps in South Africa -- but this was the young
* Kitchener's first job in the Royal Engineers). On pp. 264-265, Conder
* describes a sunset and sunrise observed from the top of Mt. Hermon,
* including the TRIANGULAR MOUNTAIN SHADOWS. But our interest is in a
* single sentence, set off as a separate paragraph:
* "The sun underwent strange changes of shape in the thick vapours --- now
* almost square, now like a domed temple --- until at length it slid into
* the sea, and went out like a blue spark."
* MANY THANKS to Andrew Alden, of Oakland, CA, for finding this!
* According to Wikipedia, Mount Hermon is 2,814 m above sea level, and
* the highest point in Syria. Conder says his observation was made from
* a height of 9150 feet. It appears to have been made on "Monday, the 8th
* of September" (1873).
* Available at
* https://archive.org/stream/tentworkinpalest01conduoft#page/264/mode/2up
* and
* https://books.google.com/books/about/Tent_Work_in_Palestine.html?id=ltiQteXzxNIC
* Henry Bedford's pre-Verne observation
* sunset and sunrise of July 14/15, 1878: ". . . the sun -- the green
* sun --- appears. A distant low range of rocks comes between us and its
* point of rising; and, as we glide on, an opening between them shows us
* the sun, a bright emerald, as pure and brilliant as ever gem that
* glistened; again we lose it, and again an opening shows it to us in
* its own golden light; and then once more it is the bright green; and
* now it rises higher, clears the ridge, and is once more the golden orb.
* This is what we saw, but another observer, our alter Ego , assures us
* that, when he first saw it, the colour was a fiery red, which soon turned
* to green. Evidently an optical effect of what is called polarization
* of light, as these complementary colours seem to show." (p.48)
* Bedford's long travelogue was serialized in Month 34, 290-304 (Ch. I),
* 395-411 (Ch. II) (1878); vol. 35, pp.43-58 (Ch. III), pp.167-184 (Ch.IV),
* 334-351 (Ch.V), 473-490 (Ch.VI) and vol. 36, 17-37 (Ch. VII) (all 1879).
* N.B.: these are volumes XV to XVII, New Series.
* Bedford was a convert to Catholicism; The Month appears to have been a
* magazine for British Catholics.
* JULES VERNE's NOVEL
* I was surprised to discover, from the facsimile of the original edition
* that was published by Hachette in 1977, that the original title was
* hyphenated. The Hachette edition also has the original illustrations,
* including drawings depicting the "ray" like narrow crepuscular rays;
* see Mulder's complaint about this on p.3 of his book.
* Cf. Moncrieff's complaints (1905) about Scottish errors.
* Thanks to Stephen Williams for turning this up!
* Fisher #144, O'C #145
* For the origin of the "legend", see the 2002 publication of Verne's
* correspondence with Hetzel, his editor -- and its actual inventor.
* (Quoted in its entirety in Rambaut's 1906 Met.Mag. paper)
* ". . . the parting ray is a brilliant emerald green."
* "The . . . effect is not produced by the sun setting behind a distant bank
* of clouds. Probably the first ray from the rising sun would be the same
* unexpected colour."
* Fisher #58
* former "EARLIEST" OBSERVATION (Sept. 13, 1865)
* William Swan observed from summit of the Rigi.
* misinterpreted as due to contrast with red sky:
* "I do not doubt the phenomenon was purely subjective, for before sunrise
* the sky was all lit up of a magnificent crimson hue."
* NOTE: This is the William Swan for whom the "Swan bands" of C2 are named.
* Fisher #141, O'C #135
* Mostly about the Krakatoa effects, but half a paragraph on GF
* (pp.601-602) says "Mr. Henry Bedford . . . in an English magazine" of
* 1878, as well as G.H.Hopkins (see above). The Bedford quote describes
* an Arctic Circle sunset and sunrise in July: ". . . the sun -- the GREEN
* sun --- appears. A distant low range of rocks comes between us and its
* point of rising, and, as we glide on, an opening between them shows us
* the sun, a bright emerald, as pure and brilliant as ever gem that
* glistened; . . . and now it rises higher, clears the ridge, and is once
* more the golden orb." (slightly mis-quoted; see Bedford, 1879)
* The Bedford quotation is pre-Verne, but no detailed citation is given.
* (in the March issue)
* Thinks it is a CONTRAST EFFECT
* "A sun seen as green or blue for hours together is a phenomenon
* witnessed only after the late Krakatoa eruptions . . . ; but a sun which
* turns green or blue just at setting is, I believe, an old and, we may say,
* ordinary one, little remarked till lately. I have a note of witnessing
* it . . . on June 23, 1877, the sunset being very clear and bright.
* "The sunset was bright this evening, the sun of a ruddy gold, which
* colour it kept till nothing was left of it but a star-like spot; then this
* spot turned, for the twinkling of an eye, a leaden or watery blue, and
* vanished."
* a GEOMETRIC CRANK -- one of de Morgan's ``paradoxers''
* Starts off by mentioning Verne's novel, and quoting the florid paragraph.
* A wonderfully ingenious and completely CRANK THEORY OF COLOR is used to
* explain the green ray as the COMPLEMENT of the INVISIBLE INFRARED rays!
* It all is based on a confusion of additive and subtractive color mixing,
* together with the mistaken notion that the spectrum contains all possible
* colors. From these mistakes, he goes on to a marvelous GEOMETRIC
* CONSTRUCTION, and hence a mechanical device to illustrate the theory:
* "Ce petit instrument . . . donne, dans la practique des résultats
* beaucoup plus exacts que le cercle chromatique de Chevreul. . . ."
* ". . . il serait particulièrement curieux de blanchir une partie de
* l'espace v'v'' avec des rayons obscurs et, inversement, de rendre
* lumineux les rayons obscurs en les mélangement avec des rayons verts."
* [Indeed it would be!]
*
* NOTE: La Nature published 2 "Semestres" per year,
* BOTH with the SAME volume number, and both starting at p.1 !!
* Extreme care is required to determine the correct half of the year;
* either the date or the issue number must be given.
* AUGUSTE TREVE's observations and simultaneous-contrast theory
* (This was the great-uncle of the modern scientist Yvain Treve)
* "Sa durée est celle d'un éclair. C'est, pour le navigateur, comme un
* adieu chargé de promesses, toujours fidèlement tenues, d'un beau temps
* pour le lendemain; il est, en effet, bien peu d'exemples, s'il y en a,
* qu'un beau coucher de soleil ait été suivi d'un mauvais temps."
* Cf. the similar claims made by Wegener (1926), and the remark of
* "Another Engineer Officer" (1904) about this being standard French
* navigational instruction lore.
* Fisher #142
* Almost word for word the same letter published in C.R.
* cited by Polo in his 1904 letter
* A short followup to the Trève paper of Oct. 1885
* He offers a mechanical theory for successive contrast!
* Thanks again to Yvain Treve for providing this reference!
* One-paragraph abstract of the 1885 Trève paper in C.R.
* "M. Trève has described to the French Academy of Sciences a phenomenon
* of a beautiful green ray which he has observed . . . ."
* Besson's sunrise observation, with a VENUS flash on setting as well
* A convert from the "contrast" idea, thanks to seeing a sunRISE flash
* in the Azores: "Voici une excellente occasion de vérifier la théorie
* du commandant Trève." He saw another (not as good) the next morning.
* "La théorie du contraste des couleurs me paraît donc fausse."
* This is Vol. 22 of the 3rd Series, 1er Semestre, dated 3 Avril 1886
* in the section "Correspondance et Chronique".
* Available at Gallica.
* SUNRISE OBSERVATIONS OVER MOUNTAINS in letter to Mascart
* "Tous les touristes qui frequentent l'Égypte et la mer Rouge ont été
* témoins de ce phénomène . . . ."
* ". . . dans le mer Rouge, plusiers fois et notamment en octobre dernier,
* j'ai assisté, moi et mon second, au lever du Soleil à l'horizon de
* la mer, et que la première impression sur nos deux rétines a été
* d'un beau vert émeraude.
* Le lendemain, assistant tous deux au lever du Soleil derrière des
* montagnes élévées de 1° à 2° au-dessus de l'horizon, la même
* impression lumineuse franchement verte a encore frappé nos yeux."
* [Note the correct altitude here, but not in his 1898 letter.]
* "Je ne puis citer le nombre de fois que j'ai observé et fait observer
* ce même phénomène au coucher du Soleil et encore derrière des
* montagnes."
* Fisher #87, O'C #237
* This is an extract from the C.R. letter
* No.707, 18 Dec. 1886
* O'C #238
* Fisher #88
* de Maubeuge's letter quoted again, in l'Astronomie
* This was *before* it merged with B.S.A.F. The full title is:
*
* L' A S T R O N O M I E
*
* REVUE
* D'ASTRONOMIE
* POPULAIRE,
* de Meteorologie et de Physique du Globe,
* exposant
* les progrès de la science pendant l'année;
* publiée par
* CAMILLE FLAMMARION,
* avec le concurs des principaux astronomes français et étrangers
* FIRST USE of term "GREEN FLASH"?
* "At sunset tonight I observed a phenomenon which has, I believe, been
* seen from on board ship, but never probably from a place with such a
* distant sea horizon as we have here -- some seventy miles. The sky for
* a short distance above the point where the sun set was perfectly clear
* of cloud or haze, and I watched carefully the last portion of its disk
* disappear into the sea. As soon as the last speck of the yellow
* vanished, a momentary bright green flash shone out. This was quite
* different from the complementary green seen after looking at the setting
* sun; brighter and bluer in tint. I have seen it stated that the cause
* of this green light is the sun shining through the water that hides
* it, and would be glad to know if such is the true explanation."
* Robert Trail Omond was a Scottish meteorologist, Superintendent of the
* Ben Nevis Observatory (1883-95) when this was written, and later (1903-?)
* Honorary Secretary of the Scottish Meteorological Society [see WW, 1909].
* Fisher #111, O'C #99
* RICCO's reply to Omond
* Fisher #126, O'C #116
* Early description of GREEN RIM
* FIRST refutation of CONTRAST EFFECT by HUE ?
* ? Joseph Solange Henri Pellat (Pogg.)
* ". . . ni à un contraste des couleurs qui, du reste, vu la teinte jaune
* d'or du disque, donnerait une couleur bleue et non pas verte."
* Pellat's report, in German
* Here is an explicit mention of THOLLON:
* "During the autumn of 1886 I visited M. Perrotin and M. Thollon, at the
* Nice Observatory, and watched the setting sun with M. Thollon on five
* clear evenings, to catch sight of the last blue ray . . . . The sun at that
* period of the year set over the bare edge of an opposite mountain, but on
* four out of the five nights I saw the blue ray, though I have only seen it
* on two other occasions from the sea-level."
* (article is mostly about Lick Obs.)
* N.B.: A. Cowper Ranyard was editor of "Knowledge" from 1904-1910;
* the editor when he published this article was R.A.Proctor.
* Ranyard was apparently impressed by John Evershed, who inherited
* Ranyard's instruments in 1894, after knowing him only a year.
* I see from the Nov. 13, 1863 issue of M.N. that Ranyard became a Fellow
* of the RAS at that time -- as Foucault and Bond became Associates.
* Fisher #124
* The ENGLISH MECHANIC series for 1889 follows.
* Note that Eng.Mech. published 2 volumes per year.
* The "Letters" section of E.M. occupied the ecological niche today held
* by Usenet: a heterogeneous mixture of professionals, amateurs, and cranks.
* Letter-writers often used only initials, or pseudonyms.
* Letters are numbered in squared brackets; I preserve those numbers here,
* as many letters in small print appear on each 9 x 12-inch page.
* One letter may touch on many topics besides the GF; rather than list the
* many irrelevancies, I simply give the number. Note that queries and
* letters have separate numbering systems!
*
* This thread was started by someone signing as "F.R.A.S." (i.e., "Fellow
* of the Royal Astronomical Society") in a previous issue. Here, "H.B.F."
* asks "F.R.A.S." for an explanation of the "Green Ray" at sunset, which
* he describes as "a drop of the most vivid emerald green". He continues:
* "My attention was first drawn to the alleged phenomenon by the perusal
* of M. Jules Verne's story, `The Green Ray,' and believing it to be
* fictitious, I set myself to observe. For about three months of the summer
* the place of my residence -- an island in the Levant -- allowed an ocean
* horizon for the setting sun. On the very first evening of observation I
* was rewarded with the sight of that wonderfully brilliant flash, and on
* successive evenings I continued the observations. About two out of every
* three observations were successful . . . . Believing that the phenomenon
* might still be a purely subjective one, I asked my wife to join in the
* observations, and, sceptical as she at first was, on each occasion,
* whether the green ray was visible or not, our observations exactly
* coincided. On the whole, out of some fifty successive observations, I
* should say we succeeded in obtaining a glimpse of the `ray' about thirty
* times."
* Eric Hutton identifies "A Fellow of the Royal Astronomical Society" as
* Captain Noble, J.P. of Uckfield, Sussex. [EM ref. No. 3105 p326]
* No. 1275, Aug. 30, 1889
* Fisher #167
* Alas, the otherwise reliable Fellow offers "H.B.F." the AFTERIMAGE theory!
* (Evidently, he had never seen a GF)
* "I fancy that the green ray of which my querist speaks must have a
* cognate origin to this, and that the eye, deadened to the sensation of red
* by the brilliant crimson of the sun's disappearing limb, must temporarily
* select the green from the more composite light illuminating the horizon."
* Eric Hutton identifies "A Fellow of the Royal Astronomical Society" as
* Captain Noble, J.P. of Uckfield, Sussex. [EM ref. No. 3105 p326]
* No. 1276, Sept. 6, 1889
* Fisher #172
* Another ignoramus offers the "WAVE" notion:
* "Surely the `emerald drop' so often seen by `H.B.F.' page 11, can be no
* other than solar light transmitted through the sea . . . ."
* No. 1276, Sept. 6, 1889
* Fisher #164
* Another vote for afterimages:
* He cites the Pears' Soap ads as an example.
* No. 1277, Sept. 13, 1889
* "H.B.F." knows it isn't an afterimage:
* "I should have explained, however, that I failed to observe it on
* occasions when the sun presented a red appearance, and only when he set
* with a pale golden colour has it been visible. Moreover the ray has
* not that dull appearance noticeable in this and in other similar optical
* illusions, nor has it the like permanency."
* He also rejects the light-through-a-wave explanation of "E.L.G.", as
* ". . . only when the sea has been exceptionally calm, has it been visible."
* COMMENT: Note that the experienced observer here quite rightly dismisses
* the arm-waving of the would-be theorists who have *never* seen a flash.
* No. 1277, Sept. 13, 1889
* Fisher #168
* Another vote for afterimages:
* "I may, however, add that if this is the correct explanation, the
* phenomenon is more likely to be observed within the Tropics than at higher
* latitudes, since the more vertical the path of the setting sun, the
* greater the rapidity of its apparent motion, and the more sudden the
* change from light to darkness."
* No. 1277, Sept. 13, 1889
* FRAS switches to the "wave" idea:
* cites HBF's 30351 letter
* Eric Hutton identifies "A Fellow of the Royal Astronomical Society" as
* Captain Noble, J.P. of Uckfield, Sussex. [EM ref. No. 3105 p326]
* No. 1278, Sept. 20, 1889
* Fisher #173
* BLUE is commonest color at sea?
* Believes flash is due to Sun shining through water
* "I have had numberless opportunities of witnessing the same appearance
* in mid-ocean, where the water appears blue, and the flash is also of an
* exquisite blue."
* "I have repeatedly drawn the attention of others to this, especially
* between the Tropics, to all of whom the flash appeared blue."
* cites E.M.50,11
* No. 1278, Sept. 20, 1889
* Fisher #166
* cites and quotes Ranyard's paper in Knowledge
* No. 1278, Sept. 20, 1889
* O'C #114
* "E.L.G." criticises "F.R.A.S." for afterimage theory
* ". . . no sunset, in any latitude, has a colour complemental to green."
* He now recognizes the problem with his model:
* "The emerald light must somehow have got a dip through sea-water; but
* how, is a great puzzle with so little refraction. It would seem, it
* must enter and leave very steep wave surfaces, though `H.B.F.' calls the
* sea `calm.' He does not give a hint of the height of his station, a most
* important element, if it is never, as he thinks, visible from a ship's
* deck."
* No. 1278, Sept. 20, 1889
* Fisher #165
* HBF's 3rd letter: he decides to accept the "wave" story, but modified:
* ". . . the last glimpse of the sun after he has passed beneath the visible
* horizon, seen through the depth of a clear and placid ocean , and not
* through a mere superficial wave or two." [N.B.: ignores refraction!]
* "The verandah from which most of my observations were made stands 664ft.
* above sea-level, at a distance of three miles from the shore."
* No. 1279, Sept. 27, 1889
* Fisher #169
* At last, "E.L.G." puts the pieces together!
* "If this is, after all, a blue ray, and can be seen, as the observer at
* Nice tells us, after sunset behind a mountain, of course the sea has
* nothing to do with it. The last explanation must be taken, and it gives us
* the first proof that air, like other refracting media, refracts the
* different colours with different indices. Now I believed, about thirty
* years ago, that I had a proof of this on watching, through a good
* achromatic glass, a very clear sunrise in the north suburbs of London.
* The sun rose . . . with so little colour that it could not be called even
* `pale golden.' It was merely creamy; but from the first emergence till
* the lower limb was up, the upper limb had a distinct edging of blue, and
* the lower one of red."
* (So we have here an independent, if uncertain, rediscovery of the colored
* limbs.)
* With this item, the *green* ray series ends. But see the next 2 items!
* No. 1279, Sept. 27, 1889
* A. COWPER RANYARD speaks up:
* "I need only remind `F.R.A.S.' of a paper by Sir G. B. Airy, published
* in the Monthly Notices for 1869, on an eyepiece for correcting the
* effects of atmospheric dispersion, to recall to his mind the phenomena
* which are always observed when a star or the sun is near to the horizon."
* "When the sun or a planet is near to the horizon the blue fringe along
* its upper limb and the red fringe along its lower limb is a very marked
* feature when it is observed with a power of two or three hundred."
* The Airy paper is probably O'C. #4
* FIRST CALCULATION SCALED TO HORIZONTAL REFRACTION ? (1/60)
* "To express it in numbers, the atmospheric dispersion from B to G of the
* spectrum is about one-sixtieth of the atmospheric refraction. On the
* horizon at the sea-level, the horizontal refraction is about 34 minutes,
* and the length of the spectrum from B to G is 34''."
* He favorably notes "E.L.G."'s observation.
* No. 1280, Oct. 4, 1889
* Fisher #125
* "FRAS" recants, with an excuse, and a damning admission:
* "There can be no doubt that Mr. Ranyard does suggest a -- or the --
* vera causa for the phenomenon of the final blue flash incident on
* sunsets; but, as far as I am concerned, it is one which I have never
* witnessed . . . ."
* [NOTE: Both this and Ranyard's item were indexed under "blue" by the E.M.]
* This apparently ends the entire episode in E.M. for 1889.
* No. 1282, Oct. 18, 1889
* Fisher #174
* Possible GREEN RAY ?? or BLANK-STRIP flash?
* ". . . den Eindruck eines vertikalen blaugrünen Flämmchens . . . "
* "Ziemlich nahe vor Sonnenuntergang war hier die Sonne durch einen
* schmalen Wolkenstreifen in zwei Theile getheilt. . . ."
*
* Leonhard Sohncke (1842-1897) was a well-known crystallographer who
* became head of the meteorological stations in Baden when he was made
* professor of physics at the Technische Hochschule in Karlsruhe (1871-1883).
* His green-flash work is rather obliquely mentioned in the DSB.
* Fisher #138
* Sohncke's paper reported in Nature; cited by Michie Smith (see below)
* March 27 issue
* Fisher #139
* Nature's report of Sohncke's paper re-reported in Science
* in the "Notes and News" department, which began on the previous page.
* April 11 issue
* SECOND MENTION OF VARIABLE DURATION
* "If the colour were due simply to refraction it would last for only a
* fraction of a second, and the colour would be much more blue than green.
* But, so far as my own observations go, the colour may last for several
* seconds, and is a bright pea-green . . . ."
* Charles Michie Smith's first appearance. He was Pogson's successor at
* Madras, and established the Kodaikánal Observatory in 1899.
* Note that Evershed, his successor, always refers to him as
* "Michie-Smith" (hyphenated) in his autobiographical note in Vistas,
* Vol. 1, p.33.
* Fisher #136, O'C #285
* April 10 issue
* GREEN RAY
* ". . . the sun had sunk behind a hill, when, suddenly, my companion and I
* both saw a flash of green light against the thickest cloud; it lasted
* one or two seconds, just long enough for there to be no doubt about it.
* We compared it to the glare thrown by `green fire,' extending over an
* area whose diameter appeared about four times that of the moon."
* Fisher #39
* First calculation of duration of green at sunset ?
* 2nd CALCULATION SCALED TO HORIZONTAL REFRACTION ?
* "Cette dispersion atmosphérique démontre que, dans un coucher de
* Soleil, le rayon vert doit persister, sour notre latitude, une
* seconde environ après la disparition du rayon jaune."
* (Prosper Henry)
* The Henry brothers, Paul and Prosper, invented the 13-inch astrograph
* used to make the Carte du Ciel , the monster project that absorbed the
* efforts of a whole generation (or two!) of astronomers.
* Fisher #55, O'C #50
* cited by F.K., who blames Fisher
* This is about crepuscular rays, NOT green flashes!
* Biart's letter is confined to p.116; but the editorial comment on the
* next page is included here.
* This was *before* l'Astronomie merged with B.S.A.F.
* Fisher #8
* SUNRISE better than SUNSET (according to Charles Mostyn)
* NO GF under INVERSION conditions; TWO TYPES of sunsets distinguished
* "The best displays took place took place when the refraction near the
* horizon was of such a character that the sun assumed a balloon, or vase,
* shape as he came close to the sea-line. When, on the contrary, the sun
* appeared flattened out in its horizontal diameter, the `green ray' was
* either entirely absent, or was seen only in an indistinct and uncertain
* manner."
* Seen 3 times as the ship rose and fell on waves in "the Southern Ocean."
* Apparently, this refers to Mostyn's trip from London to Sydney at the end
* of 1890 and beginning of 1891 (thanks to Edward Gilbert for the info!)
* This is the Aug. 13 issue.
* Fisher #103, O'C #253
* Mostyn's note reprinted (with slight editing) in "Science"
* Sept. 18, 1891 issue; the column runs from pp. 157-159.
* The 1891 E.M. series begins with E.Reginald Blakeley, who saw a
* crepuscular ray:
* "Surely it could not be the green ray Verne has written about?"
* No. 1379, Aug. 28, 1891
* A reply to E.Reginald Blakeley, pointing out that what he saw were
* crepuscular rays (though not so named).
* No. 1380, Sept. 4, 1891
* HBF's 4th letter: he continues to accept the "wave" story:
* "I have not the least doubt but that the explanation of the phenomenon
* given by `E.L.G.' (letter 30324) is the correct one . . . ."
* But there is a nice account here of a double flash at sunset made
* visible by "the sea . . . swelling in great easy rolls."
* No. 1380, Sept. 4, 1891
* Fisher #170
* Mostyn's Nature letter replayed by Scientific American
* Sept. 12 issue -- must have been a weekly then.
* Packer points out that crepuscular rays are often mistaken for green
* flashes and other things, citing Col. Markwick's letter in No.1281.
* No. 1383, Sept. 25, 1891
* Blakeley thanks Clapham and "HBF", agreeing that he saw a crepuscular ray
* and not a GF.
* No. 1383, Sept. 25, 1891
* A minor GF observation (blue, actually) from Mt. Hamilton
* This is probably an observation of a flash above a Wegener's
* "BLANK STRIP", from the description. The dark strip in the drawing is
* about 2 degrees above the apparent horizon, roughly right for the dip
* there.
* Fisher #33
* William N. GROFF's work on ANCIENT EGYPTIAN depictions
* contains some of his own observations
*
* Groff was an interesting character about whom little is known. He was
* born in 1857 in Cincinnati, Ohio, and died relatively young in 1901 in
* Athens, Greece. I'd guess he picked up his astronomical interest in
* Cincy, as the observatory there was important in the mid-19th Century.
*
* He was obviously an experienced GF observer; so we take his GF work
* seriously. He seems to have learned most of his astronomy from
* Flammarion's "Astronomie Populaire" and Burritt's "Geography of the
* Heavens". With such a weak scientific background, it is remarkable that
* he managed to figure out the correct cause of the GF on his own.
*
* Note that he describes the green flash at sea as ``le `soleil vert' des
* matelots,'' which confirms my opinion that these phenomena were long known
* to sailors.
*
* N.B.: Each volume, or "No." as it is called, was printed in the year
* after the date of the meeting in which the paper was given. Thus
* "1893" here really means "given in 1893, published in 1894".
* Fisher #50; O'C #40
* comment on Groff's paper
* Dr. Abbate pacha thinks it is an afterimage.
* His comment that "Newton . . . a été le premier à parler de ce
* phénomène intraoptique, tout en le rapportant au changement qui
* survient du rouge intense à la couleur complémentaire, le vert"
* seems to have given rise to a mistaken impression that Newton commented
* on green flashes, not just on afterimages.
* Dr. Abbate seems really to be the FIRST to believe the Verne "LEGEND":
* ". . . le charmant petit livre a J. Verne, Le Rayon Vert . . . . Ceux qui
* le consulteront, sûrement avec plaisir, trouveront comme récompense,
* outre la délicate illusion qui est produite par la peine d'observer
* attentivement le phénomène du rayon vert , un bonheur ineffable,
* mystique, qui s'y rattache, selon la vielle légende, née au pays des
* Highlanders, en Ecosse."
* O'C #1
* Groff's 2nd paper
* This is the second of two notes published as a single item; the first is
* on the Nile. These notes were additions to earlier papers.
* Fisher #51; O'C #41
* Groff's 3rd paper
* This is a short note mentioning the green flash, but associating green
* and blue with the "other world" and death (via the setting of the Sun).
* [Note that the "III" here means it is the third note in this group, not
* the third in the GF series (though it is that as well).]
* Groff's 4th paper
* This is a short note giving further examples.
* Popular summary of Groff's work
* in No.531, 30 Mars 1895
* Daressy objects to Groff's view that the Egyptians meant to depict the
* green flash: "Est-il probable qu'en peignant ainsi le caractère
* hiéroglyphique, les Egyptiens aient eu l'intention de représenter
* le phénomène du rayon vert? Plusiers arguments me semblent indiquer
* que telle n'a pas été leur pensée."
* Unfortunately, his second reason is that "On sait que le rayon vert est
* un phénomène dû à une illusion d'optique . . . d'une durée
* infiniment courte . . . ." -- and, as "mon honorable confrère parle d'un
* rayon vert au lever du soleil" when Daressy thinks "Les conditions
* requises ne se trouvent plus réunies: l'astre étant plus brillant que le
* ciel, son apparition ne peut donner lieu à une impression lumineuse de
* couleur inverse . . . ." Worse, he asserts that "Ce ne peut donc être que
* par une prédisposition spéciale aux illusions d'optique, une sorte de
* daltonisme, que certaines personnes croient voir le disque émettre une
* lumière verte à son lever." [Talk about adding insult to injury!]
* "Si donc les Egyptiens n'ont pas représenté le rayon vert avec le
* soleil couchant, il est fort improbable qu'ils l'aient reproduit avec le
* soleil levant."
* Fortunately, his later arguments are sounder; he argues that the colors
* are chosen for religious rather than observational reasons, and that
* the "sunrise" symbol is derived from the rounded shape of a box lid.
* MRS.STEEL's NOVEL
* "And Marjory, cresting the knoll, thought instantly that here, indeed,
* was a chance of the Green Ray. For ever since she had read Jules
* Verne's book the idea of this, the last legacy of a dying day, had
* remained with her fancifully. . . . Even if the legend was no legend, and
* the phenomenon simply a natural one, due to refraction, there must be
* something exhilirating in seeing that which other people had not seen
* . . . ." (p.125)
* "`I have often heard you mention this Green Ray, Miss Marjory, but I am
* not quite sure to what you allude.'
* `To a fiction of Jules Verne's, that is all,' put in Paul quickly.
* `Nothing of the sort; people have seen it,' corrected the girl,
* eagerly." (p.161)
* " `. . . it is like the Green Ray, something to dream about.'" (p.162)
* Fisher #140 says "Flora Annie Steel" but not read
* Groff's 5th paper
* This is his long paper that discusses the green flash in detail.
* GOOD QUOTE:
* "En traitant des questions scientifiques on rencontre deux difficultés:
* si l'on se borne à annoncer les résultats des recherches, on court le
* risque d'être obscur, ou même d'être incompris; si l'on donne, en
* détail, des preuves à l'appui de chaque assertion, on se perd dans des
* digressions et on court le risque d'être inintelligible."
* Well said! So, "Peut-être la meilleure méthode est-elle, tout en
* donnant les résultats des recherches, d'indiquer brièvement sur quoi
* elles sont fondées, puis, si l'occasion s'en présente, de discuter plus
* en détail le sujet et de développer à l'appui des conclusions ce qu'on
* n'avait fait qu'indiquer." So Daressy's note gives him this
* opportunity.
* TERMINOLOGY:
* "Nous disons rayon , mais il serait plus correct de dire
* zone lumineuse , zone lumineuse rouge, orange, jaune, verte, bleue
* (indigo ou violet), qui s'appliquerait à la lumière (en apparence)
* émise par le disque du soleil à l'horizon, et que differentes personnes,
* sur une même méridienne observeraient simultanément."
* Regarding AFTERIMAGES:
* "Si l'on regarde un objet rouge ou rougeâtre -- le disque du soleil,
* par exemple, puis qu'on ferme les yeux, on peut bien voir la couleur
* complémentaire verte ou verdâtre, mais on distingue bien entre le
* phénomène d'optique et la couleur verte du disque du soleil apparaissant
* ou disparaissant -- la sensation est tout autre."
* The TURNING-AROUND EXPERIMENT (this seems to be the FIRST mention of it):
* "Si plusiers personnes A, B et C par exemple, vont constater la couleur
* du dernier rayon du soleil couchant, A regarde le soleil, B et C ont le
* dos tourné vers l'occident; quand A voit la dernière partie du disque
* disparaissant prendre la couleur verte (ou bleue); il dit à B et C de
* regarder; B et C, qui n'avaient pas regardé le disque tournent et peuvent
* bien voir le disque disparaissant de couleur verte (ou bleue), mais est-ce
* à dire qu'on ne voit jamais la couleur complémentaire au moment du
* coucher du soleil? je crois l'avoir constatée, mais la sensation est tout
* autre que celle produite sur l'observateur par la couleur réelle, ou
* apparent du disque."
* HISTORY:
* ". . . j'avais espèré trouver le phénomène étudiée et expliqué dans
* des ouvrages et avoir, ou la confirmation de l'hypothèse à laquelle
* j'étais arrivé, ou la vraie explication. Mais, malgré toutes mes
* recherches, je n'ai rencontré nulle part l'étude du phénomène du
* premier et du dernier rayon (zône lumineuse) du soleil à l'horizon sur
* le désert. Mais assurément le phénomène des couleurs du soleil à son
* lever et à son coucher sur le désert a dû être étudié et expliqué
* et j'espère pouvoir compléter plus tard les indications données ici à
* ce sujet: la seule indication directe que j'aie rencontrée jusqu'ici est
* dans Jules Verne, Le Rayon vert, p. 181 s. . . . " [p.248]
* LATITUDE effect:
* He also predicted that the flash would be visible much longer in the
* polar regions: "Dans le pays du nord (et même près di pôle sud) où
* l'atmosphère est très lourde, le disque du soleil surgit et disparaît
* très lentement, le phénomène des couleurs du soleil à l'horizon (si
* l'atmosphère est assez pure), doit être plus long et plus marqué que
* dans les pays plus près de l'équateur." [Note, p. 250]
* Mostly about scattering, which the author calls "diffraction".
* Having (correctly) attributed the red color of the normal sunset to
* this, he then gets into the green (or blue) flash. The whole paper is
* purely qualitative argument from analogy -- the worst kind of sloppy
* thinking. "Relativement au rayon bleu, je pense pouvoir dire aujourd'hui,
* presque avec certitude, qu'il n'est engendré ni par la réfraction ni par
* la diffraction." He tries to observe the spectrum of the setting Sun, but
* it fades out on him; so he argues it can't be due to refraction, which
* would cause one color to be left at the end.
* "Pour démontrer que le phénomène du rayon vert ou bleu, etc., n'est
* pas engendré par la réfraction, on pourrait citer beaucoup d'autres
* faits, mais j'ai hâte de finir." Yeah, sure.
* "On peut donc conclure que le phénomène du rayon vert ou bleu est un
* phénomène intraoptique, et je crois qu'il tire son origine du contraste
* entre la couleur orangée ou jaune du Soleil et la couleur bleu du Ciel;
* ou encore, entre la couleur blanch de l'auréole qui entoure le Soleil et
* la couleur noirâtre du désert et de la mer." (!!!) All garbage!
* Groff's 6th paper
* This is the continuation of the long paper of the previous year.
* Mostly, it supplies examples of the uses of blue and green coloring in
* ancient art and writing to support his inferences about the sunrise
* and the green flash, so that ". . . par ces mentions, représentations et
* usages nous avons été induits à reconnaître que le phénomène naturel
* ou astronomique, le plus ancien dont on possède des attestations sur des
* monuments originaux, est le phénomène du rayon vert ou bleu."
* a novice's useless report
* Fisher #40
* DOUBLE BLUE FLASH due to MOTION OF SHIP
* (report of Captain Salveson of the Royal Norwegian Navy)
* Is this the first GF report in JBAA? (probably)
* EARLY CALCULATION SCALED TO HORIZONTAL REFRACTION (1/40)
* note change of year but not volume number
* Goodacre (1905) thought this was the first in JBAA; it is not.
* But it is almost certainly Whitmell's first paper.
* (Note a paper by the infamous "Leo Brenner" (Gopchevic) above this!)
* Fisher #146
* Comment by "M. le President" on Schmoll's observations of a deformed Sun
* This seems to be the first GF mentioned in BSAF.
* Fisher #30, O'C #196
* Ernst Wölffing's adds to Ekama's observation his own (useless)
* Fisher #162
* Mostly citations of earlier works, esp. in Eng.Mech., and Ranyard's
* "Knowledge" article (1889)
* Note change in volume number but not year: JBAA changed volumes
* between the Sept. and Oct. issues.
* GF refs. in Nature
* Observations of green *Sun* and refs.
* unidentified PLANET flash
* Fisher #83
* Mostly citations of earlier works
* O'C #153
* Arthur Mee indulges in purple prose
* Mostly references to JBAA reports; requests observations from SAF members.
* O'C #246
* relay of a GF report from J.F.Young; not useful, and confuses additive
* and subtractive color mixing (cf. his BSAF paper above)
* Note change of year but not volume number
* Fisher #163, O'C #245
* Not about green flash or "green ray" at all, but green *Sun*
* (Note a paper by the infamous "Leo Brenner" (Gopchevic) immediately above!)
* Whitmell corrects confusion between additive and subtractive color
* mixing, and provides some references
* Letter is dated 24 Jan. 1898.
* Whitmell summarizes his earlier papers
* The item is dated 5 March 1898, but the Journal is for 1897.
* Thanks to Ray Emery for supplying this!
* Seems to be an exact reprint of his 1896 paper in Bull.Inst.Egypt.
* Whitmell reports seeing the colored rims
* One of a series of "Miscellaneous" items, signed by Whitmell, p.93.
* (This seems to have appeared about mid-year, 1898.)
* Thanks to Ray Emery for supplying this!
* SUNRISE observation of GF over the Sinai (cf. Escher, 1930)
* ". . . ce fait, que le rayon vert ne se voit pas toujours , même dans
* les meilleures conditions de pureté d'atmosphère."
* Fisher #89, O'C #240
* Abstract of de Maubeuge's report to the Académie des Sciences
* This version reports "un rayon de couleur vert émeraude, qui a couvert
* un arc de 10° au-dessus de l'horizon." But the C.R. version merely
* says "Le sommet des montagnes était à environ 10° au-dessus de
* l'horizon." Probably this was a typo, and 1 degree was intended; in any
* case, the C.R. report makes this appear to be a normal flash, not a green
* ray. Cf. his 1886 letter, in which the altitude is 1° or 2°.
* O'C #239; Fisher #90
* Report of de Maubeuge's letter, in the account of "Académie des
* Sciences de Paris, 26 Septembre --- 3 Octobre 1898"
* O'C #241; Fisher #91
* Another remark on the shape that predicts the inf.-mir. flash:
* ". . . le spectacle est souvent accompagné de déformations du disque
* solaire, déformations des plus curieuses, imitant depuis la forme d'un
* ballon jusqu'à celle d'une ligne brisée."
* Fisher #72
* PIOT-BEY invokes Groff and de Maubeuge
* "Peu de contrées paraissent se prêter autant que l'Égypte à la
* manifestation du rayon vert."
* Fisher #117, O'C #106
* An account of Piot-Bey's C.R. paper
* MIS-cited by F.K., who gave the year as 1915!
* Fisher #118 has it right
* RED and VIOLET rims observed; photographs of flattened sunsets
* Drawings of typical sunset distortions
* O'C #109 -- he has the wrong date
* A report of de Maubeuge's CR paper, propagating the 10° error
* and giving his initial as K., not H.
* Hix sets off a thread with Question 536
* Brocard (below) says Hix refers to de Maubeuge's CR paper.
* AFAS = Association Française pour l'Avancement des Sciences
* Report on de Maubeuge's CR 127, 453 paper; cited by Plassmann
* This is issue Nr. 48
* Plassmann objects to de Maubeuge's explanation in Nr.48
* He cites the obvious objections: that solar protuberances would be
* seen easily at eclipses, and that the green would be transmitted far
* better high in the sky. He then suggests it might be due to selective
* atmospheric absorption, giving a very vague and arm-waving concept,
* and suggests "Fortgesetzte Spectralbeobachtungen".
* This is Nr. 51, 17.Dez. 1898 of Naturwissenschaftliche Rundschau,
* Wöchentliche Berichte über die Fortschritte auf dem Gesammtgebiete der
* Naturwissenschaften.
* An experienced observer supports the refraction explanation
* Comments on the items in Nr. 48 (de Maubeuge) and Nr. 51 (Plassmann)
* Fisher #134, not read
* Report on Libert's letter to Cornu in CR 127, 792 (1898)
* This is issue Nr. 3
* Report on Piot-Bey, Groff, and de Maubeuge
* This is issue Nr. 6
* Reply to Hix (Question 536)
* "L'explication, toute physico-physiologique, et, par conséquent, je le
* répète, purement subjective, est des plus simples."
* AFAS = Association Française pour l'Avancement des Sciences
* Reply to Hix (Question 536), citing Piot-Bey and Groff
* "De ses observations M. Piot-Bey conclut que le rayon vert est un
* phénomène absolument objectif." [ A nice juxtaposition! ]
* AFAS = Association Française pour l'Avancement des Sciences
* Reply to Hix (Question 536), naming (but not citing) Cornu.
* AFAS = Association Française pour l'Avancement des Sciences
* Reply to Hix (Question 536)
* A curious explanation: at sea, he will have the waves be the prism; but
* on land. "l'effet de prisme y est formé par la couche atmosphérique
* ondulée, plus dense, qui avoisine le sol . . . ."
* Perhaps we could regard this as a precursor to Fraser's INVERSION-WAVE
* suggestion?
* AFAS = Association Française pour l'Avancement des Sciences
* Final reply to Hix (Question 536)
* This remarkable letter terminated the discussion; and no wonder:
* it contains a remarkably complete bibliography.
* Brocard cites all of Groff's papers in Bull.Inst.Égypt,
* 14 references in all.
* AFAS = Association Française pour l'Avancement des Sciences
* Another reference to de Maubeuge giving his initial as K., not H.
* This is mainly about the reports of Plassmann and Schülke, however.
* Probably this is the note cited in Prometheus 14, 48 (1903), though
* the page number given there is 425.
* Note that volumes overlap years!
* 29 March, No.494
* reviews of the works of Piot-Bey, Groff and de Maubeuge
* Guébhard's talk at the 21 Avril 1899 Séance de la Soc.Fr.de Physique
* Guébhard mis-cites "Trèves" in C.R. 101, 845, as well as citing
* Dr. Abbate Pacha, Groff, and Daressy. He seems never to have seen
* a GF. His paper is contested by Pellat (see below), who cites his own
* observations in 1887. Then Guébhard cites Franceschi back at him.
* These discussions were reviewed in Ciel et Terre later in 1899
* (see below).
* Note that these are in the section "Résumés des Communications"
* where the page numbers bear a superscripted asterisk, not the
* full-length papers printed with simple page numbers.
* [This volume contains papers by the Curies and by Becquerel on radium;
* papers by Cornu on optics, by Amagat on the equation of state; by
* Poincaré and by Deslandres; by Pellin and Broca on their
* constant-deviation spectrometer; etc.! What a wonderful time this
* must have been to be a French physicist!]
* Pellat refutes Guébhard
* "M.Pellat, tout en reconnaissant que le phénomène des couleurs
* consécutives peut jouer un rôle dans la vision du rayon vert,
* considère le rayon vert comme ayant une existence réelle."
* He then cites his own 1887 paper and observations.
* Raveau's GREEN RAY BELOW the horizon
* "M.Raveau a observé un phénomène très différent de celui que
* décrit M. Pellat. Au moment où le bord supérieur du soleil venait de
* disparaître, il a vu la mer s'éclairer, pendant un temps très court,
* d'une lueur verte; cette lueur a occupé d'abord un petit triangle, ayant
* sa base sur l'horizon, à l'endroit où s'était évanouie la petite ligne
* lumineuse qui constituait la dernière partie visible du disque du soleil.
* La région éclairée s'est graduellement resserrée vers l'horizon et a
* disparu, l'ensemble du phénomène ressemblant à l'écoulement rapide
* d'un liquide lumineux."
* long, sensible account; RED FLASH DISCOVERED
* ". . . nombreuses observations que j'en ai faites."
* "J'avais . . . été frappé par ce phénomène réputé extrèmement rare
* (si l'on en croit la romanesque idylle de Jules Verne) . . . ."
* "Piqué au vif, par ces observations fréquentes et faciles . . . j'ai
* exploré avec un assez fort groissement, l'extrême bord apparent de
* l'astre radieux et j'ai eu la satisfaction de constater, au moment
* où le point opposé du limbe du Soleil quitte la Terre, un
* rayon rouge fort vif ."
* "Avec une lunette, il est facile de constater le rayon rouge et orange
* du dessous du limbe solaire, lorsque celui-ci prend contact, ou bien
* perd contact (au lever) avec l'horizon."
* "Le rayon vert est un simple phénomène de réfraction et il doit se
* produire aussi bien pour la Lune et pour les étoiles que pour le Soleil,
* aussi bien au lever qu'au coucher d'un astre suffisamment brillant, et
* le rayon rouge pourra être observé, avec certaines précautions; ces
* deux rayons complémentaires sont observables en montagne, aussi bien
* qu'en plaine et qu'en mer; . . . ."
* (Unfortunately, he then tries to connect the red ray with the color of
* lunar eclipses.)
* This is almost identical to Turquan's note in Revue Scientifique (4),
* Vol. 11:1, No. 4, pp. 122-123 (28 Jan. 1899), which evidently appeared
* before the BSAF version.
* Fisher #143, O'C #143
* Useless nonsense; contrast colors
* O'C #85
* Wordy description of mock-mirage flashes. He seems to think some of
* this has to do with the Sun's atmosphere. Nice use of colored filters to
* bring out the red and green limbs.
* Early mention of WAVELENGTH DEPENDENCE of LIMB DARKENING: he knows the
* limb is redder than the center. He also invokes atmospheric dispersion,
* but apparently is flummoxed by the mock mirages.; vague references to
* the "black drop" at Venus transits, and atmospheric scattering.
* J.J.Taudin Chabot writes German as if it were French.
* See corrections of typos here in Met.Z.16,p.523. (Fisher #19)
* See corrections of typos here in his 1900 paper, Met.Z.17,p.335.
* Fisher #18
* LORD KELVIN's incredible estimate
* ". . . in an instant I saw a blue light . . . which, in less than the
* one-twentieth of a second became dazzlingly white . . . ."
* See further discussion in 1910 !!
* This is in the 31 August issue.
* An Erratum appeared in the 1 Sept. issue, saying that 5 o'clock should be
* 4 o'clock, and that "of sunrise" should be added after "light" in line 7.
* Fisher #64, O'C #69
* Report on Kelvin's letter to Nature
* This is issue Nr. 40
* (This is a report of the discussion at a meeting of the French
* physical society, involving Guébhard, H. Pellat, and Raveau.)
* "Guébhart" is Paul Émile Adrien Guébhard, who had recently
* published several papers on vision, and as a medical man was
* predisposed to a physiological theory of green flashes.
* Guébhart's "bibliographie complète dans un mémoire
* présenté à la Société française de physique" is probably no
* more than the references cited in the "Séances" (1899).
* Is Raveau's observation that "la mer s'éclairer, pendant un temps
* très court, d'une lueur verte" a green fog below eye level?
* Seems to be a summary of Groff's work; all derivative, anyway (no refs.)
* EARLIEST VENUS GREEN FLASH?
* passengers on board the "Saint-Laurent"
* part of O'C. #303
* passengers on board the "Saint-Laurent"
* Note discrepancy in 5th passenger's name.
* 31 Mars issue
* Fisher #176
* part of O'C. #303
* translated from the Revue Scientifique account
* part of O'C. #303
* Jules Garnier refers both to the St.Laurent report and his own in 1899
* This time he omits mentioning the waves; only atmospheric refraction
* forms "un spectre . . . devant l'oeil de l'observateur, lequel ne retient
* des sept couleurs de ce spectre que le vert, qui est la couleur la plus
* intense . . . ." [Seems to be the first to claim that green is seen
* because it is "brightest" to the eye!]
* 21 Avril issue
* H.H.Turner sees a GF at the May 23 eclipse in Algiers -- see item on p.300
* J.J.Taudin Chabot, thinking the "green radiation" has something to do
* with the Sun or Moon, observes a partial solar eclipse without result.
* Footnote corrects his earlier paper in Met.Z.(1899)
* Fisher #20
* cites his earlier paper in Met.Z.(1899)
* As the Sun followed the slope of a mountain, "blieb dieses Mal eine
* grün leuchtende Stelle nahezu 30 Sekunden lang sichtbar"
* O'C #191; Fisher #21
* abstract of the 7 passengers' account in Revue Scientifique
* Fisher #177
* part of O'C. #303
* not useful
* Col. E. E. Markwick, F.R.A.S.
* Fisher #84
* Not a very useful observation; only a couple of sentences on p.5
* This is the lead article in Vol. 1, No. 1 of "Das Weltall"
* WHITMELL's first land-horizon flash (2nd GF)
* "Green Flash is a more suitable name than Green Ray."
* Fisher #147
* The same item, cut down slightly, and citing his vol. 5 note.
* reference to previous year's Intermediaire de l'Assoc.fr. pour
* l'avancement des sciences
* JANSSEN reports Hansky's GF on Mont Blanc, and adds his own
* Aleksey Pavlovitch Hansky was an assistant at Pulkovo who spent
* some time at the Meudon Observatory. He specialized in photographing
* the solar surface, and monitoring its activity. He seems to have been
* the first person to notice the relation between the shape of the corona
* and the sunspot cycle.
* Hansky is quoted as describing a morning flash, with the textbook
* explanation; but modified: ". . . s'il existe beaucoup de vapeur d'eau,
* il ne reste du spectra que le partie rouge et une faible bande dans le
* vert ; mais, si l'air est très sec, la partie verte du spectre est
* intense et c'est elle que nous voyons au premier moment de l'apparition
* du Soleil, quand le spectre passe devant l'œil de l'observateur."
* To this, Janssen adds: "Cette explication est exacte, mais il faut
* remarquer que c'est encore plus l'absence de brumes que de vapeur qui
* importe à la production du phénomène, car j'ai vu très nettement le
* Rayon vert dans le Pacifique."
* (Presumably this was during his 1883 trip to the Carolines -- too late
* to have influenced Jules Verne.)
* At the end of this volume are several scientific notes in sections
* denoted by capital letters; this is section F. The Hansky quotation
* is on pp. F.7 and F.8. The index is section I.
* Reprinted in Janssen's works, Vol. 2, pp. 544-550 (see pp. 548-549)
* in 1930. A slightly edited extract from Hansky's account was also
* reprinted in 1907 by Radau (q.v.).
* Available at Gallica. The volume is a sort of combination of the
* Rubber Bible and the Nautical Almanac, with the World Almanac thrown
* in: there are the tables of weights and measures (and currencies) of
* various countries; conversions among the Julian, Gregorian, Moslem and
* French Revolutionary calendars, as well as a variety of physical and
* chemical tables.
* a badly confused account; thinks "actinic" rays change the response of
* the eye?
* O'C #74
* PRIORITY DISPUTE; no GF info
* J.J.Taudin Chabot has a priority fight with T.J.J.See over the use of
* colored glasses:
* ". . . erlaube ich mir die Anfrage, ob sie durch eine redaktionelle Notiz
* auf meine Priorität gegenüber Professor Thomas J. J. Se [sic], U.S.Naval
* Observatory, Washington, in Sache der Einschaltung selektiv absorbirender
* Medien zur Verdeutlichung der Beobachtung am Fernrohr hinweisen wollten."
* (and cites his paper in Met.Z.16,425(Sept.1899).)
* In fact, both were scooped by Stampfer (1851).
* J.J.Taudin Chabot uses his filter method to examine colored rims, and
* finds that a smoke plume 450m away does *not* have colored edges.
* He seems not to be a "morning" person:
* "Der häufigen Beobachtung des `Sonnenaufgangs' . . . stellen sich
* Schwierigkeiten verschiedener Art in den Weg, deren nicht geringste,
* vielleicht indessen nur individuellen Charakters die ist, dass zu jener
* im Allgemeinen ziemlich frühen Tagesstunde die persönliche Schärfe
* des Wahrnehmungsvermögens sich nicht immer schon in vollem Umfange
* eingestellt hat . . . ."
* O'C #192; Fisher #22
* EARLY CALCULATION SCALED TO HORIZONTAL REFRACTION (1/200 = 10" = 2/3 s)
* Anomalous dispersion proposed: cf. the Julius file (far below).
* ". . . the physicist of the Committee, Dr. W.H.Julius, of Utrecht. . . "
* (from Nijland's account of the Expedition to Sumatra, Amsterdam, 1903)
* (Nijland was the Sec.-Treas. of the Eclips-Commissie; part of his report
* is on the Web at http://www.exploratorium.edu/eclipse/1901.html .)
* Julius proposed anomalous dispersion as the explanation of everything
* in sight: the solar limb, prominences, sunspots, stellar spectra. . . .
* (see J. Hartmann, A.N.175, Nr.4197, 341-368 (1907) for refutations.)
* Fisher #61 indicates this volume is in series 2.
* O'C #64 agrees
* not useful
* Fisher #6
* not useful; only half a sentence is devoted to GF
* The page number is mis-printed without the "2", explaining the wrong
* reference to p.56 given by O'Connell, who also mis-copied the name.
* Why did he bother with such trivia and yet reject (as he says) 200
* references?
* O'C #282
* John Franklin-Adams sees a GF like Baily's beads [WAVES!]
* ". . . the phenomenon here described may have been caused by the waves of
* the sea taking the place of the mountains of the Moon. The evening was
* calm, and the waves not large enough to make this possible unless images
* of the waves were thrown up by a mirage state of the atmosphere. I have
* twice seen from a steamer's deck mirage images of the sea waves, about
* a mile distant, thrown up sufficiently to entirely hide the horizon."
* N.B.: We often see such an effect here; I have several pictures of it.
* cf. Evans, 1914.
* This is the May 1901 paper mentioned in Admiral Maclear's 1906 letters.
* Caution: M.N. volumes do not coincide with years here (Nov.1901).
* Fisher #1
* JBAA abstracts the above
* This appears to be a reprint of J.F.-A.'s note in M.N.
* No.1892, June 28, 1901
* "F.R.A.S." comments on Franklin-Adams's observation;
* he is troubled by the "Baily's beads" allusion, taking it literally.
* Note that the heading is a sub-head within a long letter of many parts
* that begins on p.424; the main title is "Greenwich Observations".
* No.1892, June 28, 1901
* The "BILIOUSNESS" tale:
* Only the last sixth of this letter deals with the notorious GF story:
* The full heading is:
* "Sunspots and terrestrial magnetism; To ``F.R.A.S.'' -- the green flash
* a sign of biliousness"
* "I was much interested in ``F.R.A.S.'s'' observations on the ``Green
* Flash.'' I have repeatedly seen this very curious phenomena [sic] ;
* but really, I have never taken any notice of it, and it is the first time
* I have observed it mentioned in print. I remember it struck me most
* vividly when I was staying at Torquay, and I communicated my ideas to a
* medical friend, who promptly said I was suffering from biliousness, and
* there and then prescribed. I remember I looked again for it the day after
* I had taken some medicine, and my friends saying that I should not see it
* again -- at all events for some time to come -- came true, and I had
* forgotten all about it until I saw the remarks of your valuable
* correspondent."
* No.1893, July 5, 1901
* O'C #71
* Langford [44949] identifies "Treadle" as C. Mostyn, from his letter in
* Nature 44,352(1891). Cf. similar remarks in his 1906 Knowledge paper.
* I regard this identification as secure.
* EXPERIENCED: "Having been much at sea in former years, I have had many
* opportunities of observing this very beautiful and interesting
* phenomenon. . . . many scores of observations . . . ."
* EARLY RECOGNITION of the Type A sunset and mirage effects:
* "I have noticed that a particular form of refraction was most favourable
* to its appearance. When the sun, on approaching the horizon, assumed
* curious shapes as of a goldfish-globe or a pear, then there would nearly
* always be a green or bluish flash at the moment of disappearance. On the
* other hand, when the sun assumed the shape of an oval with major axis
* horizontal, the flash did not appear."
* He correctly diagnoses Franklin-Adams's "beads": "I fancy they must be
* caused by ripples on the sea-surface at the horizon. . . ."
* His triple flash was seen from "the old Macquarie , now a training-ship
* for officers under Lord Brassey's scheme."
* Edward Gilbert finds that this trip from London to Sydney was from
* October 28, 1890 to January 29, 1891, and that the ship was built in
* 1875 as the Melbourne ; renamed Macquarie in 1888, and renamed again
* to Fortuna in 1904, before being broken up in 1953. Gilbert also says
* that the pseudonym "Treadle" was taken from Mostyn's interest in treadle
* bicycles.
* No.1893, July 5, 1901
* Fisher #104
* Completely irrelevant remarks that have nothing to do with green
* flashes, as Langford [44949] soon makes clear.
* No.1893, July 5, 1901
* The citation of letter 44819 of "T.R." actually means 44919 of "F.R."
* -- an example of the numerous typos in the E.M.'s letter columns.
* "But to some eyes it was red , not green."
* No.1894, July 12, 1901
* Langford identifies "Treadle" as Mostyn, and implicitly chastises "F.R.".
* He succinctly summarizes the subject in 1 paragraph!
* No.1894, July 12, 1901
* Whitmell's 1-sentence announcement of a cloud-top flash
* No.1902, Sept. 6, 1901
* Fisher #150
* Whitmell's full report of the above observation
* Evidence of VISUAL ADAPTATION:
* "I also noticed that, before sunset, the decreasing segment of the
* setting Solar disc, originally yellow, became gradually whiter in tint.
* Mr. Scriven Bolton, who was with me, also observed the flash. We both
* used opera-glasses."
* (This seems to be vol. 9, 1901).
* Thanks to Ray Emery for supplying this!
* PICKERING's original GF note, "confirming" Franklin-Adams's observation
* -- but without the beads!
* Cited as a "minor publication" in HCO's Annual Report for 1901/02, p.15
* Caution: M.N. volumes do not coincide with years here (Nov.1901).
* Fisher #113
* JBAA abstracts the above
* Naturwiss.Rundschau abstracts Pickering's report
* Nr. 50
* Fisher #115
* PICKERING's "optical illusion" paper
* Caution: M.N. volumes do not coincide with years here (Nov.1901).
* "The effect, I presume, is subjective, and merely a case of
* complementary colours . . . . The fact that my assistant could not see it at
* sunrise . . . confirms this view."
* Fisher #116, O'C #105
* This is the NIJLAND paper that prompted HAVINGA to observe!
* EXCELLENT ADVICE to amateur observers!
* ". . . Prof. W.H.Julius and J.H.Wilterdink, and me, members of the Dutch
* expedition to observe the total solar eclipse of 18 May near Padang . . . "
* Early use of the term "GREEN SEGMENT" (it was first used by Winstanley):
* "This green segment , that I have observed more, though not so
* brilliant, is badly conveyed by the name ``flamelet''."
* ALBERT ANTONIE NIJLAND
* 530 nm given twice
* double flash observed "Durch die Bewegung des Schiffes". (WAVES)
* (For the benefit of people unfamiliar with Astronomische Nachrichten ,
* I should point out that its columns are numbered, rather than pages.)
* Fisher #107
* JBAA abstracts the above
* DISPERSION proposed (!) -- red and green rims seen
* Abstracted in JBAA 12, 299 (1902), which also mentions Hills (next).
* (I file the JBAA summary after Hills, some months too early.)
* See his obit. in M.N. 81, 245 (1921), which mentions his GF observations.
* He was VP of the RMS in 1918 and 1919.
* Fisher #4
* BLUE and VIOLET seen after green with 12x binocular
* ". . . the narrowing segment . . . is first seen to turn green at its two
* extremities; the green colour then appears to run inwards until the whole
* area of the segment appears coloured. . . . after . . . about a second the
* green fades away and is momentarily replaced by a blue or blue-violet.
* The latter is immeasurably more feeble than the green . . . ."
* Major E.H.Hills, R.E.
* Fisher #57, O'C #51
* Schmidt discusses Julius's chromospheric and GF theories, both based on
* anomalous dispersion. It seems the English word "FLASH" has led to this
* confusion (cf. "flash spectrum"). Schmidt compares Julius's theories to
* his own for the solar atmosphere, involving critical refraction --
* essentially, an early example of Hasse's ``Kimmfläche''. Schmidt doesn't
* accept Julius's chromospheric model, but seems favorably inclined toward
* his GF theory.
* cf. the shorter version in Met.Z. 19, 337 later in the year (below)
* Fisher #131
* Ricco quotes from, and comments on, Prinz:
* He seems to draw no distinction between the green rim and "punto verde".
* the 2 photos reproduced show flattening, not distortion
* WARNING: the nutty librarians seem to catalog this journal as
* "Società Astronomica Italiana. Memorie" -- though nothing of
* the sort appears in the published volumes! (That's because the Italian
* Astronomical Society took it over later.)
* O'C #118
* Belated account of Pickering's *first* paper in M.N.
* Fisher #114
* JULIUS republishes his SCALED REFRACTION calculation
* (This appears to be an exact reprint of the 1901 paper)
* NOTE: this appears to be Julius's last GF publication.
* O'C #65; Fisher #63
* Keatley Moore replies to Query No. 69
* and refers to Col. Markwick (see above, 1900)
* He believes it is an afterimage: "The ghosts persist with me about 2
* seconds, which is also the time the green flash lasted."
* Incorrectly cited by Mulder (1922), whose error was copied by
* Feenstra Kuiper (1926). Fisher has it right.
* Fisher #102
* Keatley Moore receives Whitmell's response (below)
* Whitmell counters Moore with earlier references
* Fisher #148
* HUGH ROBERT MILL's first GF report: green, blue, violet
* ". . . there was only one night on which the sunset was sufficiently clear
* to show the interesting phenomenon of the green ray. This was on Sunday,
* August 11, when, as the upper edge of the sun touched the sea-horizon, a
* beam of yellow light, almost instantaneously passing through green to blue
* and dying away in violet, was distinctly visible. It is remarkable that
* so few observers have noticed this striking appearance, which must [sic]
* be visible every time the unclouded sun dips beneath a sharp horizon."
* (pp. 418/419) -- so he evidently believed the "textbook" story.
* This was the Antarctic expedition organized by the Royal Geographical
* Society in 1901 and led by Robert Falcon Scott. Mill notes on p. 422
* that "Lieut. E. H. Shackleton undertook the salinity determinations, and
* proved a very apt and enthusiastic pupil" -- a prophetic remark that
* reminds me of Picard's remark (1680) about Römer.
* A nice halftone photo of this sailing ship is on p. 421.
* RED FLASH discovery? [No; it appears Turquan (1899) beat him to it.]
* "It occurred to me some time ago that, under suitable conditions, there
* might be seen at sunrise and at sunset not only a green flash but also a
* red flash. . . ."
* "In the belfry of the Wesleyan Chapel, on the west side of Woodhouse
* Moor, there are narrow horizontal openings, through which, at certain
* times, the setting sun can send his rays to an observer at the large
* band stand, about 300 yards away.
* "On Saturday, 26th April, between 7 1/4 and 7 1/2 p.m., I was so
* exceptionally fortunate as to observe through the openings no fewer
* than three green and three red flashes."
* (Monday, 28th April, 1902; col. 4.)
* Reprint of the above item, with minor differences in editing:
* "In the belfry of the Wesleyan Chapel, there are narrow horizontal
* openings, through which, at certain times, the setting sun can send
* his rays to an observer at the large Band stand, about 300 yards away."
* An account of Whitmell's talk appears in Obs. 25, 226 (1902).
* Fisher #149, O'C #296
* The original manuscript of the above, printed in full, it appears. The
* JBAA version is improved by editing. But this version has appended the
* text of Prof. E. E. BARNARD's letter from Mt. Hamilton, in addition to
* an observation of a red flash due to cloud, as suggested by Whitmell.
* Barnard, in his letter, says "I have seen the phenomenon (at sunset),
* many, many times in the past fifteen years." (But, clearly, never at
* sunrise.)
* Whitmell answers Query No.72, adding further evidence
* summary of Backhouse's M.N. paper in March
* A summary of W. H. Pickering's M.N. report
* This is the item mentioned by Katherine Bracher in 1992. It mentions
* Kelvin's observation "three years ago", and that "Professor Nijland, of
* Utrecht, Holland, has lately seen it several times at sea." As it says
* that ". . . Pickering calls attention . . . to what he names the `green flash'
* at sunset", one can see how the notion arose that WHP had named it.
* "Observations may be made with the naked eye, though a small telescope
* or opera-glasses will be found advantageous."
* reprinted from A.N., with typos & other editorial changes added!
* Juli 1902 issue
* Fisher #108, O'C #255
* a series of GF papers followed Nijland's:
* First, a simple visual observation of a few sec. duration.
* "Frau Marie Jautz aus Wien in St. Andra" bei Triest" sees a classic
* inf.-mir. flash:
* ". . . verwandelte sich der noch sichbare Rest derselben in ein flaches,
* grünes Scheibchen, welches auf der Meeresoberfläche zu schwimmen
* schien." [nice observation of the mirage!]
* Fisher #175 ?
* J.J.Taudin Chabot's attempt to observe a GF at a partially-eclipsed
* sunrise was clouded out.
* Fisher #23
* Condensed version of Schmidt's Deutsche Revue paper in April (above)
* Only the first half of Schmidt's D.R. paper is quoted here; the part
* comparing his solar theory with Julius's is omitted.
* Fisher #132
* Alexander Herschel's GF over cumuli (see footnote, p.294)
* Cites Hopkins (1883) and Swan.
* July 24 issue
* Fisher #56
* BOILING associated with an inferior-mirage flash
* O'C #293
* Brief review, citing Biot's text, Krifka/Sterneck, and Arctowski
* (Properly belongs in the "distorted sunsets" file; but kept here, as it
* elicited the following GF observations)
* (#1525, 16 Août 1902)
* Seems to be a GREEN FOG observation
* ". . . tout à fait à l'horizon même, l'épais rideau de nuages noirs et
* pluvieux ainsi que le fond éloingé du paysage prirent une teinte
* verdâtre bien prononcée pendant quelques instants seulement,
* comme s'ils eussent été éclairés par la lumière électrique."
* (#1530, 20 Sept. 1902)
* Whitmell corrects "H.P.", and argues TERMINOLOGY:
* "The term ``green ray'' is a bad one. ``Green flash'' is much better.
* . . . There is nothing like a ``ray.''"
* "On August 24 I witnessed three green flashes in succession, as the
* sun's tip sank behind two strips of clouds and the horizon."
* No.1957, Sept. 26, 1902
* "Sigma" corrects "H.P." in a strange way
* "What ``H.P.'' describes is not the green ray, but only a dispersion
* effect among the clouds."
* Eric Hutton has identified "Sigma" (Mr Sprague) [ref. No. 3105 p326]
* No.1957, Sept. 26, 1902
* FRAS corrects "H.P"'s crepuscular-ray observation (query 285, p.135)
* One paragraph headed "The Green Ray" in a much longer letter
* No.1958, Oct. 3, 1902
* Whitmell takes "Sigma" to task:
* "The letter by ``Sigma'' (p.154) affords an excellent illustration of
* the danger of a writer dealing with a subject about which he is ignorant."
* No.1958, Oct. 3, 1902
* Refers to Prinz's paper (1898) and Riccò's work
* (#1533, 11 Oct. 1902)
* long observations of "green ray" [probably visual illusion; see below]
* "Le 13 mars 1899, il a duré 112 secondes 1/2, et le 14 mars 1899, 364
* secondes. A cette dernière date, beaucoup de personnes ont été
* frappées de la coloration verte si prolongée. Le 23 mars de cette
* année, j'ai encore revu le phénomène pendant 107 secondes.
* . . . Dans l'ordre de décomposition apparaìt d'abord le rouge, puis
* l'orangé et le jaune et enfin le vert."
* cf. Cornsweet et al. in VISION file for probable explanation (BLEACHING).
* (#1535, 25 Oct. 1902)
* Fisher #71, O'C #80
* ADAPTATION?
* ". . . the flash was very distinct, but seemed to my vision to be such a pale
* green as to be almost white."
* No.1965, Nov. 21, 1902
* Fisher #96
* a 3-sentence abstract of Libert's La Nature 30:2, 332 (1902) paper,
* calling him "Lucian" (instead of Lucien) Libert;
* also mentions the original report in No.1525, (wrong) p. 161 (copied
* from Libert)
* also mentions Garcin's paper on p. 161 in Aug. 1902 (not naming Garcin).
* Dez. issue
* WHITE, then GREEN FLASH -- evidence for ADAPTATION
* "Da ich den Sonnenuntergang mit Rücksicht auf das eventuell auftretende
* Phänomen erwartete . . . ."
* Clearly an inf.-mir. flash: ". . . den ganzen Tag über herrschte leichte
* Bora . . . ."
* Fisher #45
* a 3rd-hand account of the GF and Julius's theory, attributed to Met.Z.
* sounds like a useless novice report, but might be a real GREEN RAY?
* "Au moment précis où le disque solaire s'effeçait derrière la ligne
* des eaux, instantanément éclata à l'horizon un foyer d'un
* vert émeraude intense projetant dans tous les directions des rayons
* qui se détachaient sur une atmosphére émeraude très clair. Notre
* correspondant insiste sur la beauté féerique de ce phénomène
* absolument remarquable."
* Nice summary of how the inf.-mir. "segment" becomes green from the ends
* and is followed by blue and violet (nameless observer using binoculars)
* Knight again, observing in Italy
* "I am inclined to believe that a change in latitude affects its colour
* to a certain extent. Such is my opinion from thirty-three observations
* made in Italy since Aug. 17 to [Sept. 25]."
* GF mentioned only in short 2nd paragraph of longer letter.
* No. 2011, Oct. 9, 1903
* Fisher #66
* Clapham is uninformative
* ". . . observed on several occasions, and always found it best to be seen
* on a clear sea horizon."
* No. 2013, Oct. 23, 1903
* Chabot seems confused -- useless
* O'C #14 -- why did he bother with this? There are mentions of
* green and red rims, and the use of copper- and cobalt-glass filters.
* But Chabot's earlier papers are more interesting.
* MOUNTAIN sunset GF from 2565m
* Fisher #36
* The interview with Jules Verne that was excerpted in "T.P.'s Weekly",
* in which Verne cannot recall the name of his novel, and has to be
* reminded of it by his wife: "'. . . a visit to Fingal's Cave . . . was the
* origin of my book, "The -- the --"' M. Verne paused. 'I really forget
* the name,' said he. 'Do you remember it?' he asked, turning to his wife.
* '"The Green Ray," was it not,' suggested Madame Verne.
* 'Oh yes, that was it, of course -- "The Green Ray." One must be
* excused,' added he, laughing, 'if, among so many titles the right one
* is not for the moment forthcoming.'"
* The interviewer was Gordon Jones.
* Available at HathiTrust:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3042632&view=1up&seq=676
* and at Google Books.
* June, 1904 issue of this monthly.
* BEGIN T.P.'s WEEKLY series
* As these items are mostly in the "T.P.'s Letter Box" section, and
* unsigned except for initials or pseudonyms, they are a bit difficult to
* give in standard bibliographical form. This magazine lacked the useful
* identifying numbers of English Mechanic, too.
*
* This is the item that started it off, merely by mentioning Verne's
* book:
* No GF, but an interview with Verne from "the current number of 'Temple Bar'"
* is quoted in which he mentions "Le Rayon Vert" -- as well as H.G.Wells.
* Some of these early issues are now (2019) available at the HathiTrust
* website:
* https://catalog.hathitrust.org/Record/000503105
*
* as well as at Google Books. From the information in their catalog,
* one learns that "T.P." was Thomas Power O'Connor (1848-1929).
*
* Note: Part II of Joseph Conrad's "Nostromo" begins on the facing page!
* No. 83, June 10, 1904
* A novice relates 2 sightings, with no useful details, and asks for an
* explanation: "I am curious to know whether it is only seen when the sun
* is setting over the sea."
* June 24, 1904
* Whitmell stirs up enthusiasm again, noticing the YELLOW stage:
* Another Southport flash!
* "The disc of the setting sun was decidedly orange. As it sunk below
* the horizon, the diminishing segment paled to yellow, the colour
* changing to a beautiful green when only the tip of the sun was left."
* No.2052, July 22, 1904
* Fisher #151
* Responses to Whitmell begin here:
* "Phusis" fails because of his "low-lying hill horizon"
* "I have looked for this phenomenon rather vainly for a long time. Is it
* necessary that the horizon should be a sea level?"
* (The similarity to "S.W."'s question in TPW is remarkable.)
* No.2053, July 29, 1904
* Whittle criticises "the crude idea that the sea water is the cause of
* the green ray, as if it were possible for light to pass through at such an
* angle."
* No.2053, July 29, 1904
* "I examined it with a binocular, and distinctly saw the feather wisp as
* described by Mr. Whitmell at the final disappearance of the sun's limb."
* No.2053, July 29, 1904
* We now interleave the letters to E.M. and T.P. in chronological order:
* Responses to "S.W." begin here:
* Another novice responds with the "Pears' Soap ad" theory, with a good
* description of the ad itself.
* July 29, 1904
* Cope reports an INFERIOR-MIRAGE flash over LAND horizon
* "Through a field-glass the last visible part of the sun appeared to
* assume an oval shape, with its longest axis horizontal, and at the same
* time the two ends became of a beautiful green colour, which extended
* towards the centre . . . ."
* No.2055, Aug. 12, 1904
* Fisher #29
* A more experienced observer refutes the "Pears' Soap ad" theory.
* ". . . several of us tested it, but with negative results. We looked
* fixedly at the red sun, and then looked quickly up at a white cloud, with
* the result that some saw a green image of the sun; but that is entirely
* different from the ``green flash,'' which is horizontal and very little
* more than momentary, whereas the visual impression of the sun on the cloud
* (and in Pears' experiment) lasts for some time."
* Aug. 26, 1904
* FIRST CLASSIFICATION?
* This issue has 3 replies. The first is a SPLENDIDLY CLEAR account of the
* difference between green flashes and GREEN RAYs:
* "In the course of sixteen years sailing the seven seas I have very
* frequently seen the green flash and also the green ray. Fine weather and
* an absolutely clear horizon are, or course, essential, but this form of
* refracted light requires other atmospheric conditions, which have not yet
* been scientifically explained, and the flash may be often looked for in
* vain when the conditions seem to be most favourable. The flash appears
* like a magnificent emerald the moment the sun sinks -- sometimes vanishes
* instantly and sometimes fades in three or four seconds. Occasionally, in
* the latter case, a luminous green ray springs from the flash and shoots
* vertically upwards to a height of about five of the sun's apparent
* diameters. Strangely enough, this phenomenon is not commonly known among
* British seamen, although it has been described for many years in a
* standard French Naval Instruction Book as a sure sign of continued fine
* weather." [cf. Trève (1885) and Wegener (1926).]
* Sept. 9, 1904
* Confusion between "green Sun" and green flash; ignore
* Sept. 9, 1904
* A beginner notices the HEIGHT effect:
* "Although both of us gave our undivided attention, there was no green
* ray visible. At the same time, however, two other friends at a distance
* of several hundred yards from us, and on slightly lower ground, declare
* they witnessed the phenomenon."
* [This is evidently the paper "Phusis" (E.M., Oct.14) had in mind.]
* Sept. 9, 1904
* a fuzzy-minded promoter of "color is entirely subjective" nonsense.
* Sept. 16, 1904
* Another refutation of "Pears' Soap"
* "I know the ``Pears' Soap'' effect well, and have seen green suns often,
* but this flash could have nothing of the same character. . . ."
* Sept. 16, 1904
* "Phusis" cites a troubling argument (evidence for ADAPTATION):
* ". . . the theory has been advanced that it is an optical illusion. How
* in else manner can any of our readers account for its visibility to some
* and its invisibility to other observers at the same time? In other words,
* is the colour flash produced by dispersion, or is it a complementary
* colour effect? If it is the former, then it should be visible to all."
* No.2061, Sept.23, 1904
* Another after-imager.
* Sept. 23, 1904
* "C.B.S." quotes an irrelevant passage from Longfellow; ignore.
* Sept. 23, 1904
* Good explanation of the standard textbook story
* "`Phusis' . . . seems to doubt whether the phenomenon known as the `green
* flash' is anything more than an optical illusion due to a complementary
* colour effect (query, complementary to what?)"
* No.2062, Sept.30, 1904
* Whitmell recommends a telescope, and mentions RED flash:
* "I have seen it once or twice, and believe I am the first to draw
* attention to it."
* No.2062, Sept.30, 1904
* "Treadle" (Mostyn) relates a beautiful sunrise flash, and adds:
* "It is never seen unless a great deal of refraction is about, as is
* evidenced by the sun assuming curious shapes --- a goldfish globe, &c."
* A clue to his identity: of the "Bedford Level Experiment," he says
* "I was concerned in it."
* No.2062, Sept.30, 1904
* Fisher #105
* Another ignoramus pushes after-images; ignore.
* "Though not having seen the green flash personally, . . . ."
* Sept. 30, 1904
* SUPERIOR MIRAGES with SUNSET drawings
* "FOG" in blank strips; GF in "cap"
* Fisher #128, O'C #272
* GREEN SUN distinguished from green flash
* "J'ai à plusiers reprises observé le rayon vert, mais le soleil vert
* en différait par sa longue durée d'abord, par la situation du soleil
* au-dessus de l'horizon ensuite, et c'est à ce titre que j'ai voulu le
* signaler."
* letter to editor from a first-time observer who claims a green flash;
* but the description clearly shows that this was only a crepuscular ray.
* An example of CONFUSION due to inappropriate TERMINOLOGY.
* "Phusis" points out some visual effects (evidence of ADAPTATION)
* "Two persons watching the sun at the same time : one sees the flash and
* the other does not, although both are careful observers."
* (attributed to T.P.'s Weekly, Sept.30, p.444 and "previous issues for
* the past few weeks.") Cf. "T.D.", Sept.9, in TPW.
* No.2064, Oct.14, 1904
* More after-imagery; though "If fatigued by a red light and then exposed
* to a yellowish light, the yellow will appear green."
* Oct. 14, 1904
* Whitmell cites some earlier works ("Phusis", Kelvin)
* No.2065, Oct.21, 1904
* Mostyn ("Treadle") counters "Phusis"
* "When I was at sea, the officers of the watch had orders to send and call
* me. . . " makes it sound as if he was the captain; but Edward Gilbert finds
* that Mostyn was only a passenger.
* No.2065, Oct.21, 1904
* This might be Rambaut? There is a reference to Froude's "Leaves from a
* South African Journal" without details; see Froude (1877).
* ". . . take care not to fatigue the eyes by staring at the setting sun. A
* wise plan is to turn the back to the sun, turning round from time to time
* for a brief glimpse, to make sure that it has not disappeared, and only
* fixing the eyes upon it finally when nothing remains visible but the upper
* edge of the disc. Unless the horizon is distant and low, the watch may be
* in vain."
* Oct. 21, 1904
* Whitmell gives several references, and confirms that "Treadle" is Mostyn
* No.2066, Oct.28, 1904
* Clearly this is Charles Mostyn, finishing the TPW series.
* "I have seen it dozens, nay, scores, of times at sunrise at sea. The
* horizon is much more frequently clear in morning than in evening."
* Oct. 28, 1904
* VIOLET flash
* ". . . what we saw was a flash that was distinctly violet in colour."
* No.2067, Nov.4, 1904
* O'C #193; Fisher #25
* Whitmell admits the simple explanation is not adequate:
* "Mr. Childe's question as to why the flash is often absent, though
* circumstances seem favourable to its production, is not easily answered."
* No.2068, Nov.11, 1904
* Mostyn ("Treadle") notices the symptoms of INFERIOR MIRAGE for shipboard
* flashes (again!)
* "I used to observe that the flash was most often seen when the sun, as
* it approached the horizon, was distorted horizontally and assumed the
* appearance of a gold-fish globe or an egg on its side . . . . On the other
* hand, when the refraction was vertical --- when the sun took on the shape
* of an egg on its end . . . --- the flash was seldom if ever to be seen."
* ("Treadle" was identified as C. Mostyn by Langford in 1901.)
* No.2067, Nov.4, 1904
* Fisher #106, O'C #291
* Wilkins proposes sunlight shining through waves (!) despite Whittle's
* July letter
* No.2067, Nov.4, 1904
* Great line criticizing the "ocean waves" notion of Wilkin [sic]:
* "The horizon may be of sea, land, or cloud. Of course, this utterly
* demolishes Mr. Wilkin's explanation, which on other grounds also is quite
* untenable. Over land the flash might with equal probability be ascribed
* to waves of grass."
* No.2070, Nov.25, 1904
* Another put-down of Wilkins's "waves":
* "If Mr. Wilkins possessed the most elementary acquaintance with the laws
* governing the transmission of light through media of different densities,
* he would see at once that a horizontal ray of light entering a wave-shaped
* body of water would be deflected downward, and therefore could not
* possibly emerge from its opposite face to continue its original course in
* a straight line to the eye of a distant observer."
* No.2070, Nov.25, 1904
* Most, but not all, of Whitmell's GF letters to E.M. during 1904;
* Contains several references to other people's letters, including Childe's.
* SCHERING refutes Julius's anomalous-dispersion theory
* See Mon.Wea.Rev.33,408-409(1905) for a translation.
* Phys.Z. strangely indexes this under "Julius" and not "Schering", which
* explains Fisher's listing it under "Julius" as his #62.
* Hartmann's long refutation of Julius's other anomalous-dispersion
* theories in A.N.4197 mistakenly gives the year as 1904.
* 1 Jan. 1905 issue
* Fisher #62 ("Julius") *and* #129 ("Schering")!
* Mentions GF only in 1 sentence: ". . . der übrigens sehr oft, aber nicht
* immer, im letzten Moment den viel erwähnten grünen Strahl zeigte . . . ."
* Feb. issue
* Fisher #100
* telescopic JUPITER FLASH
* No. 2087, March 24, 1905
* O'C #205; Fisher #41
* Whitmell's comment on Ellison's Jupiter flash
* No. 2088, March 31, 1905
* An exact reprint of Whitmell's E.M. letter [258].
* Thanks to Ray Emery for supplying this!
* Discussion of Whitmell's paper on the Sun's supposed reflection in the sea
* These two items really belong with the Ricco and Forel files, as they
* depend mainly on their work.
* "If one only occasionally watched the sun rise and set, one did not know
* what were unusual phenomena and what were not, and if one then saw an
* unusual phenomenon, one did not recognise it as such, because one did not
* know what the usual appearances were."
* ". . . it was noticeably green for a period of two seconds, not what might
* be called a flash, but lasting a sufficient time for it to be seen that it
* was green; . . . ."
* Fisher #53
* Whitmell's report on rotundity (cf. Forel and Ricco, whom he cites)
* ". . . I have left out of account the influence of refraction. Doubtless
* it would modify some of the results, but would not affect the general
* reasoning."
* "M. Ricco appears to have been the first to observe the contraction in
* the sun's image reflected from the sea." [but cf. Bravais, 1853!]
* Properly, this should be filed with either the Ricco or the
* Forel/Dufours file; but it is here as it logically follows Mr.
* Hardcastle's comments on green flashes (previous item).
* Comment on oral presentation of Goodacre's paper (next item)
* and discussion by Goodacre:
* ". . . Mr. Goodacre said he always saw the flash with unaided vision,
* though he had read that it was much better seen with a binocular."
* "Mr. Hardcastle . . . would describe the duration of the flash as being
* two seconds, but, of course, a far greater amount of the sun was visible
* within two seconds of its rising than ought to be according to the
* movement of the sun. It occurred rapidly, as one saw it rising, evidently
* due to refraction, and not to the movement of the earth."
* Joseph Alfred Hardcastle was a grandson of Sir John Herschel, and worked
* as a professional astronomer (see his obits in JBAA 28, 28-29 (1917).
* and M.N. 78, 246-248 (1918).)
* Fisher #49 (listed under Goodacre); O'C #218
* third mention of VARIATIONS IN DURATION and SIZE of flashes ?
* This is mostly a translation of Schering's Phys.Z. paper, but
* the editor has an introductory paragraph that mentions Tyndall:
* ". . . the green ray seen just as the last glimpse of the sun disappears
* below the sea horizon was originally introduced into meteorology by
* Tyndall as an evidence of the special absorptive power of the aqueous
* vapor in the lowest layer of the atmosphere." He then mentions Julius's
* paper, and Schering's review of it.
* Fisher #130
* REFRACTION SCALED:
* "If we take the horizontal refraction as 32', the factor 1/40 gives
* about 50" for the vertical length of the spectrum of a luminous point,
* such as a star or the tip of the sun when on the horizon."
* "With a telescope it is quite easy to observe, at low altitudes,
* a bluish-green fringe on the upper part of the sun's limb. The
* final development and sudden disappearance at sunset of this dispersion
* phenomenon constitute the green flash."
* Fisher #152
* useless novice observation of sunrise GF
* Fisher #101, O'C #251
* A dubious first-time observation; possible green RAY ??
* ". . . suddenly there shot out from the point where we had seen the last
* of the sun a brilliant flash like a beam of electric light.
* It appeared to flash white, blue, and green in succession . . . ."
* No. 2114, Sept.29, 1905
* Fisher #26; O'C #206? (garbled)
* Jocular account of an eclipse expedition, with passing mention of GF
* "The green flash has excited general interest, and some surprising
* observations have been made. A lady has seen a green flash extend almost
* to the zenith several minutes after the Sun went down, and it has been
* quite common to see the Sun reappear somewhat faintly, but distinctly
* green all over! It is, in fact, not quite easy to separate the real
* green flash from the effects of retinal fatigue, and the writer is not
* sure that he has ever succeeded. The last segment of the disappearing
* Sun certainly changes colour, but the result is not always a brilliant
* green. . . . it is to be wished that some observer returning from an
* eclipse could set up his instrument and get the `green flash' spectrum."
* [pp. 416-417] -- "A.R.H." may be A.R.Hinks.
* Thanks to the NASA ADS full-text search for turning this up!
* Admiral Maclear: (has some earlier refs.)
* Apparently the Admiral sent nearly the same letter to Symons's (see below).
* Here, he says "stars"; there, "planet". There are other minor changes.
* Prof. W.M.Davis's "Elementary Meteorology" cited (p.50).
* The full title is "Knowledge & Illustrated Scientific News"
* conducted by Major B. Baden-Powell and E.S. Grew, M.A.
* (N.B.: this "volume" *begins* on p.315, though it spans a calendar year.)
* O'C #234
* replies to Admiral Maclear (March issue)
* Many interesting observations described, including a sunset with
* multiple flashes. One observation notes the red lower limb.
* "I have seen the green, or rather many-coloured flash also behind the
* mountains at sunset in Egypt; but it is neither so clear nor of such long
* duration when seen over land as at sea."
* Evidence of ADAPTATION:
* "At first the whole of the visible portion of the disc of the sun
* turned intense fiery red. Then when a little more than half the disc
* had disappeared it changed to yellow."
* Good color description:
* "Then when the sun is almost down the whole visible part became greenish
* with violet flashes. Then the rest of the disc becomes a line with deep
* violet at each end, blue next to the violet, and green in the middle parts
* of the line."
* ". . . the altitude above sea level about 55 feet; weather calm, light
* S.W. wind . . . ."
* "I used no dark glass on the telescope."
* Full title: Knowledge and Scientific News (March, 1906)
* CHARLES MOSTYN again -- an experienced and careful observer.
* ". . . in a favorable display . . . the `flash' changes rapidly from green
* to blue and violet . . . ."
* SUNRISE better than sunset:
* ". . . far the finest view of the `green flash' is to be obtained,
* according to my experience, oft repeated, at sunrise . . . ."
* "And the horizon is more apt to be clear and sharp at sunrise than at
* sunset, while the brilliance of the flash to the un-tired eye is
* magnificent."
* "Also, the best shows were when the sun, on the horizon, was much
* distorted by refraction."
* [cf. his E.M. letter where this is made explicit.]
* Admiral Maclear: (has several earlier refs.)
* "The phenomenon is frequently observed, but very little has been
* published about it. . . ."
* [The Editor follows with a quote of the MWR Sept. 1905 paper, which
* mentions Tyndall. This quote continues on the next page.]
* Fisher #81
* CAREFUL about Symons's dates: last issue of each volume (ca. p.210ff.)
* was always in Jan. of following year!
* Admiral Maclear: (has some earlier refs.)
* ". . . it is stated that after sunset every solar beam will be broken up
* into a short vertical spectrum; is this the explanation? if so why should
* the last flash be green? . . . I would like to see that matter worked out."
* Fisher #82
* R.C.CANN LIPPINCOTT's crusade for afterimages begins!
* Fisher #75
* R.C.CANN LIPPINCOTT contradicted by Major George H.Courtenay
* N.B.: the 1854 date is VERY EARLY !
* "I saw it continually on my way from Tasmania, in 1854, in the South
* Pacific. But then it occurred at sunrise . I used to get up to
* observe it morning after morning."
* "[Major Courtenay's observation of the green ray at sunrise . . . seems to
* dispose of Mr. Lippincott's argument that the appearance is due to fatigue
* of the eye . . . , a suggestion often made before seeing the phenomenon but
* rarely upheld by one who has actually observed it. -- Ed. S.M.M.]
* NOTE that this is a VERY EARLY OBSERVATION, before Joule!
* Fisher #31
* Col. Markwick reports a small naked-eye flash
* This is only the last paragraph of a long letter mainly on other topics
* No. 2134, Feb. 16, 1906
* Fisher #85
* FIRST REVIEW ARTICLE -- SCALED REFRACTION calculated again (1/72)
* N.B.: cites *nothing* but English journals!
* Dr. Arthur A. Rambaut, F.R.S.; earliest refs. are to Nature in 1883.
* Rambaut had been Radcliffe Observer since 1897.
* first mention of violet as complement to yellow?
* "It was then quite unmistakable, and those who are so fortunate as to
* see it, as I and several of my fellow-passengers on the Durham Castle
* did on that occasion, will not, I think, retain any lingering doubts
* as to the objective character of the phenomenon."
* Another independent inventor of the OCCULTING DIAPHRAGM!
* "This is an observation by which any possessor of a telescope can easily
* satisfy himself that the flashes are due to atmospheric dispersion of
* light, and is at least less expensive than building a Wesleyan Chapel
* with horizontal openings in the belfry." (cf. Whitmell's RF paper.)
* The curious figure purporting to show how the textbook flash is formed
* contains only red, yellow and blue -- suggesting that Rambaut made
* the common error of thinking that blue + yellow makes green.
* Fisher #122 and #123
* Cann-Lippincott again insists on afterimages, even at sunrise!
* Lippincott pursues the same line in QJRMS
* This letter is dated March 24, 1906.
* Fisher #73
* Gregg starts a round by inquiring about the green ray's visibility
* No. 2141, April 6, 1906
* H.P.Hollis replies to Gregg, citing Rambaut's first installment.
* Note: this heading is a sub-head of a long letter of many parts; the
* general heading is "Magnitude of the fixed stars".
* No. 2142, April 13, 1906
* Whitmell replies to Gregg, and cites papers in Leeds Astr.Soc.
* No. 2142, April 13, 1906
* Variability. . .
* "It should be noted that the green ray . . . is not always seen even when
* the sun sets at sea on a perfectly clear horizon."
* Fisher #7
* Unsigned editorial by H.R.Mill, with a synopsis of Verne's story
* "We have seen it only a dozen times in twenty years. . . ."
* Mill seems to believe the "old Highland legend".
* Cited with title in Kimball's "Recent Papers," MWR 34, 219 (May 1906)
* Fisher #97 and 98
* GREEN RAY observation
* "The common `green,' or as I would rather call it `blue' flash which I
* have seen, perhaps a hundred times, is undoubtedly caused in the way
* described by Dr. Rambaut, but there is another phenomenon which I have
* seen on a few occasions, which is almost as certainly caused by
* atmospheric absorption. In it the upper part of the sun's disc when
* setting becomes a vivid green for several seconds before disappearing,
* and in the light then given objects of a green colour appear with
* extraordinary vividness. Probably closely allied with this phenomenon
* is one which I have seen here on two or three occasions, when the whole
* sky became filled at sunset with what seemed to be a green mist, which
* produced the most lurid effects." ("here" = Kodaikanal)
* Fisher #137
* (mostly useless)
* Fisher #32
* first ref. to Mrs. Steel
* "As another example of the mention of the Green Ray in fiction, I may
* instance Mrs. F. A. Steel's novel, `Red Rowans.'"
* LIPPINCOTT refuses to give up!
* Fisher #76
* Capt. Carpenter replies to Lippincott in QJ, who responds (next item)
* "The extraordinary explanation of the above . . . by Mr. R. C. Cann
* Lippincott, needs some correction. . . . a complementary coloured spot will
* only fade away slowly, whereas the green flash is momentary, seldom
* exceeding 1 1/2 seconds."
* This is in the July issue.
* Lippincott responds to Carpenter with nonsense
* Another report from Southport !
* This seems to be associated with looming; needs to be investigated.
* Cites his earlier report in E.M.No. 2114, p.183.
* No. 2155, July 13, 1906
* Fisher #27
* Lippincott again
* This is a further reply to Capt. Carpenter's letter in the July issue.
* Fisher #74
* ramblings about particulate EXTINCTION and IRRADIATION
* "[. . . the question of the infrequency of the phenomenon is an
* interesting one, on which, perhaps, more can be said. -- Ed. S.M.M.]"
* "The duration may be largely affected by the observer's latitude and the
* extent by the refractive condition of the air."
* Fisher #153
* "I cannot believe that the phenomenon has ever been seen, unless the red
* edge or red colour or red ray of the rising or setting sun has been first
* seen above the horizon."
* A "convert to the physical theory" testifies for Rambaut
* Fisher #80
* Whitmell sees a a red flash below cloud
* (Alex.Thurburn is still confused)
* Varying width of green rim (N.B.: now Jan.1907)
* Fisher #46
* Hansky's sunrise flash of Sept. 4, 1900, reprinted by Rodolphe Radau
* The GF report is an extract of Hansky's report in Janssen's Note on
* his Mont Blanc observatory in the 1901 Annuaire.
* An English translation of this item appeared in the Annual Report of
* the Board of Regents of the Smithsonian Institution, for the year ending
* June 30, 1906 [GPO, Washington, DC (1907]). Unfortunately, Radau's
* initial appears there as "H.", not "R." This error was then propagated
* by the Nov. 23, 1907, supplement to "Scientific American", which abstracted
* the English translations of this and earlier Radau articles on Janssen,
* omitting Hansky's GF observation.
* Rodolphe Radau spent much of his life working at "Revue des Deux
* Mondes". He was part of the German community in Prussia, but moved to
* Paris after studying math and astronomy at Königsberg.
* The Editor's patience is exhausted! LIPPINCOTT's last gasp
* Note the Editor's sermon at the end!
* Fisher #77
* Adrien Guébhard won't admit defeat, and gets in another lick:
* "Quant au prétendu météore du rayon vert , il n'a pas davantage
* d'existence colorée objective : c'est la simple ombre portée,
* au milieu du crépuscule rouge, d'une pointe se détachant sur
* le disque solaire à sa disparition . . . ."
* This article is mostly about color perception; only 1 paragraph on GF.
* NOT a green flash -- completely PHONY description.
* "As the sun there [Egypt] descends nearer and nearer to the horizon,
* apparently hastening to disappear behind one of the Libyan hills, as if
* burying itself in the sand at their base, the immensely enlarged flaming
* disc suddenly becomes, for an instant, of a brilliant green colour, and
* immediately a series of green rays suffuses the sky in many directions,
* well-nigh to the zenith." (All a fantasy; certainly not seen.)
* Fisher #109, O'C #98
* Joseph Offord's awful paper reprinted in E.M.
* No.2186, Feb.15, 1907
* Fisher #110
* an account of Nijland's A.N. paper; first mention of GF in H&D?
* exact citation is vol.4, no.2, Maart 1907
* Thanks to Ernst Raimond for a copy of this!
* The second half of this letter concerns a TELESCOPIC green flash
* "In watching the sun set to-night beneath a land horizon, through a
* small telescope without eye-screen . . . it was evident that this green
* border was the more refrangible part of a spectrum ."
* [Looks like No. 2203 or 2205 -- can't read date on photocopy: June ?]
* Whitmell's GF letter to E.M. published on 5 July 1907;
* refers to Allison's letter, p.494
* Whitmell discuses the prolongation of a flash at the Arctic Circle,
* calculating 12 minutes (6 each before and after midnight).
* "For such a duration the word `flash' seems scarcely suitable; but the
* disadvantage of the word `ray' lies in the fact that it conveys to many
* persons the impression that a long green streamer is seen shooting up
* towards the zenith. This is unfortunate, as observers are led to look
* for something which never occurs as part of the green flash, properly
* understood."
* Reprint of Whitmell's GF letter to E.M., 5 July 1907;
* refers to Allison's letter, p.494
* Fisher #154; not read (hence the error in journal name)
* He thinks a GF is a SOLAR PROMINENCE
* He sees flashes with 10x telescope; but thinks the last previous
* observations were those of Exner in 1902 and Dorn in 1903.
* "Vermutlich ist er veranlaßt durch aufflammende Gasausbrüche am
* Sonnenrande, sogen. Protuberanzen besonderer Art." At sunrise,
* "Grüne Randerscheinungen konnte ich . . . mehrmals feststellen.
* . . . Es handelte sich dabei um eine ganze Korona grünlicher Flammen, die
* sich auf je etwa 30 Grad heliographischer Breite nördlich und südlich
* (im Sonnenbild links und rechts) vom Sonnenäquator aus erstreckten."
* (The continuation of the article on p. 329 is about ordinary solar
* activity.)
* Aug.1, 1907 issue
* Col. Markwick's review of atmospheric optics
* One long paragraph here devoted to the GF: ". . . the sight of it is
* decidedly rare, and should be treasured up in the memory afterwards."
* "It generally lasts about a couple of seconds, and the change of colour
* is most impressive. A binocular vastly assists the eye in the observation
* of the phenomenon, which is doubtless due to atmospheric dispersion . . . ."
* No.2212, Aug. 16, 1907
* HARTMANN's refutation of Julius's wild applications of anomalous
* dispersion to everything in sight. He cites Schering's 1904
* refutation of the GF model.
* This item is followed by a letter from the infamous H.H.Kritzinger!
* Allison's letter, describing the MOCK MIRAGE phenomena
* "It was curious to note how the refraction of the air caused both
* notches and projections to appear upon the limbs -- especially the upper
* one -- which notches and projections remained permanent for one or two
* minutes. Sometimes two notches would approach one another, and finally
* cut off, apparently, a piece of the luminous disc which floated above the
* rest of the sun. . . . the uppermost part of the projections on the upper
* limb continually shot out green flakes . . . ."
* No.2221, Oct.18, 1907
* Whitmell confirms what Allison's letter, p.237, reports
* Whitmell recommends using a telescope to see the green and red "flames".
* No.2222, Oct.25, 1907
* GROFF's works reprinted
* The GF papers are on pp. 171-180, 190-196, 221-224, 225-227, 249-258 and
* 258-272. The biographical note is in pp. I-IV.
* use of PINHOLE to attenuate the Sun
* Maxwell Hall
* Fisher #52
* our "last glimpse" of R.C.CANN LIPPINCOTT !
* "I am convinced that the so-called `green flash' is the after-image or
* visionary image of the impression produced on the retina by the last rays
* of the setting, or by the first rays of the rising sun, seen in the
* complementary blue-green colour."
* (Letter dated 10 Feb. 1908)
* Whitmell relays an observation by Ivo Gregg in Egypt
* ". . . where he has been staying with Professor Flinders Petrie."
* ". . . in the Libyan desert, near Wadi Halfa, he saw, with the naked
* eye, at sunset, the Green Flash, a phenomenon for which I had asked him
* to look out. Just as the solar disc disappeared, its tip assumed a fine
* green colour."
* As Whitmell asked Gregg to observe, this might be the cause of Petrie's
* 1914 report?
* The same item, reprinted in the Leeds Trans.
* Thanks to Ray Emery for supplying this!
* 2 minor mentions of GF observations in a long article on other matters
* Prof. Ward calls it "the `green ray'" (in quotes) on pp. 335 & 339.
* Oct. issue.
* Fisher #145
* green rim + green flash
* O'C #271
* R.C.Cann Lippincott sees something at last: GF or Cornsweet effect?
* Fisher #78
* ORANGE LINE becomes GREEN BAND at Southport !
* "The disc was much distorted as it sank; for the last 30 seconds or so
* it seemed an unvarying bright orange line; then the orange simply faded
* and all but disappeared. I was just about to register one more failure
* when a distinct and bright green band took the position and apparent size
* of the orange of about 20 seconds previously; it continued for perhaps
* seven seconds and then gradually faded away."
* Fisher #70
* GF with inf.mirage, 10. August 1909 at Zandvoort
* ". . . ein Spiegelbild auf der Meeresfläche entstand. Nur ungefähr eine
* Sekunde vor dem völligen Verschwinden w u r d e d a s l e t z t e
* s e g m e n t d e r S o n n e g l e i c h z e i t i g m i t d e m
* S p i e g e l b i l d e grün."
* Not certain about details, "da mir die Erscheinung neu war und mich zu
* sehr überraschte." (typical BEGINNER'S REACTION)
* Also a good story about the "junge Dame": "Im Augenblick, als die Sonne
* verschwunden war, wandelte sie sich mit dem Ausdruck höchsten
* Erstaunens zu mir und sprach nur das eine Wort: grün!"
* Ellison Hawks reports a 6-second flash, "peacock blue" at end
* Fisher has "Hawkes" in error, and F.K. does too.
* No. 2317, Aug. 20, 1909
* Fisher #54
* Whitmell asks for an explanation of "the rarity of the flash although
* circumstances are apparently quite favourable for its appearance."
* "I have seen the green flash at least a score of times, but failures
* have outnumbered successes.
* "The difficulty of the problem is enhanced by the fact that a
* telescope directed to a low sun in a clear sky invariably exhibits
* atmospheric dispersion, the upper limb being fringed with bluish-green,
* the lower with orange-red, and the green flash is simply the ultimate
* development of the former colour upon the tip of the setting sun."
* No. 2318, Aug. 27, 1909
* Reprints of the two E.M. letters by Hawks and Whitmell
* Hawks letter [70] dated Aug. 14, 1909
* Thanks to Ray Emery for supplying this!
* Reprints of the two E.M. letters by Hawks and Whitmell
* Whitmell letter [98] dated Aug. 27, 1909
* Thanks to Ray Emery for supplying this!
* pompous presentation of GF in a description of twilight phenomena
* must be # 1035, from F.K.'s citation
* O'C #90 -- there is a second installment on pp. 753-756, he says.
* LIPPINCOTT vs. WHITMELL in E.M. (1909)
* "R. Claude Lippincott" sees a green flash at last; but maintains it is
* due to "simultaneous physiological contrast".
* No. 2322, Sept. 24, 1909
* Fisher #79
* Whitmell replies to Lippincott:
* No. 2323, Oct. 1, 1909
* Lippincott augments his description, asserting "simultaneous contrast".
* No. 2325, Oct. 15, 1909
* Whitmell replies to Lippincott:
* No. 2326, Oct. 22, 1909
* Cann Lippincott has his final say in E.M., shooting himself in the foot
* as he does so:
* "With reference to Mr. Whitmell's suggestion that I should study the
* appearance of the sun through a telescope when it is low or setting, I may
* remark that the telescope would introduce a new condition, which would
* produce a modification of the natural phenomenon. My present residence
* is not well situated for observations of either sunrise or sunset, because
* it is surrounded by hills on which there are trees, which interfere with
* the view of the sun about the time of sunrise or sunset."
* No. 2328, Nov.5, 1909
* CARLO BONACINI's early GF credential
* Short abstract of a paper presented in 1907: he saw the red and green
* rims, and realized that they should be attributed to atmospheric
* dispersion; and "that to this is connected, at least in part, the noted
* and discussed phenomenon of the `green ray'."
* Review of Groff's collected works
* Probably this belongs in the "biographies" file, but is included here
* for Ernst Andersson's comments on Groff's GF work: ". . . une série
* d'études très intéressantes." He seems to think it Groff's best work,
* and quotes at some length from Groff's conclusions.
*
* MANY THANKS to Orell Witthuber, Fachgebiet Aegyptologie der
* Philipps-Universität (Marburg, Germany) for providing this useful
* reference!
* LORD KELVIN's first GF
* ". . . the first time I saw it, it passed quickly from white through green,
* to intense violet. The sun was very clear, with very little of the
* redness which we generally see at sunset." That was in 1896, before the
* sunrise flash of 1899.
* (See next 2 papers for discussion.)
* Fisher #65, O'C #70
* little more info from Silvanus P. Thompson; comments on violet
* Fisher #24
* Whitmell quotes most of Kelvin's Nature paper; further comments on violet
* Described in part of one paragraph on p.246
* This is mostly about other weather phenomena, esp. anti-crepuscular rays.
* "Hochgebiete" turns out to be 1500-2000 m.
* Full title: Das Weltall, Illustrierte Zeitschrift für Astronomie und
* verwandte Gebiete, herausgegeben von Dr. F.S.Archenhold, Direktor der
* Treptow-Sternwarte
* ". . . about ten (or less) seconds after it had disappeared a bright green
* single flash, just like a railway signal lamp, but brighter far, met our
* view. . . "
* Fisher #5
* 3 GFs on an island horizon
* ". . . the reputed rareness . . . is a striking proof of the unobservant
* habits of most people."
* error: "Whitmill" for Whitmell
* Fisher #99
* KREBS's crank connection of green rims with solar activity
* ". . . eine grüne Umrandung besonders des Ostrandes der untergehenden
* Sonne . . . der Westrand, solange es sichtbar war, gewöhnlich nicht die
* gleiche Erscheinung erkennen ließ." He seems to have used the low
* Sun simply to make use of the atmospheric extinction to render it
* observable in a 3-inch telescope. The reappearance of an active
* region "am Ostrande der Sonne war . . . begleitet von ausgeprägter
* grüner Strahlung. Besonders deutlich trat sie auf bei dem ersten
* Akte des Sonnenunterganges hinter einer 3° hohen bleigrauen Bank.
* Diese erwies sich in der Folge als der total reflektierende Teil einer
* Sprungfläche der Atmosphäre. Denn unterhalb des etwa gradbreiten
* dunklen Bandes, hinter dem die Sonne verschwunden war, trat sie wieder
* hervor. Doch war die Scheibe erheblich breiter und kirschrot statt, wie
* vorher, orangefarbig. . . . die grüne Berandung stellt sich vor und
* nach dem Passieren des dunklen Bandes, das sein Auftreten der
* Totalreflexion verdankte, am natürlichen Ostrande der Sonne ein, während
* sie an dem künstlich von diesem Bande geschnitteten Ostrande ausblieb."
* Nov. issue.
* Kühl's "Nachbilderscheinung" with nice colored plate (Tafel V)
* He starts off by quoting Flöckher's account in full, and argues
* (correctly) that the green rim is too narrow and faint to be visible:
* ". . . durch die Absorption der Atmosphäre . . . muß schon der Farbrand
* wegen des Auseinanderziehens der Spektrum erheblich lichtschwächer
* als das Sonnenbild erscheinen und erleidet zudem eine vom Gelb zum Blau
* wachsende Absorption. Schon aus diesem Grunde scheint es zweifelhaft, ob
* die Dispersion die auffällige Erscheinung des grünen Strahles erklären
* kann." [A nice prefiguring of Dietze's quantitative demonstration!]
* But, strangely, ". . . der grüne Strahl, wenn er objektiv vorhanden
* wäre, doch leicht in einem Fernrohre bei niedrigem Sonnenstande . . . in
* Erscheinung treten müßte --- was nie beobachtet ist."
* So he knows nothing of Winstanley, Rambaut, Whitmell, etc.
* Finally, he admits that, in choosing between the two explanations, "Man
* könnte z. B. auch an eine Kombination beider denken, derart, daß die
* Nachbilderscheinung durch einen schwachen vorhandenen Farbring noch
* verstärkt erscheint." Which comes pretty close to the truth.
* His reference to p.56 of Arrhenius's "Kosm.Physik" makes no sense.
* Note that the date is 1910, but the actual publication date is 1911
* Blathwayt's DEMONSTRATION of GF
* About the middle third of this long paragraph deals with GF:
* "I find you can imitate it well by holding a little above your eye, and
* between it and a candle, an ordinary hand magnifying-glass, in such a way
* that the candle rays strike it at a very great angle on the upper surface
* of the glass. This produces two or three discs of light, and if you then
* turn the glass so that it lies nearly edge-on to the candle, the discs
* disappear, and at the instant of vanishing the last rays are all green."
* He also has the screwey notion that "in the usual condition of weather
* the various layers of air are of very different refractive powers, and
* thus act as a compound lens, and are free from colour." [!]
* But (maybe from dumb luck), he also says, "Perhaps it depends also on
* the height one is above the sea-level."
* Theodore B. Blathwayt was a noted discoverer and observer of comets;
* see his brief obituary in JBAA 45, 249 (1935)
* No. 2410, June 2, 1911
* Whitmell corrects Blathwayt's notion that the sea acts as a lens; adding,
* ". . . the sea horizon, being more definite, is apparently more favourable.
* It is possible also that the condition of the air over a water surface may
* be more favourable."
* No. 2411, June 9, 1911
* Fisher #155
* Whitmell reports a CLOUD-TOP flash
* "This is the celebrated Green Flash, so often looked for, but, for some
* mysterious reason, so seldom seen."
* (Letter dated 22 July 1911, published on Monday the 24th.)
* The previous page contains a note on "The Intense Heat", reporting that
* "Temperatures of over 90 degrees in the shade were recorded at several
* places in England on Saturday [i.e., the day of Whitmell's observation].
* Saturday was the tenth day during July on which the general level of
* shade temperature has been above 80 degrees, and the 23rd day in
* succession on which no rain fell on London."
* The letter following Whitmell's is amusing. . .
* Whitmell reports a CLOUD-TOP flash
* "This is the celebrated Green Flash, so often looked for, but, for some
* mysterious reason, so seldom seen."
* (Letter dated 22 July 1911)
* Thanks to Ray Emery for supplying this!
* Whitmell's scoreboard for 1911
* Useful for magnifications: "Binocular 9, Opera Glass 3".
* "Of 13 observations, only four . . . were satisfactory."
* The last observation was Sept. 6.
* Thanks to Ray Emery for supplying this!
* "GREEN SPOT"
* Col. Markwick comments on his Mediterranean cruise:
* "This appears quite well known to many naval officers, one of whom
* called it the ``green spot.'' He had been acquainted with it for years."
* Only the 2nd paragraph of this long letter is headed "The Green Flash".
* No. 2426, Sept.22, 1911
* Fisher #86
* Blathwayt thanks Whitmell, and adds, "I saw a brilliant Prussian-blue
* flash some time ago."
* Only the first short paragraph of this long letter deals with GF.
* No. 2430, Oct.20, 1911
* Fisher #9
* Not a GF observation, but relevant comment on CONTRAST EFFECTS:
* "Gold, orange, and carmine were the prevailing hues . . . ."
* "The street lamps looked quite green by contrast with the sky."
* (properly, this belongs in the Vision File, but is here as an observation.)
* No. 2443, 19 Jan. 1912 (note change of year near end of even-numbered
* volumes!)
* Brief account of paper presented at meeting of 6 Dec. 1911
* "M.Monte . . . présente une étude sur le rayon vert. Il en a recherché
* l'explication dans de nombreux ouvrages, où l'on avance, parfois, des
* hypothèses invraisemblables, et montre que l'explication par la
* dispersion atmosphérique seule rend un compte exact du phénomène."
* Braak replies to an earlier question from "G.L.T. te A."
* cites the article in H&D 4, Maart 1904.
* "I have read" the standard explanation, but can't judge its worth.
* BEADS again
* "About one or two seconds after the sun had set, Mr. Scholes noticed
* some ``blue-beads'' above the point where the rim had been; these remained
* visible for two or three seconds, and the green flash was seen when they
* disappeared." Could that have been a GREEN RAY?
* (This item is next to Wilbur Wright's obituary in the previous column.)
* Fisher #133
* Captain Carpenter's presentation at B.A.A. reported
* SYSTEMATIC SUNRISE OBSERVATIONS at Taormina, Sicily, 700 ft above sea
* Capt. Alfred Carpenter, R.N., D.S.O. (see Who's Who)
* "I observed every sunrise except four from the 10th December 1911 to
* the 14th March 1912. . . . Out of 91 mornings' observations the
* phenomenon of the Green Flash was observed on 21 occasions. Of the
* other 70 days about 45 sunrises were hidden by clouds low down on the
* horizon or by rain, and on the other 25 mornings, owing to mist or dust,
* the Sun rose out of the water a dull red, or gold, or white."
* ". . . I feel confident that, with a horizon clear of cloud or mist, the
* Sun will always show the Blue-green Flash on rising."
* "The prevailing wind was . . . blowing off shore."
* (These seem to be mostly inferior-mirage flashes, despite the altitude.)
* O'C #12
* Fisher #12
* summary of Carpenter's JBAA paper, citing Rambaut's 1906 review as motive;
* possibly this is what incited Lippincott's 1913 return in QJRMS?
* Fisher #13
* useful lists of earlier refs. in JBAA
* O'C #297
* Second-hand review of Kühl's paper and Rambaut's review
* Rambaut's article is the only reference cited; it is endorsed by the
* editor.
* Aug.31, 1912 issue (No.1913) of this folio-sized weekly
* E.W.Maunder's comments are most to the point
* This was the meeting at which Cann Lippincott's paper (next) was read.
* Fisher #178, O'C #243
* R.C.Cann-Lippincott has a shot at the BAA
* N.B.: the volumes and years of JBAA do not coincide!
* An EXCELLENT and eloquent refutation of Cann Lippincott
* N.B.: the volumes and years of JBAA do not coincide!
* O'C #13
* not so sound a reply, from Whitmell
* (stapled with the previous copy)
* O'C #154
* Ellison recalls his 1905 telescopic JUPITER FLASH in last paragraph,
* giving circumstances: "Jupiter . . . set behind a clear-cut ridge of
* mountain. This ridge was elevated 1,450ft above my station, and was nine
* miles distant, so the elevation was 1° 44'."
* No. 2490, 13 Dec. 1912
* Fisher #42
* Whitmell comments on Booth;
* only the last paragraph of 7 in this letter deals with the GF.
* No. 2491, 20 Dec. 1912
* WERFTINSPEKTOR WELZNIG
* later "G.Welzing" or "Melzing" -- see later Kosmos references
* One sunset and one sunrise obsn. in Indian Ocean (Sunda Straits).
* Thinks it is transmitted through the water.
* Lippincott again, this time in QJRMS
* He now reconsiders his 1906 statements: ". . . I wrongly attributed to
* successive what was in reality an example of simultaneous contrast ."
* He also now admits there are flashes ". . . occasioned by the refraction
* of the atmosphere . . . " but he still insists ". . . that in the explanation
* of the ``Green Flash'' given by Dr. A. Rambaut, Mr. Whitmell, Capt. A.
* Carpenter, and others, the three quite distinct optical phenomena above
* described have been confused . . . ."
* Summary of readers' responses to the 1912 "Welznig" article
* ". . . bei ruhiger See . . . "
* "Manche Mitglieder verglichen sein Licht mit dem unter dem Horizont
* stehenden Leuchtturms, der seinen Scheinwerfer nach oben aufblitzen
* läßt; andern schien er mehr nach Art einer Rakete emporzufliegen"
* = GREEN RAY ?? (Miethe's "Prometheus" article is cited.)
* N.B.: This is on p.XXXV in the colored pages:
* Title page says at bottom in small print:
* "Notiz für den Buchbinder : Es sind nur die f o r t l a u f e n d
* (arabisch) p a g i n i e r t e n Seiten auf w e i ß e m Papier
* einzubinden"
* Fortunately, L.C.'s bindery can't read German!
* Here, it's "Werftinspektor Melzing" (probably the correct spelling)
* Carpenter takes Lippincott's bait
* "Most of Mr. Lippincott's article appeared previously in last October's
* number of the Journal of the British Astronomical Association , and was
* fully answered by Mr. C. T. Whitmell and myself in the November number of
* the same journal. It seems a pity that Mr. Lippincott should repeat his
* erroneous descriptions of the Green Flash after his errors have been
* pointed out."
* A sea-captain sees a good display:
* Repeated green flashes due to heavy swell.
* Nice drawings of green rim (Fig.180) in mountain sunset
* a useless comment
*O'C #214
* a useless first observation between Sorrento and Capri
* O'C #221
* Lippincott tries to have it both ways
* He grants refraction, but concludes that "the Green Flash most likely to
* attract the attention of the ordinary observer is the Green Flash due to
* Simultaneous Complemental Contrast." Ah, the power of ignorance!
* Discussion of the following paper at BAA Meeting:
* There are several interesting comments, notably by M.A.Ainslie on
* variations of dip. What are the "American" observations he alludes to?
* He emphasizes the importance of height of the observer.
* Mrs. Brook's observation recalls Minnaert's later experience of running
* uphill.
* EARLY FLASH IN INFERIOR MIRAGE (cf. Evershed)
* cited by Corliss as "unusual"!
* Fisher #14, O'C #187
* utter nonsense about refraction through WATER
* a second BLUE SUNRISE flash over the ALPS
* BLUE SUNRISE flash over the ALPS
* BLUE flash of VENUS
* WAVE modulation (cf. Franklin-Adams's report)
* "I was using binoculars, and remarked that I had never seen the horizon
* so sharp. The waves could be seen on the edge of the sky."
* "The green line seemed to be broken into three, possibly by waves . . . ."
* Fisher #43
* Pogg. says Hans-Hermann Kritzinger was publisher of Sirius
* Kritzinger first cites and quotes much of Prof. Flöckher's 1909
* observation, reported in Mitt.VAP. Then he describes his own.
* Here he cites Kühl's article in "Der Sammler"; from the section quoted,
* it's plain that Kühl had never seen a GF (though Kritzinger describes one
* he had seen, along with a plain description of a SOLAR AFTERIMAGE, of
* which he says, "Daß diese . . . ein Agglommerat von Sonnennachbildern
* gewesen ist, scheint mir wohl kaum möglich . . . .")
* This is in the Sept. issue of Sirius
* Fisher #69
* WHITMELL on TERMINOLOGY
* "I venture to think that `flash' is a more suitable term than `ray,' for
* the latter may lead people to suppose that a long streamer of light is to
* be expected."
* Fisher #156, O'C #155
* FLASH IS COMMON -- W. FLINDERS PETRIE (Piazzi-Smyth's Pyramid opponent)
* "At sea I have always seen it, if the horizon is clear and not too red."
* Petrie was a famous archaeologist who made several trips to Egypt.
* (cf. Whitmell, 1908)
* Fisher #112, O'C #104
* Flash over "roof of the Russell Hill Schools, which are distant 1 1/4
* miles and only 50 feet higher than my house . . . ."
* Compared to the following observation by Edmund Clark.
* Fisher #15
* Flash over "the roofs of Banstead Asylum, nearly 4 miles distant across
* the main Brighton Road valley and of just the same elevation."
* mentions 2 flashes he had "previously seen once from the Lion's Head
* Hill, Capetown, and once on the South Atlantic."
* NOTE that both this and Capt. Carpenter's flash were seen the same
* evening.
* J.Edmund Clark
* Fisher #28
* 10-second flash; otherwise similar to the Howard-Young note in S&T, 1957
* Signed "P.Camille Melzi D'Eril"; properly (in Italian), Padre Camillo
* Melzi d'Eril -- director of the geodynamic observatory in Florence.
* FLAMMARION's flash; useless
* O'C #212
* cites the Sirius paper in Sept., partly translated into Dutch
* Also cites Kühl in "Sammler", 28 Juli 1914, and repeats his
* after-image explanation, which Kater seems to find persuasive.
* Nijland's comments on the above
* "It is really peculiar that people call the afterimage for help to explain
* the green flash again and again, without taking the trouble to find out,
* either in the literature or by their own observation, whether the
* phenomenon is to be seen at sunrise." After citing some examples of his
* own, he adds: "It is clear that the afterimage can hardly explain these
* morning observations."
* Both ADAPTATION and PHYSICS are involved:
* "It is possible that the reason why doubt has been cast upon records of
* the green flash is that the colour may arise in the two different ways
* suggested above . . . ."
* 3 GFs observed; one probably affected by adaptation; one at sunrise.
* O'C #202; Fisher #37
* a report from moderately high latitude (57.6 deg.N)
* GF explicitly connected with MIRAGE and DISTORTION phenomena:
* "Es waren dabei über der See oft merkwürdige Verzerrungen und Fata
* Morgana- Erscheinungen wahrzunehmen . . . ."
* . . . and with cold air: ". . . verbunden mit starker Abkühlung der Luft."
* A classic mock-mirage flash, in which he mistakes a duct edge for
* the sea surface: ". . . an den beiden Stellen, wo Sonnenrand und
* Meeresfläche sich berühren, der Rand sich grün färbte, diese Färbung
* lief mit großer Geschwindigkeit nach oben bis zur Vereinigung, so daß
* der ganze noch ziemlich lange Sonnenrand in leuchtendem Smaragd oder
* Malachitgrün strahlte. . . . Dieser ganze Vorgang hat etwa 2 - 3 Sekunden
* gedauert. Es war also die Sonne durch anormale Refraktion noch über den
* Horizont gehoben gewesen."
* This is Band 13, N.F.; 4. Okt.
* the infamous KRITZINGER paper, so criticized by Mulder (deservedly)
* Contradicts Riem's earlier appeal for more observations in Nr.40, saying
* that "Zunächst ist das Phänomen inzwischen bereits vollständig erklärt
* und dann sind solche Versuche recht gefährlich . . . Man weiß, daß
* Galilei durch unzweckmässige Sonnenbeobachtungen erblindete," and
* mentions cases of eclipse blindness. Then he asserts that "Vielleicht
* mißlingt aber dann gerade die Verfolgerung der an sich sehr interessanten
* Erscheinung, weil diese nämlich r e i n s u b j e k t i v ist."
* Here he cites Kühl's experiments in "Sirius", claiming that "eine
* gewisse Zitterbewegung" is required to intensify the afterimage, and that
* "Die unregelmäßige Verteilung verschieden erwärmter Luftschichten ist
* für die Hervorrufung der Zitterbewegung der Sonne wichtig, hat aber mit
* der `anormalen Refraktion' nichts zu tun."
* It's hard to find more misinformation, or bad advice, in so small a
* space anywhere else in the GF literature!
* This is Band 13, N.F.; 13. Dez.
* Fisher #67, but not read by him; he gives the N.F. vol., without "N.F."
* a detailed observation of the evolution of an inf.-mir. flash,
* observed through 6x30 binoculars
* This is a re-telling of the observation that Kritzinger objected to.
* O'C #269
* Attentive observations of GF and anti-crepuscular rays
* [of the GF]: "The topic is a good one for argument on board ship."
* No. 2598, Jan. 8, 1915
* Merely summarizes Whitmell's views briefly.
* The GF part of this LONG letter is 1 para. 2/3 down
* No. 2600, Jan. 22, 1915
* 1-sentence explanation of GF
* No. 2601, Jan. 29, 1915
* Whitmell endorses Hollis's explanation.
* No. 2601, Jan. 29, 1915
* Crepuscular rays, not GF
* No. 2603, Feb. 12, 1915
* AFTERIMAGES demonstrated
* "It would not be fair for me to dogmatize and assert that this is
* the only phenomenon which comes under the head of the green-ray. But it
* is certainly the only one which I succeeded in seeing; and
* it must always be present even on the possible rarer occasions when
* colour changes arising from dispersion are also evident."
* (See also Nature 95,194(1915) for presentation to Phys.Soc.)
* Feb.18, 1915
* Fisher #119
* refers to his 1875 observation, and others
* "Those who want to see the appearance at its best should keep one eye
* closed as long as possible, and when the sun is just about to disappear,
* shut the eye which has been watching the setting sun, and open the
* other, which is then unaffected by the troublesome after-images which
* are otherwise seen."
* Fisher #135, O'C #280
* Whitmell's comments on Porter, above; a good, concise summary of the matter.
* Refers to the 1906 debate in Symons's Met.Mag.
* ". . . I have observed the flash more than a hundred times. . . ."
* ". . . the nature of the horizon, provided it is clean-cut and low down,
* makes but little difference. It may be of cloud, land, or water, and, of
* course, the last is best."
* N.B.: recommendations in use of telescope (x100) and binoculars (x8).
* Fisher #157, O'C #156
* cites his sunrise-flash paper in Obs., Dec.1914
* O'C #203; Fisher #38
* Blathwayt slightly mis-quotes (and does not cite!) a literary reference:
* "The sun went down in the sea, and went out like a blue spark."
* (This turns out to be Conder, 1878 -- another pre-Verne observation!)
* The GF par. is in last col., p.205
* No. 2610, April 2, 1915
* just a brief description of a talk to the Physical Society
* O'C #108; Fisher #121
* This, though unsigned, is clearly T.B.Blathwayt (cf. his April 2 E.M.
* item, and his earlier one in E.M. June 2, 1911.)
* This is in the April 22, 1915 Nature.
* Fisher #10
* EVERSHED and MIRAGES and VENUS
* "It seems to me very probable that the phenomenon is in some way
* connected with the abnormal conditions which at sea produce mirage
* effects."
* (cites his 1900 Venus obsn.)
* Evershed succeeded Michie Smith as Director at Kodaikanal in 1911.
* O'C #31; Fisher #44
* useless query
* O'C #230
* Hollis refers obliquely to the Nature discussion, and quotes Evershed
* The GF part is near the end, on p.380
* No. 2618, May 28, 1915
* Porter's note from Nature 94,672 (Feb.18, 1915) reprinted in June MWR
* Fisher #120
* The reprint of Porter's paper immediately followed by a summary of
* Pernter & Exner's older treatment, by Cleveland Abbe Jr.
* Discussion; Prosper Henry and Julius mentioned
* A "crank" theory is mentioned, based on the supposition that the green
* color is due to water vapor, and that this is much more abundant near
* the horizon over the sea. This ignores the many GFs seen over land
* horizons; but the editor is apparently quite unfamiliar with the GF
* literature. Of course there are no numbers attached!
* Actually, this idea was presented by Exner on the last page of the
* 1910 edition of P&E's Met.Optik. But it was first mentioned in the
* editorial in MWR 33, 408 (1905) and there attributed to Tyndall.
* Could that be where Exner got the idea?
* A reprint of Kritzinger's awful note from Naturwiss. Wochenschrift
* Again Kühl's work via Kritzinger in "Sirius" is cited.
* Fisher #68
* GREEN RAY over a field of corn at sunset
* ". . . une ligne vert, lumineuse, horizontale, de laquelle jaillissait un
* rayon vert vertical."
* O'C #211 -- name spelled wrong there.
* Another classical SCALED DISPERSION CALC. (F to C = 1/80)
* (translated in Mulder's book)
* The entry in C. F. Talman's list of "Recent papers bearing on meteorology
* and seismology" on pp. 421-422 of the August issue of MWR confirms
* Mulder's attribution of this to the August issue, and gives Braak's
* given name as Cornelis.
* Mis-cited by Mulder (on p. 50) and Feenstra Kuiper
* German abstracts of 1914-1915 papers on the GF
* Starting with Whitmell's "red flash" paper in Nature (1914); continuing
* with Petrie, Porter, Schuster, Duffield, [Blathwayt], Evershed, (Abbe),
* Riem, Kühl, Kritzinger, "J.K.", and Nijland's remarks.
* The reviewer is "Prof. Dr. Chr. Jensen in Hamburg."
* In section 2.I, "Meteorologische Optik", Abt.3, pp. 257 ff.
* Drawings of crepuscular rays
* No. 2642, Nov. 12, 1915
* Whitmell points out that Col.Mansergh's observation is crep.rays, not GF
* "I have always strongly advocated the term flash rather than ray,
* because the latter term unfortunately led many persons to expect to see
* long green streamers shooting up into the sky."
* No. 2643, Nov. 19, 1915
* Capt. Alfred Carpenter, R.N., once again:
* "distinct blue green flickers" as the upper limb sank behind cloud.
* 2 flashes above cloud layers; "I was using an opera glass, and I do not
* think the flashes would have been bright enough for the unaided eye."
* Fisher #16
* A TEXTBOOK-QUALITY GREEN RAY
* "Within about half a second of the disappearance of the Sun the pale
* green flash rose up, rather more deliberately than I expected, from where
* the Sun had gone down. It lasted about a quarter of a second and then
* disappeared. It did not have any sharp outline, but I got the impression
* that its height was greater than its width, that it occupied less space
* than the disc of the Sun, and that the borders were paler than the middle
* and lower part."
* If this is not a green crepuscular ray, I don't know what is!
* [The GF part is only the last paragraph, on p.210]
* No.2663, April 7, 1916
* Fisher #11
* GUGLIELMO's first paper
* He comes down strongly in favor of atmospheric dispersion as the main
* cause, though atmospheric absorption (this seems to refer to Exner's
* mechanism) and contrast effects "could accompany and modify the color and
* perhaps the duration of the ray."
* He considers but rejects Exner's water-vapor mechanism: "I don't believe
* that the absorption was produced by water vapor because the amount of it
* can be deduced pretty well from the temperature and the degree of humidity,
* and it bore no fixed relation to the color."
* "It's clear that various causes can influence the intensity of the
* green ray: the great brightness of the sun, fatiguing the eye, could
* make the green ray appear less intense; the brightness of the atmosphere
* where it is produced could dilute it and render it less evident; dust
* particles could have such dimensions as to absorb just those rays of which
* it is composed; finally, because of the movement of the green rim, it
* could happen that at the instant when the green ray is produced, it would
* have a minimum width or dilute coloration which would decrease the
* intensity."
* MODULATION BY WAVES suggested:
* "The wavy motion of the green rim continually varies its width, and could
* produce an increase or decrease of the green ray. Similarly, if the sun
* sets (or rises) at sea, the motion of its surface, raising and lowering by
* the effect of the waves which could be invisible to the naked eye and
* without a fixed point of reference, could cause an increase or a decrease
* of its duration."
* "Rendiconti, Reale Accademia dei Lincei. Classe di scienze fisiche,
* matematiche e naturalï
* O'C #44
* The other Guglielmo paper, calculating latitude and declination effects
* Includes the SPECIAL EFFECTS NEAR THE POLES:
* "Finally, at the poles the rising or setting is not caused by the
* rotation of the earth but by the increase or decrease of the declination,
* and the duration of the green ray will be the time needed for the
* declination of the point considered to vary by 15'', and will be about a
* quarter of an hour.
* A still greater duration of the green ray can (theoretically) be
* reached about 11 km (6') from the pole, in the evening around the vernal
* equinox or the morning near the autumnal equinox, when the slight decline
* or ascent of the sun, due to the rotation of the earth, will be
* compensated respectively by the ascent or decline due to the increase or
* decrease of the solar declination." He finds a duration over an hour.
* O'C #45
* 1-paragraph abstract of Guglielmo's paper earlier this year
* May 11, 1916 issue
* Metcalfe triggers a brief exchange with his report (see also his E.M.letter)
* Notable for the following comment, rediscovering Evershed's idea:
* ". . . the sea plays no necessary part in the matter, for the flash can be
* seen when the horizon is a land instead of a water one, and the flash has
* also been seen as the sun has set behind a low bank of clouds, even in
* towns and cities far removed from the sea. At the same time, the sea
* horizon . . . is apparently more favourable. It is possible also that the
* condition of the air over a water surface may be more suitable."
* He continued: "The flash was observed and its appearance recorded by
* the ancient Egyptian astronomers 3,000 B.C." (Evidently a reference to
* William Groff's works.)
* Brayshaw's observation is not useful. He refers to Metcalfe's, the
* previous Saturday; and Metcalfe quotes him in E.M.104,12. (July 28?)
* Albert Alfred Buss sees a GF in his penultimate paragraph:
* "The green flash was also observed well during a few bright days' stay
* at the seaside, but a competent friend expressed his belief that the green
* colour seen at the moment of the vanishing sun is the complementary effect
* of the reddish glare filling the eye just the moments before."
* No. 2676, July 7, 1916
* Metcalfe's first letter of July 1 (bottom of col. 2)
* He reports an apparent inf.-mir. flash, lasting "two or three seconds."
* "The atmosphere was unusually clear at the time, a cold north-easterly
* wind blowing . . . ." on June 28.
* Quite a long list of previous reports in E.M. is given.
* No.2676, July 7, 1916
* Fisher #92
* Metcalfe's second letter of July 1 (top of col. 3)
* Appeals to Whitmell for explanation of the latter's report in Leeds Trans.
* 15, 67 (1907)
* No.2676, July 7, 1916
* Whitmell's reply to Metcalfe
* No.2677, July 14, 1916
* Fisher #158
* another reply to Metcalfe, from a novice
* ". . . this is the first time that I have seen it, and I must say that its
* brightness somewhat astonished me."
* No.2677, July 14, 1916
* Fisher #2
* Metcalfe thanks Whitmell [559, above] and "Alpha Ceti" [560], and
* quotes from Brayshaw's letter of 3 July in the Manchester Guardian.
* He also corrects an error in his earlier letter.
* [Date not available, but must be July 28, No. 2679.]
* Fisher #93
* Whitmell follows up Metcalfe's letter, and reports his July 22 observation
* which includes a GREEN RAY:
* "Over the point, at which the green flash was seen, there hovered for a
* moment a tiny wisp of light, too faint to have its colour determined. It
* was probably bluish."
* He adds his now-standard ADVICE: "For those who have not yet seen the
* flash I strongly advise the use of a binocular, as it is of great
* assistance."
* No.2680, Aug. 4, 1916
* Fisher #159, O'C #298
* VISUAL SPECTROSCOPY proposed [cf. Dijkwel, 1936]
* "In any case it also would materially help forward in the settlement of
* the problem if some observer favorably situated for seeing sunrise or
* sunset across really open sea, watched with a direct-vision spectroscope."
* No.2681, Aug. 11, 1916
* awkward description of mock-mirage flash (cited by Corliss):
* ". . . distinct green flames . . . serrations, as a very rough saw, the
* edges of which from time to time came together and sort of floated up in
* parachute form, again and again. . . . I cannot describe what I saw in
* technical language, but the phenomena was [sic] so striking, and my
* impression so vivid that I could quite well describe in a roundabout way
* what I saw to anyone interested."
* No.2681, Aug. 11, 1916
* Fisher #48
* ordinary inferior-mirage flash
* No.2681, Aug. 11, 1916
* Fisher #94
* Whitmell replies to Buss
* "It would certainly be of interest to observe the setting sun with the
* spectroscope as he suggests. But there would not be the flashing out of a
* monochromatic line, but merely a spectrum, gradually shortening at the red
* end, the green, and under favourable circumstances, the blue, being the
* last to disappear."
* probably No.2682, Aug. 18, 1916
* MANY interesting comments in reply to Buss's letter # 51
* ". . . I think that the further North one goes, the greener and paler does
* it become." (possible LATITUDE EFFECT ??)
* probably No.2684, Sep. 2, 1916
* O'C #217; Fisher #171
* vague ruminations about green flashes, buried in a long paragraph
* "Has not the colour of the sea and the atmospheric conditions something
* to do with the phenomenon? . . . Surely, then, when so many provisions have
* to be made in observing these flashes, such flashes are due to
* atmospherical effects."
* No. 2696, Nov. 24, 1916
* Good introduction:
* "The so-called green ray . . . has been attributed to three diverse
* causes: atmospheric refraction and dispersion, atmospheric absorption,
* an optical illusion due to contrast.
* The first of these causes, whose action cannot be in doubt, is
* certainly the most important, the other two could be involved and modify
* the color and duration of the ray."
* An experienced observer: "For many years I have had frequent occasions
* to observe the green ray. . . ." from heights of 70 and 40 m; so he sees
* mock-mirage flashes as well (see the second part, p.50).
* [This seems to be the abstract of the paper printed the previous year.]
* First part of paper read on 5 March; continues on p.49
* The main factor considered is the geometry, assuming normal refraction;
* so he mentions latitude and declination, giving numerical examples.
* Paper read on 19 March; see his 1916 publication in Atti Accad.Lincei
* Evidence for BLEACHING of GREEN CONES?
* "If the Sun is still a little above the horizon (more than 5°) and
* quite bright, and if the image is projected on a screen, the upper limb
* appears green with a little blue on the outside; if, on the contrary, it
* is observed directly under the same conditions without reducing the
* brightness too much, the limb appears blue, and the green is invisible."
* Second part of paper read on 5 March; continued from p.18
* HORIZONTAL GREEN RAY of the most explicit sort!
* After a morning drizzle, "the distance continued hazy until well into
* the afternoon." Then at sunset, with clouds forming overhead:
* "The disc remained quite sharp and showed no appearance of flattening,
* or change of colour, as it touched and passed down behind the hill line.
* Then, at the instant of disappearance of the last fragment of the upper
* segment, a bright emerald green flash shot out horizontally right and left
* at what would have been a tangent to the disc had it remained visible."
* This seems an excellent example of a green crepuscular ray.
* GREEN RAY at sunrise? (elicited by Wood's report, above)
* "Watched sunrise and noticed a peculiar blue light on top of sun,
* immediately before sun rose . . . ."
* "The clouds were only broken sufficiently for the sun to shine through
* for about ten minutes after sunrise, the sky being overcast."
* Fisher #34
* Dec. 1917: GF seen in HAZE
* ". . . the Sun was setting into the western haze, and assuming the usual
* form of concentric inverted saucers. The colour was a bluish green, very
* brilliant as the upper `saucer' disappeared, less so at the sinking of the
* second, after which the light became too weak to observe further."
* O'C #169
* GF seen from 10,000 ft. height "on the Hindustan-Tibet road".
* This may be the type associated with the Nachspiegelung?
* O'C #244
* a first-time observer concludes Chabot is right: dispersion is the cause
* Probably a "green Sun" due to smoke
* GREEN RAY distinguished from the usual "flash"; TERMINOLOGY discussed
* ". . . what Mr. Cobbold . . . describes as a green `flash' is in fact a
* change in the apparent colour of a small sector of the sun during an
* appreciable, though short space of time, and is not really to be defined
* as a flash. What I, and I think a few other Observers, have described
* was a ray or rays of light darting out from the sun's limb at its
* disappearance, and quite momentary, and so a true flash.
* "If we are to arrive at a satisfactory explanation, we must carefully
* distinguish the two phenomena."
* A nice TABLE of 22 observations: 8 flashes and 14 "failures"
* 2 of these were reported in English Mechanic previously.
* Note the following comment by Whitmell, who communicated these:
* "It will be noticed that Mr. Metcalfe has included failures as well as
* successes; an important point, if we are ever to arrive at a satisfactory
* explanation of the reason why the atmospheric dispersion is of so erratic
* a character." [p.159]
* NOTE: the two best, reported in E.M., both are accompanied by cold winds,
* so these are surely inferior-mirage flashes.
* Fisher #95
* Carpenter's red and green flashes at clouds (?? or blank strips?)
* Drawing shows Sun perfectly circular.
* ". . . the 16th May . . . after a brilliant, clear hot day . . . ."
* "I have never seen the green bands so strong, and they remained so until
* the Sun left the two cloud bands.
* "When the lower limb of the Sun first appeared below the upper cloud
* it appeared a deep red, a not unusual phenomena [sic] allied to the
* green flash."
* Fisher #17
* Whitmell reports a record:
* "This is the largest number of flashes seen by me in connection with a
* single sunset."
* Fisher #160, O'C #157
* listed here for reference only; not in the GF file, as only one
* paragraph on p.59 summarizes GF literature
* "Mitt.VAP" (as the AJB has it) apparently became "Die Himmelswelt"
* later, with the same volume numbers (=year+10)
* NICE DRAWINGS and BLANK STRIP DEPICTED
* ". . . the telescopic view showed a series of sharply defined, horizontal,
* narrow, black bands, the Sun's limb in the neighborhood of the bands
* being much distorted."
* Fisher #47
* Whitmell comments on the previous paper; urges use of TELESCOPE
* ". . . it is now twenty-one years since I first observed the Green Flash,
* and I have seen it dozens of times . . . ."
* "As Mr. Gibbs used a telescope, perhaps I may say that . . . I have again
* and again recommended this method to those who have hitherto not been
* fortunate enough to view this beautiful phenomenon with the naked eye."
* O'C #299
* COUTINHO's ARTIFICIAL GREEN FLASH (cf. Biot & Arago in Mirage file!)
* " . . . the Sun's movement . . . corresponds to 80 centimetres in a second
* for an observer 8 metres above water (average height of promenade-deck
* in a steamer of 6000 tons)."
* Mentions motion of the ship in this regard (cf. Nijland)
* O'C #21
* Whitmell comments on Coutinho
* Charles Thomas Whitmell died 10 Dec. 1919.
* O'C #158
* HUMPHREYS's precursor article -- the GF is treated only on pp.452-453.
* Fisher #59, O'C #53
* yet ANOTHER SCALED REFRACTION calculation! (1/146 = 1 sec)
* Metrologist Charles-Edouard Guillaume was the inventor of Invar, and
* received the Nobel Prize in physics in 1920 for his work.
* Guillaume was the Director of the BIPM and discussed the matter with
* Henri Chrétien. He invokes successive contrast.
* Good balance of dispersion and ADAPTATION of eye:
* "Toutefois, le seul fait physique n'expliquerait pas l'éclat
* remarquable que l'on s'accorde à reconnaître au rayon vert.
* Celui-ci relève d'un fait physiologique: le contraste qu'il forme
* avec la teinte rouge du soleil, à laquelle il succède
* immédiatement dans son action sur l'oeil."
* Good comparison of sunset and sunrise observations:
* ". . . peu de gens voient se lever le soleil. . . d'autre part, cet oeil,
* qui n'a pas été fatigué par la lumière rouge, ne
* possède pas l'hypersensibilité relative au vert, que nous avons
* vu étre une condition de l'éclat subjectif du phénomène."
*
* "Maintenant, une question se pose: puisque la cause du rayon vert est si
* simple, pourquoi son apparition est-elle l'exception et non la règle?"
* GOOD QUESTION!
* (Variable extinction is invoked.)
* But he mistakenly supposes sunrise flashes are rare or nonexistent, and
* so gives adaptation more than its share of the credit. Still, this is a
* surprisingly realistic and balanced presentation.
* This is the article quoted by Mulder on p. 130 of his book. The
* discussion he quotes on p. 129 appears on BSAF p.514.
* O'C #46, allowing for errors
* Whitmell's final report, at the 27 Oct. 1919 meeting
* "Mr. Whitmell gave an account of the Green Fringe he had seen round the
* upper part of the limb of the setting Sun about 5:45 p.m. on 26th
* October. On 27th October, about 5:40 p.m., Mr. Burnet and Mr. Whitmell
* again observed the Green Fringe, using a 3 in. telescope with power 50.
* Mr. Tetley observing with a binocular from Woodhouse Moor failed to see
* the Flash." (Charles Thomas Whitmell died 10 Dec. 1919.)
* Thanks to Ray Emery for supplying this!
* A review of Guillaume's BSAF 1919 paper, with extensive excerpts
* Guillaume's 1920 paper in "La Nature"
* Here is his conversation with Henri Chrétien, "le sagace et érudit
* astronome de Nice," . . . .
* "Le spectre du rayon vert ne semble pas avoir été observé;" but
* Danjon & Rougier were doing so just about then.
* He rejects a role for MIRAGES: "Les réflexions totales, dues à
* une stratification déterminée des couches d'air, bien que possibles,
* exigeraient un tel ensemble de circonstances peu probables en
* elles-mêmes, que l'on pourrait à peine concevoir la fréquence du
* rayon vert dans des conditions dont la plus essentielle qui nous ait
* toujours été indiquée est un horizon absolument exempt de brume."
* an adaptation experiment -- not relevant
* Translation of Guillaume's La Nature paper
* ". . . I may mention . . . that upon the discovery some twenty years ago
* of the presence of new gases in the atmosphere, it was suggested that
* the reason for this peculiar tint exhibited by the last ray of the sun
* might be found in the absorption caused by the passage through one of
* the said gases to be found in considerable quantities at the level of
* the sea."
* Here is his 1/146 factor again, from his 1919 BSAF paper.
* NOTE that Sci. Am. also had a WEEKLY mag. at this time!
* THANKS to Shaun Hardy for this reference!
* Henri Piéron's physiology paper
* This seems to be the earliest suggestion that the maximum visibility of
* green plays a part; he cites the 1917 NBS work of Coblentz & Emerson.
* Also cites Guillaume's 1919 BSAF paper, and Fortin in C.R. (1907).
* Date: Sept. 25, 1920.
* THANKS to Shaun Hardy for this reference!
* NATURWISSENSCHAFTEN SERIES
*
* a SELECTION EFFECT FAVORING OCEAN OBSERVATIONS nicely stated:
* "Da an Land die Sonnenuntergänge meist durch Verdeckung des Horizontes
* oder durch den Dunst der erdnahen Luftschichten getrübt werden, ist die
* See das geeignete Feld zur Beobachtung dieser Erscheinung."
* No. 24, 11 June 1920
* agrees with Brandt that BOTH PHYSICS & PHYSIOLOGY are involved:
* "Was die Erklärung anlangt, so scheint es mir, dass zwar besondere
* Bedingungen in der Atmosphäre vorhanden sein müssen, damit die
* Erscheinung beobachtet werden kann, dass aber die Färbung auf
* physiologischen Bedingungen beruht."
* No. 25, 18 June 1920
* GF ALWAYS visible
* "Ich bin überzeugt, dass bei klarem Horizont die Erscheinung -- die
* auch auf grossen Binnengewässern vorkommen soll -- stets sichtbar ist."
* Otto Meissner (cf. his 1940 note)
* GREEN FLASH SPECTRA TAKEN
* O'C #23; Fisher #35
* English abstract by Edgar William Woolard of the previous paper
* GREEN FLASH SPECTRA
* O'C #24
* GREEN FLASH SPECTRA (details and spectra)
* FILED OUT OF ORDER to be with the previous papers
* O'C #25
* Braak discusses visual effects
* "The phenomena, as we observe, always present themselves to us as the
* complex of two things, namely 1st of what really objectively happened, and
* 2nd of what we subjectively observe, in other words of what our senses do
* with what is objectively given."
* Maurice Farman discovers a green flash for himself.
* (The brothers Henri and Maurice Farman were aviation pioneers who
* invented ailerons. They built and flew pusher biplanes used in WWI.)
* Like most accounts by people noted in other areas, this is
* completely useless.
* O'C #209
* VENUS GF seen with naked eye (brief note)
* O'C#164
* Mercanton's GF observation near Cape Skagen, Jutland, 20 Sept. 1912
* The "rayon vert" section is on pp. 197-198. His sunset GF in the
* DRAWING was seen through 8× Zeiss binoculars: "Le ciel était
* serein, la mer calme, l'atmosphère d'une rare limpidité . . . . Le
* soleil avait montré en se rapprochant de l'horizon une teinte orangée
* et des déformations changeantes, qui en dentelaient bizarrement le
* pourtour. Après que son centre fut descendu sous la ligne d'eau et
* au fur et à mesure que sa surface visible s'amoindrissait, ses bords
* furent envahis de plus en plus par une teinte vert émeraude refoulant
* vers le milieu l'orangé de plus en plus restreint. Au moment même
* où l'astre s'abîma dans les flots, le vert, resté seul maitre de
* la surface solaire, atteignit l'intensité d'un vif éclair, puis
* s'éteignit." (The drawing shows an inferior-mirage flash.)
* He cites Evershed's 1915 Nature paper. "Mon observation corrobore
* singulièrement cette opinion plausible, également défendue tout
* récemment par C.-E. Guillaume." (citing the latter's 1919 paper in
* l'Astronomie.)
* The title pages are given in both German and French; I give only the
* German here, as de Quervain (despite his name) writes only in German
* and was the expedition's leader; and this was published in Zürich.
* Dated 1. Dezember 1920; abstracted by Brooks in MWR, 1923.
* standard inf.-mir.GF
* O'C #181
* "une curieuse observation de Rayon Vert faite du sémaphore de Jobourg"
* Camuset's original report
* GF seen 3 times at reappearance from behind hills, from train.
* "J'ai donc assisté à 3 levers de soleil successifs accompagnés du
* rayon vert et ceci à l'heure du coucher du soleil."
* Isle of Man flash seen for "five or six minutes" via hill
* O'C #295
* immediately follows Whitehead's note on same page.
* Reprinted in full from his earlier paper in La Nature.
* GF seen 3 times at reappearance from behind hills.
* O'C #186
* somewhat garbled account of Danjon & Rougier's CR paper
* Besides getting Rougier's initial wrong, we have "Die Sonne erscheint
* von einem grünen Saum umgeben, der aber durch einen dunkelroten von ihr
* getrennt ist."
* Nov. issue
* first of a flurry of notes in H&D; supports Evershed's MIRAGE idea
* another scientist suckered by Jules Verne's LEGEND:
* "There is also a legend about the green flash . . . "
* "The fairly numerous cases of ``green flash'' observed by me have left
* me the impression that the phenomenon never was observed by me with a
* completely flat or slightly rumpled water surface, and also not with
* waves of such a height that the horizon, observed from a height of 6 to 10
* m, still showed waves plainly, such as is the case with a strong wind, but
* always with a state of the sea such as occurs with a moderately strong
* wind with small wave heights, so that one placed some height above the
* water saw the horizon as a smooth, blue-black boundary."
* This is vice-Admiral G.F.Tydeman, in the Dec. issue.
* REVIEW ARTICLE, but few references
* Spends much effort in knocking down a series of straw men (improbable
* explanations).
* Green and red rims seen (pp.408-409), as well as colors on sunspots
* (pp. 415-416).
* Has "Dangeon" for "Danjon"; so I suppose he knew little astronomy, and
* had heard the name in a lecture somewhere (though he cites their paper
* in BSAF!).
* Invokes physiological effects to prolong sunset flashes, claiming that
* "Jamais en effet on ne trouve mention d'une durée plus longue du rayon
* matinal." (i.e., longer than 2 sec.) -- p.422
* But he recognises that the assumption that refraction is proportional to
* refractivity is not exact. [cf. Banakhevich (1915)]
* "Mais surtout, il est grand temps de le faire remarquer,
* l'homogénéité atmosphérique est un mythe, dont la seule utilité fut
* de simplifier nos calculs, en les faussant peut-être un peu." (p. 423)
* Because of the complications of calculating the actual refraction,
* "Expliquer le rayon vert, ce n'est pas étendre de beaucoup le royaume
* de la Science. Passe-temps de vacances, dira-t-on, ou distraction
* d'amateur." (p. 425)
* This is one of the few citations found by P.F.K. on his own; he gives
* the author's name as R.P.R.Lange; here he is "R. Lange, S. J.".
* Published by Soc.Sci.Bruxelles
* O'C #78
* passing mention of "the green ray" on p. 70
* This is a meeting of the BAA; the paper was by Lawrence Richardson,
* read by Dr. Crommelin. I have attributed this account to the
* secretaries. At the end (p. 72), "Mr. Walter Maunder read a paper on
* `The Prolonged Sun-spot Minimum of 1645 to 1715.' " (Mar.1922 issue)
* Notable for the accurate description of the Earth as seen from the
* totally eclipsed Moon (cf. Link's book). A tantalizing reference:
* "Proctor states that the bright ring into which the Sun is distorted
* will have, but for the effect of atmospheric absorption, the same
* surface-brilliancy as the Sun itself." (p.71; no citation)
* A renewed appeal for observations, with only a couple of references
* Cites and quotes from Tydeman's 1921 paper in H&D, and Conrad's
* note on Danjon & Rougier in Met. Z.
* kindly supplied by C. de Jager!
* The author was the editor of De Zee, Jonkheer J. P. F. van der Mieden.
* MULDER explains his forthcoming BOOK:
* NOTE YEAR CHANGE IN MIDDLE OF VOLUME!!
* "As far as possible, I have collected everything written about the green
* ray and treated the articles historically and critically. The book is
* written in English, because the English, as a seafaring nation, have made
* many observations and still show much interest in the phenomenon."
*
* "That the green ray is observed so much more at sea than over land seems
* mainly, though not entirely, to lie in the fact that at sea the horizon
* is unobstructed."
* MULDER's book
* Prof. Dr. M.E.Mulder, Emeritus Professor of Ophthalmology
* useful for many earlier references, quoted in full.
*
* Marten Edsge Mulder -- thanks to Brenda Corbin of USNO library for
* his full name!
*
* quotes Verne's "legend" as if it were fact (p.1)
*
* his GREEN RAY observation:
* ". . . at the same moment, at which the last tip of the sun disappeared
* below the horizon, there suddenly shot, straight upwards, a clear
* narrow green ray, which vanished as suddenly as it appeared. . . . I
* estimated the length of the ray to be about 1/10 or 1/8 of the diameter
* of the sun. . . . . . . the phenomenon lasted but a fraction of a second,
* about as long as the visibility of a lightning flash. It almost made
* the impression, that the ray was ejected from the disappeared sun,
* but it also resembled somewhat a rocket or the light from a lighthouse
* below the horizon, throwing a ray of light upwards. . . ." (p.4) "But this
* [the dispersion] explanation I considered to be unacceptable in my case,
* for then one would expect that the last green part of the segment would
* disappear slowly below the horizon, as the sun itself sets slowly.
* Instead of shooting upwards, it would sink downwards." (p.6)
*
* mentions LIMB DARKENING & reddening for first time (p.7)
*
* "There has been far more written and far more observations are published
* about the green ray than I had expected. Moreover, those articles are
* published in all kinds of popular and scientific periodicals which are
* often difficult to obtain." (P.11)
* "But also those observers, who may be considered as more competent --
* for amongst them are many astronomers and physicists of repute -- have
* generally taken little notice . . . of what had been written concerning it
* by others." (p.12)
*
* "The observations at sunrise are naturally much less numerous than at
* sunset, because only few people see the sun rise. . . ." (p.15)
*
* ". . . it clearly appears that both had a different form of green ray in
* view, and consequently did not comprehend each other." (p.37)
*
* "Still I will dwell for a moment on the three forms, in which the green
* ray usually appears.
* 1° the green or green-blue border, sometimes at the outer edge
* even violet, which can almost exclusively be observed with a telescope
* or a good fieldglass.
* 2° the flash-like appearing or disappearing green or green-blue
* ray or flash, which can easily be observed by the naked eye and from which
* the phenomenon has undoubtedly taken its name.
* 3° the green or green-blue coloration of the last segment
* itself, which in the course of a few seconds disappears below the horizon,
* and which can also be seen with the naked eye." (p.134)
*
* "Finally we have the rare and abnormal forms . . . .
* As we see, the phenomenon called green ray is far more complicated than
* is generally supposed, and a long investigation will be necessary to
* explain all details." (p.139)
*
* "As the dispersion, increases and decreases in ratio to the refraction,
* the coloured border would, in such a case, be consequently much broader."
* (p.136)
*
* "The green ray is . . . too intensive, to be ascribed to simultaneous
* contrast." (p.141)
*
*
* Thanks to the efforts of Walter Nissen, this is now available at
* Google Books. The London edition is
*
* https://books.google.com/books?id=RSMyAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false
*
* and the Dutch edition is
*
* https://books.google.com/books?id=sIkyAQAAMAAJ&printsec=frontcover#v=onepage&q&f=false
*
* The curious use of a double right quotation mark before the word
* Green on the title page appears in both editions.
*
* O'C #94
* Sir ARTHUR SCHUSTER's review of MULDER's book
* N.B.: Schuster was knighted in 1920.
* O'C #133
* Claims "about 450 observations"! (estimate reduced to 300 by Nijland)
* Independent discovery of warm- & cold-water effects:
* "When the temperatures of air and water are similar, or the
* temperature of the air is higher than that of the water, there is no
* looming or distortion; but when the temp. of the air is more than
* 1° Celsius lower than that of the water, then looming and distortion
* occur. Then when one looks at the horizon through a telescope, the
* water seems to boil."
*
* "The observations and drawings are no longer in my possession, but I
* kept copies of the general remarks and collected this article from them."
* "The carefully described, excellent, and very numerous observations of
* Mr. Havinga (together about 300 pieces), are being worked up by Mr. van
* Genne, phil.-nat. cand. at Utrecht. I don't want to anticipate their
* outcome, but all agree that next to the material that Mr. Havinga has
* given us, any other material, as far as is provided by naked-eye
* observations, can hardly lay any weight in the scale."
* This is exactly the text printed in H&D (see previous 2 items),
* including Nijland's "Bijschrift", and the figure!
* kindly supplied by C. de Jager!
* (see previous 3 items!)
* kindly supplied by C. de Jager!
* Another REVIEW of MULDER'S BOOK
* This is rather a sad piece of work. The reviewer enthusiastically takes
* up the "Scottish legend", and mis-reads "Coutinho" as "Corvalho".
* He also concludes with a paragraph warning against blindness from
* looking at the Sun, quite in opposition to the spirit of Mulder's
* discussion.
* kindly supplied by C. de Jager!
* Some 20-odd flashes observed, mostly with binoculars from 12m on ship.
* Most common color reported is blue, or blue-green; some violet.
* 2 DRAWINGS of flashes behind clouds and island.
* (According to the masthead of H&D in 1929, Voûte was at Lembang.)
* J. Edmund Clark's flash "on hills nearly two miles distant, fringed with
* trees." ". . . it lingered for some seconds, probably three to five."
* (This is the flash cited in his 1926 paper.)
* W.J.Humphreys's review of Mulder's book
* Takes a surprisingly naive view of the GF:
* ". . . an adequate description and complete explanation of the `green ray'
* can be given in a few lines . . . ."
* GREEN LIGHT THROUGH TREES?
* "Every tree projected on the disc became suddenly outlined with a narrow
* hazy border of green light, the rest of the sun retaining its normal
* colour; . . . ."
* Probably this effect is due to chromatic aberration in the 3-in. telescope.
* ALFRED W. PORTER responds to SCHUSTER's review of MULDER's book
* "There are, in reality, two distinct phenomena which go under the name
* of the green flash. The first, probably the one most usually seen and the
* only one to which the epithet properly applies, is certainly an
* after-image in an eye fatigued by the red light of the sun." [SIC!]
* The second phenomenon, which I have never been successful in seeing and
* of which I can say little, is evidently due to atmospheric dispersion . . . ."
* Query: could Porter have been color-blind? Most people find the Sun's
* after-image dark and inconspicuous.
* Cited with title in Talman's "Recent Papers," MWR 50, 492 (Sep. 1922)
* Cave and Petrie try to undo the damage Porter has done; first Cave:
* ". . . it is not due to eye fatigue, for the appearance at sunrise is
* precisely the same as that at sunset . . . ."
* Cited with title in Talman's "Recent Papers," MWR 50, 544 (Oct. 1922)
* Nov. 4 issue
* and now Petrie:
* "Moreover I have never seen the green light shift about, as an
* after-image does, by movement of the eye; it is always exactly on the
* segment."
* Agnes Fry's inf.-mir.flash, well described:
* ". . . with a pair of field-glasses (which it is quite safe to use when the
* sun is really low on the horizon) the green flash was clearly seen. . . ."
* ". . . the arc of the sun turned green, and then also the chord made by
* the sea horizon, and for a fraction of a minute these two lines enclosed
* an orange space. This rapidly disappeared and the last segment was wholly
* green. . . . if observers would use glasses the green flash would much more
* frequently be recorded."
* Goodacre's second paper (Nov., 1922) [note overlap of years & volumes!]
* ". . . a high northern latitude . . . ."
* ". . . 1922 June 11, latitude about 65 N, made from the deck of the
* R.M.S.P. steamer Avon , time 10h 45m p.m."
* "As the Sun slowly sank whilst skirting the horizon, thin linear clouds
* passed rapidly across the disk and one of these separated a narrow segment
* of the N. limb from the rest of the disk. This segment immediately turned
* to a vivid green, and remained for several seconds till the Sun dropped
* out of sight behind the cloud."
* N.B.: The BAA meeting at which this paper was presented is reported
* in Obs. 46, p. 12 (1923).
* useless account of a 3-sec.GF
* O'C #229
* EVERSHED and VENUS
* ". . . the ordinary mirage effect was conspicuous, that is, distant land
* appeared raised above the sea horizon by a small interval, due to the
* total reflection of sky and land at the surface of a thin layer of air
* of low density in contact with the sea. At sunset the last segment of
* the disappearing limb was similarly reflected and reversed, causing a
* lenticular shape. . . ."
* "The striking thing about the setting of Venus was the sudden appearance
* of a reflected image moving upwards to meet the descending image, and
* the instantaneous and conspicuous change of colour from dull red to
* green at the moment of meeting of the two images."
* "It seems to me evident from these observations that the mirage layer
* greatly intensifies the ordinary dispersion effect, by adding the light
* from the reflected image to the direct image at the moment of setting.
* The normal dispersion effect at sunset under conditions when there is no
* mirage is scarcely visible to unaided vision, although easily seen in
* a telescope of low power."
* This was the year Evershed retired to Surrey.
* O'C #32
* BAA discussion of Goodacre's paper
* "In the discussion Capt. Carpenter, Capt. Ainslie, Major Hepburn,
* and Col. Maxwell took part, one point being raised as to whether the
* green ray could be kept in view by an aeroplane rising at a rate that
* would keep the setting Sun just touching the horizon." [p. 12, Jan.1923]
* I have attributed this account to the secretaries; the meeting date was
* Nov. 27, 1922.
* Thanks to the NASA ADS full-text search for turning this up!
* 3 mountain observations, and much useless speculation.
* One might be a "green fog", but I doubt it.
* ". . . la coloration vert n'est observable que par une atmosphère exempte
* d'humidité . . . ."
* (cf. Admiral Huguet (below); both contradict Feenstra Kuiper's
* HUMIDITY theory.)
* Issue No. 2557
* FINE account of GREEN RAYS in Tibet
* A second-hand report "quoting a description given by him last year in
* the Statesman of India . . . the appearance (seen for [sic] some two
* or three minutes after actual sunset) is described as
* `very similar to a series of rapid, dark greenish shafts of light,
* cone-shaped, with their apex lying in the direction of the vanished
* sun, appearing to shoot across the horizon from right to left, and as
* rapidly disappearing. The apparition lasts from three to five seconds,
* and is not to be confused with the familiar green flash at sunset.'"
* (It would be nice to turn up that newspaper report!)
* [Note: the supposedly similar report referred to as on p. 66 of the
* same volume turns out to be a marine phosphorescent wheel.]
* May issue, in the "Monthly Record" department (pp. 385-392).
* An English summary of the Swiss Greenland expedition
* [Cf. Mercanton, 1920, in both the mirage and GF sections of this bibliog.]
* "Abnormal atmospheric refractions were observed. The setting sun was
* much distorted. Mirages were seen strongly developed over the water,
* where the surface layer of air was notably colder than that above.
* The green ray, occasionally observed at sunset, was evidently a phenomenon
* of mirage." (p. 259)
* May issue
* nice drawing of MOCK MIRAGE flashes and SKY STRIATIONS:
* "Under telescopic scrutiny this zone was seen to be not clear sky, but a
* stratified form of cirrus in horizontal lines and bands, which increased
* in density rapidly near the horizon, so that the Sun's lower limb
* disappeared before reaching the land contour. These bands were so faint
* that they were scarcely to be seen on the Sun, but they produced
* remarkable results with the green ray effect. They formed faint chords
* across the disc, at the extremities of which, in the upper segment,
* shining prominences were projected from the Sun as elongations of the
* chords. These prominences rose upwards on the circumference as the disc
* sank. Approaching the top, they turned green, and meeting there they
* united and floated clear as a tiny cloudlet of brilliant green."
* May 11 issue.
* Thinks it is all in the eye, and wanders off into the shape of the sky
* Totally USELESS
* Issue No. 2568
* Contradicts the previous report, as he has seen a double flash due to
* waves, a sunrise flash, and a flash at mountain horizon.
* Issue No. 2579
* Thinks it is due to light refracted through WAVES
* TRIPLE flash due to waves reported.
* Has never seen the flash in Pacific or Red Sea, so "J'attribue ce fait à
* l'humidité de l'atmosphère dans ces deux mers."
* (so much for Feenstra Kuiper's HUMIDITY link!)
* Issue No. 2588
* Several observations (none in detail); one double flash via a railway ramp.
* Cites the Admiral's paper in No. 2588
* Issue No. 2594
* O'C #274
* useless but typical inf.-mir.flash
* Pierre Crépy
* O'C #197
* GREEN RAY ? Possible AFTERIMAGE?
* "The flash came at the usual time, but after the limb had entirely
* disappeared, a small ball of a brilliant blue remained for two or three
* seconds."
* CARPENTER responds to Barker
* Captain Alfred Carpenter died the next year.
* O'C #188
* 5-line abstract; no useful details
* See slightly longer mention in JRASC 19, 4-9 (1925)
* O'C #152
* C.D.PERRINE makes a dumb suggestion, but reports a YELLOW FLASH:
* "It is not seen at disappearances or reappearances of the Sun behind
* ordinary clouds.
* "It is not seen at disappearances behind land."
* "The green flash is a refraction phenomenon produced by the light from
* the thin disappearing limb of the Sun shining through the prism of water
* formed by the crest of a wave or waves which extends above the general
* level of the horizon."
* BUT:
* "The yellow portion of the flash is not ordinarily noticeable as it is
* usually lost in the general red of the sunset. If carefully watched for,
* it can be detected often as a lightening of the general color and where
* the air is exceptionally transparent the true yellow can be definitely
* detected."
* Cited with title in Talman's "Recent Papers," MWR 52, 592 (Dec. 1924)
* O'C #102
* PERRINE shot down; STRATUS clouds favor the flash.
* ". . . no one at Blue Hill has ever seen the Green Flash, though many of
* us have looked, some for more than twenty years."
* ". . . if Professor Perrine means by ordinary clouds those of the cumulus
* type due to uplifting, we agree with him. But we are of the opinion that
* with clouds of the stratus type, the phenomenon may occur."
* "Finally, the significant feature in our opinion, is what we have called
* the capriciousness of the phenomenon. This indicates to our mind an
* atmospheric condition . . . . We think the phenomenon is essentially
* atmospheric, occurring possibly at times of an inversion of
* temperature. . . ."
* O'C #84
* Fisher's 1-page summary:
* Cited with title in Talman's "Recent Papers," MWR 52, 592 (Dec. 1924)
* O'C #35
* brief report of Whipple's Brit.Ass. report
* "Mr. F.J.W.Whipple of the London Meteorological Office gave a very
* beautiful experimental illustration of the green flash that appears
* under favourable conditions at sunset. It is believed to be due to the
* simultaneous action of dispersion and absorption and his experiment was
* in conformation of this view." [p. 7]
* There is also mention of "Mr. L.F.Richardson, who has been making
* a special study of turbulence in the atmosphere and who has worked out
* from theory a criterion for the increase of turbulence . . . ." [p. 8]
* Thanks to the NASA ADS full-text search for turning this up!
* Rex Clements's account -- the source of Botley's story
* "The old man used to say it was `the sun putting out his sidelights,'
* the emerald green representing a sailing-ship's starboard light."
* It appears to be one captain's idiosyncratic expression, not a term in
* general use. Clements tells this again in his "Times" letter, 1929.
* This also appears in the 1924 *first* edition by Heath Cranton Ltd.,London.
* As the subtitle is "The narrative of a voyage round the world twenty
* years ago," this is a turn-of-the-century observation, not an "old" one.
* cited by OED
* Humphreys's 1-page summary:
* Another scientist conned by Verne: ". . . whatever we may think of
* the legend that links it with love affairs . . . "
* O'C #55
* MARGARET OLMSTED as a student at Vassar!
* "All of a sudden there popped out over the edge of the island a spark of
* brilliant violet-blue light, like a big blue star, which slowly took on a
* green-blue tinge, turning to a yellow-green just before the blinding Sun
* appeared some ten seconds after the first blue flash.
* "As we were within the Arctic Circle, the Sun did not seem to rise
* straight up but swung toward the right and before the whole disk had been
* visible, disappeared with a greenish color behind a mountain, then
* reappeared in the same way as before. Passing behind another mountain
* before finally swinging clear of the land, it gave us three successive
* views of this beautiful phenomenon."
* O'C #260
* R.T.A.INNES -- GREEN RAY? or ILLUSION of motion?
* "I only saw it when the horizon was perfectly clear at the point of
* sunset, and the flash seemed to rise from the horizon for the moment then
* disappear." (appended to the above)
* O'C #222
* Second-hand accounts of other Scandinavians' observations; USELESS
* O'C #227
* DRAWING 3 shows impossible structures
* ". . . the vapour took a beautiful emerald green colour and then
* vanished. This process was repeated several times before the sun quite
* disappeared, the green colouring lessening in effect and there was no
* `green ray.'"
* ". . . a rare and beautiful phenomenon is the appearance of very faint
* coloured rays springing up from the spot where the sun is just rising or
* setting, and before the sky is very light. Often they can only be seen by
* a `sideway' observation and only last a very short time."
* As he distinguishes these from crepuscular rays ("shadows cast by
* clouds") I assume this refers to GREEN RAY displays.
* good REVIEW in French
* possible EARLIEST PHOTOGRAPH of Mock Mirage? (Fig.6, panel 6)
* Separate flashes on horns of partially-eclipsed Sun reported by
* Malburet (take that, Floor!)
* Profusely illustrated with Rudaux's dwgs. & photos
* Issue 2670
* O'C #141
* "the only occurrence during a five weeks' voyage" -- useless
* July issue
* 1-line mention; not useful
* Thanks to Stephen J. O'Meara for finding this.
* FIRST (b/w) PHOTOGRAPH OF GREEN FLASH by Lucien Rudaux
* "Le cliché montre, comme on le voit, une forte impression lumineuse
* correspondant à l'éclat vert magnifiquement intense pour les yeux
* des deux observateurs, et il fournit ainsi une pleine confirmation
* de la réalité du phénomène." (Nice inferior-mirage flash.)
* Issue 2692
* O'C #124
* mostly a German version of Touchet's paper; the source of Schröder's
* concluding line:
* "Es hat also fast den Anschein, als ob die Astronomen recht hätten,
* die behaupten, dass der grüne Strahl nur deshalb eine selten
* beobachtete Erscheinung ist, weil man sich zu Unrecht einbildet,
* dass er selten zu sehen sei."
* Most of the same illustrations from Touchet's paper!
* O'C #225
* EXCELLENT argument against the standard model !!
* "Cette observation corrobore d'une manière très nette, partant très
* précieuse, deux points sur lesquels nombre d'auteurs, et spécialement
* les deux derniers nommés [i.e., Touchet & Rudaux], insistent à juste
* raison, savoir : 1. l'apparition du rayon semble liée non à la
* réfraction atmosphérique dite `normalé, laquelle se borne à aplatir un
* peu le disque solaire à l'horizon, mais bien à des réfractions
* anormales qui déforment fortement, et irrégulièrement aussi,
* l'image de l'astre. . . . "
* O'C #87
* ABSTRACT of a paper given by RUDAUX showing distorted sunsets
* reported by Em.Touchet as secretary:
* "Les réfractions inégales de l'atmosphère donnent à certaines images
* du Soleil des apparences invraisemblables."
* These are most likely the pictures reproduced in Touchet's paper (above),
* or in Rudaux's own article in L'Illustration (1927)
* O'C #125
* K.I.LUCHAI's table of 81 flashes seen at Petrovsk (Saratovskii gub.)
* Communicated by G.A.Tikhov
* "In the literature is often written that the green ray is a very rare
* phenomenon. I don't agree with this -- we see it in our area fairly
* often." Here again the appearance is described as like "Bengal fire."
* "Mostly the blue color predominates. The green ray is often seen when
* the Sun sets behind a thick layer of stratus on the horizon."
* "In most cases this phenomenon precedes a falling barometer and bad
* weather." But there are NO USEFUL DETAILS, only the dates when it was
* seen. The summer maximum runs from June through Sept., with very few in
* March and April.
* Note that O'Connell uses the AJB's spelling of "K.J.Lucaj", and their
* translated name of journal as "Weltkunde"! He also gives the year as
* 1927, probably because it appears in the 1927 volume of the Jahresbericht.
* In Russian, this is
* К. И. Лучай
* Зелёный луч
* Мироведение 15, 58-59 (1926)
* O'C #233
* nearly useless
* SUNRISE flash "Par temps absolument calme et ciel d'une pureté parfaite."
* C.D.PERRINE again
* ". . . during my stay in Hermosa Beach, California. . . . Between March 11
* and August 27 definitely green flashes were seen on 34 occasions. Of
* these 20 were over land, 12 over water and 2 behind wet fog banks. It is
* significant that not only were flashes seen at Hermosa more frequently
* over the land but that the colors were on the average much more intense."
* O'C #103
* Davidson & Stratton report some observations from ship on return voyage
* from Sumatra solar eclipse. They notice that
* ". . . through glasses the tips of the setting segment of the Sun were seen
* as green distinctly before the final disappearance of the yellow rim."
* O'C #200
* WONDERFUL ACCOUNT of the effects of RETINAL BLEACHING! and a GREEN RAY!!
* This excellent account is accompanied by full circumstantial details:
* coordinates, barometer, air and sea temperatures, wind, sea state, etc.
* Translation given in full:
*
* On board the S.S. "Tosari", 12 September 1924, 6.15 p.m., steaming in
* the Indian Ocean, N. lat. 6° 32.'5, E. long. 78° 40.'5, corr.
* bar. 758.1, air temperature 28.5°, sea water 27.0° wind W by N 4,
* undulating sea, moderate SW swell. Very wet atmosphere, overcast sky
* with clear western apparent horizon.
*
* At sunset an especially beautiful green ray was observed. When half the
* solar disk had disappeared behind the horizon, the top part of the still
* visible Sun was light green, the lowest part harsh green in tint. This
* harsh green color moved slowly upward, displacing the light green color.
* When the last harsh green colored little segment had disappeared at the
* apparent horizon, plume-shaped green rays shot upward.
*
* The sky was almost completely clouded over, only the spot where the Sun
* had disappeared was bright. Almost all kinds of clouds were to be seen,
* nearly equally divided.
*
* After sunset it came to my attention that all sailors who had come on
* deck to see the natural phenomenon had such an intensely dark red skin
* color; arms, face, and hands had a color of dark mahogany. That was
* also true for myself. On the gilded buttons of my uniform lay a silver
* lustre, on the white uniform a pink glow. The Moon, which before sunset
* had been seen very well, was now pale and indistinct. The water was
* greyish in color, only the bow waves and the wake, which otherwise are
* white, were now harsh green. The sea phosphoresced light. Looking over
* the sea, I got the impression that a yellow haze (light topaz color)
* hung over everything.
*
* Around the West the color of the clouds was varying between chestnut and
* the light yellow-brown color of old gold, run through with strips of
* pink and pearl-gray and quite pale between the gaps through which the
* blue sky was seen.
*
* Around the East the color of the clouds was from pale to dark gray.
* After 10 minutes the whole sky was uniformly covered with stratus
* clouds. In the 10 minutes I had seen the entire cloud cover change and
* unite into one layer.
*
* The port (red light) gave its usual color; that on starboard (green
* light) however radiated a harsher green light. The aft top-light (white
* light) shone green blue; the color was approximately like that of a
* spark between two carbon points. Seen from the bridge, the lights on
* deck looked, as far as color and shape are concerned, like the blowtorch
* of an autogenous welding apparatus. Looking at the binnacle I noticed
* that the brass hood and the rose were tinted green (light emerald
* green); likewise the chart, which lay on the table in the chartroom.
* The light from the lamp above the chart had the color of absinthe.
*
* This peculiar green tint slowly faded away from all lights. At 6.34 all
* lights were again of the usual color, but much clearer. Also this
* greater brightness faded away after approximately 15 minutes.
*
* The sky cleared off and drifted to the west. At 6.45 the eastern sky
* was clear, with a few feathers which converged in the E by N. It began
* to lighten around the NE and at 7.30 p.m. a halo appeared around the
* Moon. The atmosphere was very moist. Before sunset the railing was all
* wet from the dew.
*
* At night at 12.20 H.W. Point de Galle was spotted, the air was thick
* and misty. The temperature of the sea water had fallen to 23.5 in these
* hours; there was a strong ?koraallucht? observed.
* [The observation was made just west of the southern part of Ceylon.]
* possible GREEN RAY *below* observer? CLOUD-TOP flash
* ". . . an almost dazzling emerald green, which seemed to emit rays
* downwards in a semi-circle from the last fraction of the sun's disc.
* Not only was its brilliance greater than it has been my fortune to see
* it before, even at sea in the tropics, but, instead of being an
* instantaneous phenomenon, it lasted at least two seconds or even longer. . . .
* Its duration was not quite so long as on the occasion reported to you a
* few years ago, when it was seen in a cleft between trees on the same
* ridge, but its brilliance was incomparably greater."
* [see his 1922 Met.Mag. report for the earlier one.]
* [Sounds like Bandfield's flash, but observed from slightly above the
* best height. An inversion at cloud top would be responsible.]
* Telescopic observations of green or violet rims
* Blue/violet in winter, green in summer.
* Some of the phenomena may be contaminated by lateral color in the
* eyepiece, as "je n'en laisse passer que l'extrème bord dans le champ de
* la lunette." This might affect Part C, a claimed green color interior
* to the disk where masked off by clouds & mountains.
* O'C #126
* 3 reports on contiguous pages stapled together
*
* Several GFs at successive sunsets, *except* that
* ". . . aucun rayon vert ne fut perceptible; le Soleil s'étala, du reste,
* en une longue bande plate sans être surmonté d'une calotte rouge."
* O'C #268
* MALBURET's observation of GF at PARTIAL ECLIPSE detailed
* Influence of height of observer stressed
* O'C #235
* Standard double image of VENUS at setting
* O'C #173
* Sillem, responding to Davidson & Stratton (p.156), claims the flash is
* illusory because it is bluer when the sky is clear and the Sun yellow,
* and greener when the sky is hazy and the Sun red.
* Aug. 1926 issue
* O'C #283
* Passing reference in Alice Shalek's travel fragment from Chile
* "The only compensation for living in this country is the magnificent
* sunsets." (p. 522) "Just after the blood-red ball of the sun drops
* below the horizon, the so-called `last green ray' quivers across the
* heavens. It is a phenomenon that even the oldest residents await as
* for a faithfully repeated miracle." (p. 523)
* Reprinted from Deutsche Allgemeine Zeitung, June 2, p. 6.
* "Alice Shalek is an Austrian lady who has been living in South America
* and writing home about it from time to time." [inside front cover]
* Sun set "over a long building some miles off and at a slightly lower level"
* "smoky white with a faint tinge of green" after "deep orange" sun.
* Oct. 1926
* C.J.P.Cave responds to Sillem (p.246):
* "The appearance of the last segment of the Sun as seen through a
* telescope or field-glasses is utterly at variance with the theory that the
* green ray is subjective."
* O'C #189
* refutation of Sillem's claim the flash is illusory
* O'C #26
* EVERSHED summarizes:
* "On a land horizon . . . the Flash, whether red or green, is generally
* less conspicuous than when seen on a sea horizon, partly because
* refraction and dispersion rapidly increase towards the lower sea horizon,
* and partly from another cause. At sea there is often a layer of air in
* contact with the water which causes mirage effects; distant objects on the
* horizon are reflected from it. These conditions cause an enhancement of
* the Flash, because the green segment of the Sun is reflected and reversed
* upon itself, producing a lenticular patch of green light of appreciable
* width." (O'C.#33)
* O'C #33
* PIETER FEENSTRA KUIPER's thesis
* misunderstands Wegener's model; figures drawn wrong. But a good quote:
* "It is quite remarkable that case 1 (inferior mirage) is generally known
* and understood, while case 2 (Wegener's sunset model) has been seen
* again and again, but before Wegener has never been explained."
* (Actually, this refers to the Mock Mirage!)
* Lagaaij's green-ray drawing is reproduced in color.
* N.B.: C.de Boer, Jr., in Helder, was the publisher of "De Zee".
*
* Thanks to Thierry Lombry for pointing out that
* this thesis is available on the Web as a 134 mb (!) PDF, at
*
* https://dspace.library.uu.nl/handle/1874/283890
*
* -- the full-text open-access link leads to the PDF file.
* [Unfortunately, as of Sept. 16, 2017, the pages are out of order.]
* O'C #75
* FEENSTRA KUIPER's SUMMARY
* here he again misunderstands Wegener: "In the case of upward reflection
* [i.e., superior mirage] an untransparent layer is found just above the
* horizon, behind which the Sun passes. If the lowest border of the Sun
* appears underneath this layer, it is reflected upward."
* O'C #76
* AFTERIMAGE reports
* MEYER's early atmos.-optics REVIEW -- filed separately (cf. Humphreys)
* A fine review article, or rather, popularization -- there are no
* references! This is an early example of Meyer's respect for the Dutch
* work: ". . . eine führende Stellung nimmt in dieser Beziehung Holland
* ein, . . . " (p.145)
* The GF gets only a paragraph on p.152. Everything imaginable is here:
* halos, rainbows, mirages, distortions, aurorae, meteors, zodiacal light,
* scattering, blue sky, flattened shape of sky, crepuscular rays, Moon
* illusion, Brockengespenst, coronae, heiligenschein, noctilucent clouds,
* scintillation, eclipse phenomena, glories, colored shadows, . . . !
* It seems patterned after Nijland's long article in De Zee (1902), and
* could equally well be the model for Minnaert's book.
* There are detailed instructions for observers, too.
* kindly supplied by Brigitte Hofmann, Redaction "Kosmos"!
* Many new observations:
* Hansheinrich Mehnert: "double Sun" with upper image disappearing at a
* fixed almucantar at SUNRISE: "Die Scheinsonne zeigte während der ganzen
* Zeit [ungefähr drei Minuten] ihres Bestehens jenen grünen Strahl.
* Ihr oberes Viertel war von einem nicht stark glänzenden Smargdgrün,
* das nach det Mitte zu in Gelb überging. Jedoch war der ganze Farbton
* dieser Scheinsonne bedeutend dunkler als der der darunter befindlichen
* richtigen Sonne."
* Leopold Neumann: "Ich hatte in den beiden Sommern 1923 und 1924 an die
* hundert Male Gelegenheit, den angeblich seltenen grünen Strahl zu
* beobachten, ohne mir der Seltenheit dieser Erscheinung bewußt zu werden."
* (evidence for ADAPTATION:) ". . . einmal im entscheidenden Augenblick der
* Beobachtung meine Aufmerksamkeit abgelenkt wurde, während mein Begleiter
* den Horizont nicht aus dem Auge ließ. Plötzlich rief er: `Sieh hin!',
* und es zeigte sich, daß er noch verhältnismäßig lange den grünen
* Strahl sah, ohne daß ich ihn zu gleicher Zeit gewahren konnte."
* "Dieser oberste Rand erschien sekundenlang knapp vor dem Verschwinden
* als ein auf dem Wasser schwimmender, etwas vom Horizont abgerückter
* glühend roter Feuerball von der Größe einer Kirche, aus dem dann im
* Augenblick des völligen Untergangs ohne Farbenzwischenstufen ein intensiv
* leuchtendes, hellgrünes Flämmchen in der Form eines hohen spitzwinkeligen
* Dreieckes emporlohte, da durch die roten Reflexe im Wasser ein
* blitzartiges grünes Zucken jagte." (the figure closely resembles
* Lagaaij's drawing in F.K.'s thesis!) (GREEN RAY)
* Lucien Rudaux's French article on the GF, illustrated by good B/W
* PHOTOGRAPHS of sunsets (including a nice MM) and 2 GFs, plus BEAUTIFUL
* COLORED DRAWINGS showing the visual appearance quite accurately, both for
* the naked eye and telescopically. p.183 has 2 nice photos of
* ASYMMETRICAL mirage development over an island. The center photo nicely
* shows the DARKENING of the SKY toward the horizon.
* [Rudaux was both an astronomer and an artist; he is regarded as the
* forerunner of Chesley Bonestell and other realistic space artists.]
* 27 August issue
* attempt to test Julius's anomalous-refraction theory with ionized air in
* the lab
* O'C #122
* rejects Julius's anomalous-refraction theory in favor of the usual
* scattering + dispersion
* ONE FLASH SEEN BY TWO GROUPS at MT. HAMILTON
* "The place where the Sun was last seen was at a haze line. . . ."
* O'C #287
* SAME SUNSET as above
* ". . . a narrow horizontal band of vivid green projected against the sky
* at the point where the Sun was disappearing."
* This is the double-star Aitken
* O'C #165
* Lucien Rudaux's drawings and photographs; text not credited
* The page of drawings (presumably in color -- I have only a monochrome
* photocopy) is taken directly from Rudaux's "l'Illustration" article,
* less than 2 months earlier, and is headed:
* The green ray at sunset: a meteorological "mystery"
* The explanatory drawings are also taken from "l'Illustration"; much
* of the text (p. 712) is a translation of his text there as well.
* The captions and explanations in the text are all right on the money.
* Rudaux/Ill. Lond. News item, cited with title only
* Nov. issue
* GREEN LINE OF DIFFRACTED LIGHT ?
* ". . . seemed to follow the minor prominences of the skyline, instead of
* first appearing between them."
* Nov. 19 issue
* A GOOD discussion based on numerous observations by a careful observer:
* Carlo Bonacini recognized the connection between thermal inversions and
* mock-mirage flashes. He also observed the spectrum of the green rim
* visually; realized that the phenomena are complex and depend on several
* factors, so that the textbook explanation is inadequate; realized the
* contribution of visual effects to what is seen; and connected sunset
* distortions, green flashes, and mirages. This is a thoughtful and
* insightful discussion, even though he believed that water vapor played an
* important part in producing the green color, and laid heavy emphasis on the
* variability of the rain bands in connection with his GF observations:
* ". . . our quite numerous observations [have] established a direct
* connection between the intensity of the rain-band and that of the GF:
* -- in the sense that when this is vivid, the humidity is always high.
* [Naturally, the reverse is not true, as other conditions are necessary
* for the formation of the GF.]
* "This immediately clarifies how it is that the phenomenon is more
* showy and quite sharp at sea, where the atmosphere is extremely humid:
* while on land, or in the mountains, is almost always found the blue or
* blue-violet color. . . .
* "So while Guglielmo finds in the chromatic tail of the solar disk a
* prevalence of blue in the summer and green in the winter, I find in my
* statistics to have observed magnificent blue colors in the winter too,
* but in special conditions of low humidity (weak rain-band)." (p. 121).
* He also recognized that physiological effects are not excluded by a
* physical cause: "And in fact, if it is true that the primary cause of
* the GF is real, this does not alter the fact that in particular
* circumstances of observation, that is when the observer has fixated for
* a long time, without being dazzled, the Sun can add to the sensation of
* objective green the negative image of the disk as well, of similar tint:
* since, as is known, a color appears of increased saturation when seen
* after fatigue by its complement . . . ." (pp. 122-123)
* "And so could be explained still better that particular vividness of
* the green flash that has always amazed all the observers. . . ."
* In discussing the width of the green rim and the duration of the
* flash, he seems to have confused seconds of time and seconds of arc, in
* reading the literature. (Indeed, he seems to mis-read many references
* that he cites.) Still, his general point that the observed duration
* exceeds the calculated one is correct. "This means that there is
* something else. There must be some occasional circumstance that
* intervenes to modify the phenomenon and in an essential way." (p.124)
* This leads him (in section 7) to consider the irregularities of the
* solar limb.
* That discussion focuses on the effects of "seeing", but leads to a
* discussion of static deformations of the limb (which, he says, are
* associated with the best GF displays) in section 8 (p. 126). He
* immediately attributes these structures to "stratification in calm".
* But he supposes that discontinuous images require discontinuities of
* density. "The literature, otherwise copious, is not generally
* accompanied by explanations." His own explanations largely involve
* arm-waving about "stratiform condensations" of water vapor in the upper
* atmosphere.
* In section 9 (p. 127), he describes how pieces appear to be removed
* at the top of the setting disk by irregularities in refraction, and how
* this can be simulated with a white disk and a wavy glass, or "any glass
* whatever of very bad quality, which is not flat." So these pieces
* of "the extreme upper limb, separated like a cloud," cause good GF
* displays [i.e., mock-mirage flashes]. (Sect.10, p.128) He gives
* some examples from his observing records: Fig.2 shows "the separation
* of a red segment" at the lower limb -- i.e., a red flash. "And I
* predict therefore that when the upper limb will arrive at that zone,
* there will be a beautiful GF. Indeed, 2 or 3 times we have had the
* isolated green cloud (and a little blue at the end) with a duration
* greater than 2'' and of an unusual width."
* In section 11 (p. 129) he discusses mirage effects: "The bizarre
* forms of the Sun at the horizon can in fact become still more complicated
* by this cause: indeed the duplications, the more grandiose splittings
* etc., could not otherwise be explained . . . ", and naturally cites Wegener.
* Mirage should play a part in the GF because the reflected image
* of the green cloud is added to the direct image, thus enlarging the
* colored zone and (he thinks) its duration "if the disappearance of the
* two zones is not simultaneous."
* Sect. 12 (pp.129-130) deals with high latitudes, where he thinks the GF
* is rarely seen. This fits in with his ideas about water vapor.
* Note that he discovered that "spikes" on the upper limb occur at the
* same altitudes as indentations in the lower limb, and associated these with
* inversion layers, 30 years before O'Connell! (Compare Fig. 3 here with
* O'Connell's pp.135 and 137.)
* (No.39 of the Pubblicazioni is entitled:
* NEL PRIMO CENTENARIO DALLA FONDAZIONE DELL'OSSERVATORIO - 1827 - 1927
* Thanks to Luca Lombroso for providing this information!)
* OLIVER LODGE, obviously never having seen a GF, thinks "the sudden green
* flash, seen by some people . . . , is mainly physiological; for I see . . .
* a momentary greenness when I switch off a bright lamp, with metallic
* filament, suspended over my bed."
* Dec. 3 issue
* O'C #81
* LODGE gets his comeuppance for speaking out of turn. . .
* "The literature of the green flash is very voluminous. . . ."
* "The explanation as a refraction phenomenon is so simple, and fits the
* facts so well, that it is curious that there should be such a reluctance
* to accept it."
* NOTE: Cave was President of the Royal Meteorological Society from
* 1913-1915 and 1924-1926. See QJRMS 77, 334-336 (1951)
* O'C #190
* Dec. 17 issue
* ``Much confusion has beset this subject
* because two entirely different things are unfortunately covered by the
* phrase `green flash.' If separate names had from the first been given to
* the two things, each would have been treated apart from the other and a
* great amount of controversy avoided.''
* O'C #249
* EVERSHED replies to Lodge:
* "The physiological theory of the green flash, resuscitated by Sir Oliver
* Lodge, is not now held by any competent observer who has made a careful
* study of the phenomenon."
* "I have made very numerous observations of the green flash, at sea and
* on land, and have confirmed Mr. Whitmell's conclusions."
* Dec. 17 issue
* O'C #207
* "I . . . suggested that five of us should turn our backs to the sun and
* close our eyes until the sixth should signal that the upper edge of the
* sun was disappearing. On his signal we turned, and each saw for an
* appreciable time a thread of bright green light lining the silhouette of
* the island at the point where the sun was last seen."
* O'C #281
* LODGE RECANTS
* "If in my letter . . . I am understood to have suggested that the green
* flash seen at sunset had no cause other than a physiological one, I
* withdraw any implied or hinted suggestion in that direction; for it is
* evident that a great weight of authority is in favour of a physical
* cause."
* "It was, I admit, rather hasty to send a letter on so small a point. . . ."
* O'C #82
* DRAWINGS of MM-type flashes appear more schematic than detailed.
* Possible observation of SKY BANDING?
* "Temps clair, vent très faible; quelques légères bandes de brume
* parallèles à l'horizon donnent au disque l'aplatissement et les
* déformations bien connues."
* ". . . les lignes de brume accusent l'étranglement de la partie
* supérieure, et finissent par la séparer du disque, comme le montre la
* figure 2."
* useless very brief report of Ruda's 1927 papers
* R.W.WOOD (Mar.31) -- see following papers
* "No person trained in the observation of optical effects, both real and
* subjective, who has seen the phenomenon at its best, will have any doubt
* about its reality."
* "It seems possible that the determining factor is the relative
* temperature of the air and the ocean."
* "With cold water and warm air, . . . the normal gradient of refractive
* index would be increased, the curvature of the rays augmented, and
* sunset would be delayed, giving a greater opportunity for atmospheric
* dispersion to come into play."
* (This error was propagated by Rayleigh two years later.)
* O'C #162
* WOOD's unsuccessful appeal for observations (May 12)
* Popular Astronomy reprints the Science News Letter item verbatim:
* O'C #163
* double flash (first mountain, then sea horizon) from the St. Albans
* O'C #194 (he has wrong volume)
* useless amateur report
* O'C #208
* GREEN RAY of amazing size if no error; could it be a crepuscular ray?
* "Immediately after sunset a vivid emerald green flash was observed from
* the horizon point of sunset to an altitude of about 80° in a southerly
* direction. The sky immediately above the horizon was covered with A-St
* clouds to an altitude of about 5°. The remainder of the sky was
* covered with Cu-Nb/St. Cu. clouds."
* GF COMMON in SOUTHERN CALIFORNIA
* "In some localities the green flash is by no means so rare a phenomenon
* as might be inferred from Prof.Wood's experience on the Atlantic Ocean and
* from the letters of some other correspondents of Nature. Here in Southern
* California I have seen the flash many times. . . ."
* O'C #170
* Observations at Pic du Midi
* Emphasizes the need for a high horizon to get BLUE or VIOLET.
* Admits that mirages can extend the duration, citing Evershed.
* "Si l'atmosphère était homogène, la durée theorique . . . ne saurait
* atteindre en aucun cas, sous nos latitudes, une durée de 2 secondes . . . .
* Mais it suffit d'avoir contemplé quelques couchers de Soleil pour être
* convaincu que l'atmosphère est bien souvent hétérogène , et cette
* circonstance suffit à expliquer les durées anormales fréquemment
* observées." BUT:
* ". . . la présence d'une couche d'indice minimum au point de disparition
* du Soleil est susceptible de donner lieu à une frange colorée
* exceptionnellement large. In convient toutefois de remarquer qu'elle
* ne saurait augmenter la durée de visibilité du Rayon Vert. . . ."
*
* Nice drawing of a marine mirage showing the bow-wake.
* Good advice to observers:
* "L'instrument idéal pour le bien observer est essentiellement portatif;
* je ne saurais en effet rien conseiller de mieux qu'une jumelle à prismes
* groissant huit fois."
* O'C #120
* Observations at Pic du Midi: COLOR REVERSAL
* Terminology critiqued; extreme variability of phenomena pointed out,
* including mock-mirage features.
* Discussion of "recrudescence" of green light.
* Much is made of Bellemin & Gallisot's "couche troublée";
* the interpretation is all garbage, but the observations are excellent.
* "Hypothèse du contraste ou des couleurs complémentaires . . . qui
* contient pourtant un fond de vérité."
* VENUS and JUPITER observed telescopically:
* "Parfois même il y a renversement complet des couleurs, renversement
* qui ne dure en général qu'un instant.
* "Mais le 8 février, il y eut renversement complet pendant plus d'une
* minute; le rouge occupait nettement la partie supérieure du disque de
* Vénus, avec cependant des oscillations marquées. . . . Le 11 février, le
* même phénomène s'est reproduit, mais moins nettement, et pendant moins
* longtemps." [cf. O'Connell, Plates XIII, XIV (pp.77 & 79)]
* Planetary analog of GREEN RAY?
* "De plus, il est essentiel de remarquer que la tache verte s'eloigne non
* seulement du disque, mais encore qu'elle s'élève réellement par rapport
* à l'horizon. La distance maxima entre le disque et l'aigrette au moment
* où elle va disparaître est de l'ordre de 1'."
* O'C #27
* useless
* O'C #176
* useless -- another first-time observer
* O'C #242
* 5 reports from a moderately experienced observer; some blue
* Includes a nice RED FLASH:
* "Lower limb of Sun emerged from a cumulus bank 1/2° above distant
* horizon with a ruby light."
* Many mock-mirage flashes:
* "In certain states of the sky the green ray may be formed by successive
* strata of lofty clouds forming false horizons, and I once saw the upper
* limb sinking, at 1° altitude, through a close succession of these, and
* with × 18 glass counted about a dozen separate productions of the
* green ray, which formed on each side of the upper segment, and appeared to
* chase each other to the top, unite with the ray coming up the opposite
* side, and float clear."
* O'C #220
* So brief I quote it in full here: USE of BINOCULARS
* "It is possible to see this with field-glasses when an observer could
* not see it with the naked eye. It is safe to use such glasses on the Sun
* when this is quite low on the horizon for the few moments necessary for
* this observation."
* TELESCOPE recommended; BLUE-VIOLET reported
* "This has been seen many times. . . ."
* ". . . first was of a deep green hue, but the last tiny spark appeared of
* a most intense blue-violet colour."
* O'C #219
* BLUE flash over LAND
* O'C #182
* Repeated or continuous GF for over a MINUTE of time
* "Il est très facile . . . de prolonger le temps pendant lequel le bord
* supérieur du Soleil est, pour l'observateur, tangent au parapet: il
* suffit de lever la tête progressivement au fur à mesure que le Soleil
* descend . . . .
* "Quand le Rayon Vert est visible, on peut l'observer pendant plus d'une
* minute d'une maniere continue ou, à plusiers reprises, en maintenant le
* tête au-dessous du plan parapet-bord superieur du Soleil . . . ."
*O'C #213
* GREEN better seen over LAND than over SEA in polluted air
* O'C #204
* Jacchia sees the green rim; Groubé sees a GF. Both useless.
*O'C #216
* A curious proposal and experiment (see Agnes Fry's earlier report in JBAA)
* VENUS flash seen from 700 ft.: "peacock green"
* Parker identifies Housman's RED FLASH (above)
* March issue
* O'C #262
* Fleming reports an observation by Frank T. Davies (with Byrd exped.)
* "Frank T. Davies . . . reports . . . a green flash observed off Bermuda on
* the evening of August 28, 1928:
* `Very smoky dull-red sunset . . . .' -- so much for the rule that
* flashes can't be seen when the sun is red! ` It did not look to me
* like a flash but a definite change from yellow to green lasting about
* two to three seconds.'"
* No info about water temperature; but this is plainly an inf-mir. flash.
* March 15 issue
* Mostly about crepuscular rays, except for a useless passing mention that
* "Sun set . . . with a peculiar green tint as upper segment dipped . . . ."
* VENUS GF
* refers to the Kosmoshandweiser 1926, S.13 and 1927, S.282
* kindly supplied by Brigitte Hofmann, Redaction "Kosmos"!
* typical isolated report; useless except that
* ". . . as we had protected our eyes up to the last few seconds we were
* both able to agree that the transformation to green was unmistakable
* and was not accompanied by any change of colour in the region of sky
* near the sun." (inappropriately cited by Botley, 1930)
* ". . . in most perfect conditions. The sun's disk was a brilliant deep red."
* Offers the afterimage explanation.
* "I see it fairly frequently at sunrise."
* CAUTION: horizontal refr. given as 36 deg., not minutes.
* "I have not infrequently seen grey or violet at sunrise."
* A muddled version of the standard story
* Thinks blue is seen only at sunrise
* Refers to earlier letters by Cave Orme [21 Aug.] and Druce.
* (Could "Druce" be Dence, above, on Aug.19?)
* AGNES FRY offers her indoor afterimage example again (cf. her JBAA paper
* earlier this year)
* This is the item Botley (1971) had in mind about
* "the sun putting out his sidelights"
* -- but see his book "A Gipsy of the Horn" (1925) for its first appearance!
* YELLOW stage noted
* "The setting sun was of a deep yellow colour, and when partly set was
* still trying to the sight. As the last segment of the sun disappeared it
* turned a whitish yellow tinged with a deep orange colour, followed
* immediately by the green flash of a beautiful emerald shade."
* A completely CRANK work. The author believes it is all contrast effects,
* and has a screwey theory about these, colored shadows, acoustics,
* hydraulics, electricity, etc. Basically, a well-meaning but ignorant
* amateur, who replicated Prof. Porter's experiments, but has even less
* understanding of their significance.
* Why did the editors see fit to publish this nonsense? [Oct. issue]
* The ORIGINAL ADMIRAL BYRD story from an eyewitness (Russell Owen)
* "Via New York Times radio station and Mussel Rock radio station.
* Robert Dollar Steamship Company, San Francisco. Copyright, 1929,
* by the New York Times Company, the San Francisco Chronicle and the
* St. Louis Post Dispatch. . . .
* "SPECIAL BY WIRELESS
* "LITTLE AMERICA, Antarctica, Oct. 22 -- The ``green flash,'' that
* phenomenon seen at sea and which occasionally causes debate among
* scientific men, has been seen here recently so prolonged that instead
* of flash it resembled a green flare hung in the sky where the sun had
* just set. The green flash is usually seen at sea in the tropics where
* the sun drops suddenly below the horizon and vanishes so quickly that
* it is literally a flash.
* "It comes from the last star like a point of light from the sun
* as it goes down, a point which changes rapidly in color of which
* the green is exceptionally vivid, giving the phenomenon its name.
* Atmospheric refraction causes the light to disappear in the order of
* its refractability or bending qualities. The red rays bend the least
* and so disappear first, then the green and finally the blue.
* "SUN SINKS SLOWLY
* "Here the sun descends so slowly that it seems to roll along the
* horizon and as it will be only two days until it is above the horizon
* all the time for the rest of the summer it clings interminably before,
* with seeming reluctance, dropping from sight. As its downward movement
* is so prolonged the last rays shimmer above the barrier edge as it moves
* eastward, appearing and reappearing from behind the irregularities of
* the barrier surface. It trembles and pulsates, producing a vibration
* light of great beauty.
* "The night the green flash was seen some one ran into the
* administration building and called, ``Come out and see the green sun.''
* "SEEN FOR HALF HOUR
* "There was a rush for the surface and as eyes turned southward,
* they saw a tiny but brilliant green spot where the last ray of the upper
* limb of the sun hung on the skyline. It lasted an appreciable length
* of time, several seconds at least, and no sooner disappeared than it
* flashed forth again. Altogether it remained on the horizon with short
* interruptions for thirty-five minutes.
* "When it disappeared momentarily it seemed to have been shut off by a
* tiny spurt, an inequality in the skyline caused by the barrier surface.
* "Even by moving the head up a few inches it would disappear and
* reappear again and after it had finally disappeared from view it could
* be recaptured by climbing up the first few steps of the antanea post.
* "Curiously enough at one time there seemed to be a brilliant red
* flash or spot of light a short distance from the green at just about the
* distance one would suppose the arc of the upper limb of the sun extends
* below the horizon."
* The rest of the article continues Owen's running reports on the
* progress of the Byrd expedition. Note: all strictly [sic]. Most of
* the typos can be figured out: "last star like a" was meant to be just
* "last star-like" and "vibration" was obviously meant to be "vibrating".
* But how did "antanea" get past the proofreaders? "Eastward" is a typical
* mistake of a Northern Hemisphere resident new to the South.
* Note that this was a sunset flash seen at the end of the southern
* winter night, which explains the confusion in second-hand reports.
* According to Davies (1931) and Haines (1931), the flashes were seen on
* Oct. 16, several days before the dateline of this account.
* Seen 20 times in 2 months at MT. HAMILTON
* This is the double-star Aitken
* O'C #166
* NORMALLY SEEN WITH 8X BINOCULARS in Santa Barbara
* "These observations . . . have been made through a pair of eight-power
* Hensoldt-Wetzlar binoculars, under which circumstances it is an
* exception when it cannot be seen, assuming that the horizon is clear. . . ."
* O'C #267
* Pinkhof quotes from letters, mostly a wordy report from W. Meyers Cluwen:
* "Unusually clear weather, straight horizon, sharp as I have seldom
* seen it in our country. North wind . . . Quiet sea. . . . The sun
* set without any deformation. . . . Just at the moment when the last bit of
* the sun disappeared, a green light appeared for a short moment, green
* with a touch of blue, shining to us and reflected in the water. . . . about
* 1/4 to 1/2 second, possibly 1 second. Short times are difficult to
* determine without special aids. One usually overestimates the duration of
* such observations, because the image `persists'."
* Pinkhof then reports a few of his own: ". . . the sun was quite well
* deformed: the outline looked angular and when it arrived at the horizon, a
* mirror image was formed in a layer of air, so that it was just as if the
* sun rested on a pedestal." He then adds a third-hand account of the
* Byrd expedition's observation, relayed via d'Aumérie. "Mr. d'Aumérie
* recalled a similar case that was brought about in a very different way
* (published some years ago in the Bulletin de la Société Astronomique de
* France): a hiker ran along a slope at the same pace as the speed of the
* sunset. The green flash then remained visible a long time." [NOTE: this
* must be Whitehead's report in BSAF 35,404(1921).]
* I have a botched copy of this; Berkeley's original was badly stained.
* 2 useless "pale blue" flashes
* GOOD EVIDENCE for ADAPTATION
* ". . . two of us watched the sun carefully until it had set, while the
* other two looked eastwards and on a signal from the sun watchers turned
* quickly just as the sun was disappearing. The two who had watched
* continuously saw the green flash, while to those who did not look till
* the very last moment, the sun went down orange-yellow, and no green was
* seen."
* a blurb for Rayleigh's 1930 paper, in Nature
* "A satisfactory account of the origin of the `green flash' of the upper
* limb of the sun when it disappears at sunset is given by Lord Rayleigh
* in the January issue of the Proceedings of the Royal Society. "
* Curiously, this cites the correct reference for Wood's paper, though
* Rayleigh got it wrong in his paper! So I think the attribution of
* this item to Rayleigh by his biographer Egerton (1949) is in error.
* Jan.25 issue, in the "Research Items" dept.
* a useless and ordinary report, preceded by poor drawings of a solar Omega
* in the report by T.E.Earl, "Abnormal refraction, Mediterranean Sea".
* EXCELLENT INFERIOR-MIRAGE SUNRISE FLASH -- BEST DRAWINGS EVER
* VERY CAREFUL observation of Omega-type sunrise with 3-inch telescope.
* ". . . the first appearance of the sun was a small flattened button-shaped
* spot . . . of intense green light . . . ."
* ". . . in the first stages . . . the lower edge seemed to be separated very
* slightly from the sea-horizon . . . while in the succeeding stages the disc
* seemed to be joined to the horizon-line by a connecting strip . . . .
* This connecting strip appeared to be due to some `mirage' effect, for,
* at the instant of separation from the sun's disc . . . the last connection
* took the form of flickering orange-red flames in rapid vertical motion
* between disc and reflection. Separation was complete . . . when the sun's
* disc had an ovoid form, flattened at the top, but extended and much
* pointed below, the lower edge being orange-red while the upper edge was
* still narrowly green."
* Even the red flash at the stem was noticed!
* Dumb comments by Botley on the above, comparing physiological effects at
* the SUNRISE flash with a SUNSET observation from the Times
* RAYLEIGH (younger)
* another SCALED DISPERSION calculation:
* "Thus the angular dispersion between the C and F lines, now more
* generally called @roman H sub alpha@ and @roman H sub beta@ is
* @1.04 times 10 sup -2@ of 35', or 22''."
* He also promotes Wood's (1928) erroneous suggestion that more refraction
* would make the green rim more visible.
* Note that the reference to Wood on p. 317 is badly garbled: it says
* Nature "vol. 111, p.502 (1923)", but should be vol. 121, p.501 (1928).
* [Vol. 111, p. 13 (1923) is Evershed; Rayleigh got them confused.]
* O'C #112
* This is a collection of 10 other reports, accumulated at the Carina
* Observatory in Odder over a long period. Some are recognizable (Flöcker,
* Stebbins & Aitken at Mt. Hamilton, the Byrd expedition in Antarctica)
* but most are apparently either newspaper reports or individual reports
* sent in. #6 is interesting: ". . . he had looked long at the Sun, when it
* suddenly began, and made an impression nearly like that due to an
* irritation of the eye. . . " (cf. Mike Bandfield's reports)
* O'C #72
* A year of systematic observations at both sunset and sunrise. This is
* probably the best comparison of sunset with sunrise available. The
* duration was longer at sunset, the longest being 12 sec.
* EVIDENCE for ADAPTATION
* Less interesting is Roßmann's paper on pp.368-371 of the same issue.
* He saw fewer GF's from the Feldberg, which is lower. Observations were
* timed with a stopwatch. The observations with refraction anomalies
* (superior mirages, distorted Sun, etc.) lasted longer, on the average,
* than those without.
* NOTE: Roßmann was the original owner of the copy of P&E on my desk.
* GREEN COLUMN (cf. Escher, below!)
* "In Ceylon at the end of April and beginning of May -- just before the
* break of the S.W. Monsoon -- at sunset, which is always very brilliant, as
* the sun finally disappears under the horizon, a great column of green
* light appears to shoot up into the heavens and then gradually disappear."
* B.G.ESCHER comments on Feenstra Kuiper's thesis, with some useful ideas
* (as well as some gaffes). His main weakness is having seen only 4 GFs;
* and, as he says, "A complete classification could only be given by
* someone who has made very many observations himself and moreover is
* sufficiently educated in the natural sciences."
* [F.K. (below) unaccountably takes great offense at this sensible remark.]
* Nevertheless, Escher offers his classification.
*
* Escher allows a PERSONAL FACTOR: "The phenomenon sometimes lasts so
* briefly that a complete concentration of thought is required precisely at
* the moment of sunset or sunrise. If the concentration at that moment is
* not complete, it can happen that one has seen nothing, while his neighbor,
* who was completely concentrated, saw the green flash well." [If we
* replace "thought" with "vision", we see the presence of the bleaching
* effects; see C. Vaughan Starr below.]
*
* Escher makes a USEFUL DISTINCTION:
* "In the first place, a sharp separation must be made between the
* phenomena that are seen on the Sun itself, while it still (or already)
* stands above the horizon, and the phenomena that appear immediately after
* the Sun has set or just before it has risen." [The latter are the green
* crepuscular rays, though Escher seems to include the inferior mirage as
* well.]
*
* The chief value of this paper is his detailed description of a SUNRISE
* GREEN RAY, with essential circumstances:
* ". . . I have named a green column, which I have observed on 6 July 1929
* at sunrise in the Gulf of Suez. It was easy to predict where the Sun
* would rise on the pink illuminated parts of the mountains on the Sinai
* peninsula. Just above the profile line, where the Sun rose later on,
* appeared a bright light-yellow rim and simultaneously above that a
* light-blue segment. This segment rose and changed to green below.
* Suddenly the Sun itself appeared, absolutely not red or orange, as it was
* with the green flash at sunset, but intensely shining and white,
* surrounded by a light yellow shine. At the same time the mountain
* silhouette became light colored. The light between the mountain horizon
* and the sea was obviously laden with dust particles, which is hardly
* surprising in the Sinai desert. I estimate the duration of this
* long-lasting, broad and high green flash at 2 seconds. That abnormal
* refraction and dispersion occur here is certain; they were apparently
* caused by mineral particles in the air."
* "The diameter of the green column was estimated to be about half that
* of the Sun, while the height of the green column with blue cap was
* estimated by me at 2/3 of the diameter of the Sun."
* [He says earlier he used a 5 x 20 Spindler & Hoyer prism monocular; but
* does not say explicitly that it was used for this observation.]
*
* There is also an INTERESTING MAP showing the geographical distribution
* of the observations in F.K.'s thesis. From the concentration of GF
* observations in the Red Sea, the Gulf of Aden, and the south-eastern
* Mediterranean, he suggests that "the frequency of the green ray
* observations is greatest in the regions where the precipitation is the
* least, that is, where the shipping routes pass near or between deserts."
* So he concludes that "a dry climate is favorable for the appearance of
* this very remarkable phenomenon."
*
* Note: Escher was quite a famous geologist; thanks to G.P.Können for
* pointing this out. He was the sixth president of the International
* Association of Volcanology and Chemistry of the Earth's Interior, and
* the brother of the remarkable artist M.C.Escher.
*
* Tijdschrift, Koninklijk Nederlands Aardrijkskundig Genootschap =
* Journal of the Royal Dutch Geographical Society
* The thin-skinned Feenstra Kuiper angrily takes offense . . .
* . . . and Escher then adds a few more off-base suggestions (that mineral
* crystals in the air could affect its index of refraction).
* COMMON in SOUTHERN CALIFORNIA
* "The observations of these beautiful but variable phenomena have been
* very numerous. . . . in the 32-day interval Aug. 20 - Sept. 20, 1928, I
* witnessed the flash at sunset 13 times."
* "Contrary to what appears to be the usual impression, the green flash is
* at least as easy to observe when the sun is considerably reddened as when
* it is bright."
* O'C #171
* GOOD SUMMARY of Dutch work (cf. Meyer's 1939 paper!)
* This gives a better summary of Feenstra Kuiper's thesis than F.K. himself
* gave in JBAA. The history of Nijland's effort is also outlined.
* O'C #146
* cites Wood's 1928 Nature paper
* "While descending in clear weather as a passenger in a motor-car into a
* valley in Kincardineshire I watched the artificial sunset due to the
* obscuring of the sun by a hill some three miles away, the country being
* several inches deep in snow; the sunset occupied about five seconds; the
* last-disappearing edge of the sun turned from orange through yellow to a
* grass green. . . . the sharp increase of temperature with height usual
* above a snow surface appears to have produced a sufficiently high
* dispersion."
* O'C #270
* Admiral BYRD's account (cf. Haines, below)
* GF mentioned only on p.186, in section "The `green flash' flares at sunset"
* ". . . we had a series of sunsets."
* p.193 shows a picture of "William (Cyclone) Haines, meteorologist"
* HENRY NORRIS RUSSELL reports from Egypt on the GF and mirages
* (pretty standard textbook treatment)
* std. 2-sec inf.-mir. flash
* a trivial observation, but the Editor's comment (below) is noteworthy
* the Editor's comment:
* ". . . the mist may possibly have excluded the blue and violet images more
* completely than usual, which would give a purer green than is normally
* seen. This suggestion, however, is offered with diffidence."
*(cf. Dietze!)
* This is the most detailed account of the Byrd expedition's GF display:
* "The green color lasted for about a second at a time. It could not be
* seen continuously with the head in a fixed position . . . ."
* "When the Sun sank too low to be seen from the ground, it was still
* visible from the radio towers, and the above effect was seen at intervals
* for as long as one-half hour after the first observation."
* "The above effect was seen at intervals during a period lasting over
* half an hour."
* (translated by Roßmann, 1934)
* O'C #47
* prompted by Køhl's article in 1930
* An amateur discovers the green and red rims on the low Sun
* O'C #22
* Green rim seen telescopically above cloud:
* "Au-dessus et surtout en dessous du nuage, les images ont été très
* agitées avec effilochements dans le sens horizontal."
* "Le temps était très nuageux, le vent très violent."
* O'C #236
* 2 inf.-mir. flashes
* May issue
* useless inf.-mir. flash
* June issue
* FIRST COLOR PHOTOGRAPH by Maurice de Kerolyr
* The AUTOCHROME PLATES! (These must be the ones mentioned by Minnaert)
* This is a longer account than that in BSAF the next year.
* Here, Touchet says de Kerolyr was "directeur de la Station
* astrophotographique de la Haute Provence, à Forcalquier (Basses-Alpes)."
* But it seems that OHP did not yet exist; he speaks of a later article
* "à l'occasion du projet de construction d'un grand observatoire
* français".
* This seems to have been a private observatory; the telescope was an f/10
* lens of 1.20 m focal length.
* There is a drawing made from the plate by Rudaux; but "le mode
* d'impression de ce journal ne le permit pas. . . ." so the pictures are all
* black-and-white.
* Issue of Aug. 1, 1931.
* THANKS to Shaun Hardy for this reference!
* VENUS flash
* "As planet's altitude became . . . approximately equal to its diameter it
* appeared joined to the horizon by a ray of light." [DRAWINGS]
* cited in vol.13, p.8
* Oct. issue
* Good inferior-mirage flash
* ". . . le vent, assez fort, avait tourné de l'Ouest au Nord."
* O'C #178
* Ordinary inferior-mirage flash
* NO GF stuff; why did O'Connell include this?
* Could be useful for study of visual effects
* O'C #107
* GPK has a look at the green rim
* This is a curious piece of work, done while Kuiper was a student at
* Leiden. He states that he's never seen a naked-eye green flash, but
* once saw a good telescopic one. He then relates his observations on
* one [!] evening at the 26.5-cm refractor of Leiden Observatory.
* The "cloud" sounds as if it might have been a Wegener blank strip.
* The whole argument is full of inconsistencies: if there really was a
* cloud, then his observation says nothing about clear-weather observability
* of the flash, as he claims; you can't have both less refraction and more
* absorption simultaneously; etc. The paper is notable for the suggestion
* that unspecified "waves" in the air are responsible for the pieces that
* break off the upper limb and turn green, but I doubt that he really
* understood Kelvin-Helmholtz waves at this point (and no meteorological
* data are given.) The best that can be said for it is that he recognized
* that something besides extinction is affecting the visibility of the
* flash.
* (NOTE: volume number not certain.)
* A GENUINE LEGEND at last !!
* ". . . plusiers légendes, surtout celle du voeu à formuler pendant sa
* fugace apparition et qui doit se réaliser dans le cours de l'année."
* Ignorant of earlier work: "On peur se souvenir de l'explication physique
* qui en a été donnée ici-même par notre illustre collègue M. Ch.-Ed.
* Guillaume, en 1919. . . ." [cf. his BSAF paper.]
* "L'idée préconçue, fausse et très répandue, que le rayon vert est
* un phénomène rarissime et mystérieux en a éloigné les observateurs
* sérieux, et il en est des plus éminents qui doutent même de sa
* réalité, parce qu'ils ne l'ont jamais vu."
* O'C #177
* Green rim seen with 16x telescope
* O'C #185
* FIRST COLOR PHOTOGRAPH of a green flash
* The AUTOCHROME PLATES! (These must be the ones mentioned by Minnaert)
* Touchet's shorter account of Maurice de Kerolyr's color photography
* on "Plaques ``Autochromes'' de Lumière."
* "Nous ne pouvons reproduire ici le cliché obtenu par M.de Kerolyr.
* Il faudrait pour cela une planche en couleurs -- dont le prix est fort
* élevé -- et puis . . . l'image très petite de l'aigrette verte viendrait
* certainement fort mal au tirage trichrome."
* "Après les expériences de MM. Danjon et Rougier à Strasbourg, les
* photographies de M. Lucien Rudaux à Donville, les clichés en couleurs de
* M. de Kerolyr, on peut dire que la question du Rayon vert est liquidée.
* "C'est peut-être un peu de mystère qui s'en va; mais, ajoute M. de
* Kerolyr, ``c'est si beau à voir''! Aussi continuerons-nous, toujours,
* à regarder le Rayon vert chaque fois que l'occasion sera favorable."
* O'C #142
* Gunnar Dam -- a first-timer. Nothing useful.
* O'C #199
* Comment on the above Gunnar Dam:
* "The undersigned does not agree with Hr. Gunnar Dam that the phenomenon
* `the green flash' can be a rarity. The two times I observed it, I simply
* stood and waited for it."
* (Account of 8 GFs at alternate disappearances and reappearances behind
* Lofotens mountains as Sun grazed the horizon.)
* "My opinion is that the phenomenon is far more everyday than is believed
* up to now; it requires completely clear and calm weather and an observer
* who is prepared beforehand."
* Paul Bergso/e
* O'C #175
* Double flash due to sunset behind ISLAND
* O'C #252
* GOOD detailed account of mountain sunrise with green illuminations
* RED/GREEN rims on CLOUDS as well
* Effective wavelengths estimated at 0.47 micron at start, 0.53 after 2
* sec, 0.57 after 6 sec.
* O'C #215
* GF behind mountains
* O'C #247
* Repeated GF by climbing rapidly up mountain
* O'C #198
* an impressionistic description; not useful
* (violet) GREEN RAY
* He saw the GF from the deck of a ship, but two observers on the bridge
* (2 m higher) failed to see it.
* BLUE and VIOLET flashes behind CUMULUS clouds
* with VIOLET RAY shooting up (slightly longer account of the observation
* above; so filed here out of order).
* O'C #248
* Observed from the Mauretania!
* "Immediately after the Sun set, a brilliant blue-green blaze of light
* shot up and hovered for a full three seconds at the spot where the Sun had
* been, then wavered and disappeared."
* O'C #290
* Comments on the above
* ". . . I have seen it not infrequently when conditions were favourable."
* O'C #294
* 2 GREEN RAY reports from small boats; one HORIZONTAL RAY
* "At the very moment when the Sun's disk disappeared, a beam of green
* vertical rays clearly rose up, fan-shaped, with a central angle which I
* estimate as some 20 degrees and of height approximately equal to a solar
* diameter. The color of the ray was a green which can be called
* ``metallic'' and the duration did not reach half a second."
* "Another time . . . without deformation of the Sun's disk near the horizon,
* as the Sun set into the sea, I observed a double green flash effect. For
* an instant two green beams went out to the left and right, horizontally,
* and immediately afterward another vertically, similar to the one observed
* [before]. The horizontal beams were less wide than the vertical ray."
* And a useful observation:
* "During 15 days' stay on Ibiza I saw the green ray every time when the
* Sun set behind bare mountains; but when (because of my location) the Sun
* disappeared behind wooded mountains, there was never a green flash."
* (cf. Justice, 1930)
* O'C #210
* HALDANE's paper (belongs in VISION file, but filed here for continuity)
* (cited in Rayleigh's 1934 paper)
* "Lord Rayleigh . . . devised an experimental arrangement which enabled
* this effect [i.e., dispersion] to be studied at leisure. The colour seen
* was, however, blue, not green. It now seems evident, in view of the
* experiments described above, that the cause of the actual sunset or
* sunrise coloured ray being vividly green, is the simultaneous contrast
* effect due to the light coming from round the sun being red."
* A first-time observer asks for an explanation
* A clear "textbook" explanation in reply to Tidwell Browne.
* "It is not actually essential for the production of the green flash
* at sunset that the sun be seen setting directly over the sea. What is
* necessary is a sharply defined object, low down, behind which the sun
* disappears."
* A 35-year-old observation recalled, with exaggeration:
* Possible PHYSIOLOGICAL EFFECT? (Could be BLEACHING.)
* ". . . though the ball was bright red it was not too bright to allow of
* direct vision. The ray, which tinged the whole seascape, lasted for
* about two or three minutes, and was intensely green. I had been
* looking directly at the sun before it set."
* LORD RAYLEIGH's letter to The Times:
* "I have before me a Dutch monograph `Der [sic!] Groene Straal' . . . ."
* "I was interested in this subject after a voyage home from South Africa
* in 1929 . . . ."
* "This investigation is published in the Royal Society's Proceedings ,
* Vol. 126 (1929)." [N.B.: Actual date is 1930, though received in
* Nov.1929.]
* "As a physiologist I should like to point out that Lord Rayleigh's
* inference . . . that the green colour of the `ray' seen in very clear
* weather at sunset and sunrise does not depend on physiological contrast
* is inconclusive. . . . I think there can be no doubt that the greenness
* depends on `simultaneous' contrast."
* On firmer ground:
* "I think that not only physicists, but also many physiologists, have a
* very imperfect conception of the extent to which physiological contrast
* enters into what we actually see. According to Newton's teaching the
* sensation of colour produced by light depends simply on the refrangibility
* (in more modern language, the wavelength) of the light. This is only true
* under certain physiological conditions. Under other and quite usual
* conditions it is not true at all, as can easily be shown experimentally."
* Sir FLINDERS PETRIE gets a word in . . .
* Argues (implicitly) from SCALED REFRACTION again.
* "By standing on a slope facing the sunrise the blue can be kept in view
* for some minutes by walking downhill."
* EVERSHED debunks HALDANE (temporarily)
* "subjective" phenomena:
* "It moved as I moved my eye!"
* "We may then cease to feel surprised at the constantly recurring
* discussions as to the cause of the Green Ray -- all resting on the
* assumption that this expression connotes a homogeneous phenomenon."
* HALDANE again; points out that colors seen telescopically differ from
* those seen in context (i.e., "related" colors)
* Sounds at first like a GREEN RAY, but seems to be inf.-mir.flash
* ". . . after [sic] an unusually beautiful sunset, [I] saw it blaze up.
* The brightness of the Sun's disk had been very great . . . ; the green
* flamelet, which shot up immediately after its disappearance, was also
* very bright, it had the form of a small lying-down rectangle."
* [So maybe this "shooting up" stuff is just a belated realization that
* the mirage is above the visible horizon?]
* A couple of green flashes, including at JUPITER setting
* (cites Borgesius's paper on p.281)
* O'C #261
* Possibly the EARLIEST AIRPLANE FLASH?
* ". . . lasted quite two or three seconds. . . ." [sic]
* Mary du Cauroy, Duchess of Bedford, was an early airplane owner who
* first flew in 1926 at the age of 61. In 1937, she took off on a solo
* flight, and was never seen again -- a sort of elderly Amelia Earhart.
* Possibly the EARLIEST AIRPLANE FLASH?
* ". . . lasted quite one to two seconds. . . ." [sic]
* (a "reprinted" letter from The Times of Nov.27, 1933, p.15,col.5)
* (with a remarkable alteration! WHOSE?? The Editor's, or the Duchess of
* Bedford's?)
* a textbook account; Hoppe seems only to have observed the green & red rims,
* and attributes variations to changes in opacity
* O'C #53
* HEIGHT effects:
* "The visibility of the green flash depends on the height of the eye."
* Maart 1934
* O'C #148
* NICE SUMMARY of 303 observations!
* (quotes from his 1922 H&D paper)
* HEIGHT effect:
* "Usually I observed from the lower bridge, the 2nd Officer on watch
* from the upper: when the sun set directly forward, I went and stood
* next to him. In the first case I saw the green flash a few seconds
* earlier, but it was never obvious to me that the green flash depends
* on the height of the eye. . . ."
* Comments on letters to the newspaper:
* "All the writers have heard
* of the `green flash' at least once, don't know what and how much has
* already been written about this subject, have seen the phenomenon a
* single time and suppose that they have made an important discovery worth
* reporting."
* "Now that Dr. S.W.Visser and Mr. J.Th.Verstelle have published observations,
* made on the Marnix van St. Aldegonde, in the March issue, I beg
* to be allowed to add some further details to mine (i.e. my observations)."
* [THANKS to MART DE GROOT for this last sentence!!!]
* "I made my first observation on 25 July 1902, the last on 20 Oct. 1905.
* This series, 303 observations, formed the basis of the dissertation
* of Dr. P. Feenstra Kuiper for the doctoral degree in physical and
* natural science. From that time I traveled another sixteen years, only
* interrupted by an interval of one year . . . . How many observations
* have I made in all these years? I do not know, as I kept no notes . . . .
* A ``green ray'' such as was observed by D. P. Lagaay on 22 July 1911, and
* afterward reproduced in the thesis of Dr. F. K., I have never seen, a
* proof that it occurs extremely seldom; one sees such a thing by chance ."
*
* probably April issue?
* O'C #49
* Gustav Schröder's first GF?
* A GF in the last 3 seconds before disappearing. ". . . außerordentlich
* klare Luft. . . . ein prächtiges Grün (mit bläulichem Schimmer) . . . ."
* Thanks to Gerhard Czeplak of DWD Hamburg for this item!
* probably May issue
* Good account of typical phenomena, including SQUARE SUN and a display
* like Rudaux's 1904 drawing:
* "Much more remarkable flashes appear when atmospheric stratification
* causes, as it often does, the sun's image to be distorted in such a way
* that the sides are more or less serrated like those of a Japanese lantern
* or an accordion bellows. When the serrations are sufficiently marked, one
* layer after another in succession, beginning with the uppermost, separates
* itself from the lower part of the image, becomes narrower horizontally and
* much thinner vertically, turns green or blue, often at least at the
* pointed ends first, and disappears. In the last two or three years I have
* repeatedly witnessed this phenomenon, obtaining all the way from two to
* six green and blue flashes."
* ". . . the image took on the form of a rectangle capped by an isosceles
* triangle with somewhat rounded top. The top of the triangle now came off,
* turned blue, and disappeared. Then in between the point at which this
* disappearance occurred and the flattening disk another blue flash
* appeared, where nothing had been visible before. The image then became
* more and more flattened, and thinner vertically, without changing
* appreciably in horizontal width, and disappeared red (as the image often
* does).
* "Most of these observations were made with one inch achromatic
* binoculars magnifying about six diameters."
* O'C #172
* a report from the N.R.Crt., 21 July, 1934:
* ". . . color nearly of the copper Bunsen-flame."
* cited by Kupffer
* A fairly good popular account, though marred by attributing the color
* photography to Lord Rayleigh (!)
* Some rather overdone writing: "Zur Zeit, als der Roman von Jules Verne
* erschien, nahm die wissenschaftliche Welt die geistreiche Geschichte mit
* einiger Geringschätzung auf und verbannte den grünen Strahl in die
* Rumpelkammer pseudowissenschaftlichen Aberglaubens oder erklärte ihn als
* optische Täuschung."
* And, after the textbook story, then says: "Die Wissenschaft hat wieder
* ein Stück Poesie getötet. Bleibt der grüne Strahl darum nicht doch ein
* Wunder?"
* Schindler sees 2 GFs at sea, but none at home, where "geht die Sonne
* hinter nur 20 km entfernten Gebirgen unter, und der Aufgang erfolgt unter
* noch ungünsterigen Verhältnissen."
* Heft 6 is probably Juni
* O'C #278
* Comments on Schindler's paper in Sterne 1934 Heft 6
* "An der See scheint mir dieser Strahl durchaus nicht so selten, wie es
* in dem genannten Artikel stand . . . ."
* no useful details; Heft 9, so probably Sept.
* O'C #226
* the younger RAYLEIGH's second paper. Some of the "DISCUSSION" is
* more valuable than his work:
*
* Instructor-Capt. T. Y. Baker (pp. 493-495 of the "Discussion"):
* "My objection to this explanation is that refraction through the
* atmosphere is different in its nature from refraction through a prism,
* and an explanation based upon measurements of refractive index and
* dispersion at sea-level densities alone is not adequate. . . . if the
* author's explanation is adequate the green flash should always be seen
* when the sun sets cleanly behind the horizon. . . . And it must be
* remembered that the green flash is not a common phenomenon. It is the
* exception rather than the rule.
* "The true explanation of the green flash is, in my opinion, much
* more complicated than the author suggests." . . .
* "One has only to look at the form of the integral to see that a
* change of only a few units in the ninth decimal place for the bottom
* layers of the atmosphere (say up to 200 feet) is sufficient to alter
* the value of the integral by 20" . . . The rarer occasions when the green
* flash is seen are departures from the normal. I am almost tempted to go
* further and suggest that the abnormalities conducive to the green flash
* are most probably found in the lower levels of the atmosphere. . . . But in
* support, though not in proof, of my contention I would like to refer to
* measurements of the dip of the sea horizon made by ships of the Navy a
* few years ago. In this case abnormalities of the dip were entirely due
* to an abnormal condition of an extremely small part of the atmosphere,
* some seven or eight miles horizontally and 50 or 60 feet vertically. The
* normal condition of the atmosphere shows that a ray, nearly horizontal,
* has a curvature of about 8" per mile. Our measurements of the dip, some
* three thousand in all, showed variations between 32" and -17" per mile.
* If there are these wide variations in dn/dh , which is proportional to
* the curvature, is it not extremely likely that there may be differences
* . . . in these lower levels sufficient to account for a green flash?"
* [Note observation of possible CONCAVE surface.]
*
* Mr. W. H. White: "Green flash, turning blue, seen from foredeck (20 ft.)
* and exactly reproduced from forecastle deck, 9 ft. higher, 10 sec. later;
* a longer interval than simple theory suggests." (pp. 495-496)
*
* Dr. W. D. Wright: "Moreover the effects of successive contrast are very
* much stronger than the similar effects of simultaneous contrast. . . ."
*
* Mr. W. F. Floyd: "I am willing to accept a purely physical explanation of
* the green flash, but I would suggest that the present paper establishes
* only one possible explanation. That a physiological effect may
* contribute to the phenomenon, or may even provide the sole explanation of
* it, has not been disproved, nor can it be disproved by purely physical
* arguments." [cf. Rayleigh's footnote on p.491: "I do not enter upon these
* more or less physiological questions without misgiving, bred partly of
* lack of familiarity with this field, and partly from dislike of the
* vagueness inherent in the use of words for describing subjective colour
* impression."] [See also Worley (1935) for further comment.]
*
* LABORATORY DEMONSTRATION that scattering can remove the blue and leave a
* green last ray:
* No.255, July 1, 1934
* O'C #113
* A slavish imitation of Nijland's A.N. paper (cited), including several
* repetitions of the magic 530 nm wavelength; no useful data
* "Geschlossen 1934 Sept. 4"
* O'C #257
* classical inf.-mir. flash at sea horizon
* ". . . couleur vert tendre (comme de l'herbe fraîche)."
* "Les trois fois que j'ai pu faire une observation positive du rayon
* verte à la jumelle, il s'est formé à une petite distance au-dessus
* de l'horizon, sans contact avec la mer."
* followed by a letter dated Octobre 1934
* O'C #288
* Fritz Roßmann translated Haines's report:
* and added a noteworthy comment:
* "Nach Meinung des Referenten ist in polaren Gegenden der grüne Strahl
* . . . recht selten. . . . Zweitens wird die Beobachtungsmöglichkeit aber
* weiter eingeschränkt durch das Wetter. Selbst bei Hochdrucklagen, in
* denen häufig auch günstige anomale Refraktionsverhältnisse vorhanden
* sind, ist die Lufttrübung meist gross, wenigstens an Orten geringer
* Seehöhe. Die günstigen Brechungsverhältnisse bleiben dann wegen der
* gleichzeitig fast stets ungünstigen Extinktionsverhältnisse meist
* unwirksam."
* Okt. 1934
* Blue sunrise flashes over the Alps
* "Séance du 7 Novembre 1934"
* O'C #179
* an uninformative report
* This is a bilingual publication; every item is in both English and
* Japanese. The pages seem not to be numbered; this is No. 294.
* Dec. 18, 1934
* O'C #301
* Blue and green flashes with "trainée lumineuse"
* ? May be our BRIGHT LINE in SKY at HORIZON ??
* 3 days of observations; the middle one with probable Fata Brumosa
* MYSTERIOUS "traces":
* ". . . j'ai vu une traînée lumineuse très rapide glissant de gauche à
* droite et présentant une teinte bleue très faiblement verdâtre.
* (next day): "Comme la veille en suivant à l'oeil nu le coucher du
* Soleil, j'ai vu une traînée lumineuse d'un ton vert très intense."
* 2nd & 3rd days were accompanied by "FOG": "près de l'horizon des
* bandes brumeuses avec des stries horizontales."
* O'C #289
* Botley reports a letter from the Radio Times , Nov.2 (1934).
* Report of "TWO SUNS" and each giving a flash.
* original report from Mr. Stewart:
* ". . . I saw it (the green ray) scores of times, probably because after
* seeing it once it became a temporary superstition to look for it on
* every possible occasion . . . ."
* "We saw the green ray from the first and then several minutes again from
* the second when that set in its turn, both equally vivid."
* Botley likens the observation to Applegate, Met.Mag.64,67(1929)
* Nice DRAWINGS of sunset distortions induced by inversions, with a "cap"
* flash like Rudaux's (1904)
* "The stages numbered 5, 6, 7, seemed to take a long time."
* (No doubt they did! This is an extreme Type B sunset.)
* flash seen over land horizon despite light smog
* A SUNRISE inf.-mir. flash, prolonged by HIGH LATITUDE
* "A vivid green point changing quickly to a fairly sizable ball of green
* fire. . . . lasted from two to three seconds." (in Hudson's Bay)
* "There was hardly any wind and the sea was calm."
* N.B.: Davies's 1931 note in TMAE detailed the Byrd expedition's GFs.
* THANKS to Shaun Hardy at the DTM library for pointing this out!
* 7 GFs seen in 15 attempts, with several long ones: 6, 10, 11 sec!
* (continued from AN 6056)
* ". . . die Erscheinung in unseren Breiten keineswegs so selten ist, wie
* oft behauptet wird."
* Many references to Pickering's seeing scale.
* A.N. Nr.6084
* O'C #258
* Review of recent literature, especially Rayleigh's papers
* O'C #62
* two color changes reported: first WHITE, then green.
* (observed from 8 m height "à l'aide d'une bonne jumelle . . . d'un
* grossissement de 7 diamètres . . . .")
* The "white" stage is probably the yellow flash, although bleaching
* should be important here:
* "Depuis le moment où le soleil rouge et aux rayons si puissants
* touchait l'horizon, jusqu'à sa disparition complète, nous avons observé
* le phénomène sans la moindre interruption, malgré la fatigue que cela
* occasionnait aux yeux."
* Two other observers in the same general area saw GFs when Rahir did not:
* "Le rayon vert peut donc être visible d'un point du littoral et ne pas
* se manifester à quelques kilomètres de distance. Cette diférence peut
* être due au fait que notre point d'observation est plus haut de quelques
* mètres que ceux des deux autres observateurs."
* O'C #111
* A half-hearted literature review in one paragraph
* This is a followup to Rahir's note. It mentions Guillaume, Coutinho,
* Danjois [sic!] & Rougier, Julius, and Rayleigh; no citations.
* [The item just above this is signed by Lagrange; this bears only his
* initials.]
* Another novice reports both common flashes:
* HEIGHT EFFECTS:
* ". . . from a hill about 180 feet high. On one occasion Mr. H. B. Lusk
* . . . was on the beach at sunset and reported that no green flash was
* visible, though it was clearly seen by me and by other observers from the
* hill."
* ADAPTATION:
* "Although the primary cause of the coloured flash may be atmospheric
* dispersion, simultaneous colour contrast may very considerably modify the
* subjective colour effect."
* COMMENT on RAYLEIGH:
* "The discussion following Lord Rayleigh's paper read before the Physical
* Society indicated, however, that before a satisfactory explanation of all
* the observed phenomena could be given, further observations were
* required."
* O'C #300
* EVIDENCE that RAYLEIGH never saw flashes before his 1930 and 1934 papers:
* "On a recent trip to the West Indes, I saw it three times out of a total
* of five sunsets observed, using a field glass x7. It was just about as
* conspicuous as the experimental work would lead one to anticipate.
* Circumstances unfortunately prevented my observing further sunsets . . . ."
* O'C #266
* editorial summary of GF correspondence:
* H.Carey Gibson "states that he has observed the flash several times . . .
* from . . . 150 ft. above sea level. In October 1933, while in the Gulf of
* Aden . . . , `the flash could be clearly seen, with or without glasses,
* almost any evening', and was even observed from a port-hole about 18 in.
* above the water." ** RECORD LOW EYE LEVEL?
* Northcote Thomas reports from 800 ft. that "On occasions the colour
* persisted for half a minute." ** HALF A MINUTE??
* O'C #307
* R.M.Bell of Penn.State cites Byrd's account (1930)
* O'C #174
* An ORKNEY blue flash
* "The actual colour of the `flash' under comparable conditions of
* temperature lapse probably depend on the amount of atmospheric pollution,
* in this case practically nil."
* GF over ROOF of building seen from Utrecht Obs.
* "From the time of the observation, the zenith distance of the upper limb
* of the Sun was 89° 16', taking 36' for the refraction."
* O'C #256
* This is a report of the meeting Schröder refers to:
* (abstract of Minnaert's report on the GF in Utrecht, from N.R.C.)
* Annalen der Hydrographie und Maritimem Meteorologie
* (Tafel 46) Nice colored plates of typical sunsets + GF
* Bildreihe 6 shows classical evidence of ADAPTATION
* more interesting solar distortions than in 1937 paper
* Kapitän Gustav Schröder, Hamburg-Amerika Linie
* See note at 1937 refs.
* O'C #279
* NIJLAND's revised criteria for observers
* only the 2nd part of this paper (section 4, p.438) deals with the GF
* Here we are 9 years after Feenstra Kuiper's thesis, of which he says:
* "The conclusion of the discussion is that the green flash can in general
* be explained by the following three atmospheric effects:
* 1. the normal dispersion, which forms a spectrum from the low-standing
* sun, with red below, blue or violet above;
* 2. the normal scattering, which removes the blue and violet from the
* light that reaches us from the direction of the sun;
* 3. the important absorption of yellow and orange, especially by moist
* air.
* There remains then practically only red and green; a solar image with
* red lower limb and green upper rim. Thereby a first step in explaining
* the phenomenon is made, but all sorts of details remain enigmatic at
* present and make regular observation necessary, whereby in particular
* those who live by the sea can take part productively."
* O'C #97
* A moderately experienced observer's views: "I myself have many
* experiences of witnessing the phenomena, mostly when I was on board the
* ship, in past years. . . . At present I am convinced that such
* observations on land are not quite difficult as formerly thought. . . .
* Meanwhile I have several occasions when I failed to see the green flash
* on the apparently clear sea-horizon. It is doubtless that some
* critical circumstances of floating clouds near the setting sun will
* interfere the phenomena."
* ISSEI YAMAMOTO was Director of the Kwasan Observatory.
* Pages are not numbered, but this is on 3rd page.
* O'C #302
* TIKHOV's anomalous-refraction paper in MIROVEDENIE
* Mostly about anomalous refraction, but several important parts about the
* `green ray', and some interesting observations:
* He notes that the color depends on atmospheric clarity, but subscribes
* to the "segment" model. As he calculates only a 12" width for the green
* rim, he clearly needs to make it wider. He proposes to do this by
* invoking abnormally large refraction, like many earlier workers; but
* he then models the atmosphere as a prism, using the minimum-deviation
* formula! This allows him to handle refraction up to 2° 42' (= 2 x
* 1° 21'). Larger refraction requires greater obliquity of the
* incident rays, hence nonlinearly more dispersion.
* The alternating red and green lines observed at sunrise on 11 Jan. 1926
* are interesting, and might be due to ducting. He notes that mirage was
* observed quite often, but doesn't say which kind of mirage.
* In section 9, he reports 8 GFs at sunrise and 2 at sunset in a month.
* The longest reached 9 sec.; one was blue. The horizontal refraction for
* these summer observations was from 30' to 37' (mean, 33'), though his
* winter observations reach 2 degrees.
* This is the last issue of the year (No.6) of this bimonthly.
* useless observation made with prism binocs.
* TIKHOV thought he had detected anomalous dispersion in the B band:
* N.B.: Fig.2 is an actual photographic print, now turning brown!
* Dated Feb., 1936.
* O'C #140
* A remarkably LONG GF (10 sec) associated with SUPERIOR MIRAGE
* After a detailed description of afternoon superior mirage around the
* horizon, he reports (p.69):
* "Die Sonne erschien beim Untergang ganz besonders stark abgeplattet, ihr
* vertikaler Durchmesser erreichte kaum 2/3 des horizontalen. Am
* schwindenden Sonnenrande spielten etwa 10 Sekunden lang blaugrüne
* Lichter, was sonst --- wenn überhaupt --- nur von viel kürzerer Dauer zu
* sein pflegt. Alle diese Umstände beweisen eine besonders starke
* Krümmung der Lichtstrahlen in den unteren Lichtschichten, die wohl ---
* der Jahreszeit und dem Wetter entsprechend --- unmittelbar über der
* Meeresoberfläche kühl und darum dicht, höher hinauf beträchtlich
* wärmer und darum undichter gewesen sein müssen."
* This is the S.S.Mataroa observation mentioned by Barlow (below)
* Appears to be an inf.-mir. flash, though same temp. is given for water
* and air. Color changes of Venus also reported at 2 1/2 deg. altitude.
* Dated April 1936.
* Summary of earlier reports in Marine Obs., plus mentions of Rambaut,
* Whitmell, Capt. Carpenter, J.E.Clark (1926), and Admiral Maclear.
* Only the M.O. references are actually cited. Michie Smith is called
* "Mickie" Smith. "As far as is known the first account of it was
* published in Nature in 1882." [probably meaning 1883]
* O'C #7
* VISUAL SPECTROSCOPY OF SETTING SUN AND GF -- orig. proposed by Buss, 1916
* "- The phenomenon is caused by absorption on the one side of the green
* and scattering on the other, while the red set earlier because of
* dispersion. -" [cf. Dufay]
* O'C #28
* GF with RAY
* ". . . just as the last particle of the sun's disc was visible, it turned
* a bright light green, with short and broadening rays of the same green
* shooting up from it . . . ."
* The letters from Kendrew and Evershed are excerpted and printed together
* with the remarks of the editor, Gilbert T. Walker; I list Kendrew's and
* Evershed's contributions separately, but include the same covering title
* with all:
* KENDREW reports a GREEN GLOW after the GF:
* "As the upper limb of the sun finally disappeared it assumed the same
* green colour, and a distinct green glow continued for a second or two
* after the sun itself had gone." ?? GREEN RAY ??
* John Evershed's clearest and most explicit explanation of the
* inferior-mirage flash:
* ". . . it may also be enhanced by a mirage effect, due to refraction by a
* layer of warm air in contact with the sea: this has the effect of adding
* to the green segment an inverted image of it, producing in effect a
* lens-shaped green patch."
* Gilbert T.Walker, editor of QJRMS, muddles the terminology:
* "My experience is that at sea sometimes the sun's light fades out
* steadily, being green for about two seconds, while at other times there is
* finally a sudden increase and decrease in brightness. The latter effect,
* presumably due to abnormal refraction, on a still night, constitutes the
* `green flash' while to the former the title of `green ray' is more
* appropriate."
* Cicely M. Botley provides an indirect reference to the Manx folklore
* reported in letters to the Times in the summer of 1929:
* brief mention only
* ". . . several members . . . witnessed an excellent occurrence of the
* `green flash'. At Blackpool the Sun sets behind a horizon of open sea,
* and on that date the western sky became exceptionally clear . . . ." [p.301]
* "W.H.McC." must be W. H. McCrea.
* Thanks to ADS full-text search!
* Rehash of a few older VENUS flashes on p.182
* TIKHOV's big article starts with TERMINOLOGY complaint:
* "This phenomenon bears the not very fortunate name `green ray'."
* "That which is observed corresponds poorly with the usual conception of
* a ray as something long, drawn out along a straight line."
* He believes the Rambaut/Rayleigh model, but also describes
* mock-mirage flashes.
* Table 2 shows the non-linear growth of dispersion with refraction, based
* on his 1935 paper in Mirovedeniye. So he thinks excessive normal
* refraction is responsible. There is the interesting result that the
* longest theoretical duration is almost 6 hours, at latitude 89° 56'
* (just 7 km from the Pole), where the diurnal and seasonal motions cancel
* to first order. "All these calculations are purely theoretical. In
* reality, faster and irregular changes of refraction near the horizon can
* completely violate the calculated duration of the phenomenon." He then
* cites Byrd's observation, and one from Julius Peyer (?). The last section
* shows his Pulkovo spectra of the red and green rims, which he equates to
* red and green flashes.
* This is a cut above the usual popular article on the subject, which he
* has clearly approached with much care and thought.
* The Russian reference is:
* Проф. Г. А. Тихов
* Зелёный луч
* Наука и Жизнь No.9,
* 29-33 (1936)
* Brief report of sunrise GF behind MOUNTAINS at 67° lat., on Norse coast
* Between 1 and 2 am, MET. There is a sketch of only the mountain horizon.
* Two flashes seen in low corners. "According to the captain, it had
* been an uncommonly clear observation of the green flash." Thanks a lot!
* Curious appearance; related to MOON ILLUSION?
* Or a HORIZONTAL GREEN RAY display?
* Sun set behind MOUNTAINS:
* "Immédiatement après la disparition du bord supérieur du Soleil,
* un tache verte clair, allongée dans le sens horizontal et
* dépassant dans ce sens un peu le diamètre du Soleil, est apparue
* à l'endroit où était le bord du Soleil et a duré, peut-être,
* une seconde."
* O'C #180
* 15 SECONDS COUNTED
* Kapitän Gustav Schröder, Hamburg-Amerika Linie
* "Von dem Augenblick an, als das feuriggelbe in ein grünes Oval
* übergegangen war, bis zum Verschwinden konnte ich 15 Sekunden zählen,
* und es war beinahe der schönste Grüne Strahl, den ich jemals sah."
* See note at 1937 refs.
* O'C #129
* routine inf.-mir.flash: "un globule, vert éclatant."
* O'C #273
* useless inf.-mir. flash report
* There are 2 interesting mirage reports earlier on this page.
* in April issue
* PINK SUNSPOTS at inferior mirage
* June issue
* a rather breathless account of a SUNRISE GF, 3 to 4 sec. long
* A nice inf.-mir. flash; water over a degree warmer than air; calm.
* Followed by a sunset flash the same day!
* Thanks to Gerhard Czeplak, DWD Hamburg, for this item!
* Juli 1937
* VENUS GF at setting
* in July issue
* This query incorporates observations
* "It s'agit d'une lueur verte intense qui se produit exactement au moment
* où le soleil entre dans les flots à l'horizon. Si le ciel est un peu
* opaque au-dessus de cet horizon, mais qu'il y ait cependant une ligne
* assez large de ciel bleu et clair entre l'horizon de la mer et ce début
* de nuage plus élevé, le phénomène est encore plus intense, comme
* j'ai pu le voir tout ce mois à Hendaye où je me trouvais en vacances!
* Ce rayon vert est de la couleur du cuivre en fusion lorsque le métal
* brûle par suite d'un excès de chaleur dans le creuset. C'est donc un
* vert très vif."
* He can't believe the ancients could have missed it. "Bois-Colombes"
* is the only address given.
* August issue (No. 2)
* Both common types of flash reported; seen with telescope
* ". . . the change was gradual from green to green-blue and then dark blue."
* "When about one-third of the sun was below the horizon, the upper limb
* became curiously affected: tiny strips seemed to peel off and melt away;
* some were coloured green and some violet. They bore a slight resemblance
* to flames."
* in Oct. issue
* typical account of first-time observer (Kurt Wegener):
* "war aber so wenig von der Erscheinung befriedigt, dass ich die
* bisherigen Beobachtungen für Sinnestäuschungen und die ganze Frage für
* einen Irrtum hielt, bis es mir im vergangenen Sommer auf der Insel Lopud
* bei Ragusa gelang, die Erscheinung in voller Deutlichkeit zu sehen."
* ADAPTATION: "Ein grünes Licht, das im Augenblick des Verschwindens der
* Sonne aufleuchtet, aber aus Blendungsvorgängen des Auges erklärt werden
* konnte, hatte ich öfters beobachtet."
* POSSIBLE GREEN RAY? "Ebenso habe ich öfters in der Arktis bei
* Sonnenuntergang einen breiten grünlichen Streifen beobachtet, der von der
* Sonne senkrecht nach oben wies, aber nach meiner Ansicht Teil eines Halo
* war." [Nov.1937]
* O'C #151
* Annalen der Hydrographie und Maritimem Meteorologie
* these have the "beautiful colored plates" mentioned by Minnaert on p.58
*
* "Wenn man bedenkt, dass ich den Strahl im Verlauf von zwei Monaten
* mindestens 35mal gesehen habe -- davon mehr als zehnmal bei
* Sonnenaufgängen --, muss man den Astronomen recht geben, die behaupten,
* das der 'Grüne Strahl' nur deswegen als seltene Erscheinung gilt, weil
* man sich zu Unrecht einbildet (wie die 'Morning Post' und Jules Verne),
* dass er selten zu sehen sei." (cf. Kellen!)
*
* (Tafel 61)
* Kapitän Gustav Schröder, Hamburg-Amerika Linie
*
* According to letter from H. Stüve (Public Relations, Hapag-Lloyd)
* the height of the observer's eye was about 14 m above the water line
* for both the "Reliance" and the "St. Louis".
* Issue is dated 15. Nov.
* O'C # 131a
* (Tafel 62, links)
* Kapitän Gustav Schröder, H.-A. L.
* O'C # 131b
* Dr. Wilhelm Hartmann, Hannover
* O'C # 131c
* (Tafel 62, rechts) much poorer drawings than Schröder's
* Evidence for adaptation: blue -> green at sunset
* Note that Schröder (1941) attributes the suggestion in footnote 2 to
* G. Castens; it is signed merely "Die Schriftwaltung".
* O'C # 131d
* Otto Klaehn, II.Offizier, D. "Reliance", H.-A.L.
* Kupffer was the president of the Naturforschenden Verein in Riga; Meyer
* was its VP. Kupffer says his article is based on references supplied by
* Rudolf Meyer. So this posthumous paper might be regarded as a dry run for
* Meyer's review paper in 1939. He says he has seen the GF many times,
* and his account shows it; his own flashes have run from a fraction of a
* second to 5 sec. At the end he describes in some detail 2 of his
* inferior-mirage flashes in 1934.
* O'C #228
* GF observed from south rim of the Grand Canyon
* "As it approached the point of disappearance the reddish colour
* changed to yellow and then to brilliant green. The theory ordinarily
* advanced . . . is that of atmospheric dispersion. If this is correct, then
* the green should change to blue at the last moment before disappearance.
* The fact that the blue was not observed is perhaps due to the steepness
* of the visibility curve of the eye combined with the brightness of the
* sky background." [pp. 358-359]
* Thanks to the NASA ADS full-text search for turning this up!
* William Beebe's RAY-type flash off Baja California
* "We steamed out of the quiet of San Lucas Bay into a tempestuous sea,
* a sea with so rough a skyline that we had two sunsets and a green ray.
* On deck we finished dinner at the very moment of sunset or, more
* accurately, earthrise. From almost a full half-sun it diaphragmed
* suddenly to a speck of gold, almost instantly to return to half a
* sphere again. For a second it seemed to hold steady, then vanished,
* and was replaced by a sheet of clear, pale green. Only two of us saw it,
* so it must have occurred between winks."
* TOTALLY USELESS !! Why print this stuff?
* the next page has an equally useless report by Treilhat
* GF mentioned in a textbook on philosophy
* The author thinks that philosophy can settle disputes among conflicting
* scientific disciplines, and offers examples:
* ". . . crude phenomena are often so ambiguous in status and character
* that they are bandied about among the sciences and no science wants to
* recognize them. . . . For example, when an astronomer looks at the disc
* of Mars through a good telescope under specially good conditions of
* visibility, he may see a network of straight lines, the famous `canals
* of Mars.' Is the physical reality attested by this observation?
* By no means. They may be optical illusions, because the eye at the
* limits of visibility has a trick of importing regularity into what it
* sees and so will interpret a number of irregular markings as a pattern
* of straight lines. Does the phenomenon then belong to astronomy or to
* psychology? The matter is still in dispute." [This was a reasonable
* statement in 1939.] "A still simpler case is the seeing of what is
* called the `green flash' of the setting sun at sea. If the sky is
* quite clear and cloudless, the last bit of the sun's disc, as it dips
* below the horizon, turns a vivid green. This is a fact, though I have
* always found some people who could not see it. But the explanation of
* this fact is in dispute. Is this green objective or subjective? [Not
* a reasonable question in 1939, in view of the photographs made by
* Rudaux in 1925 and de Kerolyr's Autochrome plates -- not to mention
* old laboratory measurements of the dispersion of air, and the even
* older observations of red and blue rims on the low Sun.] . . . Either
* there is a selective absorption [sic] of rays in the atmosphere such
* that those which reach the eye turn the sun green; or else the green is
* merely a contrasting colour due to the redness of the surrounding sky.
* Both interpretations seem possible, and the actual effect may be due
* to both, for they may reinforce each other. Hence there is plenty of
* occasion for philosophy to offer its mediation in connexion with ambiguous
* phenomena and the disputed territory on the border of several sciences."
* Schiller (1864 - 1937) was once a well-known pragmatist, but is now
* (for obvious reasons) largely forgotten.
* 450 nm BLUE wavelength estimated in Warnemünde, 1.Sept.1938
* "Als die gelbrote Sonnenscheibe etwa 3/4 untergetaucht war, erschien der
* Rest ganz plötzlich über der Kimm in ausgesprochen blauer Farbe, der man
* im Spektrum eine Wellenlänge von rund 450 mμ zuordnen müsste."
* "Um bei der Beobachtung etwaigen optisch-physiologischen Täuschungen so
* weit wie möglich aus dem Wege zu gehen, beobachtete der Verfasser die
* Sonne beim Untergehen stets nur mit einem Auge, während das andere erst
* dann geöffnet wurde, wenn der grüne Strahl auftrat, so dass dieser mit
* einem ungeblendeten, nicht ermüdeten Auge wesentlich leichter beobachtet
* werden konnte."
* O'C #286
* EXCELLENT REVIEW and synopsis of Feenstra Kuiper's thesis;
* first suggestion of WAVES on inversions as a cause;
* too many good quotes to give here!
* O'C #89
* ASP LEAFLET 123
* has a few interesting refs.
* This is the double-star Aitken
* O'C #5
* Osbert Sitwell thinks GFs are afterimages, but does not use that word
* ". . . just before sunset each evening, trouble would begin about
* Le Rayon Vert, the Green Ray. Recently there had been correspondence
* in the columns of The Times, and also, presumably, of certain French
* journals, concerning this mysterious and, indeed, mythical ray . . . ." All
* treated with great sarcasm. Pity this supercilious twit is misinformed.
* The original edition was published by Macmillan, London; (1939) there,
* this appears on p. 42, according to Google Books.
* Deliberate observations of SOLAR AFTERIMAGES
* (offered as explanation of GF by Ing. Hans Vogel)
* "In den Heften des `Kosmos-Handweisers' liest man immer wieder Berichte
* von Augenzeugen über eine seltsame Himmelserscheinung, die unmittelbar
* nach Sonnenuntergang auftritt und sich so darstellt, daß von der eben
* untergegangenen Sonne aus ein zuckender grüner Schein über den Himmel
* huscht, oft bis zum Zenith reichend, aber immer nur wenige Sekunden
* andauernd. Die Erscheinung wurde von vielen angezweifelt, weil sie nicht
* von allen Menschen gesehen wird."
* Maybe this is where the rare reports of green stuff up to the zenith
* come from?
* He apparently has a method of smearing the afterimage into a "ray":
* "Nicht jedes Auge scheint das Phänomen richtig bemerken zu können."
* No volume number available; this is in the section "Kosmos-Handweiser".
* O'C #86
* GF is section 2, p.264: mentions his repeated observations in 1909,
* but does not cite publication. (cf. Naturwiss.1920)
* Useless.
* Schröder reveals he is no scientist
* This is Gustav Schröder's final publication on green flashes.
* It contains comments people have sent him about his earlier
* observations. He thinks Meyer's 1939 paper can "den Leser mit fast der
* gesamten Literatur über den `Grünen Strahl' bekannt machen"! -- and
* then picks on Meyer for mentioning the Green Segment before the Green rim,
* because "Ich habe bei meinen vielen Beobachtungen nie ein grünes Segment
* vor dem grünen Saum gesehen." Then he adds some interesting further
* observations of his own:
* He and a fellow-officer saw (with binoculars) a flash over a roof only 1
* km away.
* Then, after giving credulity to Dr. Reinhold Quasig's notion that the
* green and blue colors come from emission lines of copper and nickel in the
* Sun, he cites the EARLIEST PROPOSAL to prolong a flash via AIRPLANE:
* G. Castens, Ann.Hydr.(1937) p.496, footnote 2 (see Klaehn), in connection
* with his suggestion for the use of high latitudes. Then relates his own
* observation at Murmansk "minutenlang" as the Sun skimmed a tree-covered
* ridge. "Augeshöhe 18 m" agrees reasonably well with the 14 m estimated
* in my letter from Hapag-Lloyd.
* O'C #130
* EXCELLENT EXPLANATION OF THE *WRONG* (classical) model!
* Perhaps the EARLIEST ATTEMPT to allow for EXTINCTION
* Nice drawing of Mock Mirage at upper limb;
* says SCALED REFRACTION ". . . gilt . . . mit hinreichender Genauigkeit"!
* Observed RED and GREEN RIMS at 50 deg. zenith distance (x220)
* "Dort, wo die Luft meist frei von Dunstschwaden ist, im Gebirge
* oberhalb des ersten Inversion und am Meere ist das Auftreten des grünen
* Strahles daher keine Seltenheit."
* A good popular account
* Cites Kosmos-Handweiser Maiheft 1940, S.132 as well as Kellen's 1926
* article.
* kindly supplied by Brigitte Hofmann, Redaction "Kosmos"!
* Very observant account of details, including RED FLASHES
* cites Evershed, and notes importance of mirages at inversions
* O'C #195
* Napier Shaw's Meteorology text, with long Ch.III on Atmospheric Optics
* Useful references on mirages, including naming Flammarion as the source
* of the Diodorus Siculus reference. "Since the introduction of the
* practice of making roads with a very smooth surface the inferior mirage is
* a very common experience on a sunny day. . . . The details of lapse-rate
* require investigation." (p. 65)
* The Fata Morgana is discussed on pp. 66 and 67, citing Minasi,
* Pernter, and Forel (via QJRMS 38, 219 (1912).)
* About 1 page on GF, mostly a quote of Wood's 1928 Nature paper.
* Unfortunately, they endorse Wood's wrong-way mirage theory, thus buying
* into the mistaken idea of super-refraction. (p. 68)
* This is the 1942 reprint of the 1930 first edition.
* Paper copy filed in "Textbook accounts of GF" file.
* Google Books mis-labels this as Vol. II, due to faulty OCR.
* Green rim? seen telescopically over mountains
* probably useless; fewer than 4 lines.
* Extensive quotations from "sources in the American Geographical
* Society's library": Humphreys's book, Minnaert, Wood's "Physical Optics"
* and Evershed in QJRMS (1936). No original information.
* Interesting Report of the Ordinary General Meeting of the BAA, 31 May 1944
* with a good talk on meteorological optics by E.L.Hawke
* The GF stuff starts in the last line of p.95, but there is an
* interesting explanation of Newton's numerology leading to the 7 named
* colors in the spectrum on p.89.
* He says the GF "used to occupy a great deal of space in our
* Association's Journal ." This is consistent with my observation of a
* great diminution of GF reports after the middle '30s. both here and in
* BSAF.
* GREEN RAY observations:
* "At the actual moment of apparent sunset this last segment of the disk
* sometimes seems to shoot upwards like a little tongue of flame; sometimes,
* too, it is said to give the impression of a flash from a rapidly rotated
* searchlight fitted with a green screen. I have myself seen the former
* effect over an Atlantic horizon on at least a dozen occasions, but never
* the latter."
* In the note added later, he again says: ". . . on a number of occasions I
* have seen a small ray or beam, resembling a tongue of green flame, shoot
* upwards from the Sun as it disappeared below a sea horizon . . . ."
* The subsequent discussion is of some interest.
* ignorant novice fitting Havinga's characterization
* O'C #250
* NAKED-EYE FLASH on ROOF at 440 yards
* O'C #168
* Brooks comments on Barber and recalls his 1926 observation
* DRAWINGS of GREEN TIPS and LOWER EDGE of INFERIOR MIRAGE FLASH
* Nice Omega drawings and a sketch of a stratus CLOUD-top flash.
* "details of how the colour progresses across the last remaining visible
* part of the sun at sunset."
* Tikhov reviews his work historically
* The main interest here is a short account of a GF seen by Tikhov's
* predecessor A.P.Ganskii at Mont Blanc, 4 Sept. 1900.
* Tikhov makes much of his search for anomalous dispersion and claims
* to have found it around the B band.
* The whole article on atmospheric optics runs from p.233 to 246; but the
* GF section cited here is only 3 pages.
* Professor Sir Geoffrey Taylor's CLOUD TOP FLASH problem
* This is the N.K.Johnson who wrote on optical retrieval of lapse rate
* with Roberts in 1925.
* "I had hardly expected a cloud sheet to have a sufficiently definite top
* to show the green flash, but it was a really fine display."
* The observation was in June, 1944; these are leftover letters from WW II.
* Ashmore thinks the blue color is odd.
* ". . . a beautiful blue, a trifle bluer than the deepest sky-blue seen
* with maritime polar air in spring."
* "I was viewing it through powerful binoculars. . . . Perhaps it [the
* unusual colour] was due to the use of the binoculars themselves."
* Another leftover from the War; observed Aug. 20, 1943.
* Spectroscopist ALFRED H. JOY covers the GF and other refraction effects
* 2 paragraphs on pp. 163-164 describe green flashes; a third describes
* simple dispersion at large Z.D. A little of the history of astronomical
* refraction follows: Tycho, Kepler, Newton. Modern "tables are
* reasonably accurate except at points near the horizon."
* GREEN RAY ? or afterimage?
* "There was plenty of stratocumulus about, though the sun set in a clear
* patch. Just as its lower rim touched the horizon there was a `flash' of
* pale green at `10 o'clock' from the sun's centre and about two diameters
* distant. This did not last more than a second at the most and appeared
* almost circular, with a radius slightly larger than the sun's.
* Immediately after, I noticed that the small clouds just above the sun were
* tinged with the same shade of green."
* SUNRISE FLASH "lasting about 1.5 seconds and approximating to the flash
* of a green-shaded Aldis lamp at one mile range."
* A complex display; difficult to interpret. The sunset mirages seem to
* be superior; but the sunrise phenomena appear to be inferior mirages.
* The famous compiler of 6-place math tables sees his first flash:
* "All my life I have looked . . . for the so-called green flash; I had
* conspicuously failed to catch it. To-night, over the smooth water of the
* Red Sea, I have seen it.
* "I now know the main reason for my previous failures; my conception of
* what I was looking for was at fault. I had expected something green --
* and pictured emerald green; I had expected a flash , i.e., something
* momentary like lightning, . . . and I had expected something extending
* perhaps 20' or 30' above and around the sunset point. It was none of
* these things."
* ". . . the smallness of the whole effect was contrary to my expectation."
* (reprinted in Met. Mag. the next year; see below)
* Note: this appeared only 2 years before Comrie died.
* O'C #20a
* 5 MINUTES from SLOPE OF HILL
* "The slope of this hillside was such that by walking uphill I could
* keep the upper limb of the Sun just at the point of setting, and by
* varying my pace could make it `rise' or `set' at will ... for over five
* minutes."
* (Note that years and volumes of JBAA still do not coincide.)
* O'C #183
* ". . . the fringe has been clearly photographed in natural colors."
* "The phenomenon has been very thoroughly studied in the past and there
* is quite an extensive literature on the subject, which is not really
* astronomical but belongs rather to what the French call
* optique atmosphérique ."
* O'C #134
* Houtgast sees two SUNRISE flashes over the Alps (see pp.10,11)
* He estimates the durations as 0.5 and 0.1-0.2 seconds.
* The footnote on p.11 also reports a brief WHITE FLASH at sunrise.
* described as a "witte flits". So perhaps this gave the editor the
* inspiration for "groene flits" a few pages later? (See next item.)
* The editor presents a Dutch translation of Comrie's JBAA note
* Can the introductory remarks be the first use of "groene flits" instead
* of "groene straal" in Dutch? The editor explains that it is the literal
* translation of "green flash". (The editor's note is on p. 16, under the
* heading "De groene straal"; Comrie's note begins p. 17. The editor
* refers to Houtgast's piece on Haute Provence in the same issue.)
* (I assume the script-R signature stands for "Redacteur".)
* Comrie's remarks attacked
* "Dr. J. Comrie writes me: `I seem to have stuck my head in a hornets'
* nest. Everyone is attacking me, everyone is indignant about the
* physiological explanation I gave of this phenomenon.'" The editor
* replies that Comrie's remarks were, in fact wrong; but "the readers
* should have understood this, for the piece by Comrie was put on purpose
* into the number wherein also Dr. Houtgast gave his description of the
* green flash." [Note that Houtgast's flashes were at sunrise.]
* He cites Minnaert's book.
* (I assume the script-R signature stands for "Redacteur".)
* Comrie's JBAA article reprinted
* his JBAA article reprinted again (N.B.: NOT COPIED; not in paper files)
* O'C #20b
* uninformative but temps suggest inf.-mir. flash
* May be just an enhanced green rim
* Willy Ley's GF, with a gap between disappearance and GF
* Possibly a GREEN RAY?
* "Later I experienced .. being passed over by the slowly turning
* searchlight of a distant warship. Except for the difference in color the
* two sensations were exactly alike."
* O'C #231
* Good review in Swedish, but few references
* N.B.: The GF spectrum reproduced from Danjon & Rougier shows nothing
* (all black) on the page in our library.
* O'C #42
* SUNRISE IS BETTER?
* (short reports from all over)
* "M.Gentili of the Pic-du-Midi Observatory writes that the phenomenon
* `occurs every time the Sun sets or rises behind a distant object,
* mountain, or cloud, when the low atmosphere is not much absorbing (in
* winter or spring) -- I can say, perhaps two hundred times in seven years.
* The fact that it can be seen much more frequently at sunrise proves that
* there cannot be question of a physiological ``after image'' phenomenon.'"
* (Peter Doig was editor of JBAA from 1930-1937.)
* O'C #201
* GREEN RAY for sure; probably produced by a SUB-DUCT FLASH
* "The sun . . . had been below the horizon for an appreciable time before a
* vivid green ray was seen. The ray extended 1 - 2 degrees above the
* horizon and was emerald green in colour. It lasted about 8 - 10 seconds
* and most nearly can be described as resembling a green aircraft flare
* hanging in the sky."
* "Note. . . . The radio-sonde ascent at 2000 showed a shallow layer of
* cold air from the surface to 935 mb. where a rise in temperature began.
* The temperature drop in the cold surface layer was 14°."
* CUMULUS
* ". . . seen above distant Cu . . . ."
* 3 flash sequences:
* a) flash above cloud and again at horizon (18 Dec.);
* b) "final colour violet" (8 Dec.);
* c) "blue-green to apple-green (very bright), the blue-green again."
* (30 Dec.) [probably due to effect of waves on ship]
* A first-timer sees an inf.-mir. flash
* Followed by 2 brief reports, from J.Blom and C.J.P.va Duin.
* Blom reports light blue *before* emerald green at sunset.
* O'C #265
* Classical OMEGA display described, including the introductory LINE
* explicit evidence for ADAPTATION:
* "Auparavant, je constate que lorsque je regarde à l'oeil nu le ciel
* rouge à côté du Soleil, je vois le Soleil rouge; puis, quand je fixe
* le Soleil, il me paraît par moments vert-jaune . Dans la jumelle, le
* Soleil paraît toujours jaune-orangé avant le verdissement final."
* Early AIRPLANE FLASH at 8000 ft.
* "If what I saw was a fair example of the green segment I was left with
* the impression that the phenomenon was rather fleeting and not very
* impressive, and that it would usually escape casual observation."
* PHOTOGRAPHIC DIFFICULTIES -- evidence for visual adaptation?
* EARLY MOVIE ATTEMPT
* "It was perhaps the finest example I have seen . . . . The film, when
* developed, was very sharp and clear and gave a beautiful picture of the
* sunset, but the flash did not appear."
* D. Moreau Barringer
* O'C #8
* STATISTICS: 26 yes, 13 not seen
* O'C #259
* Posthumous monograph of Frank Alvord Perret (1867 - 1943)
* Perret devotes nearly a column to "The `Green Ray'", ". . . a momentary
* flash of brightest green whose evanescent beauty invariably excites
* admiration, especially when a binocular or telescope is used.
* "Hesitant though I may be to say it, I believe the appearance to
* be purely subjective. The last-seen tiny segment of the sun's disk is
* still intensely brilliant, and its sudden disappearance leaves the retina
* abnormally irritated at this spot, yielding by reaction the complementary
* wave length, which gives us green. Yet I have seen the `green ray'
* described as wholly objective and capable of being photographed on a color
* plate. It would be interesting to know what process was employed . . . ."
* [Evidently this is an oblique reference to Kerolyr's Autochrome plates,
* as this must have been written before 1943.]
* "It will be evident that, by our hypothesis, the setting sun must
* be very red -- which indeed is normally the case -- in order to give
* the green flash. It was with interest, therefore, that I awaited
* a strongly yellow sunset, not uncommon in autumn. This, in fact,
* showed an intense violet flash without the least suggestion of green,
* and I subsequently observed a pure blue ray from a yellow-orange sun.
* There is, then, no green or other flash at the horizon or upon the sun."
* A fine example of the fact that false theories can produce true
* predictions; only contradictions can reveal and eliminate error.
* [As the low sun cannot appear yellow without retinal bleaching, which
* is stronger when the extinction is less, the observations are equally
* consistent with variations in atmospheric extinction.]
* This is Carnegie Institution Publication 549.
* Drawings showing a mock mirage off San Diego
* Nice term "crown" used to describe the piece that breaks away.
* The observer says the "edges" of the crown were initially red; I think he
* meant the upper and lower edges, not the *ends* as the Editor assumes.
* Drawings of mirages and distortions of setting sun; GREEN RAY ??
* "Finally the green flash was observed with green rays quite distinct."
* But, alas, no drawing of the "green rays"!
* "Air temperature 36° F., sea 37°."
* Some of the sunset drawings show impossible structures.
* Rear-Admiral Bongrain offers a curious phrase
* ". . . compare à un effet de capillarité optique entre les bords de
* l'arc du Soleil et l'horizon."
* So I suppose this is an Omega forming (inf.-mir. display)
* useless
* Translation of article from Bull.Mens.Soc.Astron.Pop.Toulouse
* standard account of the usual (wrong) theory.
* gross error: blue, etc. supposedly absorbed by water vapor.
* O'C #110
* SHARONOV's actual observations
* "1. A green flash can be observed repeatedly on a given evening (in
* our case, up to 6 times), accompanying the passage of the upper limb of
* the Sun not only through the line of the visible sea horizon, but also
* through the edges of cloud strips, strips of mist and boundaries of
* atmospheric layers that are invisible, but are revealed by causing
* deformations of the solar disk.
* 2. A green flash often accompanies the formation of `plumes', being
* separated from the upper edge of the disk on passage of the latter through
* the indicated boundaries. Sometimes it has the appearance of a green
* distortion at the side limbs of the solar disk.
* 3. A `plume' has the appearance of an elliptical or lens-shaped patch
* being separated from the solar disk, at first having the brightness and
* color of the Sun. A green tinge appears at the right and left edges of
* such a patch and quickly spreads along the edge, enveloping it from both
* above and below, and enclosing the red center in a bright green ring.
* Spreading to the center, the green color fills up the whole area of the
* plume, giving a bright green flash at the moment of final disappearance.
* 4. A green flash is often seen when the solar disk is weakly colored
* and very bright (dazzling), but is not seen if the solar disk is dim and
* red (evidently, owing to strong attenuation of the green rays). It is
* also not observed at `linear' sunsets, when before disappearing the solar
* disk is stretched along the horizon in a bright narrow strip, whose width
* gradually decreases.
* 5. For a moderate degree of weakening of the solar light the green
* flash is reduced in intensity, but does not change its saturated
* blue-green color, which points to the idea of a monochromatic character of
* the phenomenon.
* 6. The hypothesis, usually cited in textbooks, just explaining the
* phenomenon of the green flash by spectral dispersion in the terrestrial
* atmosphere, agrees poorly with the particulars of observed pictures at
* the edge of the sea if its usual form is borne in mind."
* В. В. Шаронов
* Наблюдения . . .
* Астр. Цирк. No. 108, 9-10 (1950)
* O'C #276
* A.D.Ross -- mentioned by title only
* This is just a meeting report: "The delegates presented in all 19 papers
* . . . [including] `The Green Flash at Sunset' by A.D.Ross (leader of the
* Australian delegation . . . )". But Rosanne Walker, the former librarian
* at the Adolph Basser Library of the Australian Academy of Science, has
* checked the conference Proceedings, and found that they do not contain
* the scientific papers.
* Ross was a solar astronomer at the U. of Western Australia; he had
* several papers in MNRAS in the early 1920s. Maybe his GF paper was
* published in Aust.J.Phys. in the early 1950s???
* This report is the lead item in the "News and Notes" department.
* Feb. 9 issue
* GF with drawings of DISTORTED SUN
* SHARONOV's excellent article
* There are some useful observations here; in particular, Sharonov has
* recognized typical sunset sequences (see Fig. 1, where a "standard" sunset
* is followed by Fisher's type B and type A sunsets, with a mock-mirage type
* B at the last. The last 2 show inf.-mir. GF and MM GF, respectively.)
* He did not understand what he was seeing, but his observations are
* careful, and the descriptions of the various types are now more detailed
* than in his Astron. Circ. note.
* Unfortunately, he chose to portray "typical" examples here rather than
* actual individual cases; in particular his Fig. 3 has all sorts of sunset
* forms run into one another indiscriminately. His observations, like mine,
* were made from 100 m above the sea, so he got to see the major types.
* "Various hypotheses have been proposed to explain the green flash, but
* not one of them can explain all the details of this phenomenon. In
* meteorology textbooks and handbooks of atmospheric optics the phenomenon
* of the green flash is usually explained as the narrow segment of the
* setting Sun, drawn out by atmospheric dispersion into a vertical spectrum,
* so that the violet color appears above and the red below. Therefore the
* red end of the spectrum sets before the green, and as the blue and violet
* rays are completely scattered in the depth of the atmosphere, then at some
* moment one green ray reaches the observer and produces the impression of a
* green flash.
* "It is necessary to recognize that such an explanation is insufficient
* to account for the actual picture of the green flash. First of all, it
* is repeatedly recorded that if the cause lay in the phenomenon of normal
* spectral dispersion, then the green flash should be observed very often,
* but in reality it seems to be a fairly rare phenomenon and it usually does
* not appear even with good atmospheric transparency at the horizon.
* Further, the order of appearance and distribution of the green color along
* the edges of ``plumes'', described above, does not correspond to the fact
* that if it were due to a single dispersion, the green rim would appear
* only on the upper edge of the ``plume'', while the lower edge should be
* red, but in reality the green border envelops the ``plume'' both from
* below and above. To fit this observed picture with the dispersion theory,
* it is necessary to assume that a ``plume'' consists of two images of a
* segment of the disk, joined at their bases. In this case, the upper of
* these would be the true segment, and the lower its inverted reflection in
* an atmospheric layer, formed like an inferior mirage".
* But unfortunately he thinks the color is independent of the extinction,
* and hence inclines toward the anomalous-dispersion theory, though he
* recognizes that there are no strong telluric lines in this part of the
* spectrum, and that Tikhov's work shows that even near the strong ones in
* the red, the anomalous dispersion is very small. The physiological
* contrast theory is even worse, so "at the present time we have no
* satisfactory theory of the green flash and therefore the question
* requires further investigations."
* The article has a fair bibliography of earlier Russian works.
* В. В. Шаронов
* о «Зелёном луче»
* Природа No.7, 53-55 (1951)
* NOTE: issues of "Priroda" are separately paginated, so the issue
* month and/or number MUST be given.
* O'C #277
* PUTILIN observes from 10, 50 and 200m and sees GF abundantly from lower
* two, using 8x binocs.
* "The observations show that the green flash does not seem to be such a
* rare phenomenon as is generally thought."
* "Both the color and form of the green flash were different on different
* days."
* CLASSIFICATION into FOUR TYPES:
* "I. Vague formless `green flash' with the aspect of a horizontal strip,
* separated by a dark strip from the horizon. . . . The strip gradually
* shrinks and disappears, not reaching the horizon. Duration not long,
* 2 - 3 seconds.
* II. The green flash has the form of an unsymmetrical oval, separated
* from the horizon. The major axis is parallel to the horizon. The upper
* part of the oval is usually more convex than the lower. The coloring in
* green light proceeds simultaneously in the whole area of the oval. . . .
* The oval disappears at some height above the horizon (does not set behind
* the horizon). Duration 7 - 10 seconds.
* III. The green flash appears to be a segment, not separated from the
* horizon. The green color in most cases begins at the corners of the
* segment, and then, as the sea reduces the size of the segment, spreads to
* its whole area. Duration on the order of 10 seconds.
* IV. The green flash appears to be a segment, not separated from the
* horizon. After becoming green, the segment gradually acquires a blue, and
* sometimes even a violet color. This type is characterized by exceptional
* brightness, distinctness, and purity of the observed colors."
* "A green flash of the 1st type is observed when conditions are not
* optimal. At this time usually there is light haze at the horizon and the
* atmosphere at the horizon is not quite calm. The setting disk of the Sun
* has an orange-red color and undergoes moderate distortions (except, of
* course, the usual flattening due to refraction).
* On the other hand, a flash of type IV (`blue flash') is observed under
* unusually good atmospheric conditions, when the atmosphere has unusually
* high transparency and tranquillity. At this time the setting disk of
* the Sun appears very bright, has a yellow color and hardly shows any
* distortions."
* "It's interesting that in the case of cloudy weather the visibility of
* the green flash often happens better than with a clear sky. Sometimes
* the flash was not observed with a completely clear sky . . . , or was
* observed very weakly.
* It's possible to think that the presence of clouds can create better
* conditions for the appearance of the green flash than with a clear sky
* because of the calmer condition of the atmosphere in its lower layers."
* Note: for details and drawings, see his 1953 paper.
* И. И. Путилин
* Зелёный луч
* Астр. Цирк. No. 18, 9-11 (1951)
* O'C #263
* std. inf.-mir. GF; water measured 2 deg. warmer than air
* Possible GREEN RAY (according to Editor's comment)
* "One and a half seconds after the sun's upper limb had disappeared below
* the horizon, a green flash was observed which lasted for 4 seconds. To
* the observers it looked like a green occulting light flaring up on the
* horizon."
* O'C #306?
* Captain Brett Hilder's letter on use of GF to determine LONGITUDE
* (see also Rawlins, 1979, in DIP file)
* This is evidently what Cotter gets exercised about in 1968 !
* The Editors reply mentions Weston's method for using sunrise and
* sunset: "Tables . . . were published by the Admiralty in 1851."
* [These must be the tables mentioned in Nautical Mag. 17, 620 (1848).]
* "It was certainly to my knowledge used in about 1925, and for the most
* part it seems to have been handed down by word of mouth."
* Hilder's letter is followed by a somewhat longer editorial comment.
* See Hilder's followup in vol. 6 (1953) in "Variable Refraction" file!
*
* N.B.: There are two things called "Journal of the Institute of
* Navigation." This one (called "Journal of Navigation" since vol.25, 1972)
* is published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC, from 1960 to 1992.
* VENUS flash in Ashkhabad
* Cites Sharonov's 2 papers (above) and Putilin in No.118.
* Remarkably, the place where Venus set (at a 50-km distant mountain) was
* 4 deg. above the horizontal! Repeated observations gave a short flash
* in every case.
* O'C #275
* GF at Sea of Azov
* Only 1 successful observation from "several meters above the sea."
* Looming allowed western shore to be seen a few minutes above the sea
* horizon. No deformations aside from flattening. The image of the far
* shore divided the Sun into 2 parts (probably this means an inferior
* mirage). The lower part disappeared first [because of perspective
* effects -- aty]; each part gave a GF on disappearing.
* Most attempts were frustrated by clouds or haze at the horizon, so
* conditions in the southern Ukraine were judged to be unfavorable for GF.
* O'C #292
* FIRST COLOR PHOTO ? (But cf. Touchet, 1932, and Dauvillier, 1962)
* METEOROLOGICAL DATA show sea 1.4C warmer than air.
* Drawing suggests Omega before GF
* O'C #48
* GOOD OBSERVATIONS, but badly confused in trying to explain them:
* (garbled explanation involving "diffraction".)
* "From numerous personal observations . . . the green flash can be observed
* under conditions of extreme cloudiness, haze and humidity so long as the
* horizon is visible . . . ."
* ". . . the flash is of very weak intensity when compared to the normal
* brilliance of the body observed."
* nice drawings of Joule's 2 types of GF
* REVERSED ORDER:
* "On one occasion, under conditions of abnormal refraction, when the Sun
* had assumed grossly distorted forms, the detached segment showed a
* bright red light at its outer edges prior to turning green. This is
* most unusual . . . ."
* "Observations of the green flash are best carried out through
* binoculars; it is quite comfortable to look at the setting Sun when
* three-quarters of its area is behind the horizon, except, possibly, when
* there is a total absence of haze; then, however, the last stages of the
* green flash phenomenon are never too bright."
*
* N.B.: There are two things called "Journal of the Institute of
* Navigation." This one (called "Journal of Navigation" since vol.25, 1972)
* is published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC, from 1960 to 1992.
* O'C #284
* DOUBLE FLASH -- sounds like a MM, then an inf.-mir.
* "Le temps était brumeux, soudain la partie supérieure du Soleil
* (en forme de petite calotte) disparuit et fut remplacée par une plage
* vert intense; puis la forme normale reparut et le Soleil se coucha
* définitivement sous la mer, en produisant au moment de sa disparition, un
* second rayon vert, mais bien mois intense que le premier."
* a popular account full of errors; at least he has SEEN some flashes
* "Editor's Notes" on p.3 says Father Raymond Devas "is at present a
* parish priest in Grenada." They spell him "Raymond" on Contents page
* but he is "Raymund" in the by-line.
* Much nonsense about refraction; but he reports seeing a 3-second flash.
* NOTE: each issue separately paginated, so issue number is vital.
* The title page of the volume says "1951-52" so we will guess 1951.
* The OED's date of 1950 is wrong. Separate issues are not dated.
* VENUS flash; no useful details
* Details of Masao Hanzawa's GF photograph described:
* "The copy sent, a half-tone reproduction, clearly shows the green
* segment of the sun on the sharp sea horizon. There is no apparent
* distortion."
* GREEN RAY? observation with DARK STREAK at sunrise
* "Jedesmal beim `Durchstoßen' einer Sprungschicht, die sich bisweilen
* durch einer zarten Dunststreifen verriet, erschien über der
* Sonnenscheibe ein kleiner grüner Fleck, der bei Vereinigung mit der
* höhersteigenden Sonne deren Farbe annahm, während das Grün nach
* links und rechts außen rückte und schwächer wurde. Plötzlich,
* offenbar bei erreichen einer besonders ausgeprägten Sprungschicht,
* plattete sich die Sonnenscheibe stark ab, hierbei erschien etwa eine
* Sekunde lang ungefähr ein Drittel Sonnendurchmesser über derselben
* ein fast ebenso ausgedehntes büscheliges zartgrünes Licht, der
* Grüne Strahl. Im nächsten Augenblick buchtete sich die Sonnenscheibe
* mit einem Ruck auf das gesamte Gebiet des Grünen Strahles aus, also
* um etwa ein Drittel ihres Durchmessers, sie war damit tatsächlich
* `gesprungen'."
* HANZAWA reports his photograph to M.O.
* "Air temperature was 30.9 F, the sea being warmer, 33.8 F."
* "As Mr. Hanzawa remarks, this is probably the first colour photograph
* taken of the green flash." Sorry, guys. Maybe third?
* Jacobsen's SPECTRUM
* As the flash is in fact dimmer than the red or yellow Sun that precedes
* it, Jacobsen's results are spurious, and probably due to inter-layer
* adjacency effects in the color film used.
* This paper was reprinted as Contrib. DAO no.26 -- thanks to
* Brenda Corbin of USNO library for the reference!
* Theodor Siegumfeldt Jacobsen -- thanks again, Brenda Corbin!
* NOTE: The L.A.Times carried Jacobsen's obituary on p. B11 of the
* Orange County edition, July 24, 2003. He was for many years the only
* astronomer at University of Washington. No mention is made of his
* connection with DAO.
* O'C #56
* evidence for FATIGUE?
* "L'observation a été suive par moi aux jumelles prismatiques 6x30.
* Madame Biemans, qui a observé à l'oeil nu, n'a pas vu le rayon vert."
* Editor's reply to the Biemans letter
* numerous references in l'Astronomie, La Nature, etc.
* Believes Jacobsen's paper.
* O'C #83
* BLUE-GREEN flash over MOUNTAINS
* ". . . there was a stream of maritime polar air; visibility was excellent
* . . . with a NW wind never exceeding force 2. The sun went down without a
* tinge of ruddiness, and at the last glimpse was bluish-green, a colour not
* often seen even in coastal observations."
* Comments on the Marine Obs.21,216(1951) report
* "It would be interesting to look for this spectrum from a position where
* Jupiter or Venus or other bright planet or star rises or sets in a sea or
* flat plain horizon." (Unaware of numerous such observations already!)
* O'C #305
* Further comments inspired by the Marine Obs. report
* "The dark spaces in such an atmospheric spectrum can be simply explained
* in terms of atmospheric layers of different densities which produce rapid
* changes in the refractive index. Such variations in refractive index are
* also responsible for the `notched' appearance of the setting sun which can
* often be seen. On these occasions it is sometimes possible the see the
* green flash several times as each `notch' reaches the upper limb of the
* sun."
* Thackeray's comments about the "dark spaces" in the spectrum must refer
* to the chromatic scintillations that run through the spectrum, as it
* is swept across the atmospheric turbulence by the Earth's rotation.
* O'C #138
* May issue
* An astute Rear Admiral's REVIEW of flashes, with a wartime OBSERVATION
* Altogether a splendid account!
* Begins with Humphreys's "proverb", and an account of a blue flash seen
* off Okinawa from the carrier U.S.S. Independence in April, 1945, that
* "after thirty years at sea, was the first I had heard of THE FLASH."
* "Now, what is this thing that no one you happen to be with has
* seen or heard of, but which is as old as the Ocean and probably has
* been obscurely mentioned in thousands of old papers and argued over in
* forecastles and cabins for centuries?"
* ". . . A recent news dispatch reports that two ladies connected with the
* University of Washington have good color pictures, taken in Hawaii of the
* green." [These would be the ones referred to by Jacobsen (1952, 1953).]
* "Without looking it up I can tell you what you need if you want to take
* pictures. A long focus camera, a telescope lens, fine grained film of 35
* mm. or larger should do the trick. A normal exposure, say one-fiftieth
* at f.8 would be enough." And this, 5 years before O'Connell's book!
* ". . . in a week or less I was able to get the last of the sun right
* in my 7× binoculars for a fine clear sight of the blue button
* that sat on the line like a bright bead and snapped out like a spark.
* From then on for the rest of the summer of 1945, it appeared many times,
* and it became commonplace to those of us who frequented the bridge.
* And I began to observe something else. `Good' conditions started of
* course with an unobstructed sky horizon clear and sharp. If the sun
* got down to within one diameter of the line and was still quite yellow,
* that meant that the air behind the horizon was clear too and conditions
* were very good. This was especially true if the sun's surface was viewed
* through glasses had a `boiling' appearance. When things were like that,
* a little blue fillet showed at each end of the line which the water cut
* across the sun. As the sun sank, the blue spots followed the sun's rim,
* receding to the maximum diameter and then approaching each other as the
* last half of the sun disappeared. Just as the thin red rim of the sun
* sank, the two sparks joined and it was this instantaneous doubling of
* the blue light that makes the appearance of a flash.
* "After the Tokyo surrender I began trying to catch this thing on
* film and immediately found out why it isn't more widely known. In the
* first place, only on very, very, good days does the joining of the
* sparks bring the intensity up to a point visible to the naked eye. . . .
* I got a good many feet of pretty sunsets and, between Midway and Iwo,
* a few fair frames of the spark.
* "Is there a scientific explanation? For me it lies in the interaction
* of two effects. Refraction. . . is least at the red end of the spectrum
* and increases through yellow and green to the blue end. And, dust and
* moisture interfere more with blue light and less with green, yellow
* and red. . . . The red strikes through better than all the rest and its
* brightness blots out the other colors. But, just for an instant, when
* the red is cut off, the blue's still showing above the waves and we get
* the BLUE FLASH.
* "The next time you are near Agrihan or north of there to Japan,
* or even up on the eastern shore of Lake Michigan and a cold front has
* swept off the dust and left a sparkle in the air -- take a look.
* "The foregoing was written three years or more before I was able,
* through the kindness of Dr. T. S. Jacobsen of the Department of Astronomy,
* University of Washington, to obtain a couple of references and to find
* those references and others at the library of the Naval Observatory. . . .
* A famous French author described, in 1882, its most usual appearance. . . "
* [here he quotes Verne's description of the color].
* "It has been widely observed and extensively written about, the
* [sic] reference alone listing no less than 178 other references."
* [That would be Willard Fisher's 1921 review.]
* "The phenomenon of the BLUE (or GREEN) FLASH is spectacular, famous,
* mysterious, controversial and, therefore, altogether the most interesting
* of the minor solar spectacles that Naval personnel have opportunities
* to see."
* NOTE: Nolan M. Kindell was Naval Aviator Number 370 in WWI, according to
*
* http://www.navalaviationmuseum.org/ExhibitsAndCollections/Exhibits/Exhibits-Frontiers/WorldWarI/Views-of-World-War-I-Exhibit-(1).aspx
*
* He was Captain Kindell when in command of the Independence , retiring
* as a Rear Admiral in 1948.
* May issue
* Followup to the previous item: another Rear Admiral mentions CALM AIR
* "The meteorological phenomenon of the blue flash is a fairly
* commonplace occurrence in the Mediterranean particularly in the summer
* months. It was observed quite frequently by this writer during the
* three years he served in Algeria and Tunisia. There, it is known as
* le rayon vert -- the green ray or beam -- and has engendered the
* superstition that it brings good luck to anyone who sights it. . . .."
* ". . . It is presumed that that clear, transparent hue is produced
* by the blending of the pure-yellow rays from the setting sun with
* the refracted or reflected blue coloration of the surface of the
* Mediterranean. [!]
* "The factors which seem to govern the possibility of observing
* the flash are (1), extremely dry atmospheric conditions which are
* usually prevalent from May through September in that locality; (2), a
* cloudless horizon which is generally a corollary of and is present under
* factor (1) at that season of the year; and (3) a practically dead calm.
* Given those three conditions, le rayon vert can almost invariably be
* observed provided the observer maintains a superlatively alert watch
* focused on the sun's upper rim as it dips below the horizon. A flat
* calm is the one factor that is most likely to be unavailable. . . ."
* (He then gives a clumsy description of the sea breeze.)
* July issue
* peculiar sunrise flash report; probably just the inf.-mir.flash
* "A brilliant green flash, lasting for some two seconds, was observed at
* sunrise. In contrast to the green tinting of the sun's upper limb which
* is frequently observed, on this occasion it was completely obscured by a
* vivid green light, distinctly round in shape, as if from a green-shaded
* searchlight. The wind was SE force 3 and the sea was slight. . . . Air
* temperature 52 F, sea 53."
* Possible Wegener's bar? Double flash at sunset
* CUMULUS CLOUD-TOP GF and another cloud-top BLUE flash (with binoculars)
* Useful editorial comment: ". . . there is a somewhat better chance of
* seeing the flash as blue or even violet, because at a little distance
* above the horizon some light of these very short wavelengths may be
* transmitted . . . . The writer of this note has similarly seen the blue
* flash at a cloud edge."
* BLUE CORNERS and sunset distortions
* DRAWINGS show MM layers above a square Sun, and a very flattened disk
* "1 minute before sunset".
* 2 GFs reported with no useful data
* "a brilliant green flash . . . duration 1 1/2 sec" 2 days in a row.
* GREEN and RED FLASHES
* A Chief Gunner proves no match for a couple of Rear Admirals (above)
* ". . . this writer has had many opportunities to observe the setting
* sun off the coast of California and on numerous occasions has seen the
* `Blue Flash.' Some flashes were very dim; others relatively bright.
* ". . . I would like to set forth a simple and obvious theory of my own.
* This theory might have been raised in one or more of the various articles
* and references on this subject, but has not to my knowledge. The flash
* is an optical illusion." [Has R. Cann Lippincott been resurrected???]
* ". . . the brightness of the sun compared to its surroundings and the fact
* that observers are staring at it as it disappears causes a complementary
* image to appear briefly at the point the sun has vacated."
* What can one say in response this ignorance, refuted many years before
* by Rudaux's photography? Why did the Proceedings publish something so
* obviously uninformed?
* "Naturally, my theory would be invalid for a flash someone has
* captured on film but I believe it will account for the vast majority of
* `Blue (or Green) Flashes.'"
* August issue
* PUTILIN's detailed observations (see his note in Astr.Tsirk.#118,1951)
* complete with numerous DRAWINGS indicating progress and coloring.
* This is written in the wordy and repetitive Soviet style, so it's
* tedious reading. However, the details of the observations are worth the
* effort. The 4 classes are described a little more than in the A.C.
* version. There was also an attempt on 13 Aug. to keep the left eye closed
* until the Sun was half set, so as to look for physiological effects;
* however, this failed, and the appearance was identical to the two eyes.
* Putilin draws a careful distinction between sunsets in which the "segment"
* touches the horizon, and those in which it is raised (a real inferior
* mirage). The former examples plainly show that a GF can be produced when
* the gradient at the horizon surface is insufficient to produce image
* inversion (either because of small temperature difference or because the
* waves truncate the lower part of the surface layer). In every case the
* green grows in from the ends, so the gradient at the surface is plainly
* visible, even if an inferior mirage is not produced.
* One can certainly agree that "From everything described above we may draw
* the conclusion that the green flash is a more complex and interesting
* phenomenon than is usually thought."
* O'C #264
* A novice asks the "Interesting question: from what height above sea
* level is the Green Ray best seen?"
* 2 well-described inferior-mirage flashes from 8 m height, and a
* mock-mirage sunset with flash.
* O'C #184
* useless; first-time observer. Volume number not certain.
* O'C #254
* "A prolonged green flash of about 2 seconds"
* Probably THE BEST article on GREEN RAY displays
* Here's an author who seems to take the term "green ray" literally!
* He appears to be a sailor who made a hobby of collecting green flashes
* -- or rather, green rays. The whole article deserves to be translated;
* but here are a few samples:
* "From 1895 to 1948 I sometimes succeeded in observing the green ray just
* after sunset. . . . sometimes from shore, sometimes from ship, and always
* with the naked eye.
* "Not once did I succeed in seeing the green ray before sunrise.
* "In the tropics the green ray after sunset sometimes was seen as a
* bundle of rays, sometimes only 3 -- 5 rays; it appeared instantly after
* sunset, lasted 0.3 -- 0.4 sec. in a vertical position, then instantly the
* top turned over to the right (in the Northern Hemisphere), so that the base
* of the bundle remained stationary, and the phenomenon vanished; the general
* duration is not more than 0.5 sec. In the Southern Hemisphere the green
* ray turned over to the left. . . . The height of the green ray or rays was
* generally not greater than the diameter of the setting Sun; the color of
* the ray is pale whitish green. The green ray, falling from its vertical
* position to the right or to the left, went out, not reaching 20 -- 30
* degrees of the horizon.
* "The green ray at temperate latitudes is almost the same at in the
* tropics, but somewhat deeper --- without whiteness; it rose in the form of
* a single ray, as if instantly blazing forth from the point of sunset,
* remained vertical 0.5 -- 0.7 sec., then fell over to the right or left
* (according to the hemisphere) and disappeared, also without reaching
* 20 -- 30 degrees of the horizontal; the width of the ray is almost
* identical from bottom to top, but the top always was more pointed; the
* height of the ray was typically the diameter of the Sun; the whole
* phenomenon lasted 1.0 -- 1.5 sec."
* (Details are given of a few of the observations.)
* "According to the color and shape of the Sun itself shortly before it
* sets, it is possible to foresee in advance whether there will or will not
* be a green ray."
* "The green ray appeared only when clear calm weather set in . . . .
* Usually 1 -- 2 days passed before the appearance of the green ray and
* as many again after it was gone, calm, clear weather. The very
* appearance of the green ray also was a forecast of good weather."
* [This is the 3rd such statement: cf. Trève (1885), "Another Engineer
* Officer" (1904), and also Wegener (1926).]
* He also claims the best time of year to see this thing is around the
* autumnal equinox, and the best month is September (in the Northern
* Hemisphere).
* There is also a claim that almost all observations were in years of
* sunspot maximum, except for 1943.
* (Based on records kept for 54 green rays, with at least another 50 not
* recorded.)
* [in the Jan/Feb. issue (no.1), 1954]
* O'C #167
* A 1954 newspaper clipping in Dutch found by R. H. van Gent in a copy of
* Flammarion's "l'Atmosphère":
* This appears to have been an Antwerp paper, to judge by the frequent
* references to Antwerp on the back side. It's a generally accurate
* account, and seems to be from a question-and-answer column. The main
* objection to this version would be the attempt to explain the loss of
* blue and violet by water-vapor absorption, which supposedly would
* explain why the GF is seen best at sea. But "It was photographed -- for
* the first time, we think -- by the French astronomer L. Rudaux. Seen
* with a strongly magnifying telescope -- e.g., 100 times -- one sees the
* ray spread out as if in a spectrum." (Evidently this refers to the
* green rim.) There is also the usual erroneous statement about "the
* American explorer Byrd, and the people of his expedition," who "could
* see the phenomenon in the Antarctic lasting 35 minutes."
* Curiously, it's signed: UNESCO.
* CLASSICAL WEGENERIAN BLANK STRIP + GF
* Gets a flash at the "lid" of the soup terrine, then a second one after
* the hourglass stage.
* "Offensichtlich hatten die parallelen oberen und unteren
* Begrenzungslinien der Erscheinung immer gleichen Abstand."
* Good description of Mock Mirage flashes.
* Thinks the intensity increases when it turns green (cf. Jacobsen):
* "Bemerkenswert ist die sprunghaft zunehmende Leuchtkraft."
* Terminology: "An sich ist die Bezeichnung Grüner `Strahl' sprachlich
* inkorrekt, ja geradezu irreführend. .. Ich konnte aber bisher stets nur
* ein Aufblinken feststellen, so daß ich die Bezeichnung `Grüner Blink'
* für richtiger halte. Leider ist diese Bezeichnung `Blink' gerade in der
* Meteorologie durch den sprachlich ebenso irreführenden Begriff `Eisblink'
* korrumpiert, so daß derjenige, der den Eisblink kennt, unter einem
* Grünen Blink wieder etwas anderes erwarten könnte."
* BLUE FLASH at SUNRISE over Atlas Mountains
* "At sunrise an instantaneous bluey-white flash occurred, followed by a
* deep red." The really interesting part is that the Sun became RED ABOVE
* and YELLOW BELOW -- see the DRAWINGS of interesting distortions.
* Note that the change in the lower part from red to yellow as the Sun
* rose is evidence for ADAPTATION.
* [This probably should be filed with the "distorted Sun" file.]
* Several brief observations from Marine Obs. follow (all on same sheet):
*
* "A cobalt-blue flash . . . about 4 sec."
* "A brilliant blue and green flash . . . lasting 2 to 2 1/2 sec."
* ". . . a brilliant green flash which turned to cobalt blue at the last
* instant. The whole phenomenon lasted for 3 1/2 sec (timed)."
* SUNRISE FLASH
* "At sunset, as the upper limb of the sun dipped behind a band of Sc, it
* turned from orange to whitish-yellow . . . , then flashed a bluish-purple or
* violet colour. Air temp. 72.3 F, . . . , sea 73.4."
* GREENISH-PURPLE ???
* "At sunset a greenish-purple flash was observed" (!)
* Probably the observer means green and changing to violet, perhaps with
* both colors visible together?
* ASYMMETRICAL FLASH (cf. ATY photo of 30 March 1998)
* "The flash started at the left-hand side and moved rapidly along the
* segment which, at the beginning was about 2 1/2' deep."
* Crepuscular rays after GF
* COBALT BLUE flash
* "no abnormal distortion was apparent", and air = water temp.
* SUNRISE flash, PURPLE --> GREEN
* 2 BLUE FLASHES over MOUNTAINS at SUNRISE
* useless
* NO GF, but useful sunset CONTRAST EFFECTS
* ". . . this same continuous cloud sheet glowed a coppery-red . . . .
* . . . the fading greens of the trees and meadows had been transformed to a
* brilliance which might be described as `fluorescent'. So brilliant were
* these greens that I developed a headache from the strain of observing."
* GF in TREES on distant hill
* "Die Sonne ging hinter einem 15 km entfernten bewaldeten Berge . . . unter
* und war dabei hell orange gefärbt."
* NOT "Green Ray" display; the "rays" here seem to be crepuscular, seen
* green only by contrast. The Editor correctly notes this, citing
* M.O.24,213.
* Note: the "Green Sun and Moon" reports immediately before this are NOT GFs
* This is a trivial and non-useful observation.
* Navigation = Journal of the Institute of Navigation (at UCLA, apparently)
* Entirely derived from Aitken's ASP Leaflet, Fisher in PA, and Groff,
* with some errors introduced (e.g., calls Danjon "Donjon".)
* N.B.: There are two things called "Journal of the Institute of
* Navigation." One (called "Journal of Navigation" since vol.25, 1972) is
* published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC from 1960 to 1992. Yet another "Navigation"
* is published in Paris!
* This is the LOS ANGELES version.
* NAKED-EYE VENUS GF that "lasted for several seconds"
* Editor notes a similar observation: M.O.23,202(1953)
* also Jupiter GF
* Possible GREEN RAY?
* "Viewed through glasses (7x) the flash could be seen for 7 to 8 sec,
* rising to several minutes of altitude, where there was a thin line of fair
* weather Cu."
* VENUS BLUE FLASH
* VENUS green flash
* What the Editor calls "twilight due to the planet" is its aureole.
* TIMED GF: "a jade green flash of 2 1/2 sec (timed)."
* The "ball of pale green, perhaps half the diameter of the sun," that
* "pulsated for at least 5 sec" after sunset was probably an afterimage?
* UNSATISFACTORY, for lack of details.
* LUNAR GF with binoculars
* Ed. notes that Moon's age was only 6.3 days.
* Classical RED FLASH below cloud
* Ed. notes the only similar report in M.O. 23, 144. July 1953
* useless: "a photograph has been made" is the only substantive content.
* Of minor historical interest in that it precedes O'Connell's book.
* "The evidence was clear that it was a morning of unusual refractive
* properties, as radar signal-echoes were being received from far beyond
* horizon-range. Downward refraction of centimetric waves is known to be
* due to low-level temperature inversion. . . ."
* MOCK MIRAGES with SUNRISE green flash (described; no figures)
* "Am 19. März 1955 ging die Sonne in einer Dunstschicht auf, die oben
* scharf begrenzt war. Beim Durchgang durch diese Schicht zeigte die Sonne
* die typischen scharfen Einschnürungen und abgerundeten Ausbuchtungen. . . .
* "Als die Sonne noch etwa zwei Sonnendurchmesser unterhalb der
* Dunstobergrenze stand, erschien auf dieser Obergrenze ein grünes
* `punktförmiges' Licht, das sich seitlich rasch ausbreitete."
* Remarkable for the large separation!
* Werner Weigel, Brocken
* superb calculation of CHROMATICITY for 3 different AEROSOL amounts
* considers BACKGROUND CONTRAST and LIMB DARKENING
* but ignores molecular absorptions, and scales aerosol to Rayleigh
* airmass
* GF + crepuscular ray (unrelated)
* Editor says that "some form of green sky coloration" of this sort has
* been "classed as varieties of the green flash at sunset"; which is
* improper (even though they have actually done this; so beware!)
* CLASSICAL Inf.-mir. RED FLASH below cloud
* ". . . a piercing brilliant red flash . . . ."
* CLASSICAL Inf.-mir. RED FLASH of Moon
* ". . . a bright crimson flash, conical . . . as the lower limb parted from
* the small image left at the horizon."
* Indexed as GF but just a green CREPUSCULAR ray
* Seen in hilly country; lasted 6 minutes
* Note that the first author is given as "Chishko" in the responses (below)
* Majendie's AIRPLANE FLASH at 22,000 ft. -- White Ray?
* Inf.-mir. mirages of Sun and Venus; not useful
* Inf.-mir. mirage of Venus
* Some possibly interesting remarks about brightness changes
* double flashes on mountain peaks, and in valley between
* Crepuscular ray, not GF -- ignore.
* An odd description leading up to a GF. No useful data.
* ". . . an intermittent light green mist of varying intensity appeared to
* drift fairly rapidly across the sun's surface . . . ." [retinal bleaching?]
* GREEN RAY? Useful details are lacking: ". . . lasted for about 1 1/2 sec.
* It extended over an arc of some 5° and had an altitude of about 7°."
* "Rayleigh to the contrary notwithstanding, light cloudiness and
* stratified inhomogeneity of the western atmosphere do not invariably spoil
* the effect. I have repeatedly seen it when the sun's disk was grotesquely
* distorted and even striated."
* "I think it is likely that observable green flashes over land horizons are
* more frequent at sunrise than at sunset, since the morning terrain is the
* nearer to thermal equilibrium with its adjacent atmosphere."
* Responses to the crepuscular-ray observation of Chishko [sic] & Tabadze
* RED and GREEN FLASHES
* Ed.: "We now have four observations of the red flash. . . ."
* Again the editor cites M.O.23,144(1953).
* BLUE FLASH
* GREEN Inferior FLASH with elongated SUNSPOTS
* "The green flash was seen all the time the upper half of the sun was
* disappearing, approximately 30 sec; not only the detached pieces appeared
* green but the edges of the main body as well."
* VENUS FLASH
* Lovell refers to his movie of a GF (JOSA, 1955)
* Clearly a SUB-DUCT green flash!
* Sounds very like the flash of Wegener's Nachspiegelung .
* ". . . I arrived at the palisades overlooking the Pacific Ocean at Santa
* Monica, California, during sunset and was amazed to see two images of the
* sun, one directly above the other. The sun had already half set, so the
* images appeared as half disks. The upper image appeared appreciably
* larger than the lower one and seemed to rest upon a clear-cut stratum of
* cloud which was separated from the well-defined ocean horizon by a narrow
* band of clear sky. . . . The upper image diminished and soon disappeared,
* leaving only the lower partial disk. . . . As this remaining image decreased
* in area it gradually ascended and seemed to disappear into the lower
* surface of the cloud stratum above. As the final strip of this image was
* disappearing upward into the cloud, it turned brilliantly green and
* remained so for a few seconds."
* PROJECTION recommended
* (Nov. issue, but filed here to keep AJP items together)
* RED and GREEN FLASHES with "considerable mirage effect" at horizon
* P.P.O.Harrison again!
* SUNRISE BLUE --> GREEN flash
* ". . . a very brilliant deep blue flash followed by a brilliant green one.
* The combined flash lasted for 1 1/2 - 2 sec."
* TYPICAL NOVICE REMARK
* "As one who has twice seen the Green Flash, at sunset in the open sea,
* I was surprised to read that Mr. Majendie saw the flash while a
* considerable portion of the sun's disc was visible."
* "MOST DIVERSIFIED"
* ". . . it exhibits many different forms and is probably one of the most
* diversified of optical phenomena."
* GREEN RAY
* "When about three-quarters submerged, the red quite suddenly changed to
* bright green and a beautiful green aura spread outwards like a fan.
* Almost before I realized what I was seeing, the fan collapsed, the green
* arc of the sun disappeared and only a red glow remained. Total time,
* possibly 7 or 8 seconds."
* METEOROLOGICAL DATA showing INVERSION for Majendie's observation
* ADAPTATION!
* ". . . the large cream building to the east was so brilliantly illuminated
* with green, that my son whom I called to see it remarked that he hadn't
* noticed the workmen were using green paint!"
* Good DRAWINGS of typical "segment" growing green from ends inward
* Another classical cloud-base RED FLASH, at sunrise, by P.P.O.Harrison
* Naked-eye Moonset GF, "bright enough to be seen without binoculars."
* G. A. Bull cites Dietze, Rayleigh, and Minnaert
* in response to 20 March letter from A. R. C. Engels
* GREEN in setting JUPITER
* GREEN -> BLUE -> VIOLET FLASH
* Sunrise GF
* GREEN RAY?
* ". . . a slight green arc of about 4° span and 3° altitude was seen."
* Sunrise GF and classical RF "lasting fully 3 sec" below cloud
* VENUS GF and counter-image
* Sunrise GF, "observed through the ship's telescope"
* ". . . a small mushroom-shaped patch, emerald green in colour, appeared on
* the highest point of the green rim. The patch then became detached from
* the limb, rising a little, but remained visible for about 10 sec."
* Ed. says there were "coloured sketches sent."
* Botley refers to Simons
* VENUS GF, observed with binoculars
* compared to Biemans (1952) in C&T, but over mountains instead of sea.
* DITCHBURN's GF article in New Scientist
* The green rim "may be seen conveniently through a telescope with a
* magnification of about 20. . . . If a dark filter is used while following
* the Sun before sunset, it should be of good optical glass. Many plastic
* filters or dark glasses do not absorb sufficiently in the infra-red and
* continuous observation of the Sun through them is dangerous.
* "On some days the colour is more vivid and the last segment of the
* Sun above the horizon looks green at the extremities. The colour may
* move in towards the centre as the Sun disappears. This green segment may
* be seen by the naked eye or with hand-held glasses and may last five
* seconds. It is almost certainly due to `mirage effects' . . . .
* "But under certain conditions, which are fairly rare in Western
* Europe, the green segment becomes detached from the rim of the setting
* Sun . . . and remains as a vivid green `flash' after the Sun's disc has
* disappeared beneath the horizon." [Here he reproduces O'Connell's
* incorrect diagram of the mock-mirage flash.]
* He also garbles Minnaert's account of prolonging the flash to many
* seconds "by running along [sic] a dyke." Misunderstanding the effect of
* height, he then supposes that "He must have been assisted by special
* conditions at the horizon because the necessary speed . . . with a flat
* road and horizon is about 600 m.p.h."
* "The true green flash is somewhat capricious in its appearance both
* over sea and over land, as would be expected if it is essentially a
* mirage effect." He mentions (but does not cite) R. W. Wood's
* observation in this connection. But, seemingly unaware of the
* importance of extinction, he is surprised that it was not seen by the
* Novaya Zemlya observer. So, a mixed bag.
* Thanks to Ken Stone (of the Times of San Diego) for finding this!
* Their "free news website" cites this at
* http://timesofsandiego.com/life/2017/01/16/rare-green-flash-at-sunset-dazzles-san-diegans/
*
* This is the book mis-cited by Mrs. Bond in 1975
* ". . . legend has it that at sunset a great flash of green light spreads
* across the horizon. . . . as the sun went down, the triumphant shout of the
* believers, all of who swore they'd seen the flash . . . was followed by a
* derisive jeer from the infidels who said they hadn't."
* Note: "Eastwards to Singapore" is the chapter title
* Another book about a ship, with a casual GF mention
* This is about the British warship Hood , sunk by the Bismark.
* Ernle Bradford seems confused about color, as well as about the GF:
* "If the horizon was quite clear and the sea unruffled the old hands
* would say:
* `Now you'll see it! Watch for the green flash.'
* Just as the sun's rim dipped, if you watched carefully enough, there
* was a brilliant green flash -- or so they said. Was there really a
* flash, at that moment when the yellow disk fused with the blue sea?
* Or was it merely an optical illusion, caused by straining one's eyes
* into the flaming path of the sun?"
* (also: Hodder and Stoughton, London,1959)
* Lucien Poncelet first quotes from 2 letters from Ch.Biemans; then
* briefly mentions O'Connell's recent book.
* "La structure thermique verticale de l'atmosphère joue, semble-t-il,
* un rôle important dans l'intensité du phénomène, par l'action
* réfléchissante de couches d'air de propriétés optiques différentes,
* et dont la surface de séparation est quasi horizontale (inversions).
* Il y a souvent des réflexions apparentées aux phénomènes de mirage.
* Parfois un petit déplacement vertical de l'observateur lui fait perdre
* la vision du rayon vert."
* After noting that blue flashes are most common in highs with northerly
* winds, he says:
* "C'est d'ailleurs assez logique so l'on tient compte de ce que
* l'anticyclone est, en principe, un lieu où l'air subsident en altitude
* est relativement sec et pur, ce qui diminue la diffraction de longueurs
* d'ondes bleus, due en partie à la vapeur d'eau et aux aérosols."
* If we leave out "diffraction by water vapor", this seems to be the
* FIRST decent EXPLANATION of BLUE FLASHES.
* VISSER's review of O'Connell's book, ILLUSTRATED with spare copies of
* O'Connell's frontispiece (facing p.57).
* Technically, this should go in the "reviews of O'Connell's book" file;
* but as Visser is one of the few reviewers to know something about green
* flashes himself, I put it here.
* "It is an extraordinarily difficult task to photograph the green flash
* in a scientifically accountable way in all its capriciousness, its
* variations in shape, color, and brightness. What Treusch, of the
* Vatican Observatory, has achieved, with experience and patience, is certain
* not to be surpassed." [But Treusch's photographs fail to show all the
* GF phenomena, because he worked at 450 m above the sea!]
*
* "My impressions, summing up: The green light phenomenon is certainly not
* limited to the moment when the upper limb of the Sun and the Earth's edge
* come into conjunction. It includes more than just the light ``ray'' that
* the naked eye supposes it sees. Long before this supreme moment, the
* green itself develops at the extremely small edges on the upper side of
* the Sun, and then can extend more and more, up to the fantastic forms of
* which the photos give many impressive examples. But there never develops
* an actual green ray of light." [A footnote says: "Father O'Connell
* would certainly never agree with the communication in the international
* cloud-atlas (World Meteorological Organization, 1956, Vol. I, p. 75):
* ``Flashes up to an altitude of several degrees have sometimes been
* observed.'' Well, this is O'Connell's loss for having not seen what is
* visible near sea-level.]
*
* And: ". . . deformations of the Sun (notchings of the limb, the obscured
* strip), which must be ascribed to diverse discontinuous temperature layers
* of small vertical extent. The radiosonde measurements, which return the
* details of the atmosphere only in a very coarse way, probably cannot
* contribute to the explanation of these."
* Gerhart S. Schwarz's response to Smiley's review of O'Connell
* (placed here slightly out of order to be next to Visser's review, above)
* "Scottish belief has it . . . " once again.
* "The green ray can be seen only when one views the horizon from an
* elevation, and this -- plus factors of latitude, season, and weather --
* probably explains why few sea captains are familiar with it."
* (see the replies to this by Palmer and Smiley, in the Oct. 23 issue.)
* (31 July 1959)
* Editor notes that a lunar GF near 1st quarter is unusual.
* Double sunset due to "Very heavy SW'ly swell."
* Cloud flash, then horizon. No useful info.
* GF in NAVIGATION:
* Lieutenant Roger E. Ekman's dangerous suggestion; cf. Cotter (1968).
* "One additional line of position . . . that has often assisted me with
* very good accuracy, is an observation of the exact time of sunset and
* solution of a time sight."
* "If the navigator uses a good pair of 7× 50 binoculars and
* observes the last segment of the upper limb of the setting sun, a bright
* bluish-green flash may be seen. This phenomenon lasts about two seconds.
* By marking the time and solving the navigational problem for an altitude
* of 00° 00.'0, he may obtain the intercept. By coupling this intercept
* with the azimuth (amplitude) previously determined, he has a reliable
* line of position. This method may also be used at sunrise; however,
* the bluish-green flash from the upper limb is not as pronounced at this
* time. In using this means of gaining an additional line of position,
* the navigator does not have to consider such correction factors as height
* of eye, refraction, or parallax." The last sentence is simply incredible!
* Note that each issue is now paged separately; the month is vital!
* DRAWINGS of DISTORTED SUN before GF:
* DRAWINGS of SUN with green moving in from ends, as in Minnaert:
* Drawn as segment; but temps. fit Inf.-mir. better. (air: 70; sea: 74)
* curious verbal description of an "Omega" (inf.mirage) from a first-timer
* Certainly a classical example of the inf.-mir. flash;
* "It was quite cold" (though 14 June)
* Replies to Schwarz's letter (31 July issue) by Harold S. Palmer . . .
* ". . . Schwarz says that the green ray can be seen only from an elevation
* but does not say how great an elevation . . . .
* . . . I have seen the green ray several dozens of times when my eyes were
* about 16 feet above sea level.
* "I have also seen the green ray from shipboard . . . .
* "Most remarkable, however, was seeing the green ray once from the
* observation platform at the rear of an eastbound train somewhere on the
* Great Plains."
* . . . and Charles H. Smiley, whose review started all this.
* Schwarz's comment "is misleading". And Smiley has noticed the
* mock-mirage flash: "From an elevation, the green flash may at times
* be seen before the sun sets. On such occasion, two notches may be
* seen on the sides of the sun, and these notches coming together at the
* top of the sun result in a green flash."
* O'Connell's summary article in SCIENTIFIC AMERICAN
* cites Rayleigh's 1934 paper as 1 of 5 references
* This is reprinted on pp.91-97 of Lynch's book (1980).
* VENUS flash
* "Air temp. 77.6 F, wet bulb 70.6, sea 80; wind SÉly, force 3;
* visibility excellent; sea slight." So, a std. Inf.-mir. flash.
* VENUS flash
* a useless first-time observation
* Description fits Inf.-mir. flash.
* "Air temp. 79 F, sea 80; wind calm."
* NAKED-EYE SUNRISE FLASH -- ATY TYPE? (no drawing)
* Peculiar phenomena -- wish there were more details
* Flash seen in binoculars -- ATY TYPE? (no drawing)
* seen at 52 ft. but not 40 ft.
* Flash seen in binoculars -- Drawing suggests inf.mirage type truncated
* by waves
* VENUS GF (belongs in Venus file but on same page as previous 3 reports)
* Nice drawing
* useless
* Adaptation phenomena?
* ". . . the margin of the cloud sheet assumed a bright green tint which
* lasted from about 30 sec before the flash to approximately 90 sec.
* after it."
* VIOLET FLASH
* Addey, the director of the BAA's Sun section, comments on Rackham's note.
* [Livesey (1968) explicitly identifies him as Addey.]
* "It could be repeated as often as one wished by performing the necessary
* gymnastics."
* B/W PHOTOS by Walter A. Feibelman
* GREEN RAY display with drawings
* ". . . the cone dissolved for about 2 sec. into a sheet of green flame
* extending 2° to 3° above the horizon."
* SATURN GF
* RF -- maybe a MM flash
* GREEN RAY observations
* Observations by Robert E. Seebold: CONTRAIL ILLUMINATION
* some GOOD COLOR PHOTOS
* misattributes first account to Winstanley;
* confuses inferior and superior mirages
* DE JAGER -- nice MOUNTAIN SHADOWS
* GF followed the mountain slope like Ricco
* Double BLUE FLASH behind cumuli
* "kingfisher blue"
* Green crepuscular rays?
* "visible for just over half an hour" -- contrast effect?
* see sketch facing p.128
* "Moonrise was observed through the bridge telescope and a brilliant red
* flash was seen for 2 sec. as the lower limb cleared the horizon . . . ."
* "Air temp. 65 F, wet bulb 62.5, sea 66.9." [so, Inf.-mir.]
* 10 flashes at clouds observed through binoculars
* "In all, ten separate green flashes were thus seen, and at one stage
* with the sun half set, the whole of the visible surface, with the
* exception of the parts crossed by the narrow bands of cloud, turned a
* bright green for about 2 secs."
* ?? possibly Cornsweet's phenomenon?
* "Air temp. 82 F, wet bulb 77, sea 81.5. Wind E, force 4."
* NOT a GF at all, but a greenish crepuscular ray. Ignore!
* ADAPTATION EFFECTS? CLOUD-TOP FLASH? Seen at an elevated (hilltop) horizon
* "The afternoon . . . had been sunny, cold, and clear" so inversions are
* involved. The "dash" is a compressed mock mirage, probably of Fraser's
* hilltop type. "All this happened in the space of about a minute."
* Nice HOURGLASS PHOTO (b/w), p.102
* indirect report of early GF photos c.1949
* "Nous en avons projeté des photographies en couleurs, obtenues au Pic,
* devant la Société Astronomique de France, en 1949."
* NOT confirmed by searching in BSAF.
* interesting drawings
* textbook flash
* B/W PHOTOS by Walter A. Feibelman
* a few green flashes and many airplane wakes crossing the Sun
* LUNAR GREEN FLASH at one cusp, not at the other
* (First flash probably drowned out by remaining part of disk)
* cf. partial-eclipse flash reported by Touchet, 1925
* NICE DISTORTED SUNSET drawings; GF at end
* VENUS GF
* VENUS GF
* GREEN RAY?
* "The flash extended over an arc of 15-20 degrees and was of an intense
* green colour."
* 3 flashes at successive cloud layers; NICE SKETCHES
* typical INFERIOR-MIRAGE RED FLASH
* GEORGE ALCOCK's GREEN RAYS and CLOUD-TOP flashes
* Notable for explicitly suggesting a GREEN CREPUSCULAR RAY:
* "On 1964 June 13 at 20.13 UT the Sun went down behind a sharply-defined
* belt of distant strato-cumulus some 1½° above the horizon.
* The last upper fringe of the disappearing limb turned a brilliant copper
* green. The visibility was about 30 miles, the air stream unstable,
* behind a cold front - these seem to be the normal conditions for a
* display of the Green Flash.
* "Such displays are the usual feature reported, but I do not consider
* this to be the true Green Flash, which I have seen only twice -
* on both occasions at sunrise. The first was off Cape Trafalgar,
* Spain, on 1942 November 17; the second at Farcet on 1950 December 25.
* On these occasions the Sun remained completely hidden behind large
* distant cumulus, until appearing suddenly behind the sharply-defined
* indented mountain-like summit. At the moment of the Sun's appearance
* a brilliant copper-green crepuscular ray shot up from the cloud top
* to near the zenith - a magnificent, unforgettable phenomenon. As the
* vivid green limb emerged the ray vanished just as suddenly. The whole
* phenomenon lasted about 1¼ seconds. I have never read any reports of
* any other observer witnessing this spectacle, which I consider to be
* the true Green Flash."
* Thanks to Guy Hurst, the current editor, for supplying a copy!
* typical MOCK-MIRAGE FLASHes with drawings
* "The whole process took about 10 min and as the last vestige of the sun
* finally passed from sight we looked for, but saw no flash." !!!
* "The elongated button-shape became separated from the main body of the sun
* by a thin translucent line and became a brilliant ultramarine colour.
* The button-shaped part reformed and separated a second time."
* "Just before passing from sight the sun lost all semblance of its original
* shape and became a pyramid of flaming ultramarine coloured vapour which
* gradually sank below the horizon. . . ."
* typical MOCK-MIRAGE FLASH with drawings
* "An unusual feature was the occurrence of a green flash on the upper
* limb, while it was still well above the horizon."
* shorter version of the following report:
* Observation by Ian C.McLennan; this version published in Feb., the next
* in April:
* AIRPLANE FLASH from 35,000 feet
* N.B.: Minnaert's new translation has 39 kft in error
* "Its width was about half the apparent diameter of the solar disk."
* Textbook green and red flashes
* "As the sun's upper limb appeared above the horizon, a very distinct
* green flash was seen . . . . When the sun had cleared the horizon it
* immediately disappeared behind the edge of the cloud sheet: a very marked
* red flash then appeared on the lower limb . . . ."
* "Air temp. 59 F, dew point 54, sea 62." [so GF was an Inf.-mir.]
* LUNAR BLUE flash
* "The atmosphere was exceptionally clear and dust free."
* The Vatican Observatory photo reproduced in this coffee-table book does
* not appear in O'Connell's book, so I suppose it had been taken since then.
* It shows a small but pure green mock-mirage flash, accompanied by the
* ``textbook'' explanation, which of course does not agree with the photo!
* Thanks to John Norris for mentioning this on Usenet!
* A remarkable assertion: "SUGGESTED ON MANY OCCASIONS"
* "The method of finding longitude from an observation of the Green
* Flash which occurs in favourable meteorological conditions when the
* upper limb of the Sun sinks below the visible horizon has been suggested
* on many occasions during the present century." He considers it too
* imprecise to use "on account of the relatively long interval which the
* phenomenon may occupy"; but cites Simmons in J.Inst.Nav.4 (1951), who
* in turn cites Capt. Brett Hilder earlier in that volume. Evidently
* Ekman (1959) is another example, though not cited.
* This book contains many errors; see
* http://www.huxtable.u-net.com/cotter01.htm
* for a list of them.
* VENUS GF
* "At an altitude of approximately 5° the colour began to alternate
* between red and green . . . . At the moment of setting there was a vivid
* green flash in the shape of a triangle."
* 4 GFs in one sunset -- CLOUDS or blank strips?
* "At sunset, three narrow bands of cloud lay across the sun's disc.
* As the upper limb of the sun sank past the upper edge of each band there
* was a distinct pale emerald-green flash and, finally, a brilliant green
* flash as the top of the sun's disc disappeared below the horizon."
* FLASH over VOORTREKKER MONUMENT (but none at horizon)
* an ordinary "emerald-green" sunset flash in ANTARCTICA
* Detailed meteorological conditions were recorded: slightly higher than
* average pressure and slightly lower than average humidity (53% at -20 C).
* From ship's position and time, the true altitude of the Sun's upper limb
* was found to be -0° 39' which indicates "normal conditions of
* refraction"
* Informatsionnii Byulleten' Sovetskoi Antarkticheskoi Ekspeditsii No.73
* "a small green spot" photographed with (apparently) an ordinary 35mm camera
* GF seen over distant hills with binoculars
* AIRPLANE FLASH
* NICE COLOR PHOTOS showing DISPERSION of HORIZON (red below).
* THANKS to Ros Austin for providing an actual reprint with the colored
* plate (filed separately in the "pictures" file)! -- Not to mention a
* first-hand account of the flight (he was there).
* ". . . no physiological causes need be considered."
* random discussion of GF and color films -- useless
* Discussion begun with Smith's drawing (see his 1971 note, below).
* A grazing observation at 78 N, around local midnight. (Cf. Baxter, 1983)
* "During the course of the next 20 minutes the Sun disappeared and
* reappeared several times between the saw-tooth peaks of the Trollheimen
* . . . . On each occasion I observed a vivid green coloration . . . through
* binoculars for, I suppose, a second or two."
* VIEZEE in CONDON REPORT
* not 100% accurate, but many useful references
* "The refracted images of the setting sun computed by Wegener's model
* agree closely [!] with those photographed and described by D.J.K.O'Connell
* (1958) . . . "
* A textbook inf.-mir. GF
* sounds like experienced observers:
* ". . . the atmospheric conditions prevailing seemed to indicate that a
* green flash could be expected at sunset and the setting sun was duly
* observed through binoculars with striking results."
* "Air temp. 59.5 F, wet bulb 52.6, sea 61.6. Wind NW, force 4."
* MOON
* Report not clearly worded: what was seen?
* probably inf.-mir. GF, not green Sun
* ". . . I was standing . . . about 15 feet above sea level."
* ". . . the solar disc changed suddenly to a distinct `spectral' green for
* a few seconds."
* probably useless
* Sunsets in CEYLON
* ". . . more often than not . . . ."
* 2 SUNRISE flashes over hills
* Possible GREEN FOG ?
* ". . . the light appeared to flood the whole landscape, and to persist for
* some 2-3 seconds . . . ."
* MARY WICKHAM BOND's book
* "We had seen it before, in Grenada and St. Vincent . . . . To my eyes,
* it has never spread across the horizon, nor is it green but blue, like
* a brilliant spark from an electric wire."
* She here mis-cites Cain's 1959 chapter as a "book," but quotes the
* passage from it. (cf. her 1975 item in NYTimes)
* Thanks to Anna M. Stevens for finding this!
* NAKED EYE BLUE FLASH
* Color reversal: "Towards the end the blue became deeper and changed to a
* blue-green before fading away."
* Air here is reported 0.9 deg. warmer than sea, though description fits
* an Inf.-mir. flash.
* Smith's letter to JBAA: probably one of Fraser's wave-flashes;
* the drawing is somewhat confusing.
* VENUS colored limbs; not a flash. Nice sketch.
* The Editor's comments are a bit garbled: "When this happens the greater
* part of the orange/yellow range of colour will be removed by absorption
* due to invisible water vapour, while most of the blue/violet will be lost
* by scattering due to very small particles within the atmosphere."
* Where's the 3rd Baron Rayleigh when we need him?
* unreliable CICELY M. BOTLEY review -- many names misspelled;
* another LEGEND believer!
* another MULTIPLE FLASH via HILLS
* Botley's letter to JBAA, commenting on Smith: here she is correct.
* Richard Scorer's cloud atlas has a page on GFs
* Section 13.5.2 describes the low-Sun phenomena and GFs. There are
* several pages of fine pictures of atmospheric-optics phenomena in this
* chapter. Unfortunately, the supposed superior mirage in Fig. 13.5.1 is
* certainly a reflection in a curved window, not a mirage at all.
* double AIRPLANE FLASH at 26,000 ft., 5 sec + 3 sec
* "There was a false horizon formed by the top of a layer of altostratus
* above which the air was very clear."
* another AIRPLANE FLASH
* BLUE FLASH from Seattle; nutty explanation
* 1 paragraph on 2nd page on GF: lone telescopic observation of green rim.
* NO GF seen in Riyadh
* ?? can this be a color-blind observer?
* Botley comments on Young's letter (above), getting the mirage wrong.
* Gerald Hawkins's passing comment:
* "On rare occasions the rim of the sun can shine a pale green for a few
* seconds. But this trick of refraction is with clear air over an open sea
* horizon. I knew there would be no green flash this morning, inland over
* rolling hills." Evidently he has never seen one.
* Thanks to Stephen Williams for turning this up.
* flashes in Alaska "looked for, and usually observed" at Geophys.Inst.,
* Fairbanks.
* CHROMATICITY DIAGRAM, DOMINANT WAVELENGTH & PURITY tabulated
* minor mention of GF in meeting; no useful information
* GF routinely seen at Las Campanas
* evidently reprinted from the newsletter of the Toronto Centre.
* "I have seen the green flash at sunset only once in Canada, yet here it
* is easily seen three or four times a week."
* Thanks to ADS full-text search.
* "electric BLUE" flash above alto-stratus
* ". . . visibility was remarkably good."
* minor mention of GF in meeting; no useful information
* SPIKES -- GREEN FLASH -- WAVES (Mock Mirage?)
* "the green rim is magnified by the proper `mirage' conditions."
* [as already suggested by Evershed (1915, 1923, 1926, 1936) and seconded
* by Mercanton (1920), Visser (1921), and also others: e.g., Clarke (1930).]
* He correctly says that inferior mirages over water "warmer than the
* overlying air" (p. 4) can work; but then proposes "Gravity Waves" as
* "the other way around the theorem". But he then assumes the inversion
* is "a kilometer or more above our eye" (p.6) to find the waves have
* ". . . wavelengths of between 200 m and 2 km." (p. 8)
* This is where "Fraser's theorem" is proved [but not the first time].
* See White's more accurate treatment (1979) of waves on inversions.
* Note: Atmosphere became Atmosphere-Ocean shortly after this, and
* seems never again to have published a GF paper.
* Rare bright GF photographed with a "small camera" (no focal length given)
* (MARY WICKHAM BOND was the wife of the ornithologist JAMES BOND,
* after whom Ian Fleming named agent 007.)
* This item was followed by 3 useless letters from writers who fit
* Havinga's condemnation, in the Aug.24 Travel section.
* NOTE: her reference to Cain's book gives chapter title, not book title
* Brief mentions of a few GF observations in the Arctic Ocean
* See pp. 112 and 182 [and note 8 on p. 293, citing Sharonov (1951)].
* There is a curious error on p. 229: "We saw the sun clearly for the first
* time after the arctic night on February 15. It rose at 1100 hours, and
* climbed to 18° above the horizon." [Obviously, 18' is intended.]
* (Thanks to David Burch for finding this reference!)
* 2 Mock Mirage flashes mistaken for "superior mirage"
* Good photographs of SUNSET DISTORTIONS
* Believes, and even cites, Jules Verne for "LEGEND"
* VENUS GF
* Distorted moonrise; seems to be an Inf.Mir.
* [filed here because of the following item on same sheet]
* Naked-eye Inf.-mir. flash
* Followed by a long quote from "The Meteorological Glossary" on GF,
* saying that "in a hazy atmosphere such differential scattering may not be
* appreciable and the flash may then appear blue or violet." This
* nonsense needs to be straightened out!
* Eloquent eyewitness accounts of two sunrise flashes
* Fred H. Stocking was an English prof. at Williams College.
* This contains a few minor errors: seconds for minutes in
* longest duration; 25 for 35 minutes of the Byrd expedition.
* Note: though this is the May issue of UpCountry, it came with the
* 29 April issue of the Berkshire Eagle
* (Note that each issue is separately paginated, so month is required)
* condensation of Stocking's GF article
* Color photo of inf.-mir. GF is BADLY reproduced
* (Note that each issue is separately paginated, so month is required)
* independent discovery of Sang/Meyer/Fraser THEOREM
* Badly confused about O'Connell's pictures
* Notes that OBLIQUE WAVES will produce "tilted" features
* This seems to be the only paper J. Met. ever published on the GF
* Cover shows a barely visible green wisp -- filed in "color images" file
* Fraser's "photograph of the green flash on the cover is one of the most
* outstanding views ever captured on film." (Hardly true, even in 1980.)
* "Blue and purple [sic] light is scattered far more strongly than red
* light. For this reason, very little blue or purple light reaches the
* observer when the sun is near the horizon."
* "To enlarge the green rim so that it can be seen, requires a temperature
* profile that causes the atmosphere to act as a giant magnifying glass.
* There are at least three classes of temperature profiles that will do
* this; one with a superadiabatic lapse rate near the surface, and two in
* the form of lifted inversions."
* Minnaert, O'Connell, Shaw, and Fraser's 1975 paper are cited.
* August issue
* a terribly oversimplified account -- poor
* But he does recognize (p.3466) that refraction does not scale with
* refractivity.
* Andrzej Urbańczyk's observation
* (translated from the Polish original in Młody Technik, c. 1979?)
* He was captain of the "Morning Star", enroute from San Franciso to
* Polynesia, south of the Equator and west of Samoa. "One evening
* . . . I heard an agitated cry from the helmsman: 'Look! There! Look!
* Green Sun!' . . . I just looked at the setting Sun, . . . and suddenly
* the remaining gelatine-red piece, beginning at the Earth, emitted
* green like a tram light and disappeared."
* "The whole crew saw the green flash five times . . . ."
* The explanation starts out with the Ancient Egyptians, moves on to
* Jules Verne and "the well-known Soviet astronomer G. A. Tikhov", and
* "two French astronomers" -- all without specifics, but with extended
* quotations; but we know who they are.
* The first observation appears to have been made in the summer of 1978,
* as he says at the end that he saw it again several times in the spring
* of 1979, including a cloud-top flash.
* There is a photograph, credited to unnamed "French astronomers".
* (in Unicode: Andrzej Urbańczyk ; Młody Technik )
* In Russian, the reference is:
* А. Урбаньчик
* Зелёный луч
* Наука и Жизнь No.7,
* 94-96 (1980)
* O'Connell's 1960 Scientific American article reprinted
* Alistair Fraser's article on atmospheric optics in SMITHSONIAN
* with a good COLOR PHOTO of a nice Mock Mirage flash on p. 74;
* green flashes are discussed only in the final paragraph (where,
* again, we have: "Scottish legend assures us . . . .")
* Enough with the phony LEGEND, already!
* But this otherwise good article is too little known.
* Superb MIRAGE PHOTOS as well as the GF picture; other pretty stuff.
* EXTINCTION comments -- good and bad!
* The observer notes that "On previous occasions such flashes had been
* either accompanied or replaced by an intense blue (topaz) flash, this
* phenomenon was not observed . . . , neither was the intensity of the flash
* so great as seen before." Fine. Then the Editor's comment claims that
* "In a hazy atmosphere . . . differential scattering may not be appreciable
* and the flash may then appear blue or violet," getting it all wrong.
* GERHARZ's Questar observations from 25 m
* GREEN AIRPLANES and CONTRAILS
* ". . . since O'Connell . . . any further analysis may have indeed become
* worthy of Sir Arthur Schuster paraphrasing this event . . . .
* However, despite these frequent assurances that everything optical under
* the sun has already been observed, recorded and analyzed, the
* interpretation of beautiful phenomena in nature must not remain restricted
* to the realm of science pundits."
* "For at least 10 minutes after sunset, and up to 5° elevation of the
* line of sight, green coloration . . . may still be observed on
* sun-illuminated, very distant airplanes in normal flight altitudes and on
* their contrails. . . ."
* 6 flashes in one sunset; BOTH INF.-MIR. and MOCK-MIRAGE (wave) flashes.
* Rather crude drawings illustrating the formation of mock-mirage flashes
* and the Omega form leading to the final inferior-mirage flash.
* "During the 28 seconds or so that it took the sun to disappear totally
* below the horizon, five separate green flashes were observed. These
* occurred when the upper limb of the sun broke away from the main body of
* the sun and formed a cigar shape approximately one-sixth of the diameter
* of the sun in length. This cigar shape almost immediately disappeared,
* turning a faint and rather watery green as it did so."
* . . . "The duration of these flashes was a split second each.
* The final and sixth flash, observed as the sun sank below the horizon
* was very pronounced. It appeared very slightly above the horizon and
* lasted approximately two seconds. A feature which the observers had not
* witnessed before was that in the centre of the green colouring (which was
* a bright emerald green) was a small circular area of a much paler green
* colour; this only occurred, however, in about the last half-second of the
* duration of the flash." [N.B.: the drawing shows the spot is
* elliptical, not circular.] (wind force 2).
* Drawings look like an inf.-mir. flash, but description is odd:
* "The flash appeared after the sun had set and then collapsed into itself
* and disappeared." But it probably is a normal flash, as "the colour was
* a brilliant emerald green." (Certainly not a green ray.)
* Bohren believes Jules Verne's "LEGEND"!
* typical MM phenomena sketched from photos
* His slide (sent to ATY) shows a *yellow* flash on Kodachrome
* a fair popular summary. He has the mirage connection right, but says
* an inversion layer is "a condition in which a cold trough of air is
* sandwiched between two regions of warm air," which is nonsense. He also
* says the "orange and yellow light is dispelled [sic] by molecules of air
* in an effect known as Rayleigh scattering," which is also wrong. There is
* a nice drawing of a mock-mirage sequence, but the explanation is all
* wrong. There's also stuff about "lighting up the entire western sky."
* And he evidently confuses the 3rd Baron Rayleigh with the 4th. Still,
* a fairly good account, apart from these serious errors.
* The "Lick" sunset is Chappell's, from Sept. 16, 1931.
* N.B.: Each issue is separately paginated, so the MONTH is essential!
* COLOR PHOTO on cover
* Remarkable flash of appreciable dimensions recorded with 50mm lens
* (cf. Mary Bond's accomplishment)
* N.B.: author is not the photographer (Mlle.Danielle Jey).
* Nice color photograph of inf.mirage flash with red-outlined tropical cumuli
* text by Elizabeth Stone, photo by her husband David M. Stone
* from timed photo series, "the flash lasted at most, two thirds of a second."
* A color copy is in the colored-pictures file.
* MULTIPLE flashes of MIDNIGHT SUN (cf. Reeves, JBAA 1969)
* "As midnight approached the Sun sank towards the northerly peaks and was
* periodically eclipsed by them . . . . Just before the trailing limb of the
* Sun passed behind a peak the Green Flash was observed. . . . we saw the
* limb turn from yellow through green to a vivid blue over a period of about
* ten seconds. This phenomenon was repeated many times. . . . The effect was
* spectacular."
* Fred Schaaf's earlier book gives the GF several pages
* Here he still believes the "old Scottish legend". Otherwise, good.
* ISBN 0486244024; Google Book offers some sample pages.
* Not knowing the literature, Zapffe proposes many things already done.
* He also has some facts wrong, completely fabricating a story about Lord
* Kelvin, with a wrong date (1889) for Kelvin's first flash (1893), which
* was at sunset, not sunrise as stated by Z. [see S.P.Thompson, 1910]
* Paul Ford reviews the Meinels' book, devoting a paragraph to the GF
* "Is the `green flash' purely an optical phenomenon or are there
* physiological effects that influence the brilliance or colour of the
* image?"
* Dale Cruikshank reviews the Meinels' book
* ". . . an excellent chapter on the green flash, with a very clear
* explanation of the phenomenon and the reasons why it is not easily
* photographed. Astronomers would do well to commit parts of this chapter
* to memory in order to provide a concise explanation to those who are
* first introduced to this most spectacular of the low-sun phenomena."
* Then the Meinels, in turn, review Corliss's book
* They have some useful remarks about second-hand reports:
* "The author often reproduces a sketch which he has redrawn . . . or
* occasionally apparently translates the word description in a cited
* reference into a drawing. While this latter procedure is useful in some
* cases, it may be deceptive in others. The weakness is that language is
* limited, and subtleties, difficult to put into words, can easily lead
* to a second-person sketch with profound differences from the real event."
* Of the GF, they say: "The tropical [sic] green flash is an example of
* an anomalous phenomenon not yet fully or satisfactorily explained. . . .
* Gravity waves in the atmosphere have been offered as an explanation,
* but we believe that simple variations in refractive index in three
* [sic] dimensions are sufficient to cause the solar rays to be injected
* into and trapped in a ducting stratum and conveyed over the horizon to
* the observer." [Interesting both for their doubts about the textbook
* story, and for their belief that ducting is required. And, "tropical"
* to describe Fraser's flashes in Pennsylvania )(i.e., the "gravity-wave"
* idea? They don't see that 1 dimension suffices!]
* Alexander Thom reports many green flashes
* "The last rays of the Sun's upper limb was often a brilliant green. It
* seemed to me to be such a regular phenomenon I did not think it worthwhile
* writing any description. . . ."
* Fiona Vincent confirms Thom's assertion that the GF is common, and
* comments on Baxter (1983):
* "I believe that the phenomenon can be observed, at any latitude, more
* often than is generally realized."
* Botley also comments on Baxter
* "CLOUD" seems to have been a blank strip (superior mirage);
* first GF above Wegener's BLANK STRIP, second GF at horizon:
* ". . . the sky was crystal clear without cloud or haze. . . . there was a
* very low thin band of cloud, not haze, with vertical columns between cloud
* and the Earth's surface . . . . [cf. d'Abbadie, 1849]
* This layer, together with the vertical columns, gave the effect of a
* road bridge and its piers, when backlit by the Sun's disc. I judged the
* thickness of the cloud band to be about one-twentieth of the vertical axis
* of the Sun's setting disc and the distance from the bottom of the band to
* ground level to be of a similar order.
* . . . When the upper limb of the Sun sank to `deck' level of the bridge,
* there was a green flash on the top of the cloud layer, while the red disc
* continued to shine between the cloud and the ground. The top limb of the
* Sun then came down below the cloud layer, and as it approached the ground
* a green glow developed on the righthand side and spread leftwards along
* the edge of the limb . . . ."
* "Instrumentation was used to provide x7 magnification. . . ."
* NOT a green flash at all, but green METEORS.
* A peculiar example of observers supposing they can estimate distances to
* remote objects: although the first one disappeared "behind low cloud at an
* altitude of 30°", "the distance from the ship did not appear to be
* great enough to be compatible with a meteor or other object entering the
* earth's atmosphere."
* FOUR green flashes in one sunset with mountains 72 n. miles away
* The sun "constantly changed in appearance from that of an `upturned urn'
* to an `hour-glass'" (see DRAWINGS). "Before, during and after these
* observations, we were experiencing extreme radar ranges with ships' echoes
* being received from over 40 n. mile and strong land echoes at the maximum
* range of 48 n. mile . . . ."
* A bizarre review of the Meinels' book; 3 sentences mention the green flash
* He calls Aden Meinel "Eden" -- twice! Then there is ". . . not always
* scientifically accurate" with no supporting evidence; and such lapses
* as "Extinction of sunlight and it's [sic] effects is [sic] . . . ."
* Apparently this is the Platt of Paltridge and Platt -- also published by
* Elsevier. Strange. Who is at fault here, Platt or Elsevier?
* COLOR PHOTO on cover
* mostly YELLOW FLASH in color on cover; some green
* ANTARCTIC INFERIOR FLASH
* SUNRISE FLASH with both INF.-MIR. and MOCK MIRAGE features
* "ORANGE HORNS" and the Omega phase is described as like "a spherical
* buoy". No temperature data.
* Willard Bascom's memoir
* "The reason the phenomenon is rarely seen from a densely inhabited
* coast is that the tiniest amount of haze or cloud will obscure the flash
* of green. However, it is often seen from ships well out at sea where
* the horizon is clear."
* MEINELS -- nonsense about GF, but showed that layers produce notches.
* [of O'Connell:] "While the pictures are excellent, some of the
* interpretation of the details of the origins of the phenomena need
* updating." (p.6)
* "Based on our siting [sic] of the green flash both in the Tucson desert
* and in Hawaii, we have come to the conclusion that there must be at least
* two different forms of the green flash: a ``green spot'' and an anomalous
* ``green flash.''" (p.9) [at this late date!]
* N.B.: November issue.
* William R. Corliss's review for mariners
* He correctly concludes that the textbook explanation is inadequate.
* Published by NOAA.
* The issue is marked "April-May-June" on the title page, but "Spring 1988"
* on the cover and in the footers.
* GF gets 1 paragraph on p.352.
* 2 good COLOR PHOTOGRAPHS of flashes and a nice OMEGA photo
* all COLOR photographs by PEKKA PARVIAINEN
* including one small GF and a fine early-stage OMEGA, and a
* near-rectangular Sun (Abb.4, 5, 6).
* Filed in sequence, as my color copy is not impressive.
* Text by Christoph Leinert; issue no.2
* GOOD REVIEW from secondary sources; believes Verne's "LEGEND"
* good COLOR PHOTOS from Pekka, O'Connell, etc.
* Nice account of GREEN ILLUMINATION of a BALLOON (cf. Seebold's contrails)
* Account of a report by Jonathan Shanklin of the British Antarctic Survey
* ". . . the green flash is occasionally seen, although difficult to
* photograph." [BAA Meeting Report]
* Thanks to ADS full-text search.
* 2 flashes with VISIBILITY = 50 km
* all sorts of nonsense, but a 14-second Green Flash reported
* Note that large variations in horizontal refraction have been known for
* several centuries; this is not a new discovery.
* Somebody ought to re-reduce these data, allowing for variations in dip.
*
* NOTE: in an e-mail dated Aug. 8, 2007, Bill Liller tells me his position
* at Viña del Mar is more accurately
*
* Lat. -32d 57' 28.1" Long. -71d 32' 45.3" Height 120 m
*
* -- the values published in this paper should be corrected accordingly.
*
* See Stephen McCluskey's 2017 study of refraction at the apparent horizon
* (in the "variable refraction" file) for useful discussion. Also, his
* 2018 paper (in the "Terrestrial Refraction" file) that cites this.
* mostly a puff piece about the above. The GF is mentioned in passing
* One of Pekka's GF photos is on the cover (Oct.13 issue)
* Many errors of optics, as well as Verne's LEGEND
* Betty Jean Miller's second GF item
* ". . . I talked about seeing `the green flash' as the sun set last
* weekend." A local biology teacher offers the after-image idea.
* The GF item follows the one in the title.
* Betty Jean Miller's third GF item cites the first item (Aug. 3)
* Mentions the 1981 item in Smithsonian and the July Discover [above]
* Writer asks about GF
* Replies to the Overend query
* Michael Berry mentions O'Connell's book.
* Replies to the Overend query
* Ken Durose cites Greenler's book.
* Explanation paraphrased (and embroidered!) from Bowditch
* Jon Carroll's column actually credits "American Practical Navigator".
* Apparently there was an earlier column in which he asked about the GF.
* meteorological details given; sunset over hills
* "Night and day, the sky is an every-changing theater of optical wonders.
* Mostly, however, we go around with our eyes to the ground."
* Katherine Bracher's historical notes turn up earliest PASP mention of GF
* (see PASP for June, 1902) -- this is the May/June issue.
* Charles B. Minnich's ``ANCIENT NAVIGATOR'' columns
* The first shows the standard textbook model. Pretty much OK
* except for ". . . atmospheric refraction has little effect on the
* high-energy [sic] red portion of solar light so it streams off into the
* atmosphere. In contrast, the low-energy blue portion of solar light is
* refracted (bent) severely, so it's not seen."
* "The Ensign" is published by United States Power Squadrons, Raleigh, NC;
* thanks to Yvonne Hill, its editor, for these 2 items!
* Charles B. Minnich's ``ANCIENT NAVIGATOR'' columns (#2)
* His advice not to use a focal length longer than 200mm is apparently
* intended for hand-held use. His suggestion to use the lens "a little
* less than wide open" and suggested exposure of a half second would
* produce greatly overexposed pictures. And: "Forget using a movie
* camera. The flash can occur between frames if your shutter speed is
* slow."
* A popular account based mostly on Bowditch (note the strange numbers)
* Incited by reader Howard R. Bird, who "saw a phenomenon called the green
* flash immediately following a sunset." Odd, how people get this notion.
* The GF treatment is only the first 2 pages of text. The advice is good,
* but the explanation is garbled, confusing inferior and superior mirages.
* Paolo Candy's mountain-wave flash
* The COLOR PHOTOGRAPHS show a few small flashes, and a good sunset
* series. The best example is enlarged on the cover.
* "Nuove Orione" is a popular magazine for amateur astronomers, much like
* "Astronomy". It does not seem to have volume numbers.
* Bob Silverberg's popular account, as originally published
* He has only read O'Connell, it seems.
* see Robert Willmerdinger's tiny flash in color in Abb.2
* (filed in regular sequence, as the flash is so puny) This is part of
* a Xi-shaped Sun (corner of top line); the image is rather overexposed.
* issue no.8-9
* PEER HECHLER reports his expedition's sighting of a GF near Shetland Is.
* The observation was made Sunday, Aug. 21, 1994. The 12 scientists found
* the display of what appears to have been a standard inferior-mirage
* flash very impressive: "`Geisterhaft' erschien uns diese optische
* Erscheinung insbesondere deswegen, weil die Farbe Grün am Himmel in
* Zusammenhang mit einem Sonnenuntergang nicht gerade die normale
* Erfahrung widerspiegelt." There is the ILLUSION of increasing
* brightness: ". . . vom gerade verschwindenden Rot über ein von der
* Intensität her zunehmendes Gelb in ein helles markantes Grün
* überging."
* At the end he quotes a section from Meyers kleines Lexikon Meteorologie
* (1987) that makes the error of claiming that blue is not seen because
* it blends in with the color of the sky!
* Thanks to Prof. Dr. Kristian Schlegel for a copy of this item!
* Coco's flashes are all small MM-type flashes, probably due to Fraser's
* wave mechanism. I now have a color copy of the article. There is a
* nice RED FLASH that appears to be a MM on p.50.
* There are some errors: he thinks Swan's paper was the first; calls the
* MM flash "the green segment"; says never look at the Sun, etc.
* AAA062.082.031
* MICHAEL VOLLMER's nice 2-part review of atmospheric optics
* GFs get mentioned briefly in last paragraph of first column on p.182;
* as this is a small part of the content, I MOVED this to the Vollmer
* file.
* An unusual observation described in strangely impersonal terms
* in Walter Stefaniuk's "You Asked Us" column. Most of the GF explanation
* is quotes attributed to David Phillips of Environment Canada.
*
* I have talked to Walter Stefaniuk now about this on the phone. He says
* the sighting is his own: a "pencil of light" he saw overhead and to the
* east at sunset. He mentioned "misty" conditions, and that the weather
* had been cloudy; so I suppose this is a very rare anticrepuscular ray
* caused by an intense GF. The sunset itself was hidden from him by an
* island to the west (this was in Panama). The duration of a second or
* less is consistent with this interpretation, at least. [June, 2000]
* Brendan McWilliams begins his GF columns
* "People who have heard of it and havelooked for it and failed to find it
* often dismissed it as a fantasy. Others who have been fortunate enough
* to see it have thought it to be an optical illusion . . . ."
* Don't they have proofreaders in Ireland? His columns are full of typos.
* Beda Tobin's response to McWilliams reports an observation (not useful)
* Frank Sargeant, the Tampa Tribune's outdoors editor, is skeptical
* But one of his correspondents is even worse: "The reason you can't see
* it in the Gulf is because the water is so dirty compared to the clear
* waters of the Caribbean." [Evidently, a through-the-waves believer.]
* (Apparently there was an earlier column on this topic, as this was "one
* of a number of readers who wrote" about it.)
* A second reader quoted from a Scientific American article.
* Book publication of George Alcock's GREEN RAY observations:
* "Just after 8pm on 13th June [1964], George witnessed the phenomenon
* known as 'green flash': 'The sun went down behind a sharply defined belt
* of distant stratocumulus some 1.5 deg above the horizon. The last upper
* fringe of the disappearing limb turned a brilliant copper green.' The
* prevailing conditions -- good visibility, an unstable airstream behind a
* cold front -- had been as expected for such a display; yet George did not
* consider it to have been the genuine article, which he says he has seen
* only twice, on both occasions at sunrise. 'I saw it at Cape Trafalgar,
* Spain, on 17th November 1942, and in my garden on Christmas morning
* 1950. On those occasions the sun remained hidden by distant large cumulus
* before suddenly appearing behind the sharply defined moutain of cloud.
* At the moment the sun appeared, a brilliant copper-green crepuscular ray
* shot up from the cloud top to near the zenith. As the limb emerged vivid
* green, the ray vanished just as suddenly. The whole phenomenon lasted
* about 1 1/4 seconds -- a magnificent unforgettable spectacle, which I
* consider the true green flash'."
* It's notable that he explicitly says it was a CREPUSCULAR RAY.
* Thanks to Eric Frappa for pointing this out! It's a limited edition
* of 2000 copies, each signed by Alcock.
* Short mention of GF in sidebar on p.66, with mistakes: "diffraction" !
* Main article "The fire that separates day from night", pp.58-66 by S.Howe
* Why is Leigh Sherman in La Jolla asking the C.S.M. about green flashes?
* Especially when there were several items in the local paper a few years
* earlier? Anyway, the answers are provided by Peter N. Spotts, on the
* "Home Forum" page; his column is evidently meant for the kiddies.
* anonymously attributed to the Boston Globe
* Could this be the mystery ref. to Usha McFarlane?
* "Green flashes have inspired literary descriptions -- from Chekov [sic]
* to Jules Verne -- and a wealth of legends. The Scots claim that . . . ."
* O'Connell and Minnaert's book are cited. Sound observing advice.
* Drawing shows "irradiation" according to R. White's comment following
* 2 unrelated GF reports are mentioned in the Editor's footnote (useless)
* Rebecca Jones has an even wackier answer than the reader's question:
* Craig Bohren is cited, but misunderstood: "You need binoculars or a
* telescope to see it. . . . The light radiating from the sun comes in
* different wavelengths. . . . But when the sun sets, and the last few
* rays come over the horizon, all we're getting are the violet-blue ones.
* The atmosphere refracts those rays just a little, so to our eyes, they
* appear green.
* "And this is the green flash. It lasts just 5 - 10 seconds at this
* latitude, but can last a couple of hours in polar regions."
* But at least Craig is quoted as saying "There's no great risk" in
* looking at a "low horizon sun" through binoculars.
* Jeff Klinkenberg's good article with a picture by Lu Rarogiewicz
* Quoting Rue Morgan: "It was like a green flash bulb going off, and it
* only lasted maybe a second, and it was incredible. I thought, `This is
* so amazing, it's going to be all over the news tonight.' I watched the
* TV that night, kept switching stations, but nobody reported anything."
* There is also much attention paid to the scoffers.
* The narrative describes an inf.-mir. flash, with "little notches" that
* "pinch off" a piece at the top: "The pinched-off part, a greenish version
* of the sun's disc, seems to float at the horizon."
* Short reply to query about the reality of the GF
* many small errors
* popular article with good pictures by KENNETH D. LANGFORD
* but a few errors
* This is the (Dec.1996/Jan.1997) issue.
* Ronald L. Speer (in Va.) thinks Florida sunsets are dull
* -- but he admits to never seeing a GF
* article for schoolteachers, full of small errors; Jan/Feb 1997 issue
* Lev Tarasov says G.A.Tikhov was interested in the flash.
* A story about skier Glen Plake, who "told us it was good luck to see
* a green flash at sunset." No GF info.
* another popularization, full of mistakes
* OK Omega photo, p.81; feeble GF, same page (March issue)
* Brendan McWilliams's second installment: the GF described
* Contains a short bio on O'Connell, citing his book
* Brendan McWilliams's third installment: advice for observers
* The advice is generally sound, but he picked up O'Connell's error:
* "An unusual thermal structure in the upper air" is said to be required.
* Verne's "legend" is quoted in full (in translation).
* Yet another popular account, derivative and with some minor errors
* A fair but derivative article; author has seen 1 weak GF
* ". . . it was not the green explosion or backlit emerald that I'd been
* anticipating -- it was more subtle, a green glow that faded in and then
* abruptly vanished. . . . I had watched the sun accelerate into the sea
* until it was nearly gone. Then, for the last ten seconds, I locked my
* gaze on the sun's rim and finally, there it was. When I saw the flash
* I turned excitedly to my wife and children, who were watching with me,
* but somehow they had missed it." [So, probably RETINAL BLEACHING.]
* Leslie Wilk has read the standard accounts, and repeats their errors,
* attributing the color to simultaneous contrast with the red sky,
* and mistakenly thinking the peak of the visual response is important.
* But he does recognize the importance of atmospheric structure.
* The publisher was bought in 1998 by Petersen Pubs, in turn bought the
* next year by emap.usa in England; but the editorial office is still in
* S.D.! (619-697-0703)
* The author's name is given on the contents page as Leslie Wilks; but as
* Dr. Les Wilk on the article. [I checked by e-mail: "Wilk" is correct.]
* By the way, he runs the "Physics Gearbag" Web site, one of my GF links.
* A SUNRISE FLASH photographed by Mischa Schirmer
* I have only a b/w photocopy, but the version on their Web site isn't
* very impressive; the flash is overexposed, due to use of automatic
* exposure setting. 4 stages from the line at the horizon to a very
* flattened Sun are shown.
* April issue
* std. Inf.-mir. flash, but maybe longer lasting?
* "The remaining segment of the sun rapidly turned a very brilliant green
* which seemed to last for several seconds."
* Bob Silverberg's account, reprinted in hardcover anthology
* This is a popular account, based almost entirely on O'Connell's 1960
* article in Scientific American . It is remarkably accurate, except for
* "green being the color least affected by the atmospheric refraction."
* His own failure to see a flash is the common one, as betrayed by the
* words "The sun, yellow to the end, disappeared behind the hills."
* (see 1992 for the original publication.)
* so-so COLOR PHOTO of inf.-mir.GF
* June, 1997
* Humphreys's couplet is quoted, in a reply by the editor of the Old
* Farmer's Almanac:
* Thanks to Jonathan Addington for pointing this out on Google News!
* ATY article on GF
* [actually FILED in "COLOR PHOTOS" file.]
* PHOTOGRAPHS with short text
* Abb.7 is completely muddied out on my b/w photocopy.
* The Web version of Abb.8 (the SUNRISE BLUE FLASH) in fact shows a
* small piece of blue rim; mostly this is overexposed. Both taken by
* Michael Kobusch. Oktober issue.
* Entertaining first-hand account of a green-flash hunt in the Caribbean
* Gary Lee takes his color chart along. . . .
* Good short summary, with quotes from Alistair Fraser
* Nice Inf.-mir. GF COLOR PHOTO taken by Steven Businger
* This "Premier issue" apparently came out late in 1997; no month given.
* AQUA is the PADI Diving Society Magazine (Islands Publ. Co.)
* (PADI = Prof. Assoc. of Diving Instructors)
* [actually FILED in "COLOR PHOTOS" file.]
* French translation of Craig's Bohren's 1987 GF chapter from "Clouds . . . "
* Thanks to Didier Renaut for a photocopy!
* Alan Whitman's multiple GFs include a CLOUD-TOP flash
* Seen Jan. 22, 1983 from Queen Charlotte Islands. There are also
* accounts of chromatic scintillations of Sirius, Canopus ("mostly green,
* occasionally pure red, frequently both red and green. . . "), and the
* crescent Venus near the horizon.
* Thanks to the ADS full-text search, which revealed this; Dec. issue
* Paolo Candy's book begins with a GF chapter
* Thanks to Paolo Candy for supplying a copy of the revised edition!
* A short 1-paragraph mention of GF
* "At the time of the green flash, the red image of the Sun has set,
* and the blue image is absorbed by the atmosphere, leaving only the green
* image to be seen."
* reprint of my Ocean Navigator article
* [actually FILED in "COLOR PHOTOS" file.]
* This probably should be in the "folklore" file . . . .
* This is the little box at the bottom left corner of the page.
* "While no one in the group could recall actually witnessing the
* phenomenon, the consensus was that if they sat gazing at sunsets long
* enough, their chances of a sighting would increase.
* "Hence, an early-bird dinner and special cocktail were born."
* The dinner menu, and the recipe for the drink, are given.
* ATY's 500 words on GF (filed in "pictures" file -- cover is my GF)
* The cover of this (June 1998) issue is my Jan.1996 GF.
* my AAS abstract
* A badly garbled version of my press release at the AAS meeting
* No. 8073
* nice summary of my press release and phone interview
* No. 2139
* Cruise-ship sunset GF (p.160)
* ". . . a prolonged two to three second emerald green flash occurred! The
* dining salon erupted in cheers . . . ."
* [June issue]
* Thanks to ADS full-text search for turning this up!
* VENUS flash and HEIGHT EFFECT
* Thanks to Axel Quetz, editorial staff of SuW, for supplying the
* page number; I have only a photocopy that omits them. (July issue)
* Neil de Grasse Tyson's book
* A simplified account of the textbook story: ". . . the atmosphere can
* act like a prism . . . ." (p. 119)
* He also touches on sunset eye safety on p. 124; and, though not as
* conservative as the extremists, is still overly cautious.
* Well-written, but (as Pasachoff notes below) prone to errors.
* Jay Pasachoff reviews the Tyson book:
* "His explanation of the green flash which is sometimes visible at
* sunset is incomplete."
* (30 July 1998 issue)
* Norman Hey's letter, cited by Harnish in the Nov. issue (below)
* In Palau, "We had three evenings in a row when . . . we saw a distinct
* green flash . . . ." "Who might have seen more?" There is a rare
* mention of YELLOW: ". . . the limb turned yellow then green . . . ."
* He also mentions "an apparent intensification just prior to the moment
* of disappearance." (This is a fairly common illusion.)
* a third-hand account, based on the New Scientist report
* (This is Corliss's newsletter)
* seems to be based on the Economist's confused version of my work
* This regular column by the assistant head of the Irish Met Service
* is called "Weather Eye". No indication where he got it from.
* short article for high-school teachers, illustrated with my Jan.7 flash
* This mag is published by the ACS
* supplemental info for the above item
* The questions on the last page don't allow a correct answer for
* what happens to red light, though.
* GF treated in last section
* nice COLOR PHOTO of one of Pekka's green flashes (Abb.13)
* "Beliebt ist das Phänomen, weil es einerseits nur selten zu beobachten
* ist, so daß es immer noch etwas besonderes ist, den Strahl selbst
* gesehen zu haben. Zum anderen rankt sich um den grünen Sonnenstrahl
* Jules Verne zufolge die Legende . . . ."
* No. 10, so I suppose October issue.
* San Diego BIPLANE PILOT Tom Harnish reports seeing many a GF here
* and cites Norman Hey's letter in the August issue.
* Nov. issue (each month paginated separately)
* This commercial travelogue treats the GF in its penultimate paragraph
* "Baja's unpolluted surroundings make it a perfect place to see a green
* flash. We saw several during the week." No details; sketchy description.
* This article is one of three under the "Sunland Secrets" head.
* "Steve Edwards is a staff writer for the Muskegon (Mich.) Chronicle"
* based on the AAS press release; slightly garbled
* Uses my inf-mir. GF photo
* William Galvani sees a flash in La Jolla, after 30 years of looking
* This is available on the magazine's website at
* http://www.48north.com/jan99/greenflash.htm
* but is accompanied by a most misleading animated graphic.
* Thanks to Greg Smart for the pointer!
* Chet Raymo finally sees a flash after 34 years
* "The atmosphere acts like a prism. . . ." And he mis-dates O'Connell's
* Scientific American article to 1965. Or does he mean he didn't see
* the article until 1965?
* Mentions the 1992 column, and one I don't have, in 1985.
* my OPN article; some COLOR PHOTOGRAPHS
* letter commenting on my OPN article
* Mainly to point out the newer edition of Minnaert
* A wrong idea popularized
* This memoir is more about Tuscany than about Kinta Beevor's childhood.
* But, alas, on p. 144, we have: "Sometimes from the beach at dusk we could
* see the `green flash'. The sky had to be perfectly clear, and just as the
* last tiny segment of the sun disappeared below the horizon, the streak of
* tangential light through the surface of the sea would produce this
* extraordinary optical effect." Extraordinary indeed!
* "Published in the United States by Pantheon Books, a division of Random
* House, Inc., New York. Originally published in Great Britain by Viking,
* a division of Penguin Books Ltd., London, in 1993." So this should
* really be moved back to 1993; but is kept here for the dangerous review
* (next below) by Jo Ann Hofheimer. Note that Kinta Beevor died in 1995.
* A wrong idea popularized again!
* Jo Ann Hofheimer's unfortunate review of Kinta Beevor's book says
* "If you're interested in . . . what causes that mysterious green flash as
* the sun sets over the sea --- this is the book for you." Arrrghhh!!
* my Zenit article: GOOD COLOR PHOTOGRAPHS, so filed in "PICTURES" file.
* Includes the 4-flash sunset from Mt. Laguna.
* Very nicely translated into Dutch by editor Eddy Echternach.
* This is the June issue (no.6)
* the "70-word article" in Frontier Airlines's magazine
* The GF paragraph is the second part of Nancy Schatz Alton's column.
* My mock-mirage photo is mis-marked "inferior-mirage", but at least the
* correct advice for observing is given.
* Science 's "NetWatch" page picks up my GF Web site
* A pretty good 1-sentence summary, though "movies" is misleading.
* Letters to Zenit, responding to my GF article there:
* letter from Cor Booy about FEENSTRA KUIPER and his GF observations.
* Here is the "held van de dag" story!
* This is the Sept. issue (nr.9)
* Letters to Zenit, responding to my GF article there:
* letter from Lodi Huider, asking why Jules Verne wasn't mentioned.
* Both of these letters have responses from ATY (translated).
* This is the Sept. issue (nr.9)
* Nice but short item in DIE ZEIT
* Christoph Drösser's reply to a query by Maria Blümel
* Succinctly put: "Bei bestimmten Schichtungen von warmer und kalter Luft
* kommt es aber nicht nur zu Brechungen, sondern auch zu Spiegelungen.
* Dann erscheint die Sonnenscheibe über dem Horizont eingekerbt und
* verzerrt. Unter diesen Bedingungen kann der grüne Rand im Moment des
* Sonnenuntergangs für kurze Zeit optisch in die Breite gezogen werden
* und wird für Sekundenbruchteile wie ein Blitz sichtbar."
* Evidently Stimmt's? is a regular column in the Wissen section.
* Alaskan pilots' accounts of GFs and mirages, reported by Fred Hirschmann
* This is a big, glossy "coffee-table" book, with lots of pictures --
* but none of mirages or green flashes! The GF stories are on p. 28;
* mirages on p.27; and a good ball-lightning story (mis-labelled as St.
* Elmo's fire) on p.31. The GF explanation is a rudimentary version of
* the textbook account: "The earth's atmosphere acts as a giant prism,"
* blah, blah,blah. Also, in discussing latitude effects: ". . . the green
* flash occurs for a longer period of time in the Arctic. Some observers
* in northern Alaska have reported seeing green flashes that lasted for
* more than one second." Amazing, isn't it? The game of repeatedly
* displaying the same flash over and over by climbing and diving is also
* described. So is the trick of playing hide-and-seek with mountains and
* valleys.
* On the other hand, the mirages are accompanied by some quantitative data
* on inversions: a square Moon is described with an inversion of 60° F
* between the surface and 2000 ft. An inversion at 500 ft. gave mirages
* of an island 30 miles away, switching between erect and inverted images in
* 50 ft. of airplane elevation. Nice description of superior mirage:
* ". . . the tops of mountains go flat and appear boxlike." [TRUNCATION]
* Eileen Schifano's little gem, describing the flash clearly in 138 words
* my appeal for source identifications
* Physics Today cites my GF Web site and shows Hank Hogan's composite photo
* Frank Deford obviously is dubious . . .
* "Or maybe it is just a Keysian Loch Ness monster."
* There is a follow-up to this in the November 2000 issue.
* Jerry Schad's good brief mention of green flashes and distorted sunsets.
* Alan Gilmore tells me this story was largely based on my Web site
* They got some details right (the hyphen in Verne's title; ozone as the
* main orange absorber) and some wrong (the 1/40 second duration seems to
* be a simple error on the part of the reporter; believing Verne's "old
* Scottish legend" is another matter!). The phony illustration is a
* shame, though. (Filed with the other color illustrations, anyway.)
* The "Listener" is basically the radio and TV schedule for the Kiwis.
* Michael Viney's observation; books by Raymo and McWilliams named
* ". . . a brilliant, emerald flash of light. Yes -- emerald!"
* A little noise in here: wrong title for McWilliams's book; wrong date
* for O'Connell's work.
* A couple of GOOD COLOR PHOTOS reproduced
* One is my April 19, 1998 mock-mirage flash from Alpine; the other was
* taken by Régis Tiercelin and shows a nice green rim. The descriptions
* are brief; the translation of Bohren's essay on GFs is cited.
* This is a special issue on numerical weather prediction. An item of
* special interest is on pp. 9-10, on numerical weather prediction in
* Potsdam; there is a fine color photograph of the Einstein tower!
* A very insipid inferior-mirage flash; shows the Omega nicely, though
* Tim Laman's sunset sequence has barely a trace of green.
* (He tells me they failed to reproduce the frame that shows the flash
* best!)
* This is in the "Geographica" section of the un-numbered pages at the
* front of the issue.
* My "visual effects" paper, mostly about retinal bleaching
* Sunset Paper III.
* Katie Burns's newspaper column on refraction phenomena
* This came out quite well, though they failed to credit my photographs of
* green flashes.
* Glen Liston's report of South Pole flashes in 1983
* The photograph on p. 17 has been "digitally enhanced to more closely
* resemble the darker and brighter green colour that we witnessed."
* It clearly shows the flattened image at the top of a strongly-refracting
* (darker) layer.
* Amy Gulick's article based largely on my website
* Peter Nichols's apparent green-glow observation mentions Eric Hiscock
* "As the red upper rim vanished, a distinct, momentary, radium-green
* glow blinked and was gone." The facing page (63) shows an old German
* postcard colored by Tacita Dean in "the perfect radium shade" --
* actually, a rather watery, pale green.
* This book is the catalogue for Tacita Dean's show at the Tate,
* 15 Feb. - 6 May, 2001. The copyright for the book is "The Tate
* Trustees" but the texts are copyright "the authors", and no author
* or editor is given for the book in the British Library catalog.
* Brief mention of green flash in a handbook of phenomena for vacationers
* with one of my COLOR PHOTOs of an inferior-mirage flash.
* Standard textbook explanation, with use of term "groene segment".
* Co-publisher: ANWB bv, Den Haag.
* David Turner's BLUE SUNRISE flash in the mountains (Las Campanas)
* GF mentioned in a textbook for French mariners, with one of my photos
* Storm Dunlop's book
* GF is covered on p.131, under "Sunrise and sunset effects"
* Foldout catalogue produced for Tacita Dean's show at Museu Serralves
* in Portugal, 2002. (Cf. her movie, in the "GF in movies" section, and
* the 2004 book based on it, in sequence below.)
* I have not seen this. It is advertised at
* http://www.bookstorming.com/fiche.asp?idlivre=2147470343&page=liste.asp&np=1&nbr=1&ttcl=
* and elsewhere.
* Beth Brust's GF article
* Good 2-page treatment, with my photos
* Kathy Morey's short mention
* This is a nice guidebook to one of the Hawaiian islands. Green flashes
* are mentioned in connection with a beach on the NW corner of the island.
* The somewhat inaccurate account on pp. 168-170 of the second (1997)
* edition has been replaced by a revised version on pp. 248-249 of the
* third (2002). There is an amusing account of ``The Tanqueray
* Flash'', attributed to her skeptical father.
* John A. Adam's book on mathematical models
* One paragraph on p. 75 is devoted to green flashes (textbook model).
* from the Boulder meeting issue of AO
* One of their rainbows corresponds to the sub-duct flash, if you
* replace the light source (rainbow) with the observer (flash).
* Hank Hogan's composite published again; 1 page of text
* Thanks to Hank for a color copy!
* Steve Ackerman's book has a short GF section
* Just gives the textbook explanation: ". . . a sliver of green appears for
* a second or two as the Sun disappears over the horizon."
* The 2-paragraph "Green Flash" section spans pp. 150-151.
* Hank Hogan's sunset composite is on p. 152, well reproduced in color.
* There is also a nice inferior mirage photo on p. 148.
* Hezi Yizhaq's GF article in Hebrew
* Has a nice GF photo in color. This is a "National Geographic"-type
* mag, but with quarto page size.
* The title translates as "The green ray -- the polygraph of love".
* Thanks to Hezi Yizhaq for a copy, and Mark Stover for transliteration!
* Tacita Dean's flip-book of frames from her video (ISBN: 3883756776)
* A rather marginal inferior-mirage flash. The film was (for my taste)
* overexposed about 1 stop, and the sky was very bright. Because of
* the combination of overexposure and excessive aerosol scattering,
* the flash is very washed-out looking; it shows, at best, a yellow-green
* color. This isn't helped by the low resolution of the film. It
* does convey well the naked-eye impression of an average flash.
* The only printing in the flip book is on the inside cover, where
* Tacita Dean says, "At the end of last year, I made a 2 minute 16 mm
* film of the green ray in Madagascar. The green ray is an optical
* phenomenon that happens at the last moment of setting sun. It is
* quite rare to see from land and you usually see it when the sun sets
* over the sea when there is a 100% clear horizon." (dated 2002).
* Apparently, from an interview with the artist at
*
* http://www.bombsitebeta.com/issues/95/articles/2801 ,
*
* the use of a marginally-visible flash was intentional. On the
* other hand, I'm reminded of Havinga's (1934) remarks! Another
* interview with the artist was published in 2007 (below).
* The flip-book is a cute idea; I'd have wished for a nicer flash.
* You can see, from the discontinuities in the waves, that about 1 frame
* per second was selected at first. Several consecutive frames show
* the flash itself. The overexposure makes the Sun white until the
* remaining segment is about 10' of arc wide.
* There seems to be a 2004 edition published by Distributed Art Pub Inc.
* A short treatment of the GF
* Accompanied by color images on the cover, which I have not seen.
* OK for GF, but unfortunately spreads the Galileo myth again.
* The reprint is available on the Web at
* http://bjo.bmjjournals.com/cgi/reprint/88/6/733
* It shows an inferior-mirage flash (as the "one") and a nice pair of
* mock-mirage flashes (as the "two").
* Mike Richey's brief summary
* This publication is the journal of the Ocean Cruising Club, a group
* of (mainly British) small-boat owners who enjoy long trips at sea.
* This letter cites the Met. Office's Manual for marine observers,
* O'Connell's book, and Brett Hilder's observations in the 1950s for
* determining longitude by using GF times to mark the sunset.
* A PDF is available at
* https://liveicomgrshot.blob.core.windows.net/occfiles/ffarticles/
* (look for article 643)
* Thanks to Dick Morris for pointing out this obscure item.
* Ronaldo Régério de Freitas Mourão discusses Verne's book, and its effect
* The author is an astronomer in Brazil who is interested in history.
* Unfortunately this is marred by several careless errors: he says Back's
* observation was Antarctic (though he correctly cites the title with the
* word "Arctic" in it!); Treusch is claimed to be "le premier astronome à
* enregistrer les phénomènes qui entourent le rayon vert;" Rayleigh's
* name is misspelled (twice, in different ways), and he confuses the 3rd
* and the 4th Barons -- thus producing the absurdity of giving the name
* and dates of the 3rd Baron, who died in 1919, with the publication date
* (1934) of the 4th Baron's second paper; Keilin & Hartree (1950) are
* moved to 1952 (and Hartree comes out "Hartrel"), and falsely credited
* with suggesting that oxygen and ozone absorption are responsible; etc.
* Thanks to Jacques Crovisier for pointing this out, and providing a
* photocopy. He says this "is from a contribution to one of the numerous
* colloquia organized to celebrate the Jules Verne year."
* Ken Langford says 2 of his GF photos are in here
* Scheduled for release Sept. 1, 2008 -- no editor named.
* Accord seems to be connected with Andrews McMeel Publishing, listed as
* "author" on some Web pages. Some familiar names are text contributors:
* Ed Darack, Fred Schaaf, etc.
* James Lock's analysis of the Byrd Expedition observations
* Much labored exposition of the positional astronomy of the circumstances,
* but a generally reasonable discussion of the observations. Both the
* author and his readers would have had an easier time if he had known
* to consult the Astronomical Ephemeris.
* Pete Lawrence's pictures and visual observations
* He seems to think all GFs are due to inversions -- which is nearly true
* for his high observing sites. Includes a visual observation of a
* cloud-top flash, and a photograph of a long red line at the horizon.
* Tomer ben Arous, Saber Boulahjar, and Stephen G Lipson make a lab demo
* Another aquarium demo, using salt water; high-school students
* DOI: https://doi.org/10.1088/1361-6404/aa90f5
*
* poor GREEN FLASH SPECTRUM and general discussion
* This is a re-hash of his JRASC paper in 1952.
* O'C #57
* WEH III & ATY observe some GF phenomena, but don't understand them
* This was the first GF observation I ever made, completely mystifying to
* me at the time. The observations were made over Belmont Hill from the top
* of Building D at HCO; evidently the phenomena are the same ones discussed
* by Fraser in 1975. The cause is probably miniature mock mirages due to
* inversions bent up over the hill. These observations certainly took
* place when the Sun was a few degrees above the astronomical horizon.
* ". . . the gradual nature of the color and brightness changes rules out an
* explanation by eye fatigue."
* SUNSET PHOTOGRAPHS -- slight notching
* full-spectrum flash: YELLOW, GREEN, BLUE, VIOLET
* "During the last few seconds of sunset, the remaining solar segment
* changed color through the whole visible spectrum: first more yellowish,
* then greenish, and finally blue and violet just before the last of the
* solar disk disappeared."
* GREEN INFERIOR MIRAGE OF VENUS
* Observations by Peter K. Nelson, Kevin Clarke, and James M. Roe
* on board the Canberra (eclipse cruise)
* GREEN INFERIOR MIRAGE OF VENUS explained correctly
* SUNSET PHOTOGRAPHS -- CLASSICAL INFERIOR-MIRAGE GREEN FLASH
* MOVIE FRAMES by Dennis di Cicco at Cape Velas, Costa Rica
* GREEN RIM photographed by George Ripley
* INFERIOR-MIRAGE GF photographed by Paul Travers at Puerto Vallarta, Mexico
* GREEN RAY observations
* Observations by Harold Hill in Italy (over Ligurian Sea)
* " . . . bright green ray shot up vertically from the sea."
* DISTORTED MOONRISE -- features both compressed and expanded
* VERBAL DESCRIPTION of "DOUBLE SUN" -- cf. Hevelius, and Applegate (1929)
* ". . . since the lower image was the brighter they concluded that the
* upper image was the mock sun."
* SUNSET PHOTOGRAPHS -- thistle shape; multiple layers
* photographed by Jim Baumgardt, Fremont Peak, Calif.
* SUNSET PHOTOGRAPHS showing flatter top than bottom, and extinction in
* lower layer
* photographed by Claude Combes at Juniyah, Lebanon
* SUNSET PHOTOGRAPHS by PEKKA PARVIAINEN
* LUNAR MOCK MIRAGE; nice SOLAR OMEGA
* VENUS DISPERSED: self-portrait with Green Flash
* SUNSET PHOTOGRAPHS + GREEN FLASHES by PEKKA PARVIAINEN and
* SUNSET PHOTOGRAPHS by Lee Coombs, Los Osos, CA (good HOURGLASS + extinction)
* General ATMOSPHERIC OPTICS with 2 GREEN FLASHES by Pekka, p. 258
* JUPITER flash
* SUNSET PHOTOGRAPH by PEKKA PARVIAINEN
* nice MOCK MIRAGE
* ". . . the green rim partially detached or even separated from the rest of
* the Sun . . . may be caused by stratified, horizontal air layers below
* the observer . . . ."
* SUNSET PHOTOGRAPHS by PEKKA PARVIAINEN
* nice DOUBLE MOCK MIRAGE; POSSIBLE GENUINE BLANK STRIP
* SUNSET PHOTOGRAPH by PEKKA PARVIAINEN -- FINAL LINE
* also similar sunrise drawings by Russ Sampson, Edmonton, Alberta
* CLASSICAL INFERIOR-MIRAGE GREEN FLASH and BLUE FLASH
* Observations by Kenneth A. Barbone at Pismo Beach and Rincon Point, CA
* MIRAGE plainly visible in first photo
* SUNSET PHOTOGRAPH by PEKKA PARVIAINEN
* PEAR-SHAPED SUN; FLAT BOTTOM; 2 SMALL NOSES
* "GREEN DOT" and other green flashes
* Observations by Paul C. Soper
* See subhead: "Airborne flashes"
* SUNSET PHOTOGRAPH by Marc J. Coco -- green corners on small segment
* "SQUARE" SUN and GREEN STRIP above TRIANGLE by Eugene Brings
* This GF closely resembles my flash of 2 Feb., 1999, including the
* diagonal features due to waves on the inversion! (see p.102)
* Note that issues are paginated separately here.
* copy in COLOR PHOTOS file, though Pekka's photos reproduced here are not
* very striking.
* AAA067.082.06
* Fred Schaaf's VENUS blue-green flash, seen with 7x50s on a roof
* "a few hundred yards" away; repeated a "few dozen" times by moving.
* Dennis di Cicco's inferior-mirage flash sequence at top of p. 95
* (This is the same sunset published in S&T 48, 61, 1974)
* Thanks to Benji Myers for pointing this out!
* The "textbook" story, badly presented in cartoons
* Thanks to Benji Myers for pointing this out!
* First installment of a small box on GFs, citing my Web pages
* This one mentions (but does not cite) my JOSA paper ("Part III.")
* Second installment of a small box on GFs, citing my Web pages
* This shows my Jan.7 GF, but hardly larger than a postage stamp.
* An overexposed picture of a mock-mirage flash
* a good inferior-mirage flash from Rome, and a very overexposed sunrise
* flash over mountains in New Mexico. There is an interesting discussion
* of Owen K. Garriott's report of a flash seen from several different decks
* of a ship.
* Good article by Fred Schaaf
* He even debunks the "legend"! Some nice color photographs here, including
* George Kaplan's "Omega" series. He concludes with a great line:
* ". . . more wondrous than even Jules Verne could ever hope to convey."
* ["Night Sky" is S&T's new attempt to compete with "Astronomy" mag.]
*
* John Muncie's shaded sidebar from the U-T (reproduces badly from microfilm)
* This reply is attributed to William Nirenberg at Scripps
* Arthur Salm's "At Ease" column
* Remarkably, this newspaper story cites both Shaw's 1973 paper and
* Gerharz's 1981 paper, both in PAGeoph.
* Restaurant review of Armando's Green Flash in P.B.
* Leslie James says "I happen to be among the non-believers."
* (Not too happy about the eatery, either.)
* Tucson isn't quite local, but George Ridge's column fits best here
* He relies mainly on O'Connell's 1960 article in Scientific American .
* "As described by those who have seen it, the flash most resembles a
* green stem on the disappearing red apple of the sun."
* "For some reason, the flash is easier to see from a ship's upper deck or
* other high point." Generally good observing advice here, including
* binoculars.
* The answer here is attributed to Sallie Baliunas
* Anthony Bucholtz's biweekly "Oceans Watch" column
* He gives Laplace his due: "The more atmosphere it goes through
* the more it is refracted." But then comes the textbook error:
* ". . . leaving only a green rim near the top of the sun. This is the
* green flash." So the variability has to be attributed to variable
* aerosol extinction: "Only when the atmosphere is fairly clean will the
* effect be seen. Since this is rarely the case, on most evenings you
* won't see the green flash." But he is one of the few to add that
* ". . . here in San Diego there are many days of the year when . . . chances
* are good that you'll see this beautiful effect."
* Thanks to Fred Talbert for first pointing this item out to me!
* Chet Raymo again
* This is in the "Outdoors" section of the Times, under the heading
* "Wild West". He still seems to think O'Connell's pictures were the
* first in color, and believes Groff's claims about the ancient Egyptians.
* The sunset photo on p. 1 shows a green artifact, not a GF.
* my picture gets a 5-column spread; the writeup is good
* Reports of green flashes seen from the Naples Princess, a local
* sightseeing boat.
* Naples, Florida is where this comes from.
* Mila Zinkova's GF photo illustrates our local paper's article
* Good treatment of GFs by Robert Krier. This article accompanies 2
* others by him on sunsets and clouds.
* A follow-up to the above, with a well-reproduced GF by Jim Grant
* The column is headed "Weather Watch".
*
* Here we have the citation of O'Connell's book, and REVIEWS of it.
* It's incredible that the book sold for a mere $6 in 1958.
*
* (Originally this was of interest to me only for SUNSET OBSERVATIONS.)
* See
* http://aty.sdsu.edu/explain/observations/OConnell.html
*
* for detailed discussion of the phenomena in the photographs.
* Note that the phrase "low Sun phenomena" was coined by W.J.Fisher and
* used in the titles of several of his papers.
* "At Specola Vaticana the Sun goes down sometimes over land, sometimes
* over the Adriatic Sea . . . "
* Yeah, right. So it isn't just Americans who don't know geography.
* ". . . this book will be an inspiration to amateur astronomers in showing
* how colour photography with a telescope can be applied to the study of
* fascinating and often ill-understood meteorological phenomena."
* Feb.14 issue
* James Paton parrots the Rayleigh party line: "It occurs when refraction
* in the atmosphere close to the Earth's surface is abnormally great, that
* is, when the density decreases rapidly with height."
* About a half-page summary with few comments, except:
* "The whole subject actually belongs to the field of Meteorological
* Optics, but -- as the author says -- it has been widely dealt with by
* astronomers, and valuable observational material can only be obtained by
* astronomical equipment." Nonsense!
* "Victoria" appears to be the Australian one. April issue.
* a one-column review by Charles H. Smiley
* "The color photographs of the green flash are particularly impressive
* when one realizes that, on the average, the phenomenon is visible only a
* few times a month and then only for a second or so. I have seen the
* green flash many times in the last 20 years . . . ."
* "Sea captains, retired after half a century or more of service, have
* told me that it was only after retirement that they had heard of the
* green flash and had observed it."
* This review provoked some discussion: see the letter by Schwarz,
* and Smiley's reply.
* May 1 issue
* 3-sentence announcement in Jan. issue of S&T
* "Astronomical telescopes that could be pointed to the horizon were used
* to procure this unprecedented series of pictures. . . ."
* S&T review by Stanley P. Wyatt, Jr. in the June issue
* "The book is surely the authoritative work on the green flash,
* containing, in addition to the photographs, data on simultaneous visual
* observations and meteorological conditions, a very complete bibliography,
* and a good account of the history and qualitative theory of the flash."
* "The photographs include a remarkable collection showing how varying
* atmospheric conditions distort the solar disk at the horizon. Perhaps the
* most impressive feature of these weird shapes is their symmetry around a
* vertical axis, indicating that small-scale stratification in the
* atmosphere occurs in essentially horizontal layers."
* One of the few mentions of the lack of a QUANTITATIVE theory:
* "Perhaps better balance would be achieved, and the book's utility as a
* complete and compact summary would be enhanced, if the story of the theory
* of the green flash were accompanied by a quantitative presentation. . . .
* For it is always satisfying to know that theory and observation are in
* accord."
* Obs. review by M.A.Ellison, an old scintillation observer:
* "The study of meteorological optics has been under a cloud for many
* years; this work by an astronomer will do much to initiate a revival of
* interest in the field." [cf. the review in QJRMS, below!]
* "There is also a fine bibliography of 313 entries, being an extension of
* the earlier lists of papers and observations compiled by Fisher and
* Mulder."
* in June issue
* ". . . perhaps the most striking of all atmospheric optical phenomena."
* "The chief remaining doubt is the precise meteorological conditions
* which favour the appearance of the effect. Its notorious capriciousness
* suggests the need for atmospheric super-refraction (as when an air stream
* is cooled from below); the suggestion is strongly supported by the
* radiosonde temperature data quoted in the book but it is not supported to
* a significant degree by the measure of refraction afforded by a comparison
* of actual and theoretical sunset times on occasions of the green flash.
* It is rather disappointing that there is only scanty discussion of this
* aspect of the phenomenon."
* July issue
* Simmons, who published his own short review of this subject in 1951,
* makes several relevant remarks:
* "It is remarkable to think that a phenomenon as common as the Green
* Flash should daily pass almost unnoticed."
* "Although many observations of the Green Flash have been made, it is by
* no means certain that all the causative factors are known."
* "There are indeed many variations of the so-called Green flash . . . . On
* rare occasions the last segment of the Sun turns red just before the
* appearance of the Green Flash; this has been very clearly shown in at
* least three photographs. No concrete explanation is given for this
* unusual phenomenon and it certainly does not correlate with the main
* causes of the Green Flash."
* "Detailed meteorological data have been appended to some photographs but
* correlation between the two is not clearly explained, nor is it evident
* to the novice!"
* N.B.: There are two things called "Journal of the Institute of
* Navigation." This one (called "Journal of Navigation" since vol.25, 1972)
* is published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC, from 1960 to 1992.
* Another complaint about TERMINOLOGY:
* "The author and many other observers of the phenomenon known in English
* as ``the green flash'' are unhappy about nomenclature. . . . Both
* ``flash'' and ``ray'' are poor, even wrong, descriptions. Would ``flare''
* be a more appropriate term?"
* "Weather data are given for some of the occasions that are illustrated
* by photographs. Here the standard of exactness, so evident in the
* photographic work, has fallen. Some of the synoptic weather maps are
* badly drawn and a few have serious errors. A number of radiosonde ascents
* are tabulated but nowhere are we told the units of wind speed. These are
* unfortunate lapses, all the more so as it was unnecessary to print these
* data since no attempt is made to use them to illustrate the causes of the
* phenomena."
* a short paragraph endorsing the textbook explanation
* "edited by D.J.K.O'Connell."
* Jacobsen in PASP
* "The work differs distinctly from all other treatises so far published
* on this borderline subject between astronomy and meteorology in
* containing, for the first time, color photographs of
* the actual flash itself -- all other published color pictures known to
* this reviewer being at best photographs of the green or blue upper fringe
* of the solar image preceding the flash."
* "There are no new or strikingly unexpected phenomena described, as every
* type of sunset and flash has been drawn, photographed (though not in
* color), or mentioned before by observers using low-power telescopes . . . ."
* "Forms like ``lamp shades,'' ``mushrooms,'' ``harmonicas,'' etc.,
* reminiscent of J. F. Chappell's photographs in the December 1933 issue of
* these Publications , are reproduced in great profusion. They show the
* detailed development of the solar limb as it passes inversion layers in
* the atmosphere . . . ."
* "With this magnificent material one can see what is visible in a small
* telescope at the exact moment of sunset, a spectacle that so far few
* persons have bothered to look at directly."
* ALLER explicitly credits mirages
* "Atmospheric dispersion, refraction, mirages, and inversion layers
* all combine to create a class of phenomena that rank among the most
* beautiful in nature." He also mentions absorption of yellow and orange
* (though without saying "water vapor"); but credits Jacobsen for "a mirage
* condition or reflection from an inversion layer".
* Remarkably, he "has never seen a green flash".
* Sept. issue
* a good, short, one-paragraph summary
* Some trenchant remarks:
* "Most of the coloured photographs show very clearly the green upper rim
* of the sun . . . . The author claims by implication that these photographs
* are proof of the objectivity of the Green Flash, but one may doubt whether
* the case is sound. Nobody doubted that the upper rim of a heavenly body
* near the horizon was green --- this can be seen on any clear evening with
* a small telescope. What the opponents of the objective theory said was
* the green fringe was too narrow to be perceptible to the naked eye, and
* certainly too narrow to cause a striking flash, and it is hard to counter
* this argument with photographs taken through powerful telescopes."
* "The book reproduces radiosonde ascents and synoptic charts . . . and, as
* it were, invites the reader to interpret the sun's appearance in terms of
* meteorological conditions: but the author does not attempt to do so
* himself."
* "There is an adequate index and a bibliography of about 300 papers.
* Alas, not one of them appeared in the Quarterly Journal , and few in any
* meteorological periodical." [N.B.: we now know this is due to O'Connell's
* oversight, not to lack of meteorological papers!] "Perhaps this book may
* persuade meteorologists that there is still meat on the carcass of
* meteorological optics."
* A belated and slightly erroneous unsigned review in American Scientist
* "Joule's own observations of the flash are recorded by Winstanley."
* "The skill of the Vatican observers . . . makes it certain that the
* green flash is objective, its appearance explainable by the ordinary
* laws of optics." (Explainable, yes; explained, no.)
* The subtitle of the column says "By Hugh Taylor, the Associate Editors,
* and Guest Reviewers." No hint as to who was responsible here.
* A SCOFFER relents:
* ". . . we saw no such event, and our informant was accused of pulling our
* legs. Until seeing this book I thought no more about the matter, but it
* now seems that we had been unjust to our informant, and in spite of the
* time elapsed since publication this annotation is offered."
*
* There is a small mock-mirage flash in the final scene of THX 1138
* Thanks to Robert Roosen for pointing this out!
* Eric Rohmer's film "Le Rayon Vert" ("Summer") has a REAL GF!
* The sunsets were photographed by Philippe Demard; his inferior-mirage
* flash is perfectly exposed.
* There is also an Omega-type sunset earlier in the film, with no GF.
* The Jules Verne novel is described, along with the standard textbook
* explanation of the GF, in the middle of the film.
* "Green is the color of hope," says someone in the film. Is this French
* folklore? The "legend" is not mentioned; its content, though, is
* attributed to Verne. This would actually be an acceptable
* introduction to the subject.
* Distributed with English subtitles as "Summer" by Orion Classics, and
* on videotape by Pacific Arts videos. The tape is copyrighted 1986,
* though some references give 1985 as the film's date.
* Charlie Huisking's column about movies made in Sarasota, Florida
* John D. MacDonald's "A Flash of Green" ". . . was turned into a motion
* picture in 1983 by independent Tallahassee filmmaker Victor Nunez." . . .
* "Nunez's cameras captured evocative images of the mythic Florida --
* great stretches of isolated beach, herons gliding above the water, and
* the green flash of the film's title -- that brief, brilliant illumination
* that sometimes occurs just as the sun dips into the Gulf."
*
* But, alas, I have seen the movie; the "green flash" is a clumsy special
* effect that bears no resemblance to any green flash ever described by
* any eye-witness -- the setting Sun is optically superimposed on a scene,
* and a green filter over the lens fakes something the movie makers
* imagined. (Apart from this, the movie is a faithful adaptation of the
* book.) The movie was made for the PBS series "American Playhouse",
* which I suppose accounts for the cheapness of the effect used.
*
* [in the "Arts & Travel" section]
* Charles Taylor's extended movie review of Eric Rohmer's 1986 film
* published by salon.com in "Arts & Entertainment" on June 21, 1999 at URL
*
* http://www.salon.com/ent/col/tayl/1999/06/21/summer/index.html
*
* and still there as of July, 2001.
* The film originally was "Le Rayon Vert"; "Summer" is the American title.
* This is Taylor's "Home Movies" column for videos; the film is
* available on tape. The interesting part for us here is:
* "Rohmer banked the entire movie on the off chance that he would be able
* to capture the green ray on film. He filmed sunsets for months."
* The sunsets were photographed by Philippe Demard; he tells me they got
* the nice GF sunset (in the Canary Islands) the very first evening they
* tried!
* Tacita Dean's sunset movie
* Tacita Dean is an artist with an interest in green flashes.
* Evidently she was one of the tourists who went to Madagascar for the
* solar eclipse; cf. Paolo Candy's GF taken at that time.
* Supposedly this runs 2 min 30 sec -- just the duration of the sunset.
* A short 16mm movie. I have not seen this.
* Interview with Tacita Dean about her GF movie, etc.
* Mainly useful for Tacita Dean's acount of her CLOUD-TOP FLASH seen
* from an airliner.
* Her quoted remarks contain some nonsense about green flashes, and
* a strange claim that Eric Rohmer "faked it! It looks fake. . . ."
* -- which confirms my impression that her experience of green flashes
* is very limited. The interview appears on the magazine's website at
*
* http://www.bombsitebeta.com/issues/95/articles/2801
*
* P. 32 shows 2 frames of the GF movie, discussed on pp. 32-33.
* Another Tacita Dean interview, published later but probably done
* earlier than the above, as she says "I've just made this little film"
* (about the GF). Her 5 GF observations are described on p. 102.
*
* Mario Castelnuovo-Tedesco's piano piece
* Reprinted in 1994 by Masters Music, Boca Raton, Fla.
* Thanks to Paolo Candy for turning this up!
* A critical appreciation of the works of Castelnuovo, and others
* "One of the compositions that fill us with a most bountiful sense of
* this tranquil emotion in the presence of Nature is Il Raggio Verde
* (The Green Ray), technically one of the most finished of Castelnuovo's
* works and, in its inspiration, one of the freest. Here the musician is
* alone with his own emotion. . . . It is said that the sun, when sinking
* into the sea, sends out a final green ray; it was, therefore, a sunset
* that the musician had in mind to describe. . . ." (p. 450)
* 49 SHADES OF GREEN
* From musicdiv@nypl.org Wed Sep 25 10:52:34 1996:
*
* According to the Library of Congress's "Catalog of Copyright Entries,"
* "Forty-Nine Shades of Green" was copyrighted 11 September 1956
* (EP102142). The entry states only, "Words and music by Sid
* Tepper and Roy C. Bennett." We regret that we did not find a listing
* for the song in our collections and so cannot check the lyrics for you.
*
* ASCAP says: by Roy C. Bennett and Sid Tepper
* recorded by the Ames Brothers, with Hugo Winterhalter's orchestra
* ". . . the greenest green you've ever seen. . . ." (as aty recalls)
* OK, so it doesn't have anything to do with green flashes; it's still
* a great line!
* (see Jules Verne & F.A.Steel refs. in main GF file)
*
* A Scotsman complains about Verne's treatment of Scottish places
* ". . . let me borrow from the ingenious M. Jules Verne, who in
* his Rayon-Vert gives a remarkable account of this region and its
* inhabitants. It is always well to see ourselves as others see us,
* especially through the eyes of a famous story-teller. This story of his
* is intended to be amusing, and he appears to succeed in being funnier
* than he knew by reading up Sir Walter Scott and other works of fiction,
* then `combining his information.'" Our native guide points out the
* various errors committed by Verne, while summarizing the plot of
* his novel. "All of which, if one skips the guide-book passages, makes
* a very striking account of Scottish manners and customs, but prompts
* some doubt of the author's accuracy when he comes to deal with such
* more remote regions as the moon or the bottom of the sea." Remarkably,
* not a word is said about the supposed "ancient legend."
* The copy I saw said "Published November 1904 / Reprinted with slight
* alterations November 1905" on the back of the title page.
* Laurens van der Post's description of a green ray
* "Then the sun disappeared. For a second the sea caught its breath at so
* great a loss of light, the horizon went dark with anguish -- and then
* it happened. From below the horizon, from the other side of the gulf a
* tremendous flash of bright, emerald green light shot up across the sky
* in the most solemn, urgent, majestic, and defiant wave of farewell. It
* came right over the edge of the sea like a flight of burning arrows shot
* straight at the breast of the advancing night by an army marching not
* in defeat, but victoriously homewards." [p. 231]
* Well, a bit overwrought; but probably based on somebody's observation.
* In the same year, Morrow, in New York, published an American edition.
* Thanks to Alison Ford for pointing this out!
* JOHN D. MACDONALD's novel
* This is the modern work that has done most to popularize the GF.
* Unfortunately, it's apparent MacDonald had neither seen a GF himself nor
* talked to anyone who had; the description on p. 173 is most unrealistic.
* Interestingly, this is the only fictional account to associate seeing a
* flash with the making of a wish. Did he get it from some old Cajun?
* The ILL Team in Venice, Fla., says this is "loosely based on an actual
* event of criminal history."
* HERMAN WOUK's NOVEL
* minor mention, but correctly described
* JEAN RHYS uses ``EMERALD DROP'' in passing
* "And when she said, `Look! The Emerald Drop! That brings good fortune.'
* Yes, for a moment the sky was green -- a bright green sunset. Strange.
* But not half so strange as saying it brought good fortune."
* (This phrase first appeared in the English Mechanic in 1889.)
* [This is on p. 561 of the 1985 Norton "Complete Novels".]
* Thanks to Charles Freehling for pointing out this usage.
* short story, republished
* GF mentioned in Alec Waugh's semi-autobiographical novel
* (The writer was Evelyn Waugh's older brother.)
* The characters don't see a GF, but talk about it, and look for one.
* A nice touch: another character says to the writer, "In how many of
* your stories have you made your lovers look for that," and he replies,
* "More often than I've seen it myself."
* Apparently it was released simultaneously in England by W. H. Allen.
* GREEN FOG or just ADAPTATION?
* IMPROBABLE that this guy spent so much time at sea and only saw 3 GFs
* ". . . just a split second after the sun's upper tip sinks below the
* horizon, and the sun shines through the sea, the whole sky shimmers in a
* pulsing deep-emerald glow. . . . The colors all about -- the sea the clouds,
* the boat itself, my skin -- all glowed brilliant green."
* This guy is known for his exaggerations and embroidery of stories . . .
* A very brief bibliography of GFs in French literature
* "La formation du rayon vert dépend de tant de facteurs qu'il n'est
* surprenant que son apparition semble capricieuse." Verne's book
* ". . . semble avoir élargi l'intérêt porté à ce photométéore par
* les hommes de science, du moins si l'on en juge par le nombre d'article
* consacrés au rayon vert la parution de cet ouvrage. Cet exemple
* relativement rare, pour ne pas dire exceptionnel, d'une influence probable
* de la littérature sur la science mérite d'être noté."
* After quoting Verne's description, he then quotes passages from
* Simenon's Maigret et la vielle dame and four less-famous authors,
* who all give only a passing mention, with no description. Then,
* surprisingly, we find:
* "Selon un vieux dicton écossais, le rayon vert est un signe de beau
* temps:
* « Glimpse you ever the green ray
* Count to morrow a fine day. »
*
* And then, of course, ". . . suivant une légende écossaise . . . ."
* Winston Graham wrote the popular "Poldark" historical novels, as well
* as "Marnie" (made into a movie by Hitchcock). Here he pays a curious
* sort of homage to Jules Verne: though the flash is mentioned only
* briefly a few times in the middle of the book, its use in the title
* evidently is a reference to Verne's phony "legend" -- and the lovers
* here never see the flash, even in Barbados (much less in Scotland, where
* some of the action is set.)
* The flash is introduced on p.170 of this 383-page book. On pp.173-175
* it is (in passing) dismissed as an illusion. After brief mentions of
* its failure to be seen, on pp. 180 and 211, it appears the final time
* on p.242, where one remarks, "I was talking about it to someone in Paris
* not long ago, and he said it was an accepted natural phenomenon, not an
* optical illusion or a subjective fantasy." "Like love," replies the
* other.
* Oddly, some editions of this are entitled "A Green Flash" and others
* "The Green Flash".
* VIVID DESCRIPTION of a inf.-mir. sunrise; but the characters look for a
* green flash at the END of it instead of the beginning. This has been
* corrected in the seventh printing (1999) of the paperback, which now
* (correctly) mentions the red flash as the Sun leaves the horizon.
* Mentions Bowditch. See pp. 201-203 of this revised edition (which still
* bears the 1989 copyright for St. Martin's Paperbacks).
* Thanks to Robert Roosen for pointing out this interesting book!
* David Poyer
* (see 1997 for the English translation, below)
* ". . . tandis qu'à la proue, au point où le ciel tombe à la mer, comme
* un doigt entrant par les les pupilles et touchant le fond de la tête,
* éclatait le rayon vert!" (p.16)
* Randy Wayne White's murder novel set in South Florida
* A minor character in this uninspired potboiler sees a green flash (but
* off-camera, so to speak). The author, evidently, has not: "Like a green
* flashbulb had gone off. I mean it was bright!" (p. 64) The
* know-it-all hero asserts that "It has something to do with the distance
* sunlight travels at the earth's horizon. The light travels farther,
* something like that. The distance bends and separates the light, makes
* the sun seem visible after it has already sunk below the horizon. If
* conditions are just right, the yellow of the sun mixes with the blue of
* the sea, and it's like a chemical reaction." (pp. 66-67) The character
* recalls it as "Great big sun ball. Yellow . . . red . . . orange . . .
* oily purple, then -- poof! -- green . (p. 138) Yuk. Well, what can
* you expect from a part of the world where the food is so bad?
* Passing references occur on pp. 90, 203, and 229 as well.
* Thanks to Christine Francescani for pointing this out.
* A wrong idea popularized
* This memoir is more about Tuscany than about Kinta Beevor's childhood.
* But, alas, on p. 144, we have: "Sometimes from the beach at dusk we could
* see the `green flash'. The sky had to be perfectly clear, and just as the
* last tiny segment of the sun disappeared below the horizon, the streak of
* tangential light through the surface of the sea would produce this
* extraordinary optical effect." Extraordinary indeed!
* "Published in the United States by Pantheon Books, a division of Random
* House, Inc., New York. Originally published in Great Britain by Viking,
* a division of Penguin Books Ltd., London, in 1993." This entry is here
* for the original English edition; see the 1999 Pantheon reprint in the
* main GF file. Note that Kinta Beevor died in 1995.
* Isabel Allende's memoir records the "make a wish" folklore
* "Every evening, my mother took my hand and walked with me to the rocks
* to watch the sunset. We waited to make a wish on the last ray, which
* sparks green fire at the precise instant the sun sinks below the horizon."
* passing mention in Steve Martini's thriller set in Puerto Rico
* "Maybe catch the setting sun, the green spark as it flashes on the
* horizon." (p.317)
* Thanks to Hank Hogan for pointing this out!
* Alison Anderson's translation of Le Clézio
* ". . . while at the bow, where the sky drops into the sea, like a finger
* through a pupil to probe the depths of the head, the green flash exploded
* in sudden brilliance." (p.5) [not copied, as this is the only GF use.]
* Alison Anderson explains the difficulty of translating the GF passage:
* "This was perhaps the most difficult paragraph in the novel. . . . Finding
* the translation, initially, for `rayon vert' was quite difficult, as I was
* not familiar with the expression in English."
* Mention of GF in a poem rates the "Literature" file, though it's from
* The C.S.M., and mostly about jellyfish.
* "The orb we see / is merely phenomenal.
* The sun as noumenon has already sunk. . . .
* "By hugging that globe with our eyes as it plunges,
* we hope for a vision of spurting green." Etc. Sounds as if
* Colin Campbell understood refraction, but hadn't seen a flash.
* Carol Wolper's novel about sex and Hollywood
* The passages of interest here are on p. 47, where screenwriter
* Elizabeth West and her friend Andrew are in an art gallery "in front of
* a large canvas . . . entitled Green Light .
* `It's the green flash created when the setting sun hits the ocean,'
* Andrew explained.
* `It is? How come I've never noticed that?'
* `It's out there,' he said." CUT TO: p. 271, where they are at the
* beach, on the penultimate page of the book:
* "The sun had just hit the water, and for a second it was as if a
* horizontal band of green light was drawn across the horizon."
* So it's like Jules Verne all over again, though the GF hasn't played
* any visible part in between. (Or Dorothy being told she can go back to
* Kansas any time she wants.)
* "Riverhead Books / a member of Penguin Putnam Inc."
* Hezi Yizhaq's translation of Jules Verne, with my 1997 flash on cover
* The original illustrations are reproduced in this well-produced volume.
* This website is mentioned at the bottom of p.10.
* ISBN 0 04340001574 8.
* Don Lee's stories set in Southern California use the GF for local color
* Thanks to Kathryn Neal of the SDSU Library for pointing this out!
* Pat Murphy's physics lessons, disguised as fiction; Verne would have approved
* The GF page is 237; cites Bowditch. No useful details.
* JULES VERNE's last mention of GF
* This is the English translation of Verne's unpublished manuscript.
* The GF appears on the last 2 pages, as part of the climactic scene
* (pp. 186-187). This is the 3rd time the GF appears in Verne's works
* -- always as a symbol of hope for the future, so I suppose that is
* how he felt about it.
* "Originally published in France as En Magellanie . . . 1998."
* Translated by Benjamin Ivry. Thanks to Hezi Yizhaq for finding this!
* The true origin of the "old Scottish legend" revealed
* in letter 535 from Hetzel to Verne (pp. 139-143).
* Olivier Dumas, Piero Gondolo della Riva & Volker Dehs, the editors
* of Jules Verne's unpublished correspondence with his editor Pierre-Jules
* Hetzel, have uncovered the actual facts: Hetzel invented the "legend",
* and Verne adopted almost the exact wording that Hetzel proposed.
* The phrase "rayon vert" appears without hyphenation in their early
* letters; it is not until the text is almost ready for the printer that
* we find Verne writing it as "Rayon-Vert" (p. 153).
* Some library catalogs list only Verne as the author here; others
* list Hetzel as well; WorldCat lists the editors also. Olivier Dumas
* seems to be the main editor; he signed the introduction. Most of
* Hetzel's letters to Verne were collected by della Riva.
* Many thanks to Eric Frappa for telling me about this!
* A local writer features the GF and related San Diego attractions
* Éric Frappa shows how Verne probably learned of the Green Ray
* "Avec Le Rayon-Vert , Jules Verne nomme pour la première fois le
* phénomène, qui acquiert ainsi un statut d'objet scientifique à part
* entière et attise la curiosité des férus de nature et de science."
* But how did Verne learn of this phenomenon? The few published reports
* before 1877 (when the flash first appeared in Verne's writings) were
* in English or Italian, neither of which Verne could read.
* "Ainsi, pendant longtemps, l'origine de la connaissance précoce du
* rayon vert par Jules Verne est restée un mystère . . . ."
* The link appears to have been Winstanley's 1873 report, which was
* translated in a Sept. 1874 article by Abbé Moigno in Cosmos-Les Mondes ,`
* a journal readily available to Verne -- who is known to have read it.
* Furthermore, Moigno was the Paris correspondent of The Chemical News ,
* which had reprinted Winstanley's report only a month after Winstanley
* had read it to the Manchester Literary and Philosophical Society.
* However, Moigno used the French translation of the Chemical News report
* that had appeared in L'Institut in July, 1874; in this process,
* Winstanley's name was garbled by a typo, and other errors were
* introduced. (As often happens with refraction phenomena, the effect
* of these errors was to make the phenomenon seem much more spectacular
* than it really is.)
* However, because the descriptions of green flashes in Verne's
* 1882 novel go beyond the brief and misleading French translation of
* Winstanley's report, it seems likely that Verne obtained additional
* information about them from seamen, or from friends in the Yacht-Club
* de France. In particular, in his 1877 novel Les Indes-Noires , he
* describes the flash as visible both morning and evening, while both
* Joule and Winstanley mention only sunset observations.
* Indeed, there are hints that Verne might himself have seen a green
* flash or two. He describes the "Etruscan vase" shape typical of an
* inferior-mirage sunset in his 1882 novel. And he recorded seeing
* the green of a green flash (but not in an actual flash) in a notebook
* entry dated 19 June 1881. These are tantalizing indications, but not
* conclusive evidence.
* However, it seems very likely that the French translation of
* Winstanley's report really is what got Jules Verne interested in green
* flashes: "La découverte, pour la première fois, d'un article sur le rayon
* vert en français qui précède Les Indes-Noires, dans une revue lue par
* Jules Verne, fournit une explication plausible à la prise de connaissance
* du phénomène par l'écrivain."
*
* Possible reference to GF in Indian astronomy or astrology?
* Just a passing reference in a long letter on the Krakatoa Green Sun:
* "The native astronomers say that there is a planet wholly absorbed in
* the sun, and that if it leaves the sun a green light will appear. Or,
* according to others, if Venus comes in contact with the sun, which,
* according to their calendars, is the case now, a green light will be
* seen."
* HUMPHREYS (who believes the "LEGEND" as well!)
* ". . . according to Highland legend . . . "
* "In proverb form:
*
* Glimpse you e'er the green ray,
* Count the morrow a fine day."
*
* I suspect he made this up himself.
* According to Dean Newman, this couplet also is quoted by a character
* in some novel -- but which one??? If a reference before 1923 could
* be found, it would disprove my assumption that Humphreys invented this
* "proverb".
* Here are the actual letters to The Times that set off Botley and a
* host of others:
*
* Hints of the legend:
* "In the Isle of Man a belief existed formerly, and is not yet quite
* forgotten, that a momentary gleam or tincture of the light from the
* rising sun, of a special and significant character, occurred at rare
* intervals -- once perhaps in two or three years."
* "Literary use made of the actual phenomenon, as by Jules Verne and
* William Black, belongs to a different category."
* QUERY: What did William Black write about the GF?
* DETAILS of the SOILSHEY-BIO story:
* ". . . something like the green flash appears occasionally in Manx
* folklore. The old Manx name for it was soilshey-bio , or `living light';
* and I have gathered the impression, without having been actually told so,
* that it was thought to be an emanation of the sun's life . . . ."
* "In several fragments taken down by me from Manx fisherfolk, the `flash'
* was seen at sunrise on the morning preceding the wreck of one or more
* boats . . . ."
* ". . . the `flash' certainly also had its beneficial side in popular
* belief . . . . I had this belief directly from a very old man who was, I
* should think, about the last of the `charmers,' . . . . if any person could
* find what he called `the herb of lifé at the moment when it was touched
* by the soilshey-bio , death would never touch him or anyone to whom he
* gave a portion of the herb to eat."
* (Mona Douglas was a well-known authority on Manx folklore.)
* FRANCES ELLA WHITMAN attributes the green-ray couplet to Humphreys
* in her Master's thesis from Boston U.
* "The association of green with the dead and with witches, and the
* familiar superstition that green is unlucky. . . " (p.176)
* ". . . green is a fairy color and of ill omen, and is, moreover,
* associated with witches and the dead. . . " (p.178)
* "In British folksong the color green is occasionally associated with the
* dead or with death." (p.240)
* ". . . the ill omen that in general attaches to green." (p.241)
* Dover reprint of U. of Chicago Press, 1928 edition:
* "GLIMPSE YOU EVER THE GREEN RAY, count the morrow a fine day."
* Thanks to Dean Newman for alerting me to this phrase!
* Contains 2 not very useful GF observations, but more on folklore,
* including both the verse and that "whatever you wish on the green ray
* will come true." (cf. J.D.MacDonald's "A Touch of Green".)
* This column by Gilean Douglas has about 8 column-inches on GF in the
* Sunday supplement to the Victoria Daily Colonist .
* suggests the GF is connected with the "kelpie" that vanishes in a blue flame
* (According to Admiral W. H. Smyth's "Sailor's Word-Book", a kelpie is
* "A mischievous sea-sprite, supposed to haunt the fords and ferries of
* the northern coasts of Great Britain, especially in storms.")
* Another fool fooled by Jules Verne's "LEGEND"
* ". . . it has also become a part of folk legend. The Scottish
* Highlanders, for example, say . . . ."
* Also quotes Humphreys's verse, without attribution.
* Thanks to Keith Heidorn, "the Weather Doctor", for this reference!
* J. Glyn Ford's strange book review, placed here for its odd notions
* The book reviewed leans heavily on A. Thom's now largely-discredited
* claims of extreme sophistication and accuracy in Stonehenge (and related)
* alignments. That's urban-folklore enough in itself; but now read this:
* "The major objections concern the solar alignments, for it is charged
* [?? by whom ??] that observations of solar risings and settings would be
* rendered impossible by the dazzle." (Obvious nonsense to anyone who has
* ever observed sunsets!)
* Then the weirdness really sets in: "One solution which would overcome
* the problem of dazzle is that Neolithic observers were looking for the
* phenomena [sic] of `green flash.' These phenomena occur due to the
* atmospheric dispersion of sunlight when only a minute segment of the sun
* is above the horizon. Under ideal conditions this segment is observed
* to change in color from orange to green so that the final glimpse of the
* sun is a flash of green. . . . J.H.Mathers (`The Green Flash,' Hermes 13
* [1966]: 112-14) has suggested that some Celtic tales indicate that these
* phenomena were observed. Therefore, this seems to provide a possible
* answer to the critics." A far-fetched "solution" to a far-fetched
* "problem" is crazy!
*
* Some of W. H. Julius's nutty papers on anomalous dispersion are here
*
* The beginning: note that this precedes the 1901 eclipse expedition,
* despite Minnaert's assertion in the DSB.
* The paper is dated 1900 August; the issue closed on 15 Nov.
* But it seems to be a German translation of Julius's paper in the
* proceedings of the Kon.Akad.v.Wetenschappen te Amsterdam 8, 510-523
* (24 Feb.1900)
* He mentions Schmidt's theory, and cites Wiener's 1893 mirage review.
* Already here in col. 444 there is the confusion about ir/radiance,
* couched in the tell-tale language of "rays", when he tries to explain
* why sunspots are dark.
* The English version of the same paper:
* [According to J.Hartmann, whose 1907 AN paper is in the GF file, this
* also appeared in Dutch, and in Physik. Zs.!]
* The revised sunspot proposal
* . . . and its German translation
* And now the English version (though now the sunspot story is put off)
* This version has some weasel-wording: ". . . explanations . . . on which
* we shall not now insist." And: ". . . must be deferred to a separate
* paper." Looks as if the Editor or a referee leaned on him here.
* In this paper, the ir/radiance confusion is obvious
* "Wegen ihrer schliefen Einfallrichtung haben diese Strahlen geringe
* Intensität; sie entsprechen dem Kernschatten."
* (Lecture-demonstration given at the 4th meeting of the International
* Solar Union at Bonn, 4. Aug. 1913)
* Now Julius has become a full-fledged crank: no equations, just wild
* stuff. Here he is fighting not only Anderson, but St. John, and
* Adams and Burwell, and others.
* Klaus Hentschel's review of Julius's folly
* Julius was a student of Buys Ballot, and the thesis advisor of
* Minnaert (in his second Ph.D.!) and van Cittert. He founded the
* solar-physics laboratory and program in Utrecht, in an attempt to find
* support for his bizarre theories.
* This has a complete list of Julius's publications; but beware:
* Hentschel is a social scientist, and doesn't understand any of the science
* involved. So he fails to see why everyone who knew anything about solar
* physics regarded Julius as a crank, or nearly so. This, despite the
* fact that he notices something odd about Julius's presentation, and so
* has a whole section devoted to Julius's rhetoric. Hentschel seems to
* think Julius's explanations were as plausible as the solar astronomers'
* at the time; his arguments are as qualitative as Julius's were. So there
* is no discussion of the quantitative side of the dispersion relation;
* no mention that many of the effects Julius was "explaining" were lost
* in the errors of measurement at the time; no awareness of the role of
* polarization in the discovery of Zeemann splitting in the sunspot lines
* -- or, for that matter, the recognition (from line ratios of neutral
* and ionized states of the same element, and the presence of molecular
* absorptions) of spectroscopic evidence for the lower temperature in
* sunspots than in the photosphere.
* Hentschel has missed several comments on Julius's GF theory, and adds
* no new references; so I didn't make a copy of this 192-page item.
*
* BONAVENTURA CAVALIERI's trig and log tables
* This is most likely what Cassini used to compute his refractions,
* as it was published in Bologna just a few years before he began working
* for Malvasia, and is reputed to be the book that introduced logarithms
* into Italy. I'd think Malvasia would have bought himself a copy for his
* own library and observatory.
* There is an elaborate title page, too complicated to simulate here; see
* either Google Books or the better (color) copy available at the Swiss
* electronic library, at e-rara.ch (part of E-lib.ch.) The author is
*
* FR. BONAVENTURA CAVALERIO
* MEDIOLANENSI
* Ordinis Iesuatorum Sanctti Hieronymi
* Ac in Almo Bononiensi Gymnasio Primario Matbematicarum
*
* NOTE: G.D.Cassini was Cavalieri's successor to the professorship of
* mathematics and astronomy at the U. of Bologna after Cavalieri died.
* MARALDI's invention of the "refractive medium"
* From observed heights of the mercury column at several places with known
* heights (supposedly, from surveys), he decides that the mercury column
* is one line lower at 60 feet above sea level, and that the increment in
* height to produce the next line drop in column height is 61 feet, and so
* on. This arithmetic progression makes the heights a parabolic function
* of the pressures, which allows him to calculate that the pressure goes
* to zero at a height of 12796 toises, or 6½ leagues!
* As this is much larger than the height determined from astronomical
* refractions, he says the discrepancy "donnerent lieu de conjecturer
* qu'il pourroit y avoir quelque matiere fluide répandue dans la partie
* inférieure de l'air, & peu élevée sur les plus hautes montagnes de
* ll terre, qui fut la cause principale des réfractions des Astres."
* So, from two wrong estimates of the height of the atmosphere, he
* infers that the refracting material is different from air???
* The history of the Paris Observatory, with Cassini's autobiography
*
*
* This is Jean-Dominique Cassini's account of the Paris Observatory; but
* it includes the autobiographical memoir of Jean Dominique Cassini (his
* great-grandfather, or "Cassini I"), which contains some recollections
* of the construction of the San Petronio meridian/heliometer. There are
* also accounts of his trip to England to see Herschel's telescope, and
* other papers relevant to the instrumentation and finances of the Paris
* Observatory in the early post-Revolutionary Republic. I was bemused
* at seeing the correspondence about the secret of making flint-glass,
* and a mention of Bouguer's binocular heliometer.
* The title page rambles on and on, with "suivis de la vie de J.-D.
* Cassini, écrite par lui - même, et des éloges de plusieurs académiciens
* morts pendant la révolution", including J.-D. Maraldi (the nephew of
* J.-P. Maraldi who observed looming and mirages), and Le Gentil.
* The title is often truncated at "sciences".
* Note: Hachette republished this in 2016.
* First mention of using sunrise/sunset to determine LONGITUDE
* "Captain Weston has proposed that the opportunity afforded by the
* glorious appearance of the setting sun, shall be made use of for obtaining
* ship time, and thence with a chronometer shewing Greenwich time, to get
* the longitude! . . . The tables are preparing for publication by the
* Admiralty,. . . . Capt. Weston has been rewarded by the Admiralty for his
* ingenuity . . . ."
* Visual estimates of altitude good to a degree or two
* Buist's collection of published accounts of meteorite falls in India
* includes Capt. Shortrede's provocative statement from the Journal
* of the Asiatic Society of Bengal , Part II, vol. xi, pp.959-962
* (1842?):
* "The observations themselves are very easily made when a person
* knows exactly what he has to do, and does not allow himself to be
* distracted by attempting too much. Besides general attention, the most
* useful qualification I believe to be, the ability readily to estimate
* altitudes at sight. I know by experience, that persons in the habit of
* such observations may train themselves to estimate altitudes at sight
* within 2° of the truth, for I have practised it along with another
* person, proving our estimates by an altitude and azimuth instrument."
* (reprinted by "G. Buist, LL.D., F.R.S.L. and E. &c." on p. 204)
* NOTE: Captain Shortrede was 1st Assistant, Grand Trigonometrical
* Survey of India.
* Buist notes in his introduction: "I found as I proceeded, that by
* causing notices of meteors to be inserted in the Bombay Times ,
* gentlemen were induced to write accounts of such as they had seen, who
* otherwise might have remained silent ; and the multitudes described
* during the two past years compared to the small number of notices we
* have anteriorly to this, sufficiently indicate the conveniency of the
* practice, and its adaptation for eliciting intelligence."
* Janssen's sunset spectroscopy and visible-IR report
* In his 1868 passage through the Red Sea, he took advantage of the
* high dew-points (26 to 30° C) to observe water bands at sunrise and
* sunset with a special low-dispersion spectroscope:
* "Observant avec cet instrument les levers et les couchers du Soleil
* dans cette mer, j'ai été surpris de voir que ma vision s'entendait
* loin dans la région obscure, au delà de A, et je vis alors les bandes
* obscures Y, Z de Brewster, extraordinairement accusées; ce qui montre
* bien qu'elles sont dues à la vapeur aqueuse; car dans les circonstances
* atmosphériques ordinaires, ces bandes sont bien difficilement
* perceptibles."
* NOTE: Brewster's Z is the clump of water lines at 8228 Å ,
* according to the Rubber Bible; and Y is another group at 8990.
* HISTORY of the ALMANACs, biographical notes on everybody at USNO and RGO,
* an account of Wallace Eckert (1902-1971) and computing and . . . !!!!
* Everybody involved with the Almanac is here: the heads of the US and
* HM NAOs; the people involved on both sides with refraction calculations
* (Myles Standish, Catherine Hohenkerk) or star catalogs (Dorrit Hoffleit);
* George Kaplan and modern instrumentation; computing (T.J.Watson Sr. and
* the IBM 650); Simon Newcomb, E.W.Brown and G. W. Hill, Bessel's
* refraction table, etc. are all mentioned in this 400-page book.
* This SESQUICENTENNIAL SYMPOSIUM is full of good stuff. See the Table
* of Contents (pp. ix - xi) for a fascinating look at the recent past.
* Available at https://apps.dtic.mil/sti/tr/pdf/ADA470556.pdf
* Pabitro Ray, David Salido Monzú, Robert Presl, Jemil Avers Butt,Andreas Wieser
* A good modern review of 2-color methods. Errors of a few parts in 107
* are demonstrated. References to other modern papers.
* DOI: 10.1364/oe.514997
* [see also Cassini's memoir, published by his great-grandson namesake]
*
* Biot's story about LAPLACE
* This tells how he became Laplace's proofreader, and "il est aisé de
* voir." But the main point is the anecdote about his discovery in
* analysis, and Laplace's responses to it.
* This was reprinted in Biot's Mélanges Scientifiques et Littéraires
* (M. Lévy, Paris, 1858), pp. 1-9.
* [This may be vol. 212; dated Fev. 1850]
* CLAUDE LOUIS MATHIEU (1783-1875)
* (Not to be confused with the mathematician Émile Mathieu, of the
* eponymous functions.) Mathieu was a carpenter's son, but managed to
* acquire an education, and the ambition of attending the École
* Polytechnique. Mathieu lived in Delambre's observatory as a student,
* in 1801. He and Delambre became friends, and Delambre left him the
* History of Astronomy in the 18th Century to complete. He met Arago
* at the École Polytechnique, and later married Arago's sister; their
* daughter in turn married Laughier. When Arago died, Mathieu took over
* the supervision of the Connaissance des Temps and the Annuaire
* of the Bureau des Longitudes. When he died in 1875 at the age of 92,
* he was the last living link with the founding of the metric system,
* having served as Biot's assistant in the Dunkirk survey.
* [See also the notes in C.R. 80, 581-583 (1875).]
* FRIEDRICH WILHELM BESSEL (1784-1846)
* An English translation of Heinz Klaus Strick's biography of Bessel
*
* https://www.spektrum.de/wissen/friedrich-wilhelm-bessel-1784-1846/999405
*
* is available at the St. Andrews website:
*
* https://mathshistory.st-andrews.ac.uk/Strick/Bessel.pdf
*
* A longer article at
*
* https://en.wikipedia.org/wiki/Friedrich_Bessel
*
* as well as Strick's short account is evidently based on Bessel's own
* short memoir, which is cited in his obituary in Astronomische Nachrichten.
*
* https://adsabs.harvard.edu/full/1919AN. . . .210..161R
*
* Bessel's "Kurze Erinnerungen an Momente meines Lebens" was published in
*
* "Briefwechsel zwischen W. Olbers und F. W. Bessel" (A. Erman, Leipzig, 1852)
* which is available on the Web at
*
* https://www.digitale-sammlungen.de/de/view/bsb10061073?page=13
*
* An English translation is available at
*
* http://www.probabilityandfinance.com/sheynin/098_bessel.pdf
*
* WILLIAM SCORESBY (1789-1857)
* Contains a short biography of Scoresby, and a summary of his work.
* Available at
* https://www.euppublishing.com/doi/pdfplus/10.3366/anh.2019.0551
* FRIEDRICH WILHELM AUGUST ARGELANDER (1799-1875)
* Argelander's father was Finnish, but his mother was German. The German
* royal family stayed in their house after the battle of Jena. After
* Gymnasium at Elbing, Argelander attended the University of Königsberg,
* where he was attracted to astronomy by Bessel's lectures. He asked to be
* allowed to do some work for Bessel, who was so pleased by the results that
* he called him "one of his most distinguished pupils." He became Bessel's
* regular assistant Oct. 1, 1820, and made the refraction observations
* at low altitude early in 1821. In 1823 he became the director of the
* new observatory at Abo, which was moved to Helsingfors after the fire
* of 1827. In 1837 he became director of the new observatory at Bonn,
* where, beginning in 1852, he undertook "that great Durchmusterung
* . . . with which his name will be for ever associated."
* [based on a longer obit. by Schönfeld in VJS AG 10, part 3.]
* This is the notice by William Groff's sister, Florence Groff, in his
* French collected works. She concentrates on his Biblical studies, and
* does not mention his GF work.
* JAMES GLAISHER (1809-1903)
* A detailed biography of James Glaisher by "a grandson of Glaisher's
* only daughter". Though he "did not receive much formal education,"
* Glaisher became both an FRS and a FRAS; he was "the first President of
* the Royal Microscopical Society, President of the Royal Photographical
* Society for more than 20 years, and a member of the Council of the Royal
* Aeronautical Society from its foundation in 1866 until his death."
* A friend of the family with connections at the RGO got Glaisher
* training in astronomical instruments while John Pond was A.R. After 2
* years' work with the Ordnance Survey in Ireland, Glaisher became an
* assistant to Airy at Cambridge in 1833. When Airy became A.R., he "made
* arrangements for Glaisher, then his First Assistant, to transfer . . . to
* the Royal Observatory at Greenwich." [Impressive that the finicky Airy
* was so pleased with Glaisher's work!]
* "In 1840 Airy appointed Glaisher Superintendant of the Magnetical
* and Meteorological Department on its formation, a post he was to retain
* for 34 years."
* Glaisher's discovery of the stratosphere is mentioned, but not his
* affirmation of nocturnal inversions.
* AUGUSTE BRAVAIS (1811-1863) references
* This is his own annotated bibliography, which was used to support his
* application for membership in the Académie des Sciences
*
* [See
* Maurice Crosland
* Assessment by Peers in Nineteenth-century France: The Manuscript
* Reports on Candidates for Election to the Académie des Sciences
* Minerva, Vol. 24, No. 4, pp. 413-432 (December 1986)
*
* which is available at Stable URL: https://www.jstor.org/stable/41820664
* for an explanation of such "Notes". There, Bravais is discussed on
* pp. 419-420.]
*
* Bravais began his career as a sailor, and was sent as a naturalist on
* several expeditions. This required him to study botany; a study of the
* symmetries of flowers and leaves led him into the study of minerals and
* crystals. His work in navigation clearly stimulated his study of
* refraction. [I am reminded of the career of Minnaert, who went from
* photobiology to solar physics, with excursions into atmospheric optics.]
* Bravais was a co-founder and first President of the Société
* Météorologique; he presided at its first meeting, on 14 Dec. 1852.
* This "Notice" outlines his most productive years.
*
* He discusses his interest in atmospheric optics on p. 8 of this Notice,
* beginning with rainbows and halos. The mirage publication is described on
* p. 10, where he summarizes it as follows:
* "Je passe en revue toutes les anciennes observations venues à ma
* connaissance ; je rappelle les travaux de Woltmann , de Wollaston ,
* de M. Gergonne et de M. Biot .
* "Mirage inférieur . -- Rôle important de la caustique. -- Rapport de
* grandeur des deux images . -- Explication du mirage inférieur . -- Cas de
* la caustique rectiligne . -- Cause de la moindre étendue de l'image
* inférieure dans le sens vertical. -- Effet de la courbure de la terre.
* "Mirage avec simple élévation des objets. -- Il ne peut y avoir de
* caustique dans ce cas . Couche dont la densité fictive est un minimum .
* "Mirage supérieur. -- Cas des trois images. -- Cause de la disparition
* fréquente de l'image supérieure. -- Cas où l'image moyenne disparaît .
* "Mirage latéral. Mirage multiple. -- Combinaison des deux espèces de
* mirage. -- Phénomène rare ; ce phénomène a été vu par M. Bravais dans le
* nord de l'Europe.
* "Depuis cette époque , j'ai fait, à Royan (Charente-Inférieure), de
* nombreuses observations sur le mirage observé à l'horizon de la mer ; ces
* observations ne sont point encore publiées ; elles sont accompagnées de
* plusieurs dessins, représentant l'apparence de la rive gauche de la
* Gironde, et celle de navires entrant dans le fleuve ou en sortant."
*
* Then comes the reference to his paper on the horizontal ray:
* "Explication théorique du relèvement des trajectoires lumineuses dans
* le mirage ."
* The footnote here cites his abstract in "L'Institut" 21, p. 193. His
* interesting comment is:
* "Ce phénomène paraît avoir embarrassé les géomètres, et en a conduit
* plusieurs à admettre la réflexion totale. Je montre qu'il n'y a point de
* réflexion totale , et que le relèvement des trajectoires est une
* conséquence naturelle de l'application de la théorie des ondes à la
* marche du rayon ."
* (That paper was not published until 1856.)
*
* Bravais's "Notice" is available at Google Books, at URL:
*
* https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Bravais+Notice+Travaux&btnG=
* and at HathiTrust.
*
* PROSPER HENRY (1849-1903)
* FRANÇOIS-ALPHONSE FOREL (1841-1912)
* Prof. Dr. Henri Blanc's long obituary of Forel
* NOTE: the obituaries are paginated separately from the main part of
* the volume. To get this, tell your librarian that the pages you need
* are in the "Annexe" or "Anhang" that contains the obituaries.
* Although the long bibliography was compiled by Forel himself, it is
* not complete, and contains many errors.
* FRANÇOIS-ALPHONSE FOREL (1841-1912)
* FRANÇOIS-ALPHONSE FOREL (1841-1912)
* This contains Forel's autobiography, written for his grandchildren;
* it lay unpublished in the family archives for a century, before being
* transcribed from his scribbly handwriting and published in 2012.
* The section of interest here is pp.146-154, which cover the refraction
* phenomena. Unfortunately, there is an error of transcription in the
* description of inferior mirages: in the 3rd line from the bottom of
* p.148, "au-dessus" should be "au-dessous". [see the correct (and
* similar) wording on p. 475 of Forel's 1911 lecture on the Fata Morgana,
* or pp. 523 and 525 of his 1895 monograph.]
* Thanks to Eric Frappa for useful discussion of this book.
* ROBERT TRAILL OMOND (1858-1914)
* Omond seems to have been the first person to use the phrase
* "green flash" in print. He was a student of Tait's but did not earn a
* degree (his LL.D. was honorary).
* Many thanks to Marjory G. Roy, Hon Secretary, Scottish Centre,
* Royal Met Soc, for the reference to this item!
* ANNIBALE RICCÒ (1844 -1919)
* not very informative
* ANNIBALE RICCÒ (1844 -1919)
* Much better! He began life as an architect; his work at the
* Agricultural Station at Modena involved meteorology; in 1872 he became
* assistant at the observatory there. Most of his work after 1879
* involved solar observations. He became co-editor of the Memorie degli
* Spettroscopisti Italiani with Tacchini in 1899.
* See the JHA article by Nali (2022) for another biography.
* CHARLES THOMAS WHITMELL (1849-1919)
* "Mr. C. T. Whitmell, the well-known amateur astronomer . . . ."
* "His interests lay in the mathematical rather than in the observational
* side of astronomy, though his long series of observations of the
* phenomenon known as the ``green flash'' are almost unique."
* Whitmell died Dec. 10; this paragraph appeared in the Dec. 18 issue!
* CHARLES THOMAS WHITMELL (1849-1919)
* CHARLES THOMAS WHITMELL (1849-1919)
* "In 1897 he was transferred to Leeds, where he lived for the remainder
* of his life.
* "When he settled in Leeds, Mr. Whitmell found several opportunities
* for scientific occupation. . . . There had been a Leeds Astronomical
* Society 30 or 40 years earlier, established under the honorary
* presidency of Sir George Airy, to whose proceedings Sir John Herschel
* had contributed a remarkable essay: `The Yard, the Pendulum and the
* Metré; but this society had not fulfilled expectations, and did not
* endure, but had been revived in 1892 . . . . Mr. Whitmell joined this new
* society in March, 1897 . . . . He was elected President at the end of the
* year, and held that office until 1900. He joined the British
* Astronomical Association in 1897, and was a member of its Council for
* some years. . . . Mr. Whitmell was elected a Fellow of the Royal
* Astronomical Society in December, 1898."
* Thanks to Ray Emery for supplying this! -- On the back is a title page
* for the journal, for the next year (1920).
* CHARLES THOMAS WHITMELL (1849-1919)
* "He was held in the highest respect and esteem . . . for his courtesy,
* considerateness, and charm of manner."
* ". . . the patient, careful manner in which he dealt with the difficulties
* of inquirers in the columns of the English Mechanic .
* "Phenomena of colour greatly interested him, and he wrote several notes
* in explanation of the green flash at sunset . . . ." as well as ". . . his
* useful handbook on colour, published in 1888."
* CHARLES MICHIE SMITH (1854-1922)
* Smith succeeded Pogson at Madras; founded the Kodaikánal Observatory
* near there; and was succeeded by John Evershed on his retirement in 1911.
* See Report of Kodaikánal & Madras Observatories, MN 72,286(1913)
* Note that Evershed, his successor, always refers to him as
* "Michie-Smith" (hyphenated) in his autobiographical note in Vistas.
* ARTHUR ALCOCK RAMBAUT (1859-1923)
* Rambaut became Radcliffe Observer in 1897, soon after publishing his
* big 1895 paper on atmospheric dispersion, which must have influenced
* his choice as the author to review the Green Flash -- as well as his
* mental model for it! His main work was the attempt to measure parallaxes
* from simple direct photographs -- enshrined in vol.53 of the
* Radcliffe Observations -- but this was largely a failure.
* CAPTAIN ALFRED CARPENTER (1847-1925)
* Colonel ERNEST ELLIOTT MARKWICK, C.B., C.B.E. (1853-1925)
* This long obit is prefaced with a fine portrait of Col. Markwick.
* He was interested in solar work, which may have given him his
* introduction to green flashes. His main astronomical accomplishment
* was to organize the Variable Star Section of the BAA, after which
* (his biographer here claims) the AAVSO and other like organizations
* were patterned. "In 1879 he became a Fellow of the Royal Astronomical
* Society and in October, 1912, he was elected President of the B.A.A."
* He discovered T Cen and RY Sgr, the latter an R Cor Bor star, using
* only the charts of Gould's Uranometria Argentina and binoculars,
* while stationed in Gibraltar.
* WILLEM HENRI JULIUS (1860-1925)
* Einstein's obituary, "written with the hope that his views on taking
* refraction into account in explaining solar phenomena may not be
* temporarily forgotten by oversight," refers to him as an "old friend".
* ". . . in 1891, a work of A. Schmidt . . . turned his attention to the
* field of solar physics, to which he thereafter devoted his entire life."
* His treatment of Julius's explanation of "the distribution of intensity
* in sun-spots", as due "to refraction of light from the photosphere",
* indicates that Einstein, like many others, did not understand the
* distinction between radiance and irradiance. Fortunately, he excuses
* himself by saying "I am not competent to render judgment on the reach of
* Julius' ideas . . . ."
* WILLEM HENRI JULIUS (1860-1925)
* Minnaert's biography of Julius in the DSB:
* "His observation of the solar eclipse of 1901 was the turning point in
* Julius's activity" . . . "The darkness of sunspots was explained by
* regular refraction. In these conceptions the importance of refraction
* was vastly exaggerated."
* So Minnaert, too, seems not to have realized the physical impossibility
* of Julius's ideas about sunspots.
* The DSB was edited by C.C.Gillespie and published by Scribner's, New York.
* MARTEN EDSGE MULDER (1847-1928)
* Mulder, who had been a student of Donders and Snellen (inventor of the
* familiar E / F P / T O Z / . . . eye chart) in Utrecht, founded the 4th
* eye clinic in the Netherlands in 1879, where he treated over 50,000
* patients. His pride was the library which he managed himself, and whose
* catalog he published. He resigned from his professorship at the
* University of Groningen in 1913, an unusual step at the time, to devote
* himself to travel and his interests in the natural sciences. [Note that
* the GF articles in Kosmos that provoked his interest appeared just at
* this time.] He and his wife then moved to the Hague, and he published a
* series of works on popular science.
* Many thanks to Dieneke de Vries for sending a photocopy!
* CARL AUGUST von SCHMIDT (1840-1929)
* Includes a COMPLETE BIBLIOGRAPHY of Schmidt's publications.
* Schmidt's papers cover a wide range: geophysics, meteorology, astronomy.
* His principal field seems to have been geophysics and seismology.
* He spent 32 years teaching at the Realgymnasium in Stuttgart, where he
* taught physics, chemistry, and mathematics. This career as what we
* would call a high-school science teacher was followed by several years
* as head of the Stuttgart weather office. Though he is primarily
* remembered for his work in seismology, we are concerned here with his
* papers on refraction in the atmospheres of the Earth and (supposedly)
* the Sun.
* Note: p. 238 is numbered 338 in error.
* CARL AUGUST von SCHMIDT (1840-1929)
* Kleinschmidt's other obituary of Schmidt. This one is shorter, but
* seems to recognize more of Schmidt's errors; it mentions his value
* of 14K/km for the adiabatic lapse rate, for example -- and says
* "Die nach ihm benannte Sonnenhypothese -- scherzhaft wurde er oft der
* ``Sonnenschmidt'' genannt -- . . . ."
* On the other hand, here he's introduced as "Geh. Hofrat Prof. Dr."
* ALFRED WEGENER
* ANTONIO GARBASSO (1871-1933)
* Garbasso was a physicist who studied under Heinrich Hertz at Bonn.
* He worked at Turin, and later at Florence, in both mathematical and
* experimental physics, primarily connected with the electromagnetic theory
* of light, such as circular polarization, birefringence, and spectroscopy.
* Later, he was President of the Italian Physical Society.
* PDF available at ADS.
* KARL REINHOLD KUPFFER (1872-1935)
* Kupffer was a colleague of Rudolf Meyer's; his obituary gives some
* insight into the German community in Riga, as the plunder of the library
* after the Bolshevik Revolution and disquieting effects of the German
* occupation during WW I are alluded to.
* Kupffer is a minor figure in our story. Still, he is an interesting
* character; and his complete bibliography at the end of the obituary is
* remarkable for its breadth. The obituary gives the German and current
* names of places; some of Kupffer's publications are pleas to preserve the
* German place-names.
* Sir W. M. FLINDERS PETRIE (1853-1942)
* (knighted in 1923, at age 70)
* [This book is in the library: DT 76.9 P4 D7 1985]
* He is a minor figure in our story, but a major figure in archaeology;
* his measures of the Great Pyramid showed that Piazzi Smyth was a crank.
* He also wrote an autobiography, ``Seventy years in Archaeology'' (1931).
* Margaret Drower's book will tell you more than you want to know about him.
* ROBERT JOHN STRUTT, 4th BARON RAYLEIGH (1875-1947)
* Contains a useful anecdote about the 1929 trip to South Africa that
* aroused his interest in green flashes (p.525): "The writer remembers
* one evening when Rutherford saw it on the deck above and we who were
* standing just below did not see it. Rayleigh . . . came to the conclusion
* that `everything depends on the location' of the observer."
* There is also a quote (from where???) about reactions to Rayleigh's
* GF papers. (p. 526)
* WILLIAM JACKSON HUMPHREYS (1862-1949)
* Humphreys was President of the AMS in 1928-29, and served in many other
* offices both there and in the AAS, of which he was one of the founders
* (though you can't find that here). He served on the Councils of both
* societies. He took an oddly simplistic view of both ball lightning,
* which he thought did not exist, and the GF, and was conned by Jules Verne.
* He studied under Rowland at Johns Hopkins; his most notable student was
* E.W.Woolard. Meteorologists remember him for his work in understanding
* the stratosphere; astronomers have forgotten him.
* H. R. MILL (1861-1950)
* Mill became editor of Met. Mag. from 1901 to 1919, after G. J. Symons
* died in 1900. He was a distinguished meteorologist and geographer:
* President of the RMS in 1907 and 1908; v.p. of the Royal Geographical
* Soc. in 1927-31; author of many books. This obit. is a good summary.
* He was also Shackleton's biographer. For a review of his
* autobiography, see QJRMS 78, 117 (1952). (cf. Who's Who as well.)
* Followed by a brief mention of Humphreys's death.
* OBIT for GUSTAV SCHROEDER, with publication list
* Dated 1958, though it reports his death on Jan.10, 1959
* JAMES DE GRAAFF-HUNTER (1881-1967)
* Contains an extensive (but incomplete) list of his publications.
* A much shorter version of this appeared in QJRAS 8, 292-293 (1967);
* very similar versions of it were in J.of Geodesy 41, 83-84 (1967)
* and Geographical Journal 133, 282-283 (1967).
* MARCEL MINNAERT (1893-1970)
* Memorial brochure produced for the dedication of the Minnaert building.
* Leo Molenaar's very attractive brochure, commissioned by Utrecht
* University for the opening of the Minnaert building on 5 March 1998.
* Contains a short biography of Marcel Minnaert, and reminiscences of him
* (all in Dutch) by various people he worked with.
* P. 27 has a nice photo of Minnaert "in action" with the inferior-mirage
* ray drawn on the blackboard behind him. P. 30 reproduces the GF drawings
* from his book, with the original Dutch captions. The back cover shows
* the Taylor-Matthias flash sequence.
* Nicely illustrated with photos of and drawings by Minnaert, and the
* covers of his many publications.
* Many thanks to Leo Molenaar for providing a copy!
* Leo Molenaar's monumental tribute to Minnaert
* At slightly over 600 pp., this tells you all you want to know about
* Minnaert. There is an Appendix that explains how Minnaert fell under
* the influence of Julius, and outlines Julius's crazy anomalous-dispersion
* theory of solar phenomena. Green flashes get a paragraph on pp. 255-256;
* a footnote mentions my Zenit article. There are numerous references,
* and a name-index, but no subject index.
* Thanks to Steven M. van Roode for pointing this out!
* LUTZ HASSE (1930-2016) obituary
* Lists his major accomplishments, but no bibliography.
* DOI 10.1007/s10546-016-0197-y
*
*
* ABSORPTION COEFFICIENTS and BAND PROFILES in LIQUID and GAS
* LOW-SUN SPECTRA with good resolution
* but only down to 3 degrees altitude
* Ignores refraction in estimating airmasses!
* O'C #29
* LIQUID O2
* (O2)2 seen in ATMOSPHERE
* GOOD ABSORPTION DATA
* more ABSORPTION DATA
*
* (SEE ALSO his 1887 Nature paper in GF file)
*
* (SEE ALSO the Hunt (1863) and Budde (1885) papers in Mirage File)
*
* Riccò's first mention of OMEGA shape
* INFERIOR MIRAGE OF SUN
* H.Faye presented the paper of A.Riccò, so this is occasionally
* mis-attributed to Faye.
* A German summary is in Naturwiss. Rundschau 3, 632 (1888).
* WOLF calculates the image flattening in response to Ricco's paper
* He does a parametric calculation as a function of the position of the
* reflecting point on the sea, and produces a table showing that the
* flattening is extreme at the horizon and rapidly diminishes.
* Note that this connection had been made empirically by Bravais in 1853!
* Followup to above; REFLECTION in sea claimed
* See Whitmell's reprise of this in JBAA, 1905 (filed in GF file).
* See the figure captions on p. 220, and the corresponding Plates,
* Tav. CCXXIV and CCXXV.
* Mem.Soc.Spett. was actually printed (according to the title page)
* in the year after the one conventionally assigned. Evidently the
* papers were given at meetings in the previous year, at the end of which
* they were all printed.
* A.Riccò
* O'C #115
* Followup to above; REFLECTION in sea
* Adolfo Venturi models the reflection in the sea, including standard
* terrestrial refraction, and finds less contraction of the image than
* observed by Riccò and Forel. He thus concludes that the additional
* contraction of the image is due to the waves on the water; here he
* adopts a very small slope (2.5 minutes of arc!) for the typical wave
* slope, which of course pushes the reflection of the Sun's upper limb
* toward the horizon -- assuming it is at the near face of the wave.
* He finds that refraction decreases the image reduction [as one could
* have seen more easily by adopting the point of view that refraction
* increases the effective radius of curvature of the Earth].
* Venturi was Professor of Geodesy at Palermo.
* N.B.: printed in 1890.
* Riccò replies to Venturi
* Riccò summarizes the principal points, noting that the refraction is
* uncertain because the water "in general has a temperature different from
* that of the air." He thinks the tops of the waves are flat and should
* give the same image as a flat sea, as only the very tops can be seen
* near the horizon. Otherwise, the waves would make a broken-up image,
* which is not observed. He thinks his observations are due to the
* "celebrated calmness of the water of the Gulf of Palermo".
* [This argument is partly correct: actual reflections on waves are
* broken up; so the "reflection" here must be an inferior mirage.]
* N.B.: printed in 1890.
* A simpler derivation, neglecting refraction.
* N.B.: printed in 1890.
* Venturi replies to Riccò
* Refraction and curvature don't suffice to explain the observed image
* contraction; therefore it has to be the waves, even though an exact
* analysis is difficult. . . .
* Preliminary note on DIP
* A.Ricco
* DIP and diurnal variations; horizon highest during sirocco
* A.Ricco (actually filed in DIP file; see followups there)
* FLAMMARION's note on sunset flattening and Earth curvature
* He attributes it to Riccò (see above entries), accepting the "surface
* tranquille de la mer" idea. He also refers to Forel's drawings of the
* shrunken reflections of ships' sails on Lake Geneva, as well as
* Ch. Dufour's predictions in 1874.
* The whole argument is faulty, not only because the inferior mirage is
* the "reflector", but also because terrestrial refraction of the
* "reflected" rays is neglected.
* SUNSET DEFORMATIONS; drawings & photographs; cites Colton
* Many GREEN FLASHES at sunrise; good account of photographic difficulties
* several DOUBLE HORIZONS; ". . . FOG or MIRAGE . . . "
* Note the additional observations made by T. Zona, pp. 102-103.
* A.Ricco
* Fisher #127; O'C #117
* Pier Franco Nali's recent discussion of Riccò's work, Earth curvature, etc.
* This is mostly about the supposed "reflection" from the sea surface.
* He mentions the various works above, and discusses the attempts by all
* the players to force a reflection to fit the facts.
* Alfred Russel Wallace and his fight with Hampden get mentioned, and
* the Bedford Level story; but not the lawsuit: "Wallace won the wager."
* Some hollow-Earth fanatics also appear; but no mention of Symmes.
* There is an interesting discussion of Ch. Dufour's reduced images
* of sailboats and Forel's confirmation of them, in connection with the
* curvature question. The appearance of these images is associated with a
* calm lake surface, but without realizing that it is the calm air that
* allows a thermal inversion to modify the images.
* Even Bravais and Woltman are cited; but the details of atmospheric
* refraction are largely passed by. So the differences seen over water and
* land surfaces are mentioned, but not attributed to different roughness
* lengths.
* The difficulties of photographing the Sun at the horizon with
* 19th-Century means are vaguely mentioned, but not explained. The
* compressed image beneath the low Sun is supposedly justified by a
* deeply saturated digital-camera image (Fig. 2), with no awareness of the
* artifacts of digital cameras, charge spill, etc. The partly hidden feet
* of an Omega at the edge of an island are shown as evidence that Riccò
* was correct, without realizing that the perspective that applies to the
* inverted image (which is "seen" from beneath the sea) greatly modifies
* the effective profile of the island.
* Venturi's mistaken notion that the reflected Sun is due to the wave
* facets facing the observer is mentioned without objection. This leads
* into a discussion of the reflections from waves, where a 1968 textbook
* is cited. But there's no direct mention of Cox & Munk, nor any reference
* to Shoulejkin. The glitter problem is treated as if it were separate
* from the average reflectance of the water. (No mention of Fresnel
* reflection, either.) And the lowest parts of the glitter pattern
* are attributed to the surface elements "more slanting toward the
* observer". (p. 108) The closely related issue of the variation of
* brightness over the sky and the brightness and color of the sea
* surface is not mentioned.
* Near the end of the text, Wegener's mirage model is described as
* "standard"; but the modern treatment by Kattawar and Bruton is missing.
* No mention of classic works like Pernter & Exner, or Humphreys, or
* the many works on low-altitude refraction, like Fletcher's review. . . .
* So, much interesting detail; but odd omissions and errors as well.
* The discussion is mostly qualitative, and often physically off the mark.
* In particular, the complexity of refraction phenomena makes the
* simplistic arguments advanced by the observers (and the author here)
* often misleading or wrong. Still, the details of the exchanges among
* Riccò and his critics are interesting to read, and go well beyond the
* references I have included in this bibliography. And the biographical
* note on Riccò at the end is very welcome.
* Thanks very much to Pier Franco Nali for a PDF of his paper!
* Henryk ARCTOWSKI
* Distorted Sun drawings (cf. Colton/Chappell/Fisher file)
* The "Belgica" was the first ship to winter over in the Antarctic pack
* ice, at about -71 degrees latitude.
* SCINTILLATION:
* "Pourtant, je crois pouvoir dire que, dans la région de notre hivernage,
* la scintillation des étoiles est relativement très faible toutes les fois
* que le ciel est dépourvu de nuages et qu'il n'y a pas de brume à
* l'horizon." p.19
* also 2 GREEN FLASH reports (p. 26)
* Fisher #3a
* extract from the memoir, full illustrations
* Many references to thin "CLOUD LAYERS" near the horizon,
* correlated with solar distortions.
* O'C #2
* Fisher #3b
* extract from the memoir, fewer illustrations
* O'C #3
* Fisher #3c
* Dr. BAER's first report: EARLY RECOGNITION of MIRAGE involvement
* From his verbal description, I would have made this sunset a simple
* inferior mirage; but his drawings in Met. Z. (1905) show it to be
* quite otherwise. Part of this is excerpted in the Met. Z. report,
* which includes a mock-mirage sunrise as well.
* Two features are notable: (a) the smallness of the waves (``das Meer
* machte nur ganz kleine Wellen''), mentioned twice (``Das Wasser war von
* leichten Wellen bewegt,'' -- not reprinted in the Met. Z. paper); and
* (b) his firm suggestion that mirage phenomena were involved: ``. . . der
* Auffassung, als handele es sich um Spiegelungserscheinungen auf der
* Meeresoberfläche, möchte ich vornherein entgegentreten. Das Wasser
* war von leichten Wellen bewegt, aber das untere Sonnenbild hatte
* nichts Schwankendes, Unbestimmtes, sondern ebenso scharfe Konturen wie
* das obere, und es stand in jeder Phase ganz symmetrisch zu ihm; nur war
* es zuerst viel kleiner, schmaler wie das obere, um erst am Schlusse
* breiter zu werden. Nach meiner Meinung hat sich der ganze optische
* Vorgang in der Luft abgespielt.''
* THANKS to Kristian Schlegel for sending a copy!
* BAER's early DRAWINGS of Mock Mirage, and perhaps a sub-duct sunset:
* "Das ganze Schauspiel war so sonderbar, so merkwürdig, dass ich sofort
* seine einzelnen Phasen in meinem Taschenbuch aufzeichnete. Aber allen
* Personen, die ich in den nächsten Tagen auf die Erscheinung anredete,
* selbst gebildeten autochthonen Borkumern, war sie unbekannt. Der Wärter
* auf dem Leuchtturme, dem ich ein Interesse an allen meteorologischen
* Erscheinungen zutraute, hatte sie gar nicht beachtet and erklärte mir,
* um Sonnenuntergänge bekümmere er sich nicht; das hätte ja gar keinen
* Nutzen."
* He mentions "meine Mitteilung in der Schlesischen Zeitung." After
* reporting (and drawing) a mock mirage at sunrise, he adds:
* "Um gleich dem Einwande zu begegnen, daß meinerseits eine
* physische oder optische Täuschung bei diesen Beobachtungen vorliegen
* könne, bemerke ich, daß ich Temperenzler bin, also alkoholischen oder
* sonstigen narkotischen Einflüssen nicht unterstehe, und daß ich zwei
* gesunde, emmetropische (normalsichtige) Augen mit etwa 5/3, also
* übernormaler Sehschärfe besitze. Ich kann demnach mit bestem Gewissen
* die Wahrheit der hier mitgeteilten Tatsachen bekräftigen."
* Here Dr. Baer's address is given as ``Hirschberg i. Schlesien''.
* O'C #6 -- but NO GF reported.
*
* See also Agatharchides near beginning of file.
* See also Rogers in DIP file, 1926.
* See also Weidefeld in Refraction Observations file, 1904.
*
* DIODORUS SICULUS again, with early distorted sunsets
* Speaking of Arabia Felix, he says of the sun:
* ". . . when out of the midst of the sea, as they say, it comes into view,
* it resembles a fiery red ball of charcoal which discharges huge sparks,
* and its shape does not look like a cone [footnote: `Agatharchides says
* "discus-shaped" '], as is the impression we have of it, but it has the
* shape of a column which has the appearance of being slightly thicker at
* the top; . . . ."
* This is from Book III.48; perhaps it is what Lalande (1792; sect.2247)
* had in mind, though he says "Diodore de Sicile parle avec étonnement
* d'un pays du nord où le Soleil ne paroît point rond (liv. III,
* ch. 19); on croit que ce fait étoit emprunté d'Agatharchides."
* But nothing else in Diodorus seems to come close.
* KEPLER's calculation of solar flattening at horizon (1604)
* This is translated from Kepler's "Ad Vitellionem paralipomena" (p. 131)
* by William H. Donahue (p. 144 of his translation):
* "Thus the refracted figures acquire an oval figure, like that of a coin
* thrown into water, if viewed from a very oblique angle. . . . Let it be that
* the lower edge of the Sun graze the horizon: its refraction will be 34'.
* But the refraction of something higher, such as has an altitude of half
* a degree, will be 29'. Thus, in place of the Sun's diameter, 30', there
* will be seen a quantity of 25 minutes, while the transverse diameter,
* or that parallel to the horizon, will be 30'."
* CHRISTOPH SCHEINER remarks on solar flattening
* Strange that he does not acknowledge Kepler's earlier work, though he
* cites it. He claims to have discovered the elliptical Sun for the
* first time in 1612.
* We have this only on P-10.
* German translation of Scheiner's book [so, placed here out of order]
* P.2 reproduces Scheiner's title page.
* The volume bears a full-page ad for the Hypo Bank on the back cover.
* This is Veröffentlichungen der Universität Innsbruck, Band 226.
* English translations of both Galileo and Scheiner
* Only the "sunspot letters", the Rosa Ursina , and Scheiner's 1612
* note on sunspots are provided here -- not the "Sol Ellipticus". A
* mirage is mentioned on p. 13, and "Sol Ellipticus" is briefly mentioned
* on p. 311.
* ROBERT HOOKE describes seeing, scintillation, and low-Sun distortions
* in his MICROGRAPHIA (1665), correctly attributing all these effects to
* the varying density of the air!
* DISTORTIONS at the horizon: "Since the invention (and perfecting in
* some measure) of Telescopes , it has been observ'd by several, that the
* Sun and Moon neer the horizon, are disfigur'd (losing that
* exactly-smooth terminating circular limb, which they are observ'd to
* have when situated neerer the Zenith) and are bounded with an edge every
* way (especially upon the right and left sides) ragged and indented like
* a Saw: which inequality of their limbs, I have further observ'd, not to
* remain always the same, but to be continually chang'd by a kind of
* fluctuating motion, not unlike that of the waves of the Sea; so as that
* part of the limb, which was but even now nick'd or indented in, is now
* protuberant, and will presently be sinking again; neither is this all,
* but the whole body of the Luminaries, do in the Telescope , seem to be
* depress'd and flatted, the upper, and more especially the under side
* appearing neerer to the middle then really they are, and the right and
* left appearing more remote: whence the whole Area seems to be
* terminated by a kind of Oval." (pp. 217-218)
* He discovers empirically the consequence of Laplace's extinction
* theorem: ". . . I have always mark'd that the more the limb is flatted or
* ovalled, the more red does the body appear, though not always the
* contrary." (p. 218)
* Astronomical and terrestrial REFRACTION, and MIRAGES: "It has been
* observ'd and confirm'd by the accuratest Observations of the best of our
* modern Astronomers, that all the Luminous bodies appear above the
* Horizon, when they really are below it. So that the Sun and Moon have
* both been seen above the Horizon, whil'st the Moon has been in an
* Eclipse. I shall not here instance in the great refractions, that the
* tops of high mountains, seen at a distance, have been found to have; all
* which seem to argue the Horizontal refraction, much greater then it is
* hitherto generally believ'd." (pp. 218-219)
* "I have further taken notice, that not onely the Sun, Moon and
* Starrs, and high tops of mountains have suffer'd these kinds of
* refraction, but Trees, and several bright Objects on the ground: I have
* often taken notice of the twinkling of the reflections of the Sun from a
* Glass-window at a good distance, and of a Candle in the night . . . .
* and upon the whole, I find much reason to think, that the true cause
* of all these Phænomena is from the inflection , or
* multiplicate refraction of those Rays of light within the body of the
* Atmosphere , and that it does not proceed from a refraction caus'd by
* any terminating superficies of the Air above, nor from any such
* exactly defin'd superficies within the body of the Atmosphere ." (p.219)
* He then demonstrates the phenomena by using two liquids of different
* densities in a rectangular glass tank, just as Wollaston did 135 years
* later, and many others since then; and also mentions (p. 221) "The
* veins of Glass, nay, of melted Crystal , found, and much complained
* of by Glass-grinders, might sufficiently demonstrate the truth of it to
* any diligent Observator. . . . It remains therefore to shew, that there
* is such a property in the Air, and that it is sufficient to produce all
* the above mentioned Phænomena , and therefore may be the principal,
* if not the only cause of them." He does this on the following pages,
* using several elegant and simple laboratory experiments to demonstrate
* the relation between the density and the refraction of air. And, as
* the density seems to be inversely proportional to the pressure,
* ". . . there is a continual increase of rarity in the parts of the Air,
* the further they are removed from the surface of the Earth: It will
* hence necessarily follow, that (as in the Experiment of the salt and
* fresh Water) the ray of Light passing obliquely through the Air also,
* which is of very different density, will be continually, and infinitely
* inflected, or bended, from a streight, or direct motion." (p. 228)
* Using Tycho's refraction table (p. 230), he shows that the
* FLATTENING of the Sun at the horizon is due to the differential
* refraction of upper and lower limbs, so that "the apparent refracted
* perpendicular Diameter of the Sun, will be . . . consequently six or seven
* minutes shorter then the unrefracted apparent Diameter."
* "I shall . . . proceed to shew, that the mass of Air neer the surface
* of the Earth, consists, or is made up, of parcels, which do very much
* differ from one another in point of density and rarity; and consequently
* the Rays of light that pass through them will be variously inflected,
* here one way, and there another, according as they pass so or so
* through those differing parts; and those parts being always in motion,
* . . . they do by this their motion inflect the Rays, now this way, and
* presently that way.
* "This irregular, unequal and unconstant inflection of the Rays of
* light, is the reason why the limb of the Sun , Moon , Jupiter ,
* Saturn , Mars , and Venus , appear to wave or dance; and why the body
* of the Starrs appear to tremulate or twinkle, their bodies, by this
* means, being sometimes magnify'd, and sometimes diminish'd . . . ." (p.231)
* "And that there is such a property or unequal distribution of parts,
* is manifest from the various degrees of heat and cold that are found in
* the Air; from whence will follow a differing density and rarity, both as
* to quantity and refraction . . . ." The thermal effects are also shown
* experimentally.
* Then (p.234) he asks "Whether the disparity between the upper and
* under Air be not sometimes so great, as to make a reflecting
* superficies; I have had several Observations which seem to have
* proceeded from some such cause, but it would be too long to relate and
* examine them." (Perhaps he had seen some superior mirages?) "An
* Experiment,also somewhat analogous to this, I have made with Salt-water
* and Fresh, which two liquors, in most Positions, seem'd the same, and
* not to be separated by any determinate superficies, which separating
* surface yet in some other Positions did plainly appear."
* On p. 236 he takes up LOOMING: "Whether the appearance of the Pike
* of Tenerif , and several other high mountains, at so much greater a
* distance then seems to agree with their respective heights, be not
* attributed to the Curvature of the visual Ray . . . . I think it is very
* rational to suppose, that the greatest Curvature of the Rays is made
* nearest the Earth, and that the inflection of the Rays, above 3. or 4.
* miles upwards, is very inconsiderable. . . . Whence, I suppose, proceeds
* the reason of the exceedingly differing Opinions and Assertions of
* several Authors, about the height of several very high Hills."
* The Dover edition is a facsimile of the original 1665 edition, published
* by Martin and Allestry, London.
* JACQUES CASSINI's OMEGA SUNRISE, with drawings, 7 Dec. 1694
* This has to be Cassini II, as he begins by speaking of "le Voyage
* que j'ai fait avec mon Pere en Italie, d'y faire des Observations pour
* contribuer à la perfection de l'Astronomie & de la Géographie. . . .
* Nous partîmes de Paris le 23 Septembre de l'année 1694. . . ."
* They began observing in early December:
* "Nous allâmes le 6 sur les Montagnes qui environnent le Port,
* pour voir la Mer. Le Mesco, qui est une petite Isle à l'embouchure de
* Porto Venete, se voyoit de la Montagne de S. Giorgio en forme de Navire,
* plus étroit en bas qu'au milieu, & élevé sur la surface de la Mer.
* "Le 7 au matin le vent parut favorable. . . . A 7h 30' étant à
* la hauteur de Chiavari, le Soleil parut se lever à la pointe du Cap de
* Mesco; il avoit la figure d'une colomne de feu, arrondie par le haut . . . ."
* (pp. 18-19) He then describes the Omega-shaped sunrise, complete with
* crude drawings of the various stages. On pp. 19-21 he describes his
* interpretation of the inverted image as being a reflection by ". . . la
* surface de la Mer, qui étoit alors tranquille. . . ." (p. 20)
* The problem that the sea horizon itself was not seen at the image-fold
* line is arm-waved away: the eye "ne la voit pas distinctement jusqu'à
* l'horizon sensible, où arrivent les rayons visuels qui la touchent,
* mais seulement jusqu'à un certain terme . . . au-delà duquel, l'eau
* faisant l'effet d'une glace de miroir disparoît à la vûë, & fait
* voir à la place où elle devroit paroître par la réfraction, le Ciel
* & les objets élevez, où les rayons visuels . . . réfléchissent & se
* terminent. L'on peut expliquer par cette raison l'apparence de l'Isle
* de Mesco, que l'on voyoit élevée sur la surface de la Mer, de même
* que nous l'avions remarqué le jour précédent de la Montagne de S.
* Giorgio . . . ." On p. 21, he cites Picard's Voyage d'Uranibourg for
* similar observations.
* Thanks to Luc Dettwiller for a copy of this!
* The details of Jacques Cassini's Omega sunrise (again)
* This is the version provided by Gallica. As this has the earlier date
* of publication, it must be the original, and the previous entry, a reprint.
* Occasional footers say neither Hist. nor Mem., but Rec. de l'Ac., Tom.VII.
* In this version, the report is on pp. 483-487.
* Note that both Cassinis are credited here in the Table des Matieres .
* DE MAIRAN's anomalous flattening observation
* A naked-eye observation through strongly reddening haze (probably smoke):
* "Je l'avois jugée auparavant telle que le diametre horisontal pouvoit
* avoir sur sept à huit parties, une partie de plus que le vertical."
* Cites Scheiner's Solis Elliptici Phænomenon .
* Actually published in 1735.
* A similar observation, at 17 or 18° altitude
* This first-person account has no signature. I suppose it was written
* by the perpetual secretary himself, whoever it was. The curious way
* of estimating the flattening does not sound like an astronomer.
* De Mairan's observation is cited, in the Hist.
* LE GENTIL's 1769 observations at Isle de France [Mauritius] and Pondicherry
* Here are his observations of the effects of INFERIOR MIRAGE:
* ". . . je parle des réfractions horizontales pendant l'été & pendant
* l'hiver dans la Zone torride, & d'une inégalité que j'ai en même
* temps remarquée dans le lever du Soleil; inégalité qu'on ne peut bien
* observer que sur le bord de la mer." (p. 394)
* "On avoit long-temps pensé, avant que l'expérience le confirmât,
* que vers l'Équateur les réfractions étoient différentes de ce
* qu'elles sont en France; . . . on croyoit même la réfraction horizontale
* aux environs du pôle, double de ce qu'elle est en France; on se fondoit
* principalement sur les observations de Spole & de Bilberg, faites en
* Lapponie en 1695 . . . ." (p. 394)
* He also cites Maupertuis's book on the figure of the Earth;
* "Mais M. de Maupertuis . . . ne rapporte que des observations faites à
* deux degrés de hauteur au-dessus de l'horizon; or, à cette hauteur les
* réfractions commencent à n'être plus si inégales. C'est à
* l'horizon que se font remarquer les grandes variations; & dès que
* le Soleil est élevé de deux degrés, ces grandes variations & les
* différences ne se font presque plus sentir, même d'une saison à
* l'autre . . . ." (p. 395) [VARIATIONS CONFINED to 2° interval]
* ". . . j'ai constamment trouvé, à Pondichéry, par mes observations,
* la réfraction au lever du Soleil, sur le bord se la mer, d'environ deux
* minutes plus grande en été qu'en hiver . . . .
* "J'avois commencé, des l'Isle-de-France . . . or, en faisant ces
* observations, je remarquerai, que quoiqu'il fît le plus beau temps,
* quoique le ciel fût sans nuages, que l'horizon fût de la plus grande
* netteté, je remarquerai, dis-je, que le Soleil qui, à la vue simple,
* m'avoit toujours paru se plonger dans l'horizon de la mer, se plongeoit
* réellement dans un horizon élevé au-dessus de celui de la mer, d'une
* quantité assez considérable . . . ; cette quantité . . . pouvoit aller à
* quatre ou cinq minutes: ce phénomène me surprit beaucoup la première
* fois que je l'observai . . . ." (p. 396)
* "Qui pourroit décrire le beauté du ciel, à Pondichéry, pendant
* les mois de Janvier & Février? . . . malgré ce beau ciel, qui n'a rien
* de comparable, sans un seul petit nuage, un horizon superbe : le Soleil,
* pendant tout l'hiver, n'a pas paru se lever une seule fois à l'horizon
* de la mer, mais toujours au-dessus, d'une quantité même assez
* considérable : l'effet en étoit très-singulier, comme on va le voir
* dans le détail des observations.
* "Et au contraire pendant les mois de Juin & de Juillet, qui sont à
* Pondichéry le temps des grandes chaleurs, pendant lequel temps le ciel
* n'est plus à beaucoup près si beau ; que l'air au contraire est
* toujours rempli de vapeurs, le Soleil se lève constamment à l'horizon
* de la mer . . . ." (p. 397) To this he adds that in winter he could
* view the Sun directly up to an altitude of a degree, while in summer he
* had to use a smoked glass as soon as it rose. (cf. pp. 406-407)
* [?? Perhaps this explains why he reported no green flashes??]
* In summer the upper limb took 59 seconds to reach the astronomical
* horizon after its appearance, while in winter it took only 35 seconds,
* the difference representing the difference in altitude of the effective
* horizons.
* He then gives several examples taken from his journal of
* observations. Some descriptions are of interest:
* 7 Jan. 1769: "J'attendois le Soleil à l'horizon de la mer que je
* voyois fort distinctement; mais lorsque cet astre a commencé à
* pointer, il a paru au-dessus de l'horizon de la mer, chose assez
* singulière & que j'avois déjà remarquée à l'Isle-de-France.
* Lorsque le Soleil a été à moité levé, l'horizon de la mer s'est
* abaissé, & a paru moins élevé qu'auparavant d'environ les trois
* quarts des 50 secondes trouvées avant le lever du Soleil,
* c'est-à-dire, de 36 secondes environ : le centre du Soleil étant
* tout-à-fait levé, le bord supérieur a paru refluer des deux côtés
* de l'horizon de la mer, & former comme le haut d'une urne : enfin le
* bord inférieur a quitté l'horizon bien au-dessus de la horizon de la
* mer. L'effet en a été singulier : il m'a semblé qu'une partie du
* haut de l'urne est rentrée sous l'horizon, & que le reste s'est joint
* au Soleil comme deux morceaux qu'on auroit détachés avec le ciseau."
* (pp. 399-400) So here is the EARLIEST DESCRIPTION using the URN image,
* as well as the rest of the OMEGA shape!
* 9 Jan.: "Le quart-de-cercle ayant été placé comme le 7, j'ai
* trouvé comme ce jour-là, l'horizon de la mer abaissé de 10' 50''.
* "Le Soleil a pointé beaucoup au-dessus de l'horizon à 6h 5' 58''
* 30''' ; à mesure que le Soleil paroissoit monter, l'horizon de la mer
* s'abaissoit de façon qu'il s'est trouvé moins élevé d'environ le
* quart des 50 secondes trouvées ci-dessus ; c'est-à-dire, de 12 ou 13
* secondes : enfin le second bord du Soleil s'est dégagé de l'horizon
* bien au-dessus de l'horizon de la mer à 6h 8' 25'' ½ ; ce qui a
* produit l'effet de deux soleils qui se détachoient & se quitoient, dont
* l'un retournoit du côté de l'horizon & n'a disparu que 5 à 6 secondes
* après s'être détaché du véritable." (p. 401) (So what he is
* calling the "horizon" at sunrise is really the fold-line between the
* erect and inverted images of the inferior mirage.)
* 14 July: "Le Soleil a paru subitement & précisément à l'horizon
* de la mer, c'est-à-dire, que j'ai aperc,u un petit trait ou filet de
* lumière qui a doré l'horizon ; & ce filet étoit le Soleil." (p. 406)
* So, as noted by Fisher (1921), the summer sunrises were of Type B, and
* the winter ones of type A.
* He cites and discusses the horizontal refractions found by Bouguer
* in Peru (p. 414); and, as Bouguer's values are appreciably less than his
* own, adds: "J'aurois desiré que M. Bouguer nous eût donné le détail
* de ses observations, & non pas seulement des résultats comme il a
* fait."
* Title of section:
* Article Troisième
* Observations sur les Réfractions horizontales au bord de la mer,
* à 46 pieds au-dessus de son niveau ; avec quelques Remarques sur
* l'Observation des Hollandois dans la nouvelle Zemble.
* (The latter part is pp. 416-426.)
* This section bears the note: "Ces Observations ont été lûes à
* l'Académie Royale des Sciences, dans son assemblée du 27 Novembre
* 1774." [See Mirage File and General Refr. file for other sections]
* DELAMBRE -- [more in Simpson/Bradley/Mayer file]
* This was the standard textbook at the time. He goes through the
* standard exercise of comparing the refractions at the upper and lower
* limbs of the Sun at the horizon, and finds a reduction of the vertical
* diameter of 4' 17", or about 1 part in 8; so "le disque du soleil
* déformé par la réfraction, est sensiblement elliptique; et c'est
* ainsi que je l'ai vu très-souvent, surtout lorsque d'une tour ou d'une
* montagne élevée je le voyais se lever à l'horizon de la mer ou s'y
* coucher. Souvent même la demi-ellipse inférieure m'a semblé plus
* aplatie que la supérieure. Quelquefois la supérieure seule paraissait
* elliptique et l'inférieure était singulièrement défigurée, ce qui
* indiquait des réfractions très-irrégulières pour les différens
* points du bord inférieur; mais cet effet cesse dès que le soleil est
* sorti des vapeurs de l'horizon."
* German translation of Dangos's 1806 paper with early OMEGA report
* The main part of this report is about the looming of Aetna as seen from
* Malta, so that it looked like an island. The last paragraph describes
* the Omega at sunrise.
* [I have put the original French version in the Mirage File.]
* Henry Salt's observation (cf. Agatharchides)
* "In the evening, we observed the sun before it set put on a very unusual
* appearance. At the moment of emerging from a dark cloud, when its disk
* touched the horizon, it seemed to expand beyond its natural dimensions,
* became of a palish red hue, and assumed a form greatly resembling a
* portion of a column. This is one of the many singular effects produced
* by the refraction of the atmosphere common in this part of the world;
* and something of the same kind may have given rise to the extraordinary
* appearances of the heavenly bodies mentioned by Agatharchides, to have
* occurred at the mouth of the Red Sea [he quotes the original passage in
* Greek] which have been too hastily discredited by succeeding writers.
* Our latitude at noon was 4° 53' 30" N., long. 49° 0' . . . ."
* No doubt this reference to Agatharchides explains Burstein's citation.
* (The copy I have seen is the American reprint of 1816 by M.Carey,
* Philadelphia; but I suppose it is identical to the original.)
* Absolutely CRANK paper by an F.R.S.!
* Surely even in 1821 this must have been regarded as absurd.
* He correctly notes the reddening and deformation of the Sun and Moon at
* the horizon, including the greater flattening of the lower limb, and
* its "considerable fluctuations, and variations of outline, contracting
* and enlarging in different points at the same time." But then . . .
* He finds the atmospheric heights of 40 to 75 miles found from twilight
* observations "exceed all reasonable estimate." He supposes that
* because air is "one continuous body," there "are in fact no atmospheric
* refractions" (and denies there is any refraction where crown and flint
* glasses, optically contacted, meet!) He believes the Moon illusion is
* not an illusion but a real effect due to "inflections": "The principal
* phaenomena of inflections, more than thirty years ago, I observed and
* explained, correcting some very important errors of great authority,
* . . . ." Right. The astronomers are all wrong in supposing that
* refraction takes place in the vertical plane, and have brainwashed the
* observers into faking their data to agree with this mistaken theory:
* "Such are the defects of the astronomical schools on this subject."
* The Moon illusion is bigger for the Sun than for the Moon because of
* "the weaker marginal light of the moon being extinguished, and her size
* more reduced by the atmosphere through which she appears, than that of
* the sun." The width of the rainbow at the horizon is greater than high
* in the sky "in consequence of the increased sizes of the united drops."
* The atmosphere extends only a little above the summit of Mont Blanc,
* about 3 miles. And "he who can continue to believe that the apparent
* increase of size of the sun and moon, in the horizon, is a deception . . .
* may ascribe all the other concurrent appearances and changes, change of
* colour, change of place, change of figure, undulatory changes of limb
* and outline, to delusions, not only ocular but mental . . . ."
* Wish this had been published with his figures!
* He cites Biot's Astronomie Physique for plates.
* Jules Janssen's early sunset photographs (not reproduced, of course)
* "Les photographies nos 7 et 11 montrent des effets très intéressants
* de coucher de Soleil." (p. 1166)
* These might be the EARLIEST PHOTOGRAPHS of sunset distortions?
* Or are they merely images of crepuscular rays?
* KRIFKA with hacek over the r
* colored drawings in Tafel III -- cf. Pernter & Exner
* O'C #73
* Drawing of Omega-shaped sunset
* This was *before* l'Astronomie merged with B.S.A.F.
* Crude drawings of Omega-shaped sunset, with oval stage
* There is a curious error in the Omega stages: he draws the horizon at
* the notch, instead of under the feet -- i.e., what he thinks he sees.
* But the final blob correctly is drawn floating above the horizon.
* Refers to Daguin's paper in April issue
* This was *before* l'Astronomie merged with B.S.A.F.
* ANTONIADI's distorted sunset drawings, seen near Constantinople
* "Les figures n'ont rien d'exagéré et représentent fidèlement ce
* que j'ai observé." A textbook example; cited by Galli (1908).
* This is the old l'Astronomie, *before* it merged with BSAF.
* The LC number for this is QB 1.A5; the other (BSAF) is QB 1.S58.
* COLTON
* Explicitly associates the distorted sunsets with the hot weather of
* August. "Nebelstreifen":
* ". . . am 8. Juli was einer dieser Streifen so undurchsichtig, dass er die
* Sonne in zwei scharf begrenzte Teile schied; am 8. und 9. August is die
* Sonne durch Refraktion aus den oben erwähnten unsichtbaren
* Wolkenschichten vollständig geteilt."
* O'C #19
* COLTON
* O'C #17
* O'C #18
* M. F. Beuer's distorted sunset
* "An diesem Tage was es wohl kalt aber ausnehmend ruhig, so dass man
* sehr wohl im Freien zubringen und sich einmal ordentlich satt sehen
* konnte. . . . Besonders aber fesselte mich diesmal der Untergang der
* Sonne, den ich in der Zeit von etwa ½5 bis ¾5 Uhr verfolgte und
* in 16 verschiedenen Phasen aufgezeichnet habe. . . . Überraschend
* und sonderbar genug sind die durch die Strahlenbrechung erzeugten
* Formen, jedoch ganz naturtreu."
* The figure shows the Sun setting through 2 or 3 inversions; the
* drawings keep features that should be at constant altitude nearly so;
* so I believe the drawings are fairly accurate.
* Beuer is listed as "Bürgerschullehrer (Reichenberg)".
* Thanks to Kristian Schlegel for a copy of the text AND the figures!
* Nice drawings of classical inversion-layer shapes, including MMs
* "The phenomenon was so striking and constant that every evening near
* sunset my children begged me to be taken to see the grimaces of the
* Sun."
* "The figure of the Plate represents the matter perfectly: the Sun
* at first, approaching the horizon, assumes the well-known elliptical
* shape; then from below an appendage emerges, which elongates and widens,
* and then the whole Sun is squeezed and widens, assuming hundreds of
* symmetrical forms, rapidly and continually varying, of which the plate
* represents but the principal ones, as they were drawn during the
* phenomena by me and the assistant Mr. Sartorio Gaetano at Monte Cuccio;
* every day the phenomena undergo the same phases."
* NOTE: Monte Cuccio is about 8 km west of the Palermo harbor. Measured
* coordinates from the 1943 U.S. military maps (1:50,000) of the area put
* the summit at about +38 06' 50'' N, 13 15' 54'' E of Greenwich.
* The height is marked as 1050 m. There are several lower peaks and
* ridges to the west that prevent observations from much lower down.
* NOTE: The "Atti" are all separately paginated, but not numbered.
* Full title: Atti della Reale Accademia di Scienze, Lettere e Belle Arti
* di Palermo, Terza Serie (Anno 1900-1901)
* This paper is dated 18 Nov. 1900, and is the first in the volume.
* Arctowski (?) suggests comparing the "Belgica" obsns. with Tissandier's
* The Tissandier ref. is back in 1878, but seems useless.
* COPIES OF KRIFKA's drawings
* BLACK LINE or "schwarze Strich": (cf. his paper in Weltall later in 1904)
* "Diese pflegt, entsprechend der Entscheinung des `schwarzen Strichs', im
* allgemeinem zu etwa 1000 m Meereshöhe angenommen zu werden."
* See his further details of green edges in Phys.Z.11, 645-648 (1910).
* MUSHROOM-shaped sunset, as well as a FINAL LINE lasting 3 min. or more
* also some drawings of mirages -- see Tafel 10 (good DRAWINGS)
* The claimed LATERAL MIRAGE is probably towering of distant low coastline
* EARLY PHOTOGRAPHS of distorted forms
* O'C #123
* Fairly good drawings of a Type B sunset, probably with a small mock mirage
* from "the Hamburg American Line steamer Belgravia".
* O'C #119
* Nice DRAWINGS of distorted sunrises from 203.5 m height
* First is a classical bi-lobed mushroom; second also shows inversion
* features. Note haceks and accent over the a in Krcmar.
* DRAWINGS of a classic DISTORTED SUNSET
* This is an account of discussion at a meeting. The comments by RUDOLF
* MEYER are particularly interesting, and much longer than Doss's short
* paragraph. "Assistent Cand. R. Meyer" first points out the similarity to
* the drawings in a recent issue of Met.Z. (presumably the previous item,
* but could be Baer's paper in 1905).
* ". . . man erkläre es durch anormale Refraktionsverhältnisse, die . . .
* wichtige Schlüsse über die Temperaturverteilung in der Atmosphäre
* zulassen. . . . Verzerrungen des Sonnenrandes sind nicht ganz selten. In
* der ersten Woche dieses Jahres, während des starken Frostes, konnten sie
* mehrere Tage nacheinander beobachtet werden. Die Annahme einer
* horizontalen Schichtung der Atmosphäre hat für die Erklärung der
* Erscheinungen mehr Wahrscheinlichkeit für sich, als andere Hypothesen; die
* erwähnten Beobachtungen . . . haben bei windstillem Wetter stattgefunden."
* After suggesting that the vertical sides might be related to ice-crystal
* sun-columns: "Es scheint auch nicht ausgeschlossen, dass die
* Geradlinigkeit der Seiten des Sonnenbildes zum Teil auf einer optischen
* Täuschung beruhe."
* Prof. Pflaum points out the similarity to "sehr ähnliche Zeichnungen in
* derselben Aufeinanderfolge in Pernters Meteorologischen Optik II (S.133)
* vom Jahre 1902 . . . und dort ebenfalls auf Luftspiegelung zurückgeführt
* werden." Then there is a long and largely erroneous attempt by "Direktor
* Schweder" to explain the details with known mirages (the final drawing
* shows a double MOCK MIRAGE -- quite an EARLY EXAMPLE.)
* Curiously, the dates are given in both Old and New Styles.
* This must be one of the earliest appearances of RUDOLF MEYER in print!
* Formal publication of Doss's sketches
* Here he explicitly states that the Met.Z. drawings he had been apprised
* of in the Riga meeting were those of Krcmar, Met.Z.,23,461 (1906).
* But he finds the resemblance closer to Arctowski's drawings from the
* Belgica (as reproduced in Pernter's M.O., S.133 (1902).
* (No mention of Meyer.)
* SKETCHES of distorted sunsets
* Account of paper at RASC meeting by "Dr. Chant" (probably C.A.Chant)
* (no mention of Colton)
* The Frontispiece of the Sept.-Oct. issue, facing p.273, shows
* "Forms of the setting sun as seen from the summit of Mount Hamilton, Cal."
* dated June 27, June 29, and July3, 1907
* IGNAZIO GALLI's review article -- many good refs.
* Observer was deceived by optical illusions, supposing the image became
* wider when distorted. The shapes drawn appear overly geometric and
* simplified.
* Cites Antoniadi, Daguin, Scheiner, Payer, and Fontenay-le-Comte.
* Mentions Biot & Matthieu [sic -- no reference; probably Mathieu's
* edition of Delambre's 18th-Century Hist.]
* "Sessione IIa del 19 Gennaio 1908"
* THANKS to Gerardo E. Milesi for providing a lead to this!
* Nice DISTORTED-SUNSET DRAWINGS much like Krifka's
* This would have been put in the green-flash file for its opening
* sentence: [the "HANGING DROP"]
* "Ich hatte wiederholt auf Seereisen Gelegenheit, sowohl den `hängenden
* Tropfen' wie den `grünen Strahl' zu beobachten." The footnote says:
* "Wenn die Sonne am Meereshorizont bei völlig klarem Himmel untergeht,
* so hat man kurz vor der Berührung des Sonnenrandes mit dem Horizonte
* den Eindruck, daß plötzlich ein glühender Tropfen den Sonnenrand
* mit dem Horizont verbände. Der letzte Strahl der verschwindenden Sonne
* erscheint in wunderbar smaragdgrünem Lichte."
* Despite this GF mention, it belongs here in DISTORTED SUNSETS because of
* Meyer's reply, below.
* He was 3m above the water, but "mein Sohn beobachtete dieselben
* Erscheinungen direkt vom Strande aus."
* "Die Zeichnungen sind sofort nach Untergang der Sonne aus dem
* Gedächtnis angefertigt. Eine Vergleichung von mir und meinem Sohne
* (Primaner) ergab ziemlich genaue Übereinstimmung." I take this as
* evidence for an internal boundary layer.
* The image below the apparent horizon is almost surely a reflection on
* the shallow water, as Meyer suggests -- one of very few such cases.
* "Von Realgymnasial-Direktor Prof. W. Wetekamp"
* MEYER explains Wetekamp's sunset in Weltall 9, no.9
* This is a SPLENDID article, showing great understanding of sunset
* effects at a remarkably early time! Too much good stuff to quote!
* His main weakness is that, not knowing of the mock mirage, he finds
* some sunsets inexplicable, and then blames time-dependent refraction.
* Also, he neglects curvature of Earth. Still, he recognizes that the
* effects are due to "Lichtbrechungsverhältnisse der unteren
* Luftschichten", in contrast to O'Connell. . . .
* "Von Rud. Meyer, Dozent am Rigaschen Polytechnikum"
* Alfred WEGENER's 1906-1908 observations in GREENLAND (part I)
* These reports are in the 42nd volume of the Danish journal
* "Meddelelser om Grønland", which is available at BHL, as a PDF.
* Supposedly the scans are from the New York Botanical Garden; but the
* images show library stamps and a barcode from Woods Hole.
* This item is Wegener's 76-page account of the kite and captive-balloon
* ascents, dated 1909. It has a hair-raising account of the expedition's
* difficulties and narrow escapes, with photographs of their primitive
* equipment. Our main interest here is in section III, "Diskussion der
* Beobachtungen" -- specifically, the subsection "Temperaturschichtung
* bei Refraktionsstörungen" that begins on p. 60, and particularly the
* temperature profiles ("Zustandskurven bei Luftspiegelungen") on p.65.
* The detailed descriptions of the mirage displays are in Part IV, which
* was published two years later (see next bibliography entry).
* The temperature profiles are discussed in the next subsection, "Die
* Höhe der Föhnwolken" (p. 64), where Wegener connects the wiggles in the
* profiles with the layers in the clouds: "Bemerkenswert ist der Aufstieg
* vom Oktober 13 (1907). Hier wurde beim Aufstieg eine Inversion um
* 0.9° zwischen 1250 und 1400 m gefunden, beim Abstieg aber war diese in
* 6 allerdings sehr kleine Teilinversionen zerlegt. Diese blätterige
* Temperaturschichtung dürfte der Eigentümlichkeit der Föhnwolken
* entsprechen, bisweilen in mehreren, dicht über einander liegenden
* Etagen aufzutreten, wodurch sie bei der ihnen eigentümlichen Form den
* Anblick einer Reihe auf einander gestellter Kugelsegmente darbieten
* (siehe Abbildung)." (p.66) Here he identifies the upper edge of the
* clouds with "eine typische Diskontinuitätsfläche". On the next page,
* he identifies these clouds as standing waves.
* In the next subsection (on fog), he notes that the mean height
* of the top of the fog is 225 m, the same height where a temperature
* increase was found, on average. The structure of the fog over the ice
* was seen as the ship was leaving on 31 July 1908: "Beim Austritt aus dem
* Eise plötzliches Ansteigen der Temperatur um 4° (siehe Thermogramm).
* Gleichzeitig verschwindet dar Nebel. Von aussen sah man dann den Nebel
* (nur ca. 100 m hoch) über dem Eise liegen, nach dessen Aussenkante hin
* flacher und flacher werdend." (see sketch, p. 68)
* The subsection "Der Zustand der Atmosphäre bei Föhn" on p. 69 discusses
* specific offshore and mountain flows.
* Alfred WEGENER's 1906-1908 observations in GREENLAND (parts 2-8)
* These reports are in the 42nd volume of the Danish journal
* "Meddelelser om Grønland", which is available at BHL, as a PDF of
* the copy at New York Botanical Garden (though I see a library stamp on
* p.157 that says "Marine Biological Laboratory, Woods Hole". This chunk
* is numbers 2-8, dated 1914 on the cover. (Part I is Wegener's 76-page
* account of the kite and captive-balloon ascents, dated 1909.)
*
* This is Parts 2 - 8 of Vol. 42; it has the subtitle (on BHL image 11):
*
* D A N M A R K - E K S P E D I T I O N E N
*
* TIL GRØNLANDS NORDØSTKYST 1906--1908
*
* under ledelse af
*
* L. MYLIUS-ERICHSEN
*
*
* BIND II
*
*
* See the table of contents on image 13, which tells which chapters
* have associated "Tavle" and the "Kort" ("cut"). Here we have Wegener's
*
* III. Meteorologische Beobachtungen während der Seereise 1906 und 1908
* (dated 1911) pp.113-124
*
* IV. Meteorologische Terminbeobachtungen am Danmarks-Havn
* (dated 1911) pp.125-356
*
* VI. Meteorologische Beobachtungen der Station Pustervig (with W.Brand)
* (dated 1912) pp.447-562
*
*
* PDF image 73 shows a translucent overlay identifying features of the
* photograph on image 75 (showing that printed books still have superior
* multimedia features not available on Web and PDF pages!)
*
* In the weather journal (p. 202), three periods each day are denoted:
* I 8 am
* II 2 pm
* III 9 pm
* These are used in the daily records.
*
* There are numerous references to both distorted images of the low Sun,
* and mirages and/or looming of mountains on the horizon. Search the PDF
* for "Sonne" or "Refraktion" (usually in "Refraktionsanomalie".)
* Section 3, "Wetterjournal" begins on p.202 and describes the daily
* phenomena in detail. It has several figures that show the temperature
* and pressure recordings during events of interest.
* P.224: Feb.15, 1907: "Vormittags wurden am südlichen Horizont starke
* Luftspiegelungen nach oben gesehen, bisweilen auch nur Vertikalverzerrung.
* Am deutlichsten erschien die Spiegelung, wenn man etwa 10 m über dem
* Meereise stand, sie verschwand aber fast ganz, wenn man auf das Meereis
* hinunterging."
* P.226: "beim Sonnenaufgang (9" 5) wird eine eigentümliche
* Refraktionsanomalie beobachtet: Der Oberrand der Sonne tauchte zuerst
* über dem oberen Horizont (dem Spiegelbilde) auf, verschwand etwa nach
* ½ -- 1m wieder vollständig, tauchte ungefähr nach einer gleichen Pause
* am wahren Horizont auf, verschwand wiederum vollständig und tauchte
* --- wieder nach einer ähnlichen Pause --- nun definitiv gleichzeitig
* über dem 'doppelten' und dem wahren Horizont auf, 2 parallele Striche
* bildend. Das Bild war sehr beweglich, eine Zeitlang konnten sogar
* 3 solche parallelen Striche gesehen werden, von denen der mittlere
* erheblich kürzer war als die andern beiden [entsprechend dem häufig
* auftretenden 3-fachen Horizont]. Besonders verblüffend wirkte das
* zweimalige langsame Wiederverschwinden, das täuschend dem wirklichen
* langsamen Sonnenuntergang glich." (BHL image 174)
* P.230: 1907 Mar. 10: "Solange das Licht es zulässt, werden
* Luftspiegelungen (meist doppelter Horizont) beobachtet, welche wohl ebenso
* wie die Temperatur- schwankungen auf eine Inversion zurückzuführen sind."
* P.230: 1907 Mar. 11: "starke Luftspiegelung . . . Charakteristisch
* ist das Verschwinden der Luftspiegelungen beim Anstieg der Temperatur
* (vergl. Fig. 25). Bei den schnellen Schwingungen der Temperatur gibt
* das Stations-psychrometer heute mitunter ganz sinnlose Werte: Um 8a
* steht das Eisthermometer um 1.1°, um 2p um 0.9° höher als das
* trockene Thermometer!"
* P.237; 1907 Jul. 5: Fig. 29 is a nice drawing of the superior mirage
* with multiple images and flattening of Koldeway Island, seen from 132 m.
* "Die Spiegelung machte dem normalen Bilde Platz, als der Beobachter 25 m
* vom Gipfel abgestiegen war. Das Thermogramm zeigt mehrmals an diesem Tage
* Schwankungen zwischen 2 bestimmten Werten (vergl. Fig. 30). Anscheinend
* ist also eine Inversion vorhanden, welche in geringer Höhe liegt
* und bisweilen die Station passiert, so dass diese abwechselnd in
* die untere (kalte) und in die obere (warme) Schicht versetzt wird.
* Diese Schichtgrenze durfte auch die Ursache der Luftspiegelungen sein."
* P.240; July 17: Inversion with strong temperature swings. "Gegen 3
* Uhr nachmittags, als die Station nach dem Thermogramm ausgesprochen im
* Bereich der kälteren unteren Schicht lag, wurden auch Luftspiegelungen
* nach oben am südlichen Ende der grossen Koldewey-Insel gesehen, wobei
* aber der untere Teil des Berges ungestört sichtbar war, und die Störung
* nur die oberen Teile desselben betraf. Dies scheint darauf hinzudeuten,
* dass die Schichtgrenze in grösserer Höhe über dem Boden lag, und damit
* stimmt überein, dass um 3p nur noch eine Inversion um 1.1° bis zur
* Ausguckstonne gemessen wurde, während um 1p, als die Schichtgrenze
* offenbar noch niedriger lag, eine solche von 5.6° vorhanden war. ---
* Gleichzeitig wurde weiter östlich am Kap Bismarck ein 3-facher Horizont
* über dem Meereise gesehen."
* July 24: "Abends wird eine interessante Luftspiegelung nach oben
* an der grossen Koldewey-Insel gesehen; die wechselnden Formen konnten
* durch Zeichnungen festgehalten werden (Fig. 36). Von besonderem Interesse
* ist es, dass die Spiegelung hier unmittelbar über der Oberfläche des
* Nebels erschien; sie ist offenbar durch die hier herrschende Inversion
* hervorgerufen. Wegen der Einzelheiten sei auf die Notizen bei den
* Zeichnungen verwiesen."
* P.241: series of commented drawings of the island miraged on July 24.
* P.250, Sept. 14: Drawings of inferior mirages.
* Tafel VIII, IX, and X (between pp. 252 and 253) show photographs of
* inferior mirages. See p. 253 for descriptions. [Wegener thinks these
* might be "die ersten Photographien von Luftspiegelungen überhaupt";
* but R.W.Wood published a mirage photograph in 1898.] He used a weak
* yellow filter to cut the haze.
* P.256: several mirages in October, including inf. and sup. mirages
* simulataneously on the 21st; "Die Breite des spiegelnden Streifens
* wurde mit dem Pulfrich'schen Kimmtiefenmesser zu 4 Bogenminuten
* gemessen." [This may be the first appearance of that term!] And a
* drawing of the inferior mirage that day. "Von 9 oder 10 Uhr ab wurde
* gleichzeitig auch eine Spiegelung nach oben an der grossen Koldewey-Insel
* gesehen; der fernste (südlichste) Teil der Insel erschien stark gehoben,
* wobei er mit dem normalen Bilde durch Vertikalzerrung verbunden war. Der
* obere Rand der Insel erschien ausgefranst und war in ständiger Bewegung,
* wobei er oft Brücken bildete. Auch direkt unter dieser Spiegelung
* oder Hebung, aber durch einen Streifen mit normaler Refraktion von
* ihr getrennt, war der spiegelnde Streifen der 'Spiegelung nach unten'
* zu erkennen, wenn auch hier wegen des Fehlens des Himmels weniger
* deutlich. Auf Tafel XI und XII ist einerseits der normale Anblick und
* andererseits die Hebung bezw. Spiegelung der grossen Koldewey-Insel nach
* einem Aquarell von Achton Friis wiedergegeben. Ein mittags ausgeführter
* Drachenaufstieg bis 930 m Höhe zeigte, dass bis zu dieser Höhe eine
* Temperaturumkehr um mehr als 13° herrschte, was offenbar die Ursache
* der Spiegelung nach oben bezw. Hebung war. Nachmittags wurde der
* nordwestliche Wind stärker mit föhnähnlicher Erwärmung (vergl. das
* Thermogramm Fig. 56), gleichzeitig traten auch Föhnwolken auf. Offenbar
* bedeutete diese Temperatursteigerung die Wegräumung der untersten
* kalten Luftschicht." (Ending on p.257.)
* The two colored plates named in the paragraph above nicely illustrate
* the looming.
* The mirages continued on the 23rd: "Mit den tiefen Temperaturen
* (vergl. Fig. 56) hat sich sogleich wieder die Luftspiegelung nach unten
* eingestellt. Bei der Morgenablesung konnte festgestellt werden, dass
* diese Spiegelung am deutlichsten war, wenn der Beobachter sich auf dem
* Meereise befand, während sie in dem Masse abnahm, wie er auf das Land
* hinaufging. Von 5 m Seehöhe aus verschwand sie gänzlich." Inferior
* mirages continued the next 3 or 4 days, accompanied by heavy
* hoarfrost formation. On the 28th, "Die Luftspiegelung nach unten
* ist verschwunden, statt dessen wird eine stark wogende Bewegung
* aller Objekte, namentlich der kleinen Koldewey-Insel, beobachtet.
* Ein Drachenaufstieg zeigt starke Temperaturumkehr." (p. 260)
* These October, 1907, mirages are discussed further in Wegener's
* discussion of the temperature profiles in issue No.1 (see the
* previous bibliography entry). The two should be read together.
* P. 266: Drawings of "Hebung und Spiegelung nach oben", Nov. 26.
* P. 286, Feb.15, 1908: "eine Luftspiegelung nach oben an der Schäre
* und der kleinen Koldewey-Insel gesehen die grosse Koldewey-Insel ist
* ohne Störung."
* Feb. 17: "Starke Luftspiegelung nach oben. Schon vormittags werden
* Spiegelungen nach oben an relativ nahen und niedrigen Objekten, wie der
* Schäre und der kleinen Koldewey-Insel beobachtet, die sich durch starke
* Unruhe auszeichnen. Mittags ist der Wind erheblich stärker geworden, es
* herrscht dauernd Schneetreiben, und das ganze Landschaftsbild ist in stark
* flimmernder Bewegung. Die Flimmerwellen laufen mit dem Winde. Deutlich zu
* erkennen ist noch die Vertikalverzerrung an dem nördlicheren Teil der
* kleinen Koldewey-Insel, auch die Schäre zeigt meist einen Steilabfall,
* der nicht existiert; aber die Bilder sind in beständiger schneller
* Bewegung und werden auch noch durch das Schneetreiben, das aus der
* Entfernung als Dunst erscheint, undeutlich gemacht. Die Konturen aller
* Objekte zeigen eine wilde Wellenbewegung mit zeitweiligem Emporschlagen
* einzelner Wellen. Auch die grosse Koldewey-Insel zeigt diese
* Erscheinung, es liegt also der seltene Fall vor, dass die Erscheinung
* sich gleichartig an den niedrigeren und höheren Objekten zeigt, und dass
* auch verhältnismässig sehr nahe Gegenstände diese flimmernde Bewegung
* zeigen. Die grosse Koldewey-Insel ist ausserdem noch gehoben und zeigt
* älinliche Bilder, wie früher beschrieben, nur schneller wechselnd. Bei
* der Schäre kann man bisweilen Andeutungen einer regulären Spiegelung
* nach oben sehen, meist sieht man aber nur ein Chaos von mit dem Winde
* dahinstürmenden Wellen, aus dem man nur entnehmen kann, dass jedenfalls
* die Verlikalerstreckung des Bildes grösser als normal ist." (p.287)
* Feb. 21: ". . . es wurden starke Luftspiegelungen sichtbar. Um 12 Uhr
* mittags wurde eine Photographie der Vertikalverzerrung an der mittleren
* Partie der kleinen Koldewey- Insel erhalten (siehe Tafel XIV). Um 2p
* wurde das südöstliche Ende der kleinen Koldewey-Insel stark entstellt
* beobachtet, wovon die Skizze Fig. 78 ein Bild gibt. Diese Abbildung
* zeigt nur denjenigen Teil der Insel, welcher von der Station gesehen
* links von der höchsten Erhebung liegt. Die letztere selber sowie der
* dahinter liegende Teil der grossen Koldewey-Insel ist in der Skizze
* Fig. 79 dargestellt. Bemerkenswert ist dabei, dass auch die grosse
* Koldewey-Insel nach oben spiegelt, ohne wie sonst dabei gehoben zu sein.
* Das über der höchsten Erhebung der kleinen Koldewey-Insel schwebende
* Spiegelbild variierte stark, wenn auch verhältnismässig langsam;
* zuerst glich es einer auf dem Felskopf stehenden dicken Säule, dann
* bekam diese Saule ein Kapitäl und wurde zugleich dünner und dünner,
* bis sie einen ganz feinen senkrechten Verbindungsstrich zwischen Objekt
* und Spiegelung darstellte, der dann schliesslich verschwand, so dass die
* Spiegelung frei in der Luft schwebte. Bisweilen traten auch rechteckige
* Abflachungen auf, wie sie besonders schön an der Insel Maroushia
* beobachtet wurden, von der Fig. 80 zwei Zerrbilder gibt." (p. 288)
* Feb. 22: "Spiegelung nach oben und nach unten; . . . Sehr merkwürdig
* ist das heutige Auftreten der Luftspiegelung nach unten, von welcher eine
* Skizze (Fig. 82, nächste Seite) erhalten wurde. Bald nach Anfertigung
* derselben trat zu der vorhandenen Spiegelung noch Vertikalverzerrung,
* die aber zwischen sich und der Spiegelung einen ziemlich breiten Streifen
* des direkten Bildes liess, so dass nur eine Überhöhung des oberen
* Teiles der Insel resultierte. Ausserdem traten am Oberrande des
* überhöhten Streifens auch bisweilen kurze Ansätze einer Spiegelung
* nach oben auf. Während die Vertikalzerrung und Spiegelung nach oben
* ziemlich schnell variierten, war die Spiegelung nach unten die ganze
* Zeit über, wo das Licht eine Beobachtung zuliess, vollkommen konstant."
* P. 289, Feb. 25: "Den ganzen Tag über schöne Luftspiegelungen
* nach oben, vormittags bei Windstille mehr an der kleinen Koldewey-Insel
* (hiervon, freilich nicht während der stärksten Phase, wurde die
* auf Tafel XV wiedergegebene Photographie erhalten), nachmittags bei
* Schneetreiben mehr an der grossen. Bisweilen wurde an der kleinen
* Koldewey-Insel ausser der Spiegelung nach oben gleichzeitig auch die
* nach unten gesehen (auf der Photographie nicht vorhanden), die nur einen
* ganz schmalen Streifen am Fuss der Insel bildete. Nach oben schloss sich
* daran ein breiter Streifen mit Vertikalverzerrung, und darüber erschienen
* wieder die in Fig. 78 -- 80 dargestellten überhöhten Stufenkonturen,
* Ansätze zu umgekehrten Spiegelbildern u. s. w. Der schmale Streifen mit
* Spiegelung nach unten war nur vom Meereise aus sichtbar und verschwand,
* wenn man am Lande um einige Dekameter emporstieg; dagegen war die
* Spiegelung nach oben von etwa 10 m Seehöhe aus mindestens ebenso schön
* ausgebildet wie vom Meereise aus." (p.290)
* WEGENER and BRAND report meteorology at the Pustervig station
* Many reports of mirages, and occasional MULTIPLE HORIZONS:
* Superior mirages on pp. 518-521; inferior mirages on pp.523-524,
* and a superior mirage again on p.524, and a strong superior mirage and
* thermal inversion on 525. P.577 reports double horizons on 2 days,
* one with a very strong inversion, and a triple horizon, p.579.
* BRAND reports temperatures (and mirages) from the crow's nest:
* P.577 reports double horizons on 2 days, one with a very strong
* inversion, and a triple horizon, p.579. P.580: inferior mirages,
* one with a simultaneous superior mirage, "separated by a strip of
* normal refraction", with a 13° inversion. On April 16, the wind was
* calm, followed by light variable winds; "Die Feuchtigkeit war dauernd
* gering. Mit einer Ausnahme ist zu allen Zeiten Inversion vorhanden, deren
* maximaler Wert 4.9° beträgt, während ihr durchschnittlicher Wert 1.8
* ist. Am 17. um 8a wurden schwache Luftspiegelungen nach oben beobachtet."
* In June, 1908, "Auch ist stets Inversion vorhanden, die
* durchschnittlich einen etwas grösseren Betrag als im gleichen Monat des
* Vorjahres erreicht. Wiederholt herrscht eine Inversion von 4° zwischen
* Eis und Tonne. Gleichzeitig wurden wieder Refraktionsanomalien und
* Spiegelung beobachtet. Ein am Abend des 15. ausgeführter Ballonaufstieg
* ergab ebenfalls Inversion in den untersten 200 m." (p. 582)
* There is a discussion of inversions, p. 587, and of mirages, p. 591.
* The general conclusion is that the lowest 300 meters are normally
* inverted.
* HAT-shaped sunset (but no drawings!) and comments on mirages
* ". . . at Ostend on or about September 20, 1907 . . . I was on the sea
* parade near sunset time, and suddenly heard a group of men shouting out
* `Un chapeau, un chapeau.' Looking towards the sea I saw on the horizon
* the sun in the decided shape of a hat with a large brim."
* Cites Nansen, and refers to "The South African Pilot" for mirages along
* the coast of western Africa, and recurrent Fata Morganas at Cape St. John.
* HANS HENNING's curious paper, with DRAWINGS by his brother
* This is mostly about the MOON ILLUSION, so has been FILED SEPARATELY
* with those papers.
* The distorted-sunset drawings begin on p. 293; those are not
* attributed. The ones on p. 294 are by his brother, Georg Henning, and
* made in a 500-m high hill near Samaria, looking out over the Saron plain.
* He describes the mock mirages in Fig. 7 as "Erhöhungen der
* untergehenden Sonne mit Aufsatz" -- that is, "headpiece". The drawings
* are very schematic; and as some of his other sunset drawings, purporting
* to show a tree 50 km away (which would make the tree 250 m high!) are
* incredible, I don't put much stock in these drawings.
* I have 2 really bad copies, apparently from the same torn original.
* The full journal title is: Zeitschrift für Psychologie und Physiologie
* der Sinnesorgane. 2. Abteilung, Zeitschrift für Sinnesphysiologie".
* Thanks to Helen Ross for pointing out this reference in her book!
* Comments on "COLTON PHENOMENA"; TYPE A and Type B sunsets; MIRAGES noted
* "Type A occurs always when mirage is perceptible . . . . As the descending
* sun, vertically compressed by atmospheric refraction, approaches the sea
* horizon, a protuberance . . . grows out below, and almost simultaneously a
* line of light appears in the sea horizon, which lengthens horizontally and
* thickens upward till the protuberance and the line join . . . . For about
* half the duration of sunset the sun presents the appearance of an inverted
* fish globe, whose mouth widens to the sun's diameter; from then on the
* vanishing disk looks like an ellipse much flattened below, and vanishes as
* a small elliptical spot. . . . This spot does not sink below the horizon; it
* `goes out.'"
* Type B never occurs simultaneously with a perceptible mirage. . . . The
* descending sun flattens below as it approaches the horizon, which is not
* easy to see under it, being comparatively dark. The corners of the disk
* as it passes below the horizon are rounded, instead of projecting like the
* rim of a fish globe, until about midsunset; then the remaining half-disk
* begins to show a rim, so that it looks for a time not unlike the `tin hat'
* or trench helmet of the American Expeditionary Force. This flattens down
* in the middle faster than it shortens horizontally, becomes a line of
* light, and disappears in dots and dashes among the waves, if the horizon
* is near. The disappearance is slow, not like the vanishing of the spot at
* the end as in type A.''
* Fisher's appeal for info about Janssen's 1875 report to Brit. Ass.
* "In the Sections reports of the meeting of the B. A. A. S., Bristol,
* 1875, p. 26, M. J. Janssen gave a brief summary of his observations and
* conclusions with regard to mirage at sea. As this happens to connect
* with a phase of low sun phenomena in which I am interested . . . ."
* (No. 1367, 11 March 1921)
* Fisher's papers reported in JBAA
* GREEN FLASH HISTORY and BIBLIOGRAPHY
* Type A and B now more succinctly described:
* "Type A occurs always when mirage is perceptible . . . . As the
* descending sun, vertically compressed by atmospheric refraction,
* approaches the sea horizon, a protuberance . . . grows out below, and
* almost simultaneously a line of light appears in the sea horizon, which
* lengthens horizontally and thickens upward till the protuberance and the
* thickened line join . . . . For about half the duration of sunset the sun
* presents the appearance of an inverted fish globe, whose mouth widens to
* the sun's diameter; from then on the vanishing disk looks like an
* ellipse much flattened below, and vanishes as a small oval spot. . . .
* This spot does not sink below the horizon; it `goes out,' above it.
* Type B never occurs simultaneously with a perceptible mirage. The
* descending sun flattens below as it approaches the horizon, which is not
* easy to see under it, being comparatively dark. The corners of the disk
* as it passes below the horizon are rounded, instead of projecting, until
* about midsunset; then the remaining segment begins to show a rim, so
* that it looks for a time not unlike the `tin hat' or trench helmet of
* the American Expeditionary Force. This flattens down in the middle
* faster than it shortens horizontally, becomes a line of light and
* disappears in dots and dashes among the waves, if the horizon is near.
* The disappearance is slow, not like the vanishing of the spot at the end
* of type A."
* "Not the least argument against the contrast theory arises from its
* [i.e., the flash's] ill understood capriciousness." (p.263)
* ". . . the psychological explanation seems much more convincing to persons
* who have seen the sun's departing flash only once or twice, or who have
* only read about it.
* The simple dispersion explanation is accepted, nearly as it was first
* put forward by Winstanley . . . , by W.J.Humphreys . . . and by A.A.Rambaut . . . ,
* as explaining the green flash. F.M.Exner, however, holds that the
* phenomenon is not yet completely explained. Some of its difficulties are
* variable duration, capriciousness, appearance on a cloud but not at a
* clear sea horizon below, and occasional lack of color." (p.265)
* Note that the final installment appeared in 1922.
* O'C #34
* FISHER's summary in Nature, with DRAWINGS of the 2 types
* "While the sun is the source of light in such observations, and the
* Nautical Almanac and four-place logarithms have to be used in computing,
* the subject is not astronomical but meteorological, and, I believe, has to
* do with temperature distribution in the atmosphere. We have here one of
* those residual phenomena the study of which may lead to the discovery of
* interesting facts and which can be forwarded by amateur observers, the
* more and the more widely scattered the better."
* editorial report of the Nature paper, with DRAWINGS reproduced.
* (See also Fisher, 1926 PASP, in GF)
* Fisher's table of SUNSET DURATIONS
* ". . . for any year there are two maxima about the solstices and two
* minima about the equinoxes. The maxima are sharper than the minima. In
* low latitudes the summer maximum is less than the winter, due to the
* smaller semi-diameter of the sun; but in high latitudes, beginning above
* N. 52°, this is reversed, due to the unsymmetrical and exaggerated
* effect of refraction, which makes the sines of summer solstice hour-angles
* less than those of the winter solstice."
* "Elevation above sea-level would have an effect like refraction."
* Fisher discovers Le Gentil's work, and classifies his observations as
* Type A ("which is a mirage type") or B
* Fisher's papers reported in JBAA (on same page as the previous, so filed
* before the P.A. paper, though noted here, after it.)
* Described as "a very comprehensive and suggestive summary" by JBAA
* "He promises a more detailed memoir, but there is sufficient in this one
* to give much food for thought."
* A summary paper, repeating much of the previous:
* This appears to be mostly a reprint of the first 2 papers in Nature.
* Fisher's detailed reduction of Le Gentil's observations, and of Colton's
* (Sept.-Oct.1922 issue)
* FISHER's important H.A. paper, with "79 cases, including those observed
* in Luzon, with corrections and additions. . . ."
* Here are important details about instruments, timing, and calculations.
* Also an extract of a letter from W.W.Campbell (Director at Lick):
* ". . . on midsummer evening, what we call the cigar form of the setting
* sun . . . ." [i.e., Chappell's final long line]
* ". . . type B was often not as brilliant as type A." [airmass effect.]
* also a Prefatory Note by Alexander McAdie, p.38
* Drawings showing effects of 2 or 3 inversions; SQUARE SUN
* "Le temps était ce jour-là, tres beau, sans nuages et sans vent."
* Very schematic drawings of the geometrical phases
* Dec. issue
* SUNSET OBSERVATIONS
* ". . . the final singular long line, which oddly enough is substituted
* for the small tip of light that could reasonably be expected as the
* final glimpse of a bright descending sphere."
* O'C #16
* typical distortions from an inversion above observer, with DRAWINGS
* "I cannot recall the exact details of the change from the `mushroom'
* shape of figs.2-4, to the `Bowler Hat' shape of the later phases."
* SUNSET DISTORTIONS with RECTANGLE and HOURGLASS
* Also, possible INFERIOR MIRAGE of 22-deg.HALO (Fig.3)
* fair DRAWINGS of a rather typical Type B sunset from 50 ft. above sea level
* "The bright spot . . . below the main portion of the sun and detached
* from it was very striking, but short lived, as it rapidly expanded to form
* a `mushroom stalk' reaching from the sun to the horizon." (Mock mirage)
* "This finally degenerated into a faint red line on the horizon which
* persisted for perhaps 30 sec. before disappearing."
* Distorted moonrise and sunset; DRAWINGS
* Possible GREEN RAY 1 minute long at sunset?
* "The sun was greatly distorted at sunset on that day, being accompanied
* during the last minute or so before it disappeared by a greenish-yellow
* drapery immediately above the orb . . . . This greenish-yellow curtain of
* light set below the horizon a few minutes after the sun."
* DISTORTED SUNRISE
* Possible DARK LINES in sky ("cloud")
* DISTORTED SUNSET ending with small GREEN FLASH
* Photographs of an extreme OMEGA sunrise
* This is Charles A. Federer's account of the 1956 Astronomical League
* (amateur astronomers') convention.
* The pictures (reproduced in b/w) extend across the top of the first page.
* The caption says, "The strking mirage as caused by a temperature
* difference of 28° Fahrenheit between the atmosphere and the air close
* to the warm ocean water."
* "Most dramatic was the presentation . . . of colored sunrise motion
* pictures by Matt F. Taggart, of Ft. Lauderdale. He has recorded
* little-known mirage phenomena associated with dawn; when the temperature
* difference between the cold air and the warm water is greatest, these
* effects are particularly striking." (p. 485)
* Thanks to Jim Mosher for pointing this out!
* Note that volumes and years do not come out even at this period in S&T.
* Classical OMEGA sunrise roughly sketched
* Apparently (from the DRAWING) a narrow BLANK STRIP
* This is an amusing example of the MOON ILLUSION at sunrise;
* the text says "two images visible, one on the horizon and one 2-3°
* above." But the drawing shows the second image only about 2/3 solar
* diameter, or 1/3 degree, above the horizon!
* The drawing is crude but a reasonable basis for a simulation.
* MYSTERIOUS UNEXPLAINED PHENOMENON, or else bad description
* Drawing unfortunately shows circular Sun images
* ". . . a `double sun' with the `lower sun' being semi-transparent in that
* the waves could be seen through it. The two `suns' kept the same position
* relative to each other."
* [Editorial comment that this "is due to a strong temperature lapse rate
* in the vertical, as confirmed by the presence of cumulus cloud" is
* nonsense.]
* Sounds like a ghost reflection in window or glasses???
* MYSTERIOUS UNEXPLAINED PHENOMENON, or else bad description
* Again drawing is all arcs of circles, so unreliable. Sounds vaguely
* like a mock mirage, but description doesn't fit.
* Nice but small OMEGA PHOTOGRAPH
* "On 31 July 1981 Leo Aerts (Heist-op-den-Berg, Belgium) took the setting
* sun from the Belgian coast. The temperature of the sea-water was higher
* than the air temperature. Thus the horizon looked notched rather than
* rectilinear. At the same time there appeared a mirage, which caused the
* omega-form of the setting sun."
* cites Zenit 8, 70 (1981)
* An OMEGA with large temperature difference and large inverted portion
* Ruud Keller won the "optical phenomena" category in the photo contest:
* "Travelling on the motor ship Leliegracht on 27 January 1985, he
* made a number of photos of a remarkable sunset over the Gulf of Bothnia
* near the Swedish port of Vaija (fig. 6). As the sun approached the
* horizon, while coming out from behind a cloud bank, its mirror image
* rose up! Sun and mirror image approached one another and then formed a
* sort of hour-glass (omega-form). The photos give a clear example of a
* sun reflected on a (relatively) warm layer of air above a water surface.
* The air temperature lay between -20 and -25 C; the seawater temperature
* at about -1 C. The sea was partly covered with ice . . . "
* Jan. 1988 issue; the pictures are on p. 7 and the text on p.8.
* photographs of an OMEGA-shaped sunset
* ". . . taken on 5 November 1988, with cold and quite clear weather
* conditions."
* Cites Floor's Zenit 8, 72 (1981) paper.
* Fine example of OMEGA SUNSET, with cloud across middle
* Photographed with 600mm telescope
* April 1993 issue
* TEXTBOOK EXAMPLE of OMEGA SUNSET [N.B.: actually filed in COLOR file]
* Photographed by Torsten Damme at 1400mm f.l.
* This is probably the finest Omega sunset ever photographed -- and in
* color, too. The maximum extinction at or just below the fold-line
* is particularly striking. There is also a curious pseudo-reflection of
* the inverted image on the water. . .
* Abb. 6 a-f: Sonnenuntergang über der Wesermündung in Bremerhaven . . .
* issue No. 12 (Dez.)
* Observer draws what he *thinks* is there (not a realistic drawing)
* but does mention ``a sort of hourglass appearance''. -- i.e., OMEGA.
* This is clearly an Inf.-mir. sunrise:
* "air temperature 10.0, wet bulb 8.6, dew-point 7.1, sea 13.5, . . .
* wind NW'ly, force 4."
* Two Romanian physicists observe and model flattened sunsets
* The calculations are the crude ones typical of physicists. No info
* on the photographic equipment used, but looks like short focal lengths
* were used.
* Dip of the horizon was not taken into account in the Indiana observations;
* but the discrepancies between theory and observation are mostly due to
* adopting the Standard Atmosphere's lapse rate (Biot not mentioned).
* The "textbook" GF is briefly mentioned. O'Connell's book is cited, but
* his name is misspelled. Pretty typical Am.J.Phys. effort.
* [see Siebren van der Werf et al.'s Novaya Zemlya paper (2003) for a
* much better treatment of the same problem.]
* Sergey Kivalov and I bring Biot and Chauvenet up to date
* This expands on Biot's magnification theorem, as well as dealing with
* the effects of the convergence or divergence of the vertical circles
* near the horizon.
* Stephen J. O'Meara's ducted Botswana sunrise
* Unfortunately, what looks like good photographs of a DISTORTED SUNRISE
* turns out to be just an artist's drawing based on naked-eye observation.
* Apparently, waves on an inversion made the Sun appear and disappear;
* the refraction was unusually large.
* Though the title refers to the N.Z. effect, I don't think the
* refraction was really big enough to deserve that name. The nocturnal
* inversion in a dry desert salt pan is the obvious cause, in any case.
* Thanks to Mila Zinkova for bringing this interesting observation to
* my attention! For a somewhat similar low-Sun display, see her video of a
* prolonged ducted sunset at https://www.youtube.com/watch?v=5fwGs-bP68w .
* Thanks, too, to Stephen O'Meara for explaining to me that the images are
* not really photographs; the editors "created their own caption" without
* telling him.
* Available at
* https://www.astronomy.com/observing/secret-sky-tropical-novaya-zemlya-effects/
*
* Emil Schnippel
* SUPERIOR MIRAGES with SUNSET drawings
* best seen 3 m above the sea, not from the slopes or heights of the dunes
* BRIGHT STRIP, looks like FOG
* This is probably the most complex sunset display on record! Many
* interesting features.
*
* (See also Shackleton, 1962, in Novaya Zemlya file.)
* (See also Wales, 1770; Huddart, 1797; Reinecke, 1800; and Kelly, 1846,
* in Mirage file; and de Vanssay de Blavous, 1944 in modern Refraction.)
*
* DIP of the horizon seen from a mountain used to measure the Earth
* According to this history of geodesy, this method was invented by
* Al-Biruni (see p. 182) c. 1017
* This is Chapter 8, "Geodesy", in Part 1, "Islamic Cartography", of
* Book 1, "Cartography in the Traditional Islamic and South Asian Societies",
* in Volume 2 of "The History of Cartography"
* The FIRST DIP TABLE is supposed to be the one by EDWARD WRIGHT
* This is the original edition (1599). The table is given to minutes
* only, for every 5 ft. of height. The basis of the calculation is
* not explained. The pages are not numbered; the dip table appears on
* folio O, verso: "For the higher the eye is aboue the water, the
* greater is the angle intercepted betwixt the two visual lines, whereof
* one toucheth the conuex superficies of the sea, the other passeth on
* to the sun or starres : And the lower the eye is, the lesser is the
* foresayd angle : and then onely it sheweth the true altitude, when the
* center of the sight is in the same line of leuell with the superficies
* of the water. But if the eye be higher then the water, that angle is
* greater then the true altitude, and therefore subtraction must bee made
* accordingly, that you may haue the true altitude. For this purpose I
* haue made this table here adioyned, the vse whereof is this: when you
* obserue the heigth of the sunne or starres at sea with the crosse staffe,
* you shall also find out how many foot high your eye is aboue the water
* with a plumb-line or otherwise : seeke that heigth of the eye in the
* first columne of this Table : and in the same line in the second column
* (intituled Minutes to bee subtracted ) you shall find what number of
* minutes are to be subtracted from the apparent heigth of the sunne or
* starres . . . ."
* This is immediately followed by a curious table of the solar parallax.
* From his praise of Tycho, I assumed it would be Tycho's table, based
* on a horizontal parallax of 3'; but instead, it is 2' 59" at the horizon.
* After that, one finds: "Hereunto some do also adioine the fourth
* cause of errour by reason of refraction of the beames of the sunne or
* starres through thickness of the ayre : which for aught I can finde
* by obseruation with large instruments is little to be regarded in anie
* meridian altitude of the Sunne heere at London : But in the starres I
* haue many times found it to be some thing, especially when they come
* neere the horizon, and sometimes scarce any thing being but a few
* degrees aboue the horizon. So as I think it not greatly needefull at
* this time to trouble the mariners conceipt herewith any more, for whose
* sake especially this labour was vndertaken."
* Concerning Tycho, he is copiously cited as an authority in the Preface
* as ". . . that magnificall Tycho in his Vraniburg . . . ", and that
* ". . . Astronomie hath much aduauncement by Tycho Brahe alone, who
* for his deserued renowne cannot be too oft named." (Preface, fol. 3r)
* The state of the art in his day is shown by reference to "large and
* exact instruments, wherin both minutes and half minutes might be easily
* discerned." (Preface, fol. 2r)
*
* I have seen only the 1974 facsimile reprint edition:
*
* Edward Wright
* Certaine Errors in Navigation: . . .
* (Theatrum Orbis Terrarum, Ltd., Amsterdam, 1974)
*
* co-published by Walter J. Johnson, Inc., Norwood,N.J. This is Number
* 703 of "The English Experience -- its record in early printed books
* published in facsimile". It reprints the original title page:
* Wright's revised dip table appears on p. 96 of the 3rd edition
* The title page shows the instruments of the day, with a curiously
* formed map of the world: "America" is the southern one only (the northern
* continent, "Virginia", subsumes Canada); California is an island near the
* longitude of Texas; China and India are small peninsulas; "Nova Zelandia"
* is 2 hours east of its true place; etc.
* Item 7 in the list of "Additions To this Edition that were not in the
* former" is the table of dips; item 8 is Tycho's refraction table.
* [However, Bob Graham tells me the 1599 edition did have a dip table.]
* Wright deduces the size of the Earth from the dip measured from Mount
* Edgecombe, 375 ft. high, and finds a radius of some 18.3 million ft.
* or about 5582 km; so the dips are a bit too large. He calls them
* "the angle of dipping", and I suppose this must be the first use of the
* term in English.
* It appears that Wright's measurement was first published by Richard
* Norwood in "The Seaman's Practice" in 1637.
* The "refraction of the Beams of the Sun or Stars" is "by reason of the
* Vaporous thickness of the ayre that is betwixt us and them, especially
* when they are neer the Horizon."
* There is also a table of solar parallaxes, based on 3' at the horizon.
* 3 series of DIP and TEMPERATURE DIFFERENCES
* ". . . l'observateur le plus exercé et muni des meilleurs instrumens, peut
* se tromper en plus ou en moins d'une minute, sans que les circonstances
* météorologiques puissent lui fournir ne les moyens de calculer l'erreur,
* ni même lui faire présumer dans quel sens elle a eu lieu."
* ". . . la seule conséquence qu'on puisse déduire de l'ensemble de ces
* déterminations, est celle-ci: l'erreur de la dépression calculée ne
* sera positive dans nos climats, qu'autant que la température de l'air
* surpassera celle de l'eau."
* Reprinted in: Œuvres Complètes de François Arago, Tome Onzième
* (Gide, Paris, 1859) pp. 662-670 [which is available at Gallica].
* REFRACTION AND DIP
* "..the late Mr. Henry Atkinson . . . proposed to himself to demonstrate,
* 1st, That the fluctuations in the state of the atmosphere near the
* surface of the earth are not only fully adequate to account for the very
* great variations which have been observed in the horizontal refraction,
* but even for still greater variations.
* 2dly, That the variations of the dip of the horizon at sea are caused
* by the fluctuations of the atmosphere, and can be calculated when the
* latter are known."
* ". . . draws the conclusion, that the variation of refraction arising from
* any conceivable derangement if this middle portion will be inconsiderable,
* compared with that which may be produced by changes in the lowest portion
* [the bottom 50 feet]."
* Here is Henry Atkinson's incomplete paper:
* In the Appendix he says: "To estimate the effect of refraction on the
* dip, I have shewn, in my former paper, that the small portion of the curve
* AEF, described by a ray of light in the problem under consideration, does
* not sensibly differ from a circular arc." He then employs a diagram
* similar to Wegener's.
* Short note connecting DIP and MIRAGES, copied from Kelly (1846)
* "Every one who is acquainted with nautical astronomy is aware that some
* uncertainty always attends observations made with the natural horizon,
* from the varying amount of the dip occasioned by terrestrial refraction.
* The cause of these variations is very obscure. The best authorities seem
* to regard differences of temperature in the air and water as the sole
* cause of the irregular density of the lower strata of the atmosphere on
* which the varieties of the dip depend. It is known that in general, when
* the water is warmer than the air, the dip is greater than that given in
* the nautical tables; and that when the water is colder than the air, the
* dip is less. But cases occur where the deviations from the tables are
* found to bear little relation, at least in amount, to the relative
* temperatures of the air and water. Some other property of the atmosphere
* must therefore be sought after, by the influence of which the effects of
* temperature are modified." (p.271) [He thinks it is the humidity.]
* "We know of no place where the dip is more affected or mirages more
* frequent and extraordinary than on the northeastern part of this
* continent, in the Gulf and River St. Lawrence. These phenomena are of two
* kinds. In one (the mirage of arctic regions), the horizon is elevated, the
* forms of objects distorted and inverted, sometimes two, three, and even as
* many as five mirages of the same object are seen, alternately erect and
* inverted —— the lowest always being erect. This kind of mirage is only seen
* when the water is colder than the air. In the other kind of mirage (the
* mirage of the desert), the horizon is depressed, distant points of land
* seem raised into the air, the form of objects is seldom materially
* changed, there are never more than two images of an object, and when a
* second is seen, the lower is inverted and the upper erect. When this kind
* of mirage is seen, the water is usually warmer than the air." (p. 272)
* "The mirage is constantly seen with a depressed horizon, when the water
* is warmer than the air. . . . The occurrence of either form of mirage, and
* its intensity, seem to be affected by other circumstances besides the
* relative temperature of the air and surface of the water, and the
* hygrometric state of the air." (p. 272)
* "Either the elevation or the depression is comparatively greater in a
* calm and less in a breeze." (p. 273)
* ". . . it is pretty plain that the elevation or depression of the horizon
* is chiefly influenced by the relative temperature of the air and surface
* water, and only in a minor degree and perhaps less regularly by the
* hygrometric state of the air, and either elevation or depression is the
* greater in calms." (p.274)
* All of this is copied nearly verbatim from Kelly's article in the Nautical
* Magazine 15,p. 393 (Aug. 1846).
*
* Capt. John H. Bell ran the "Nautical Department" of this magazine.
* This is item 3 of 6 short notes in his column for March, 1859.
* Google Books has Vols. 1 and 2 together; not copied.
* VARIABLE DIP and TERRESTRIAL REFRACTION
* This could as well have been filed under "Terrestrial refraction" or
* "Variable refraction", but is here because of the dip data.
* This 50-page paper has 2 Tafeln at the end, showing the observing
* geometry, figures for the derivations, and the instrument used. About
* the first 20 pages give observations of apparent depressions to the
* nearest second of arc. While the weather data are provided, there are
* no estimates of water temperature, so the data are not very useful
* today.
* Perhaps the most interesting result is that the dip of the apparent
* sea horizon was more than twice as variable as that of the lighthouse.
* There is also a useful discussion of theory, in which he shows that the
* formula given by Delambre assumes that k2 can be neglected, which is
* by no means true. Not surprisingly, he finds that objects (such as
* the shoreline at the base of the lighthouse) that should be invisible
* occasionally appear, and that the sea ``horizon'' is occasionally above
* the astronomical one. [NEGATIVE DIP] (Cf. McCluskey 2018; Tschudin 2019)
* The light was about 30 km, or very nearly 16' of arc, from the
* observer. Heights are given in Rhenish feet and inches; the observer
* was 78 ft. above the sea, the light about 130 Rheinl. Fuss. Evidently
* it is the penetration of the visual ray into the surface layer that
* makes the dip of the horizon more variable than that of the light.
* (The light typically appears some 4' above the apparent horizon.)
* There is the promise that "Die Discussion a l l e r Beobachtungen
* hinsichts des Zusammenhanges zwischen dem jährlichen und täglichen
* Gange der Refraction und den atmosphärischen Zuständen soll in einem
* zweiten Theile erfolgen, so bald das genauere Datum der Höhe des
* Heláer Leuchtthurmes über der See durch die neuen Pegel-beobachtungen
* der Admiralität bekannt geworden ist," but this seems never to have
* happened.
* These "Hefte" are separately paginated; this one has 50 pp of text,
* plus 2 Tafeln, and is available at
* https://www.biodiversitylibrary.org/item/50937#page/333/mode/1up
* Mentioned, but not cited, by Forel in his 1899 C.R. note.
* NOTE: Friedrich Ernst Kayser: 27 Mar. 1830 - 12 July 1907.
* A detailed biography is in the Schriften (N.F.) vol.12, No.2, pp.58-70,
* (1908), followed by a complete bibliography of his publications.
* DIP and diurnal variations; horizon highest during sirocco
* A.Ricco (in DIP file)
* Continuation of similar measures by SAIJA at Catania
* Continuation of similar measures by BOCCARA at Catania
* PREVIEW of VERUDELLA
* VERUDELLA
* DIP depends on DIFFERENCE between AIR and WATER TEMPERATURES
* Karl Koss, k.und k. Linienschiffs-Lieutenant
* Emerich Graf Thun-Hohenstein
* ``. . . ein sehr merkwürdiger Fall'' on 17 March 1899, when the dip changed
* from 6'6" below the true horizon to 1'7" above it, between 1:03 pm and 4:57.
* On this day, ``Sonne im Untergehen (6h10m) stark flach gedrükt.''
* FLATTENED SUNSET; WAVY HORIZON
* ``4½h sieht man mit freiem Auge die Kimm gewellt . . . und diese Wellen
* wandernd.'' (p. 395)
*
* footnote, p.364:
* "Es ist hier der Platz, eine Bemerkung über solche abnorme Hebung der
* Kimm zu besprechen, nämlich die Frage: Wieso kommt es, dass man von
* solchen Fällen (Hebung über den Augeshorizont), die sich ja doch
* öfters ereignen müssten, noch nie etwas gehört hat? Die Antwort ist
* die, dass wohl schon mancher Navigationsofficier hin und wieder aus einer
* Höhenbeobachtung eine augenscheinlich um 10 -- 15' irrige Position
* erhalten hat, dass er aber in einem solchen Falle eher eine grobe Irrung
* im Ablesen oder Aufschreiben angenommen hat als einen Fehler in der
* Kimmtiefe, zu dessen Feststellung er zudem keine Zeit gehabt hätte,
* überdies auch keine Mittel. Dass sich bei den vorliegenden
* Beobachtungen nur zwei solche Fälle ergeben haben, wiewohl sie ein Jahr
* umfassen, ist eben dem örtlichen Wetter zuzuschreiben, das im
* Winterhalbjahre entweder südlichen oder Nordwestwind, im Sommer zumeist
* Nordwest bringt, und dem Zufalle, der von 48 Beobachtungstagen des Jahres
* eben nur zwei so ausgezeichnet hat. Von Kimmfehlern bis zu 5' berichten
* übrigens R a p e r, Practice of Navigation und M a g n a g h i, Gli
* strumenti a riflessione." (p.364) [cf. Cornelis, 1924; Ramforth, 1973!]
* [see also Reinicke, 1903; Havinga, 1905; Baker, 1922).]
*
* (Wind was from the NW this day, they say.)
*
* Dr. J.B.Messerschmitt's review, including Koss
* including many references: Helmert, Th.v.Oppolzer, Budde, Forel, etc.
* But Forel's results can't be directly compared with those of Koss,
* because "die Temperaturverhältnisse über einem Binnensee komplicirter
* als am offenen Meere sind. . . ."
* The historical background that led up to the "Pola" project is
* summarized, and the results discussed. The physical description
* is remarkably modern, considering that this pre-dates the concept of
* a boundary layer; the increased lapse rate due to heat exchange over
* water warmer than the air, and its reduction over colder water, are
* plainly stated.
* Revised dip formulae and tables are presented; but "Dabei ist
* vorausgesetzt, daß die Luft gut durchmischt ist, also eine Briese
* von mindestens der Stärke 2 bis 3 weht. Bei schwächerem Winde kann
* sogenannte Temperaturumkehr eintreten, wobei sich warme Luft in der
* Höhe sammelt, ohne daß der Wind sie mit der unteren kälteren zu
* durchmischen vermöchte. Dadurch entsteht eine . . . starke Hebung der
* Kimm bis auf 3' über die durchs Auge gedachte Horizontalebene, also
* eine Hebung der Kimm um 10'." Then the temperatures must be measured
* with the best instruments; the air temperature "mit einem Aspirations-
* oder mit einem Schleuder-thermometer." In this connection, notice the
* complete neglect of "der Korrektion der Kimmtiefe wegen des Seeganges"
* which can exceed 20" when the wave height between crest and trough exceeds
* 2 m, which can limit the accuracy of altitudes measured at sea to 2'.
* [Note: corrections for the sea state were not introduced until 1960.]
* Therefore the use of a gyroscopic sextant or "Libellensextanten"
* (apparently an early bubble sextant) is recommended, to make the
* determination of the dip superfluous; or to measure the dip directly
* with any of a variety of instruments named: Steinheil prism circle,
* Troughton's dip sector, Pistor & Martin's reflecting circle, Amici-Magnaghi
* prism circle) which all assume the refraction conditions are the same on
* opposite sides of the horizon -- which is certainly not always the case.
* Auxiliary tables are included to correct for the temperature
* difference. There is a special table for near-calm conditions, assuming
* that in addition to measuring the temperature of the water surface,
* the air temperature is measured just above the water as well as at eye
* height. "Auf die Messung der Temperaturen ist dabei besondere Sorgfalt
* zu verwenden."
* This volume of Ann. Hydrog. is available at Google Books.
* TEMPERATURE DIFFERENCE and DIP
* "Even when neither land nor ships are in sight, the miraging can be
* determined by the unique moving appearance of the horizon seen through a
* telescope. The water seems to wave unnaturally and seems to flicker
* like flames along the upper surface. It does this with a strongly
* increased dip. I have never been able to see the least miraging so long
* as the ``extra dip'' remained under 30"." [This agrees well with Havinga's
* 1 deg.C] " . . . the ``boiling'' horizon." [cf. Forel, 1890. Forel has
* a nice drawing of the wave effect on p. 520 of his 1895 monograph.]
*
* "The danger is the greater because such cases [cold sea and warm air]
* generally seem to go together with a clear sharp horizon, from which one
* should never expect anything abnormal." (So much for Hornstein et al.!)
*
* Lieut.-Commander JOHN B. BLISH and his PRISM, with measurements
* The observations are off the coasts of the Californias in October,
* 1901 (Santa Ana season!), and show the Table to be wrong by from +7' 08"
* to -3' 18" -- a range of 10' 26". The large positive value is noted as
* being seen in "cloudless and hot" conditions -- typical Santa Ana.
* The positive value had air 5° F warmer than surface water; the
* negative one, 4° colder. All just as expected! (But, alas, no
* info on sea state or wind.) The photographs of the mustachioed gent
* taking observations are quite charming.
* Thanks to George Huxtable for a copy, originally from Brenda Corbin!
* Whole number 105, dated March, 1903.
* DIP and REFRACTION (cf. Havinga's dip review)
*
* Here we have a horizon 8' or 9' above the dip of 5' calculated from
* the measured water and air temperatures, using Koss's formula.
* Evidently this is a case of Hasse's "Kimmfläche" -- i.e., the observer
* is *in* a duct. In this case, it must be caused by a strong inversion
* overhead, out of reach of the air-temperature measurements.
* Comments on the occurrence of these phenomena: ". . . recht oft
* mögen wegen gehoben erscheinender Kimm falsch gemessene Kimm-
* abstände zu Ergebnissen geführt haben, die man auf
* Stromversetzungen, Änderungen der Deviation oder dergl., wenn nicht
* gar auf Unachtsamkeit geschoben hat. Wie im vorliegenden Falle, so wird
* man allerdings in vielen anderen Fällen erkennen können, sei es
* durch irgend welche verzerrt erscheinenden Objekte, sei es auch nur
* durch auffällig ausgezackt scheinende Kimm, daß
* außergewöhnliche optische Verhältnisse herrschen." . . .
* "Auch in den deutschen Gewässern kommen Luftspiegelungen oder doch
* gehobene Kimm gar nicht so selten vor, wie sich aus den meteorologischen
* Tagebüchern der Normalbeobachtungsstation der Deutschen Seewarte zu
* Neufahrwasser ergibt; . . . ."
* See p. 568 for a correction to one sentence.
* uses temperature gradient info -- see Freiesleben (1948) for update
* Note the formula for distance to the horizon on p. 543, which he relates
* to the dip variations and surveyors' k (refraction coefficient).
* On the next page, he considers the possibility of seeing infinitely far:
* ". . . das heißt der Lichtstrahl behält diese Höhe bei, soweit er auch
* läuft; daraus ergibt sich, daß man in dieser Höhe h' unendlich weit
* sehen kann und daß Punkte, die über oder unter dieser Höhe liegen,
* überhaupt keinen Kimmstrahl haben." This might count as a
* prefiguration of Hasse's Kimmfläche, except that he continues:
* "Da dies Resultat von der Erfahrung aber nicht bestätigt wird, . . . ."
* another instrument
* DIP REVIEW; mentions Kohlschütter's instrument and others
* "Different researches and theoretical demonstrations have led to the
* conclusion that difference in temperature between the water surface
* and the height of the observer's eye has a great influence. . . .
* "The observation of the temperature difference . . . still does not give
* complete certainty. The following case may serve as an example, which
* was published in the German 'Annalen' of December 1903, p.511. . . .
* [That would be Reinicke, above.]
* All these heights must thus have been too small by 8' or 9'. Every 4
* hours the temperatures of air and water were taken, the greatest was at
* 4 p.m. 1.0 degree and at noon it reached 0.6 deg. . . .
* "Between 12 and 1:30 in the afternoon there was an explanation of the
* phenomenon, when on the north side several ships came into view, whose
* forms were seen distorted in the most grotesque ways by mirage."
* (cited in Havinga's 1934 paper)
* Havinga's DIP and TEMPERATURE data
* "A remarkable case, which can well serve as an example, occurred the 19
* April in the Gulf of Suez. A strong mirage was visible, so that one saw
* inverted images above land, towers, ships and other objects. . . . Two
* hours later . . . while still always at the horizon, where no other objects
* were found, there was nothing unusual to see. The measurements showed,
* however, that there was no more dip, but an elevation of the horizon of
* 7'0".
* Had one at that moment taken an altitude, then one on almost all
* ships, making use of the usual tables, would have subtracted 6' for the
* dip, while one really should have added 7' and thus would have made an
* error of 13' in altitude."
* N.B.: this change from 4'40" to -7' dip occurred with only 0.3 degree
* change in the air-water temperature difference! So, the inversion here
* was well above eye level.
* A fine tutorial article on refraction and dip; much on mirages as well
* He distinguishes among Luftspiegelung, Hebung, and Senkung.
* Many specific examples, as well as naming places where mirages are
* common (e.g., Newfoundland bank, water warmer than air by 13 deg or more
* in winter; west coast of Africa, air warmer by 16 deg or more.)
* At the end is an extended extract from Woltmann.
* April, 1905
* a nice NOMOGRAM to make use of Koss's formulae
* Bemporad finds the dip should differ at Etna by 15" from meridian to
* prime vertical, owing to shape of ellipsoid (AZIMUTH EFFECT)
* Cites Riccò in Mem.Soc.Spett.18, p.210 in the 204-213 (1899) paper.
* A fuller account of observations from Etna is promised in Mem.Soc.Spett.
* Remarkably large NEGATIVE DIP (Wegener's strip occulting horizon)
* A fine example of Lutz Hasse's Kimmfläche, years before its invention.
* Much space devoted to instrumentation for measuring air temperatures
* accurately at sea. The case reported here (27' elevation of the
* apparent horizon above the real one!) is unusual; it is backed up by
* temperature data.
* "FOG": "Diese wogende Luftschicht über dem Wasser machte den Eindruck
* einer weißlich gelben Dunstmasse, die von der darüber befindlichen
* `kälteren' Luftschicht durch eine flimmernde Linie getrennt erschien."
* The thickness of the disturbed layer seems to have been 4 meters above
* the surface.
* [Note observation of CONCAVE surface.]
* Contains useful refs. to earlier papers in Ann.Hydrog., usw.
* The article ends with good ADVICE to observers: what to record.
* Kapitän Frhr. v. Schrötter
* nice LITERATURE REVIEW; looks like a student's thesis
* Mostly about dip, but contains some survey reductions
* and a useless lab experiment based on the assumption of a
* constant temperature gradient.
* Attempts to decide between Koss and Kohlschütter. Unfortunately, the
* field measurements between Neuwerk and Helgoland were complicated by both
* instrumental problems with a heliotrope, and the different heat-transfer
* properties over the "Wattenmeer von 1 meter Tiefe, welches zur Ebbezeit
* stundenlang trocken liegt. Da nun die Wärmeabgabe des Sandes eine
* andere als die des Wassers ist, so ändert sich das Temperaturgefälle
* der Luft gegen Eintritt des Niedrigwassers beträchtlich . . . ." (p. 321)
* So (p. 322) Kohlschütter's model works only for a wind of at
* least force 2; "geringe Windstärken oder gar Windstille bringen
* außerordentliche Abweichungen hervor."
* There are many good historical references on dip measurements in the
* introduction. At the end is a fairly comprehensive list (6) of dip-
* measuring instruments. (p. 323)
* An appendix tabulates the measurements from 1878 of observed zenith
* distances on the sight-line Helgoland-Neuwerk, for which Kohlschütter's
* method fails because of small wind speed.
* a somewhat confused presentation of dip, based on Chauvenet's treatment
* Thinks there is no refraction for an isothermal atmosphere.
* ". . . when the temperature increases upwards at the rate of 0.066 ° F.
* per foot the dip is zero. For more rapid increase of temperature the sea
* surface will appear concave , and there will be no true horizon."
* [This wording is lifted verbatim from de Graaff Hunter, 1913 -- who got
* it from Professor Everett (1873)!]
* [Note observation of CONCAVE surface.]
* Donald W. Horner, F.R.Met.Soc.
* DATA DO NOT FIT KOSS FORMULA
* Good comparison of instruments for observing dip directly
* [The smaller variations here must be due to the higher waves at sea.]
* Havinga's chastising people who mis-use "dip":
* DOUBLE HORIZON and DOUBLE SUNSET
* "The double horizon was not uniform all round the compass. At some
* parts only the lower one was visible, and at others gradually merged into
* the upper one, this merging showing up as two clearly defined horizons.
* At sundown the sun assumed some very grotesque shapes, but a peculiar
* feature of its setting was that it completely set on the upper horizon
* first, then reappeared on the lower one and proceeded to set there."
* Separation of horizons was "ten to fifteen minutes of arc at its greatest."
* N.B.: land "was distant some 40 miles."
* DOUBLE HORIZON and separate sunsets at each
* Summary of March Marine Observer report
* Instructor-Captain Thomas Yeomans Baker, R.N. (ret.)
* FIRST discussion of DUCTING?
* shows a DIP DIAGRAM, with axes interchanged: Figs. 3, 4, 5, 7, etc.
* There is also a clear discussion of the resulting "triple horizon";
* see Fig. 9 (p.977), where "the true horizontal appears half-way between
* the lines" that mark the lower erect and (middle) inverted horizon
* images. "The phenomenon of the triple horizon is well known to anyone
* who has had to take astronomical observations for navigation purposes.
* It is generally referred to as mirage without any very satisfactory
* explanation of how it is caused. Not infrequently the navigator assumes
* that the detached strip of sea is a layer of low-lying haze or cloud."
* "As the point X [in Fig. 8, p.976 -- where the horizon rays cross]
* moves upwards towards B [where the observer is] the two [lower] horizons
* merge into one another and at the point B have just disappeared. It is
* therefore wrong to say, as was done above, that the observer at B sees
* the earth as flat. He sees it hollow, the line dividing sea from sky
* being . . . the indistinct line coming from the extreme range of visibility.
* As the observer goes higher still he ultimately reaches a height at which
* he is at the culminating point of an inclined ray which started from the
* extreme range of visibility. He then has a 'dip' value of zero and for
* greater heights the sea-horizon is depressed below the horizontal."
* (p. 978) So the observer in the inversion sees only a false horizon;
* the duct here extends to the surface, but the inversion does not.
* [Note observation of CONCAVE surface.]
*
* Much of the paper is concerned with radio-wave propagation; that part
* is obsolete, and he did not know about the fast phase speed in ionized
* media (there is much discussion of the Heaviside layer).
* Comparisons of various dip tables with observations
* H.R. was published by International Hydrographic Bureau in Monaco
* GOOD REVIEW of DIP with many citations of earlier papers
* He finds the Pulfrich instrument much better than Blish's prism.
* MANY GOOD QUOTES: recognizes the BOUNDARY LAYER as important.
* Explains how Freiesleben got into this business.
* "Es gibt Geophysiker, die behaupten, die Theorie habe immer recht."
* "Aber die Frage, wie man diesen Temperaturgradienten bestimmt, die
* so harmlos erscheint, blieb mehrere Jahrzehnte lang ungelöst."
* "Diese Schicht ist als Prandtlsche Grenzschicht mit laminarer Strömung
* aufzufassen."
* DIP FORMULA
* Hans Christian Freiesleben
* Note his use of the unusual term "geodätische Kimmtiefe"
*
* NOTE: DHZ was the successor to Ann.Hydrog.; this is its first volume.
* After 2000, it became "Ocean Dynamics".
* "surface" is about 0.5 m above WAVES, comparable to 0.4m WAVE HEIGHT
* BEAUTIFUL PHOTOGRAPHS of DOUBLE HORIZON with "FOG" in between,
* and large-scale structure ("crest") along the upper horizon
* Alas, no useful supporting data! The Editor comments on the "fog".
* DRAWINGS of MIRAGES
* This report is flanked by several other mirage reports.
* FOG reported:
* "A bank of mist appeared to lie around the whole horizon. . . . The
* phenomenon lasted until about 1530, when the mist cleared and objects
* resumed their normal appearance."
* Air was 4 F warmer than sea.
* GOOD DRAWINGS of DOUBLE HORIZON and WAVY HORIZON
* This report is flanked by several other mirage reports.
* Air was 7 F warmer than sea.
* Freiesleben's fine REVIEW article
* Several classic references are discussed; the treatment is excellent.
* But his Fig. 3 shows he does not understand double horizons; clearly
* the notion of "Kimmfläche" was not in his head at all.
* He concludes that the effective "surface" layer of air is less than
* a meter above the water, and "As it is impossible to obtain accurate
* measurements of temperature at such low heights, it is impossible for
* practical navigators to compute reliably the dip of the horizon from
* measurements of temperature."
*
* N.B.: There are two things called "Journal of the Institute of
* Navigation." This one (called "Journal of Navigation" since vol.25, 1972)
* is published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC, from 1960 to 1992.
* DOUBLE HORIZON TRANSITION
* notes "the sensitivity to variations of the temperature gradients";
* "Hence, it is practically impossible to compute the course of a ray of light
* with precision from temperature measurements; one may, however, be able to
* obtain an insight into the thermical structure of the lowest atmospheric
* layers by optical measurements."
* [Cf. Kurzyńska, 1987.]
* BROCKS COMMENTS on Freiesleben's paper
* He supplies the missing factor of α before T in the denominator
* of F.'s equation for the refractivity gradient, and adds the effects of
* the water-vapor gradient. He promises there will soon be a full report
* on the importance of the water-vapor gradient.
* Hans Christian Freiesleben has by now found the other "Navigation"
* journal. This is a one-page summary of his 1952 empirical study:
* mostly just the formulae for the results.
* N.B.: There are two things called "Journal of the Institute of
* Navigation." One (called "Journal of Navigation" since vol.25, 1972) is
* published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA and
* was produced in Washington, DC, from 1960 to 1992. Yet another "Navigation"
* is published in Paris!
* This is the LOS ANGELES version.
* TIME-VARYING DIP
* "24 per cent of sight points deviate by 2 min. of arc or more, and ½
* per cent by 5 min. of arc or more, from interpolated curves."
* ". . . there is often change of sign of deviation . . . when the azimuth
* changes very quickly and the telescope sweeps over large stretches of the
* horizon between two consecutive sights."
* "Morning sights show the lowest deviation frequency. . . ."
* NICE WORK on effects of WAVES and SUPER-REFRACTION for log profiles
* introduces concept of the Kimmfläche, where ray curvature = Earth's
* Uses Koss & Graf Thun-Hohenstein as first example
* Note: DHZ became Ocean Dynamics in 2001
* shorter English version of Lutz Hasse's thesis, placed here out of order:
* Shufeldt's paper on DIP measured with a dip-meter and high magnification
* Notable for the Prefatory Note and the Discussion, both by D. H. Sadler,
* Superintendent of H.M. Nautical Almanac Office.
* "During the study, it became increasingly evident that the great
* accuracy achieved by the high-powered telescopes in measuring the
* altitude of a body above the horizon made it most desirable to determine
* the value of the dip accurately and consistently, which is not possible
* with the tables available at present. Even when the height of the eye
* was accurately established, anomalies in the value of the dip were
* encountered, although full allowance was made for barometric pressure,
* and air and water temperatures." (p. 303)
* The dip-meter used was Gavrisheff's; see his patent for details.
* "The depression of the visible horizon below the horizontal at the
* eye of observer can readily be calculated. However, the line of sight
* from the observer to the horizon is affected by terrestrial refraction;
* the amount of this effect varies with changing weather conditions.
* Differences in air temperature along the line of sigh from the observer
* to the horizon seem to be the chief cause of this variation. Where the
* water temperature differs from that of the mass of air above, the air
* immediately adjacent to the water is cooled or warmed. The effect of
* this difference is usually particularly strong on a calm wind-less day.
* "Many attempts have been made to establish a direct relationship
* between the difference of temperature of air and sea and the value for
* the correction for dip; however, the results obtained by different
* investigators differed so greatly that no definite conclusions can
* be drawn." (p. 306)
* [Hasse's English summary would not appear for another 2 years.]
* ". . . Considerable differences between sea and air temperatures were
* encountered, and had a marked, but by no means consistent, effect on
* the dip. Such celestial observations as could be obtained during this
* period, when corrected for dip as obtained by the dip-meter, always
* resulted in lines of position lying much closer to Loran fixes than
* those corrected by means of the dip tables." (p. 306)
* "Using the value of the dip as obtained by dip-meter in correcting
* the altitudes, the mean distance from the known position was 0.115
* miles; when the tabulated value of the dip, corrected for barometric
* pressure and temperature was employed, the mean distance was 0.85 miles.
* These anomalies in the value of the dip are particularly interesting
* as the winds were extremely strong (up to 65 knots) during much of
* this period, and because many of the dip measurements were made with a
* height of eye of over 80 ft. Both these factors theoretically reduce
* any anomalies in the dip at sea." (p. 307)
* Capt. Henry H. Shufeldt was one of the editors of the 12th Ed. of Dutton.
* Note: Cover of the issue reads:
* The Journal of the Institute of Navigation
* Available on Cambridge Journals website.
* DIP
* DIP over LAKES (cites Forel and Minnaert)
* ". . . sightings of the horizon were made with a laboratory cathetometer
* . . . on Lake Huron near Kincardine." It was mounted on "a concrete pier
* on the shore six feet above the water line. . . ."
* "An unexpected but regular feature came from small, but significant
* changes in the morning and the evening." (A few points are graphed.)
* Yositada TAKENOUTI, Masaaki HYUGA and Yurin SAKAMOTO use a Pulfrich dipmeter
* to determine thermal structure
* Data are shown for two ocean cruises spanning a large range in latitude.
* Cf. Johnson & Roberts (1925) in "Terrestrial refraction" file.
* Dip and Earth radius
* Historian-of-science Dennis Rawlins seems unaware that dip was once
* used to determine the radius (cf. Edw. Wright, 1657; also Al-Biruni).
* Despite the title, he used a stopwatch. Notable for mentioning the GF
* as a timing marker; cf. Brett Hilder (1951).
* "All you have to do is sit for the first sunset and then stand up to
* view a repeat performance." [Too bad Brad Smith (1997) hadn't read this.]
* Contains a useful estimate of the WAVE HEIGHT off San Diego (0.6 m),
* and convenient tables to allow for latitude and solar-declination
* effects. However, the treatment of refraction is simplistic and not
* very accurate. He is aware that "if the setting solar disc exhibits a
* visibly stratified shape (obviously indicating density gradient
* discontinuities [sic]), then it will be naive to assume that the
* correction b refraction factor is a constant . . . .", but does not
* realize that the absence of these features usually implies a convective
* surface layer and hence subnormal refraction -- especially below eye
* level. (The variation of ray curvature with height further spoils the
* method, in the real world.)
* There is a good short discussion of azimuth effects on the geoid;
* he adopts 6386 km as a good average radius of curvature. But he fails
* to point out that the radius of curvature enters into the corrections,
* which in practice should be applied iteratively, to avoid a circular
* argument.
* SUNSET Paper II (the DIP DIAGRAM)
* Siebren's 2015 dip paper
* Makes no mention of temperature effects; but there are good references
* to the navigation literature, and a discussion of wave heights.
* Marcel Tschudin's dip analysis
* Nice re-working of old observations, as well as adding many new ones.
* Uses Siebren's wave correction.
*
* See also Lutz Hasse (1960, 1964); Freiesleben (1949);
* Franklin-Adams (1901) and de Graaff-Hunter (1913) for wave effects;
* also Siebren's 2015 dip paper.
*
* GLITTER patterns analyzed long before Cox & Munk
* Glitter is relevant to the Smiley-Clemence fight, as the glitter path
* might contribute to irradiation at moderate solar altitudes, but not
* the last few degrees at the horizon.
* Thanks to George Golitsyn for mentioning this!
*
* 1913 NATURE series
*
* Meteorologist Backhouse requests a general formula
* Sept.25 issue
* Tizard replies that "Atmospheric refraction is such a varying quantity
* that no rule respecting it can be laid down applicable in all
* circumstances; as in cases of mirage, for instance . . . ."
* He cites Parry, mentions Biot, and gives empirical examples from the
* 1871 survey of the Gulf of Suez.
* Sept.25 issue
* John Ball cites various textbooks of surveying, including Jordan
* "It is not temperature per se which affects refraction, so much as the
* vertical temperature-gradient in the air . . . ."
* "It is easy nowadays to measure the vertical angles well within 5" of
* the truth . . . ."
* Nov. 20 issue
* Tizard refers to Gillespie's California data on diurnal variations
* Nov. 20 issue
* R. Langton Cole offers a simple formula
* Dec. 11 issue
* SIMPLISTIC TREATMENT by a physicist -- exponential atmosphere assumed
* Curiously, section IV of this is also called "Distance of the visible
* horizon"!
* REALISTIC treatment by GOLITSYN (what a contrast with French's paper!)
* Golitsyn's first paper on distance to the horizon for Venera pictures.
* Useful for reference [10], the first known application of Monin-Obukhov
* theory to refraction. Notice that the integrals start at z0 -- this
* assumes that the observer can see down to this level.
* The translation of that paper:
* A clear explanation of the use of Monin-Obukhov scaling for convective
* and near-stable conditions. The z0 business is briefly discussed in
* the paragraph following Eq. (4.1) on p. 990:
* "We will take as the reference level the roughness height z0 . . .
* since the universal functions of the surface layer in Eq. (2.10) are
* defined only to this level. The height z0 is proportional (it amounts
* to some fraction, usually ~0.1) to the height of obstacles on the
* surface. We will see below that the range to the horizon l is
* very slightly dependent on the exact value of z0."
* Note that the page numbering differs from that of the Russian original.
* REALISTIC treatment by GOLITSYN (what a contrast with French's paper!)
* Remarkably, this is buried in a little section near the end, starting
* on p. 300. He applies Monin-Obukhov theory, and gets reasonable
* results. Cites his fuller treatment in Izv. Atmos. Ocean. Phys. 18, 1282
* (1982) but I file this here because of the emphasis on the closed-form
* solution for the distance to the horizon -- a neat trick -- using
* confluent hypergeometric functions. [Note that due to translation
* from English to Russian and back again, they appear here as "degenerate"
* rather than "confluent" hypergeometric fcns. There are some typos as
* well, most of them obvious.]
* Thanks to George Golitsyn for pointing this paper out to me!
*
* See also Perrault (1674), Huygens (1690), Jacques Cassini, 1714;
* Maraldi (1722/24), Nettleton (1725), Bessel (1823), Bauernfeind, etc.
*
* CHABOT shows pictures of discrepant sunsets in a nice COLOR PLATE
* showing the solstice Sun setting on different sides of a distant church
* in different years.
* (See Tafel 2 at end of Nov. issue)
* Finds quasi-periodic motions of equatorial stars (Z.D. about 41°)
* with periods of a few minutes of time and peak-to-peak amplitudes of
* about one second of arc, in agreement with Schlesinger (vol.3, 1916).
* Cf. Fletcher's 1952 discussion, below; and Fraser's 1975 paper.
* Date uncertain; I first adopted 1926, but ADS says 1929.
* THANKS to Shaun Hardy for this reference!
* LECKY -- "WRINKLES"
* DIP variations:
* ". . . owing to the uncertainty of the effects of refraction, the
* apparent position of the sea horizon can never be depended upon. It is
* found to be sometimes above its normal place, and at others below it.
* The rule seems to be, that when the sea is warmer than the air, the
* horizon appears below its mean place; and when the sea is colder
* than the air, the horizon appears above its mean place. The known
* capriciousness of terrestrial refraction has prevented the formation of
* a table of values in connection with this subject."
* [Marginal note: "Sea horizon not reliable." -- p. 81 of 19th edition,
* revised and enlarged by William Allingham (1918)]
*
* cites errors in limits of lighthouses of 14 and 17 miles (=minutes of
* arc), in and before 1881; pp. 681, 682
* HORIZONTAL REFRACTION (in the sense of "lateral") discussed
* (cf. Fletcher, 1952, below)
* This is a textbook for geodesists. Refraction in the horizontal
* direction is discussed in about a page:
* "The errors caused by horizontal refraction may be of considerable
* size. Night observations have occasionally been found to be in error
* by five or six seconds because of horizontal refraction and daylight
* observations by two or three times that amount." (p. 136)
* BEGIN SMILEY - CLEMENCE dispute
* Smiley's first paper -- Suggestion that std. tables are wrong:
* N.B.: There are two things called "Journal of the Institute of
* Navigation." One (called "Journal of Navigation" since vol.25, 1972)
* is published in London by the Royal Institute of Navigation. The other
* (now called simply "Navigation") was published in Los Angeles at UCLA
* and was produced in Washington, DC, from 1960 to 1992.
* This is the latter, sometimes called "Navigation (Los Angeles)".
* Smiley's claim refuted by Clemence:
* abstract
* Clemence's full article:
* ". . . the indeterminacy is a geometrical one, and the refraction at any
* instant may differ by several minutes of arc from the most accurate value
* that can be calculated."
* Smiley's SECOND paper (Temperate zones) . . .
* . . . Smiley is immediately refuted by Clemence . . .
* "Smiley's results disagree with both the theory and the observations,
* and I conclude that they are subject to such large systematic errors as
* to be valueless . . . ."
* This is the paper in which Clemence says the upper-limb discrepancies
* are due to irradiation (a term apparently invented by Plateau -- see
* http://www.mhsgent.ugent.be/engl-plat8.html )
* . . . and Clemence is immediately followed by Willems:
* Captain Raleigh C. Willems is concerned about tables for use in the
* Air Almanac, where even surface temperatures are not available. He
* seems largely ignorant of the theoretical side: "Most formulae for
* computing astronomical refraction are based on the work of Lord
* Rayleigh. . . ." (p. 42)
* Smiley's THIRD paper (POLAR regions).
* Note change of year within volume!
* A proposal to test the Smiley-Clemence arguments with stellar
* separations measured at night, to avoid irradiation problems.
* [Immediately followed by short notes from both Smiley and Clemence.]
* (Sept. 1952)
* FLETCHER's great review article -- really EXCELLENT !!
* This really belongs in the General Refraction file, but is here for
* its extensive discussion of the Smiley-Clemence controversy.
* This SUPERB review article does everything right: it mentions the
* increasing importance of temperature gradients near the horizon, gives
* lots of numerical values, points out that refraction can be abnormally
* large but not very small; it even discusses TILTED layers, pointing out
* that "a tilt of the layers by 6' would alter refractions near the zenith
* by about 0."1. It seems fairly certain that the effect cannot be much
* larger than this under normal weather conditions. In the first place the
* standard deviation of the effective tilt in one coordinate can hardly be
* as much as 2', or the standard deviation of the irregularities in
* refraction would be more from this cause alone than it is found to
* be from all causes. . . . Secondly, in observing stars near the zenith
* with the photographic zenith tube . . . the zenith distance residuals are
* small enough to rule out refraction anomalies . . . much greater than 0."1.
* Thirdly, the sort of meteorological information contained in an ordinary
* synoptic chart rarely suggests tilts of more than one or two minutes of
* arc, except under extremely violent conditions.
* "Thus it seems that tilt is normally less than what at first sight may
* seem the rather small value of 0.°1. But it must be remembered that
* refraction changes with zenith distance nearly a thousand times faster
* near the horizon than at the zenith (at the rate of about 14', instead of
* about 1", per degree). Thus variations of one or two minutes of arc in
* the horizontal refraction are perhaps indicated, although it cannot be
* very accurate to reckon so simply at low altitudes." (pp. 320-321)
* [cf. Hudson's 1926 paper, and Gossett (1950), above.]
* He also points out the latitude and azimuth effects due to the geoid;
* that measurements made over land may not apply at sea; that diurnal and
* seasonal variations are large (giving numbers and citing references).
* Dispersion, humidity, and wind are given their due. (Oct. 1952)
* There is a section on dip, citing Freiesleben's paper in this Journal.
* Cites Varnum (1922); but Sugawa's work is not mentioned.
* This is now called the "Journal of Navigation" and is published on
* behalf of the Royal Institute of Navigation by Cambridge U. Press; see
* https://www.cambridge.org/core/journals/journal-of-navigation/all-issues
* Captain Brett Hilder gives the results of his proposal to use GFs.
* [This paper is mostly about refraction at the horizon, with comments
* on the Smiley-Clemence argument and on Fletcher's review. In turn,
* there are extensive replies by both Fletcher and Clemence interpolated
* in the present very interesting note.]
* The 103 sights were all in the SW Pacific at low latitude, so we can
* argue that the water was generally warmer than the air. [If these were
* (nearly) all Type A events, the disappearance is at the mirage level
* and not the geometric horizon; this probably accounts for the 2.8-minute
* mean discrepancy (which Hilder supposes is an error in the tabulated
* refraction), as well as the agreement of upper and lower limbs.]
* The larger discrepancy with land in sight is explained by coastal
* effects on refraction, by about 1'. As there is a smaller difference
* with the tables at sunset, the apparent refractions being less than the
* tabular ones, he decides "there is more refraction at sunset than at
* sunrise (as attributed to Delambre by Dr. Fletcher)".
* He specifically discusses variability of refraction (p.316), and
* recalls errors of 15' and even 30' at a storm front; Fletcher comments
* that these must be due to dip rather than refraction errors.
* Hilder points out that Clemence's "irradiation" explanation must be
* wrong; Clemence replies that the systematic error (though not really
* explained) is in the data and so the correction should be in the
* Almanac, whatever its cause.
* Greenbaum's observations in Clearwater, Florida, July - Aug., 1951
* The mean temperature was 80° F but no correction seems to have been
* made for humidity! (Or wavelength.) Only 7 nights of data.
* "The observations fully support the modified Garfinkel theory . . .
* The value [2' larger at 3.5° altitude] found by Smiley is not
* substantiated."
* The claim is that observations were made down to 0.5° altitude; but
* as Fig.1 does not show this, and "one was rejected", it appears the lowest
* point did not fit.
* George Wallerstein's secret past as a positional astronomer is revealed!
* Unfortunately, he mistakes Clemence's "irradiation" for "irradiance".
* The method of observing was to determine latitude from Noon altitude
* of the Sun, then use lower culmination to find refraction. A Wild T-2
* theodolite was used, and individual observations are given to 1"
* precision.
* "These results agree with Garfinkel's theoretical table quite well down
* to 2°. However the effect that Smiley has observed, of differences
* changing from positive to negative as the horizon is approached is
* confirmed by this investigation."
* Cites both Smiley and Clemence.
*
* NOTE: I was able to discuss this work with George Wallerstein himself
* at the Jan. 2001 AAS meeting here in San Diego. He says he himself
* made all the measurements, which were referred to the astronomical (not
* the apparent) horizon, using the theodolite. A 25-second systematic
* error in the measurements was never explained; but this is negligible
* compared to the effects under discussion.
* Mostly a check on the Smiley-Clemence controversy, confirming Clemence
* This contains summaries of data sent in from ships, based on sextant
* observations -- so dip errors are included. The observations between 5
* and 10° altitude were used to correct for position errors.
* No data on water temperatures or wave heights.
* Conditions of unusual refraction were probably eliminated by rejecting
* data with large runs of residuals between 5 and 10°: "Only 42 sets
* out of the original 76 were retained in the main analysis." (Censored
* data.) So the confirmation of the Almanac values is not surprising!
* SCHAEFER & LILLER REFUTED
* See Stephen McCluskey's 2017 study of refraction at the apparent horizon
* (in the "variable refraction" file) for useful discussion.
* N.B.: Archaeoastronomy no.17 = JHA 23, special section
* RUSS SAMPSON's M.S. thesis (filed separately, but belongs here)
* A nice independent rediscovery of the main features of horizontal
* refraction through careful observations and analysis of sunrise/sunset
* timings. This is a fine piece of work; it should be a model for other
* graduate students! The presentation is clear; the graphs are easy on the
* eye; the work is well done. And the data are all neatly tabulated.
* 244 sunrises (!) plus 125 sunsets.
* There is a nice drawing of LOOMING of the distant horizon on Jan. 14,
* 1993, in Fig. 2.5.3 on p.18: the surface was raised by a low-level
* thermal inversion, while the astronomical refraction was increased
* even more, making the apparent sunset occur at a more northerly azimuth.
* Ch.4 is on applications to archaeoastronomy; cf. McCluskey (2017).
* Sampson points out the effects of variable refraction on the "equinox
* sunrise" azimuth
* Giuseppe de Donà's observations of sunset times
* The presentation of "formulas" for refraction is superficial and
* useless; the value of this article is in the 17 sunset observations,
* and the nice photos of DISTORTED SUNSETS (could have been filed there,
* but is so similar to Russ Sampson's work that I put it here). 10 of the
* observations have (p,T) values as well. The observed refractions at the
* sea horizon vary from 29' 59'' to 49' 43''; mean, 36.65'. A nice touch is
* the flattening observed when the lower limb touched the apparent horizon.
* The individual observations are tabulated. Good photo sequence of an
* OMEGA sunset on p. 5; interesting comments on distortions.
* "Astronomia, la rivista dell'Unione Astrofili Italiani" seems not to
* use volume numbers. This is "n.1 gennaio/febbraio 2003".
* Thanks to Katia Alboresi for providing a copy through ILL!
* More Sampson
* Here he compares the observed refractions with model calculations based
* on radiosonde profiles. ". . . the inverse solution (i.e., extracting
* the temperature profile from refraction measurements) may produce
* no improvement on U.S. Standard Atmosphere adjusted to the surface
* conditions." (But no mention of Fraser & Hemler.) However, the
* comparison really shows that this simple adjusted model fits the
* refractions better than the noisy radiosonde data, which are useless.
* (They keep the tropospheric lapse rate fixed.)
* 20 Jan. issue
* Further analysis of Sampson's observations
* Contains good evidence of seasonal and DIURNAL (sunrise vs. sunset)
* variations: "variable but not at all random." Lapse rates are even
* mentioned. About 3% of the data show refraction over a degree. The
* large sunrise refraction in June & July is surprising.
* Russ is still at it. . . .
* ". . . it seems reasonable that the standard deviation of the surface
* vertical temperature gradient may be used as a climate proxy for the
* standard deviation in the LAAR."
* Stephen C. McCluskey's study of refraction at the apparent horizon
* He explains the effects of refraction on rising and setting times
* more clearly than the Explanatory Supplement does, and shows that
* refraction in the surface layer *at* the apparent horizon is
* significant, even for elevated horizons at distant mountain ridges.
* This effect is much larger for level-surface horizons (plains and seas),
* which explains why much larger variations are observed in rising and
* setting times (and azimuths) there than at elevated horizons.
* A good list of references from the literatures of geodesy,
* meterorology, and navigation.
*
* Most of their publications were in
* Bulletin des séances de la Société Vaudoise des
* Sciences Naturelles [usually just "Bull.Soc.Vaud."]
* Many volumes are available at the HathiTrust:
* https://catalog.hathitrust.org/Record/000504901
*
* Charles Dufour's "non-symmetrical mirage" is probably similar to my
* own observation of the boundary layer of a mountain just after sunset.
* He supposes it to be a lateral mirage; the Sun had not yet risen.
* (A letter from him, read by R.Blanchet at a meeting of the society.)
* [This is also reported in C.R. 33, 121-122 (1851).]
* Available at HathiTrust:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3085875;view=1up;seq=79
* Bulletin No. 23
* Charles Dufour's identification of the miraged objects
* He begins with the visible effects of the Earth's curvature, seen
* across the lake. "Cependant cette espèce de dépression
* mathématique causée par la rondeur du sphéroïde terrestre,
* est singulièrement modifiée par les réfractions et les
* réflexions anormales éprouvées par les rayons lumineux qui
* passent près de la surface du lac."
* His account of the Fata Morgana displays begins on p. 130, after
* discussing the inferior mirage, "un mirage tout à fait analogue à celui
* que l’on observe dans les plaines d'Egypte. Ce mirage a lieu toutes
* les fois que l'eau est plus chaude que l'air et c’est ce qui arrive
* presque constamment pendant les mois d'octobre, novembre et décembre;
* le plus souvent pendant les mois de septembre, de janvier et de février,
* et presque toujours quelques heures dans la matinée pendant les autres
* mois de l'année."
* Now comes the more interesting part:
* "Cependant, dans les circonstances où sur le lac on ne peut voir
* que des mirages, les observations n’ont rien de frappant. Il serait
* sans doute intéressant de mesurer la grandeur de ces mirages et noter en
* même temps la température de l’air et celle de l'eau. Mais j’avoue
* que pendant la dernière année, je n’ai pas spécialement porté mon
* attention sur ce point. J’ai plutôt observé dans les moments où
* les mirages avaient cessé. Alors les phénomènes qui se présentaient
* étaient bien plus variés et bien plus compliqués, et c’est surtout
* sur ceux-là que je me propose d’appeler ici l’attention.
* "Plaçons-nous à Morges par un beau jour du printemps ou de
* l’été. Mettons l’œil à 3 ou 4 mètres au-dessus du niveau du lac,
* et suivons du matin au soir, l’apparence que présentent soit la côte
* savoyarde, soit surtout le voisinage de Vevey, avec les villages et les
* maisons du cercle de Montreux.
* "En général le matin, il y a un mirage qui cesse vers 9 ou l0
* heures. Dès lors jusqu’à midi ou une heure, les objets paraissent
* demeurer à peu près à la même hauteur au-dessus du lac, mais il
* y a souvent une agitation des couches d'air, qui rend le pointé et les
* mesures angulaires bien difficiles.
* "Depuis une heure après midi, suivons spécialement la localité
* de Montreux et les villages voisins (distance de Morges 32 à 34
* kilomètres). Toute cette contrée ne tarde pas à sortir de l'eau. Il
* semble presque à certains jours qu’il y a une puissance magique qui,
* avec un cordon, soulève tout ce territoire.
* "Ce mouvement ascensionnel, d’abord assez lent, devient fort rapide
* vers 3 1/2 heures ou 4 heures, Dès lors il se ralentit de plus en plus et
* dure quelquefois jusqu'à l'approche de la nuit. D'autres fois, depuis
* 6 heures du soir, les objets paraissent retomber un peu dans l’eau
* jusqu’au coucher du soleil. Mais dans tous les cas, depuis ce moment,
* l'obscurité est telle que tout ne tarde pas à disparaître. Pour cette
* raison, je ne sais pas à quelle heure de la nuit et en combien de temps
* ces objets, ainsi soulevés dans l'après-midi, retombent à leur place,
* pour paraître le lendemain sortir encore du lac et donner ainsi tous
* les jours la même apparence avec la même régularité.
* "Ce grand mouvement est accompagné de déformations apparentes
* assez considérables de tous les objets qui paraissent ainsi déplacés.
* "La première fois que je remarquai ces déformations, je fus
* étonné, en arrivant à une heure après midi au lieu ordinaire
* d’observation, de voir du côté du Chatelard, une ville magnifique qui
* paraissait sortir du sein des eaux. C'étaient des palais, des édifices,
* des monuments superbes, remarquables surtout par leur hauteur. Tous ces
* objets, beaucoup moins brillants que ceux qui étaient plus élevés,
* paraissaient ainsi dans un demi-jour, qui ne faisait que réhausser leur
* éclat grandiose.
* "Malheureusement, toutes ces belles images n’étaient pas de
* longue durée; elles changeaient plus ou moins rapidement, mais elles
* conservaient, en général, l'aspect que je viens de décrire. Cependant
* leur forme était tellement étrange qu’il me fut impossible de
* reconnaître là aucune des localités de la contrée. En prenant avec
* soin la direction de ces objets agrandis, et en la rapportant sur la
* carte fédérale, je pus me convaincre que ces palais, ces édifices,
* ces monuments nouveaux n’étaient autre chose que la Tour-de-Peilz,
* dont les bâtiments, qui en réalité n’ont rien d’extraordinaire,
* prenaient ainsi une apparence féerique sous l’influence des
* circonstances météorologiques dans lesquelles j’étais placé.
* "Mais les objets un peu plus élevés au-dessus du niveau du lac
* avaient un aspect fort différent. Bien loin d’être amplifiés dans le
* sens vertical et de n’être que faiblement éclairés, ils éprouvaient
* au contraire une dépression considérable, et ils étaient en même temps
* extrêmement brillants. Il en était de même pour des objets tels que
* les maisons de Montreux et de Veytaux, qui paraissaient au niveau du lac,
* mais qui en réalité en sont plus éloignées que celles de la Tour, et
* qui ne semblent être aussi bas qu’à cause de la rondeur de la terre
* et de la plus grande distance qui les sépare de Morges. --- Cependant, il
* est arrivé quelquefois que les maisons de Veytaux et de Montreux m’ont
* aussi paru amplifiées dans le sens vertical, mais ce fait n’a jamais
* été de longue durée. Je citerai comme exemple, la pension Henchoz à
* Montreux, qui, le 7 mai 1854, à 3 heures 50 minutes, me présentait une
* hauteur angulaire de 3’ 10". A 6 heures du soir, elle n’avait plus
* que 30". Et en ne supposant aucune réfraction anormale d’après sa
* hauteur et d'après sa distance de Morges, cette maison devrait avoir 56".
* "Je pourrais multiplier les citations d’observations analogues,
* et pour m'assurer qu’il n’y avait ni erreur de l'instrument que
* j'employais, ni inhabileté dans la manière de m'en servir, j'ai à
* diverses reprises mesuré la largeur de plusieurs bâtiments dans le
* sens horizontal (largeur qui n’éprouvait aucune variation), et j’ai
* toujours trouvé, à 2 ou 3" près, une même valeur, qui s’accordait
* avec la détermination trigonométrique." [pp. 130-132]
* P. 134: in discussing the Fata Morgana, he makes the usual mistake
* about RADIANCE and IRRADIANCE: "On comprend très-bien que les
* objets ainsi agrandis paraissent plus sombres, puisque la lumière
* s’y distribue sur un plus grand espace, et par la raison inverse,
* on comprend de même que les objets déprimés dans le sens
* vertical paraissent aussi plus lumi-. . . " [missing line, it seems.]
* "Chacun sait que les Italiens nomment Fata morgana, des images
* fort bizarres, qui de temps en temps apparaissent en mer près du
* rivage de Messine. On voit des colonnades, des monuments, des palais
* faiblement éclairés, et qui paraissent changer de forme d’un instant
* à l'autre. On les attribue généralement à l’existence de ruines
* placées au loin sur les bords de la mer. Mais je ne sache pas que l’on
* ait jamais montré pourquoi ces ruines qui ordinairement doivent être
* presque invisibles par leur petitesse et presque cachées par la rondeur
* de la terre, apparaissent ainsi de temps en temps, pourquoi elles ne sont
* quà moitié éclairées, pourquoi elles sont agrandies, enfin pourquoi
* elles changent ainsi de forme d’un instant à l’autre. Il me semble
* que ce phénomène est peut-être analogue à celui que j’ai constaté
* depuis Morges, quand la ville de la Tour-de-Peilz, qui ordinairement
* est presque invisible, apparaît comme une ville magnifique, et je crois
* que la même explication pourrait être admise."
* (cited by Forel, p. 545)
* The title page of the volume says it contains the years 1853 - 1855, and
* gives the date of publication as 1856. This paper is in No. 34, which
* begins on p. 97, with the annual meeting held on 22 juin 1854. The
* Google scan is available at the HathiTrust website:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3085876;view=1up;seq=149
* Louis Dufour's paper on a "non-symmetrical mirage"
* Again, it seems an image of the boundary layer, not really a mirage.
* (Bulletin No. 36; meeting of 3 Jan. 1855)
* His brother's comment on the above item in "Procès-verbaux":
* "Mr C. Dufour ajoute, à l'occasion de la communication de
* Mr son frère, que les phénomènes du mirage sont bien connus
* des pêcheurs et qu'ils les expliquent en disant que ce cas
* l'eau trouble l'air."
* (Bulletin No. 37; meeting of 5 Dec., 1855)
* good discussion of INFERIOR MIRAGE over WATER, and how to
* distinguish the mirage from the REFLECTION on water (cf. Floor, and Bravais)
* First observations of REFLECTIONS on water after Büsch?
* Notice his use of the phrase "ligne de partage" for the fold line.
* He got this term from Bravais (1853), who is cited on p.391.
* This is No. 37, containing memoirs for 1855: "Séance du 4 juillet 1855."
* Available at the HathiTrust:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3085876;view=1up;seq=418
* My copy has "1857" written on it -- probably the date it was received.
* TEMPERATURE PROFILES for INFERIOR MIRAGES over WATER
* This paper is the continuation of his previous paper. It has the
* TEMPERATURE measurements.
* He is aware of the difficulties: "La recherche des températures de
* l'air est toujours une opération difficile. . . . " (p. 26)
* "Les recherches que j'ai faites au-dessus du Léman avaient pour objet
* la connaissance de la température de l'air à diverses hauteurs au-dessus
* de la surface jusqu'à une distance de 1m50 à 2m. Les difficultés sont
* ici nombreuses et variées. Il s'agit d'avoir un instrument assez
* sensible pour apprécier facilement des différences ne s'élevant qu'à
* quelques dixièmes de degré; observer au-dessus de l'eau à une distance
* assez considérable du rivage; se garantir autant que possible des effets
* de rayonnement; agiter le thermomètre dans l'air en demeurant pourtant
* dans une même couche sensiblement horizontale et enfin prendre la
* température aussi près que possible d'une nappe d'eau qui n'est que bien
* rarement tout à fait immobile.
* "Je me transportais avec un petit bateau un peu au large et je me
* servais d'un thermomètre Fastré à graduation arbitraire. Chaque
* division, de la longueur de 5/9 millimètre, équivalait à 0°,1816. Le
* thermomètre, suspendu par une ficelle à l'extrémité d'un bâton, était
* alors suspendu dans l'air à une certaine distance du bateau et à des
* hauteurs variables au-dessus de l'eau. Enfin, par un léger mouvement
* communiqué au bâton, que je tenais le bras étendu comme un pêcheur
* tient la ligne, je faisais décrire à la ficelle et au thermomètre
* une oscillation conique, de manière que l'instrument agité dans l'air
* demeurait cependant dans une même couche horizontale. Une règle
* graduée servait à mesurer la hauteur de cette couche au-dessus de
* la surface de l'eau." (p. 27)
* So the measurements ought to be fairly reliable. And, indeed,
* the temperature and density plots in the plates seem quite plausible.
* His "surface" data in the tables correspond to about 5 cm above the
* water surface.
* Furthermore, his discussion of the temperature data (pp. 31-32)
* leads him to reject both Biot's parabolic profile and the exponential
* suggested by Bravais; and he decides that "Il est à remarquer que la
* variation des densités est en général rapide près de la surface, puis
* beaucoup plus lente à une certaine hauteur. . . . En d'autres termes,
* la vitesse du décroissement des densités, qui est une certaine fonction
* de la hauteur, décroit en même temps que cette hauteur augmente. Il
* faut donc que l'équation qui représente des variations de la densité
* soit telle que sa différentielle, prise par rapport à la hauteur,
* décroisse en même temps que la hauteur augmente, ou bien que la
* différentielle seconde soit négative.
* "D'après cela, le cas qui apparaît le plus simple est celui où
* l'équation différentielle serait de la forme :
*
* dδ/dz = b + c/z
*
* b et c étant des constantes. En intégrant, on trouve :
*
* δ = bz + c. l. z
*
* . . . ." (p. 32)
* -- in other words, he discovers the correct log-linear law for
* convective boundary layers! But, unfortunately, he rejects it, because
* of its large residuals when compared to some of his data. (This poor
* fit seems to be due to the low-lying lake inversion on some days.)
* On p.36 he offers the first suggestion to derive temperature profiles
* from optical measurements:
* "Les observations optiques peuvent se faire avec beaucoup plus de
* précision et de certitude que celles de la tempèrature et c'est ici un
* de ces cas où les faits d'un certain ordre peuvent être plus sûrement
* et plus exactement connus en les abordant d'une manière indirecte et
* par leurs conséquences, qu'en cherchant á les examiner eux-mêmes et
* indépendamment de leurs effets. Avec un théodolite ou une lunette de
* Rochon, on apprendra à connaitre les variations de la température de
* l'air, suivant la hauteur, beaucoup mieux qu'on ne pourrait le faire
* avec le thermomètre le plus irréprochable."
* On p.36, he describes his method of measuring the "size" of the
* inferior mirage.
* P.37: he comments on the "lack of sharpness of the apparent horizon.
* One sees a line which, most of the time, is not very sharp; it is a sort
* of serrated ridge, with mobile and oscillating summit, presenting
* elevations and depressions that move and change at every instant. One
* would say that waves of great size collide and clash on this crest.
* This lack of sharpness on the line of the horizon is the greatest
* obstacle to observations of the mirage."
* Vol. V contains the years 1856 and 1857. This is available at the
* HathiTrust website:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3085877;view=1up;seq=44
* Louis Dufour compares his measurements with Bravais's formula
* Presented at the 4 Feb. 1857 meeting.
* at HathiTrust:
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3085877;view=1up;seq=265
* Charles-Th. Gaudin's mirage drawings
* This is a letter sent from Palermo in Feb. 1858. There is a nice plate,
* with numerous drawings of inferior mirages, some showing the
* contraction of the inverted image.
* No. 43.
* Early observations of "REFLECTIONS" on water
* (has the diagram reproduced by Riccò (1888))
* This may be the earliest calculation of the expected size of the
* shrunken image produced by reflection on a convex surface with the Earth's
* radius of curvature; the effect was already mentioned by Bravais (1853)
* for the inferior mirage. Dufour mentions the observation of the effect
* by "mon ami" Forel on a sunny afternoon; it is surely the inferior mirage
* and not the reflection on the water itself. In the numerical example,
* Dufour assumes the observer at Morges is 20 m above the water, and
* calculates a reduction factor of 3.5.
* [cf. Büsch, 1783/1800, for an early observation of this mirage.]
* Reprinted in Arch. Sci. Phys. Nat. (Ser.2) 53, 131-137 (1875).
* See Whitmell's reprise of this in JBAA, 1905 (filed in GF file).
* Charles DuFour describes the reflection clearly in l'Astronomie:
* ". . . les images ne se font pas sur un plan, mais sur une
* surface convexe , à cause de la rondeur de la Terre . . . ."
* Refers to "moe ami M. Forel" as having called his attention to it.
* This was *before* l'Astronomie merged with B.S.A.F.
* Forel replies to Riccò's note in C.R. (see RICCO file)
* Note that he has the wrong volume for Riccò's note.
* "La seule erreur possible serait une confusion avec des faits de mirage
* dans le cas de réfractions anormales. Mais nos études sur ces
* derniers phénomènes nous ont assez bien fait connaître toutes les
* possibilités du mirage, pour que nous soyons assurés de distinguer avec
* certitude les deux indices d'apparitions; et cela d'autant mieux que, sur
* une nappe d'eau aussi bien limitée que notre lac, les conditions
* thermiques et hygrométriques sont assez simples pour que nous puissions,
* dans chaque circonstance, prévoir d'avance quel type de mirage nous
* devons avoir devant nous. Les images de réflexion ainsi déformées
* ne sont nettes et précises qu'en l'absence de toute espèce de mirage."
* Abstract on mirages -- probably DUCTING and FATA MORGANA
* With air much warmer (25 C) than water (12 C), he observed strong
* towering or Fata Morgana from a steamboat: "Les rives, réellement
* basses apparaissaient comme se terminant par des falaises élevées; mais
* ce phénomène présentait une grande variabilité d'un instant à
* l'autre."
* Cites Ch.Dufour (1854) for a DARK BAND in the image: ". . . en regardent
* une chaloupe . . . on voyait nettement les voiles supérieures, très
* blanches et d'un grand éclat; au-dessous les voiles inférieures
* paraissaient déformées, allongées dans le sens vertical, sombres et
* donnant l'impression de deux images confuses superposées."
* WHITE FOG or "smoke": "Mais l'apparence qui a le plus frappé M.Soret,
* parce que, à sa connaissance, elle n'a pas encore été signalée, est
* . . . on voyait du côté du golfe d'Anthy, comme des fumées blanches
* dont les bouffées juxtaposées se seraient rapidement transportées vers
* le sud-est, sous l'impulsion du vent." He connects this with the
* mirage, and suggests that the appearance of "le mirage ordinaire" when the
* water is colder than the air might be "rattache à l'état hygrométrique
* de l'air." (and mentions Forel in particular as having seen this.)
* Cited by Forel (below)
* Evidently part of the minutes of a meeting of Soc.Phys.Hist.Nat.Genève;
* the meeting must have been in July, as it is followed by the 2 Aug. one.
* Abstract on mirages
* Very insistent that the air can be up to 7° above the water and still
* have an inferior mirage, but with very compressed inverted image.
* Also: "Dans ce cas de mirages anormaux, l'image inférieure est souvent
* très fortement déprimée, tellement qu'elle apparaît plus brillante
* que l'objet réel." Which is nonsense.
* Cites Soret.
* Evidently part of the minutes of a meeting of Soc.Helv.Sci.Nat.
* Meeting abstract on inferior mirages and WAVES on the apparent horizon
* THINNESS of the mirage layer measured: "Les mirages sont encore
* parfaitement développés à 10 centim., à 5 cm., 2 cm. au-dessus de la
* nappe des eaux; à 1 cm., M. Forel croit les avoir vus; à un ½ cm.,
* l'observation lui a échappé, le lac n'ayant par été assez calme pour
* le miroir ne fût pas mouillé par quelque vague à cette très petite
* distance du plan de l'eau."
* Perhaps the most interesting part: "M. Forel donne ensuite
* l'explication des dentelures des vagues à l'horizon en cas de mirage
* d'hiver. Ces dentelures sont à leur maximum de développement quand
* l'air est le plus calme: point n'est besoin que les vagues soient fortes
* ou aiguës; la vague de refoulement d'un bateau à vapeur donne peut-être
* la plus belle apparition du phénomène. . . . le rayon visuel, parti de
* la crête de la vague, est moins réfracté que celui du cercle de
* l'horizon et le sommet de la vague apparaît ainsi comme un point suspendu
* en l'air. Un plan de réflexion en dessous du plan de partage transforme
* l'image de ce point en un losange à grand axe vertical qui est
* l'apparition parfaite des dentelures en question." [cf. Ferguson, 1902]
* Forel tries to estimate the strength of an inferior mirage with a ratio
* I don't understand. . . .
* He also remarks on the rapidity with which the surface layer assumes the
* water temperature, in the offshore flow (8 to 20 seconds).
* under "Procès-Verbaux: Communications Scientifiques"
* Abstract on Fata Morgana
* This is all about the striated zone -- maybe its first mention by Forel?
* Evidently part of the minutes of a meeting of Soc.Helv.Sci.Nat.
* Léman
* Limnological monograph in 3 volumes on Lake Geneva
* (republished by Slatkine Reprints, Genève, 1969)
* "Déformation de l'image réfléchie sur la surface sphéroïdale du lac.
* Images de Charles Dufour." (pp.509-511)
* "Réfractions normales et anormales dans l'air atmosphérique en contact
* avec le lac." (pp.514-559) (extensive mirage & Fata Morgana observations)
* On p. 520 he has a drawing of the waves at the inferior-mirage
* apparent horizon; cf. Forel (1890), and Ferguson (1902).
* On p. 526, he points out the lack of waves on the apparent reflecting
* surface of the inferior mirage; cf. Büsch (1800) & Abbott (1854).
* P. 532: an account of inferior mirage over ice; cf. Greenler's photo.
* Note his remarks on the concave appearance (p. 541) of the lake, in
* refractions over cold water; cf. Brandes (1806), Everett (1873), and
* Thompson (1916). Forel notes the negative dip, and the recession
* of the apparent horizon. "La réfraction n'arrive cependant pas à
* éloigner indéfiniment le cercle de l'horizon. Par les plus belles
* réfractions du printemps, nous ne voyons pas la grève à vingt ou
* trente kilomètres de distance, et le corps d'une barque qui navigue
* dans ces régions éloignées reste masqué à notre vue, alors même
* que la nappe du lac nous semble concave et parait se relever jusqu'à
* la rive de la côte opposée." (p. 541) Furthermore (p. 542),
* "Les objets situés sur l'eau en dedans du cercle de l'horizon
* apparent sont déprime's. Le corps d'une barque ou d'un bateau est
* réduit en hauteur; souvent il ne parait plus qu'un trait horizontal,
* presque sans épaisseur."
* Then comes the historical anecdote about the visibility of the
* château de Chillon in 1851, which drew Charles Dufour into the matter.
* This leads to the discussion of the Fata-morgana (pp. 543-544); notice
* that he says it is "Le phénomène le plus fréquent" of those seen
* over cold water.
* The striated zone "est très remarquable et son aspect est
* caractéristique. Elle est limitée en bas par le plan du lac qui ferme
* sa ligne inférieure, en haut par une ligne plus ou moins bien dessinée,
* généralement horizontale." Its width is 2 to 5 "et même 10 minutes"
* of arc.
* On p. 546, he twice remarks that the concave appearance of the lake
* is usual for these apparitions.
* [Note observation of CONCAVE surface.]
* Pp. 551-553 describe the Fata-brumosa.
* Notice that on pp. 561-565, he carefully examines the "lateral-mirage"
* story of Soret and Jurine. I fully agree with his conclusion.
*
* Now available from Google Books, at:
*
* http://books.google.com/books?id=LMNZAAAAQAAJ
* or
* https://books.google.com/books?id=LuMPhZFIhCAC
*
* There is a photograph of Forel on p. 246 of the book at
* https://books.google.com/books?id=Nou4BAAAQBAJ&dq=%22Physics+of+Lakes
* with a brief biog. note, and account of his invention of "Limnology".
* authors: Kolumban Hutter, Irina P. Chubarenko, Yongqi Wang
* Further details of Lake Geneva mirages and refraction over warm/cold water
* ". . . le fait encore inexpliqué du mirage sur eau froide , lequel
* se montre quand la température de l'air s'élève progressivement
* au-dessus de la température de l'eau. Le mirage sur eau froide a les
* mêmes caractères que le mirage des réfractions sur eau chaude, sauf
* que l'image inférieure n'est pas symétrique; elle est bien opposée à
* l'image réelle, mais elle est fort réduite dans ses dimensions
* verticales; souvent elle n'a pas le tiers de la hauteur de l'image
* réelle."
* "Je crois avoir constaté que l'apparition des palais de la fée Morgane
* n'a lieu dans toute sa beauté que lorsqu'une brise légère passe sur le
* lac, après une matinée de grand calme."
* Perhaps his "mirage over cold water" is an inferior mirage in the
* residual layer, confined by a very low capping inversion?
* Forel's popular summary in La Nature
* He begins with a useful remark:
* "Les réfractions et mirages sont d'apparition très fréquente,
* car il est rare que le sol ou l'eau soit de même température que
* l'air sous-jacent; on les reconnaît aisément quand on a appris à les
* observer. L'observation en est le plus facile sur une nappe liquide,
* celle-ci ne présentant pas les irrégularités d'une plaine terrestre;
* sur un lac, elle est plus instructive que sur la mer, car les distances
* de la côte opposée d'un lac sont connues, tandis que l'éloignement
* d'un navire qui passe au delà de l'horizon marin est indéterminé."
* Accompanied by his standard drawings of the 4 types, showing their
* effects on sailboat sails: "Voici la suite des phénomènes qui se
* développent successivement sous nos yeux; pour en illustrer la narration,
* je représente dans une série de croquis A B C D les mêmes deux barques
* marchandes, aux voiles latines, qui sont censées naviguer sur le lac
* au delà de la ligne d'horizon apparent, disons à 10 kilomètres de
* distance."
* NOTE: John Tyndall has a very similar drawing of miraged sails at
* Lake Geneva in his "Glaciers of the Alps", pp.31-34.
* Finally: "La Fata morgana se déplace dans le sens de la brise
* régnante; quand elle a parcouru tout le cercle de l'horizon, il ne reste
* plus que l'apparition des réfractions sur eau froide, caractérisées
* par l'éloignement du cercle de l'horizon, l'apparence de surface
* à concavité supérieure que prend la nappe sphéroïdale du lac,
* le soulèvement de l'horizon apparent, l'apparition d'objets très
* éloignés masqués en réalité par la rotondité de la terre, enfin la
* compression verticale des objets bas sur l'eau, à grande distance. En
* D, se trouvent les voiles latines des barques réduites à l'état de
* triangles tellement surbaissés qu'elles sont presque méconnaissables."
* The issue is dated 12 Dec. 1896; but the reference is often cited as 1897.
* (available at Google Books, and at
* http://cnum.cnam.fr/CGI/fpage.cgi?4KY28.48/23/100/536/0/0 .)
* another summary of the mirage phenomena on Lake Geneva
* Good drawing of the peculiar horizon with inferior mirages, reprinted
* from his monograph.
* Dated 1896 on p. 167; but sometimes cited as 1898.
* Cites the La Nature paper (above).
* Delebecque's reprinted comments on Forel's C.R. paper
* With a reproduction of an obviously faked "mirage" photograph!
* "Nous reproduisons dans la figure ci-jointe une photographie qui a été
* faite par MM. Picard, de la Chaux-de-Fonds, à la fin de 1896, et qui
* nous montre un effet de mirage obtenu avec une barque sur le lac Léman.
* On remarquera la dissemblance des voiles du vrai bateau et de son image."
* Indeed! (The sails are set quite differently in the two images of the
* boat.) And the perspective indicated by the waves on the water, and the
* mountains in the background, would put the "mirage" 10 degrees or so
* above the horizon. . . . (No inverted image appears in the "mirage"
* picture, by the way.)
* Apart from the inserted sentences quoted above that describe the
* "mirage" picture, and the omission of the phrase "de l'Académie"
* from the first sentence, which would have given away the true source,
* the text is a word-for-word reprint of his 1896 C.R. note. Is this
* self-plagiarism, or entirely due to the editor? This reprint appears
* to be a comment on Forel's note in the 12 Dec. 1896 issue; but it was
* in fact a comment on Forel's note in C.R. 123, p. 161, (1896). Who was
* responsible for this deception?
* Thanks to Eric Frappa for calling my attention to this.
* The issue is dated 13 Fév. 1897.
* The fake photo explained as a double exposure
* Here, André Delbecque disavows the inserted image, acknowledges that
* his text had already been published in C.R., and says:
* "La photographie paraît, à première vue, représenter un effet de
* mirage sur le Léman ; mais ce mirage est imaginaire, et d'après ce que
* m'écrit mon ami le professeur Forel, très versé dans ces questions
* d'optique, la double image du bateau résulte simplement d'un accident
* photographique qui doit être produit pendant l'overture de l'obturateur."
* The editor ("H. de P.") says: "Par suite d’une transposition, on a
* effectivement placé dans le texte de M. A. Delebecque plusieurs lignes
* qui auraient dû venir en note à part et qui servaient d’explication à la
* photographie que nous a envoyée M. Picard, de la Chaux-de-fonds. Cette
* photographie, comme nous l’écrit de son côté M. Picard, et ainsi
* qu’il l’a reconnu après coup, résulte d’un double déclenchement
* de l’obturateur. D’où les deux images superposées. L’épreuve
* de M. Picard offre un curieux exemple de double impression et de faux
* mirage."
* Found on the Web (with some typos) at
* http://www.gloubik.info/sciences/spip.php?article878#nb2
* The issue is dated 6 Mar. 1897.
* Forel comments on Delebecque's double exposure, and his forthcoming
* work on changes in mirages
* Charles Dufour reports a Fata morgana seen at Morges
* "Le 2 juin 1896, vers les quatre heures du soir, à Morges, j'ai vu
* sur le lac un mirage supérieur fort remarquable. L'air était calme,
* et l'on voyait une belle Fata morgana sur tout le littoral d'Evian
* à Villeneuve." [Meeting of 20 juin 1896]
* A steamboat about 10 km from Morges appeared to be only 3 or 4 km
* away. With a telescope he saw an inverted image above it, joined
* at the mainmast: "C'est exactement le phénomène observé par Vince
* à Ramagate [sic] . . . et celui observé par Scoresby dans les mers
* du Groenland." He was about 10m above the lake.
* Another meeting abstract of mirage observations: "mirage parallèle"
* Cites Ch.Dufour (1854)
* Preliminary report on VARIABLE DIP
* "Pour mieux préciser les valeurs de ce déplacement de l'horizon
* apparent par rapport à l'horizon vrai, j'ai installé, dans une chambre
* au bord du lac, à Morges, sur un pilier en maçonnerie, une lunette
* astronomique dont j'ai établi l'axe à peu près suivant l'horizontale.
* J'ai déterminé l'angle formé par l'axe de ma lunette avec l'horizontale
* en visant le sommet d'une montagne (la Dent d'Oche), successivement la
* vision directe, puis la vision réfléchie dans un miroir d'eau; la
* moitié de l'angle ainsi obtenu me donne l'horizontale. . . .
* "Enfin je vise l'horizon apparent et, avec le micromètre à fil
* d'araignée, je mesure la position de l'horizon du lac en secondes de
* degré."
* [NOTE: This technique of measuring absolute altitudes by using a water
* surface as a horizontal mirror was actually invented by Mariotte, and
* published in his "Traitté du nivellement" (1672).]
* In the 5 months from 25 Oct. 1898 to 31 March 1899, the range was from
* +476" to -272" or 12' 38" relative to the geometric horizon.
* "Le facteur le plus important est la stratification thermique, laquelle
* dépend essentiellement de la différence de température entre l'air et
* l'eau. J'apprécie celle-ci en mesurant avec le thermomètre la
* température de l'air qui entoure la lunette ta et celle de l'eau du
* lac, au rivage te ." He gives a table of group means for the middle of
* each degree difference from ta - te = -6.5 to +4.5 degrees.
* Séance du 5 avril, in the Seances de la Société Vaudoise.
* Note that he cites p. 560 of his monograph, where earlier relative
* variations in the position of the horizon amounting to 14' were reported
* by using a method similar to Riccò's (whose work in 1889/1890 was not
* mentioned).
* Title page says Archives des Sciences Physiques et Naturelles,
* Cent Quatrième Année, quatrième période, tome huitième, Genève
* Available at the Biodiversity Heritage Library, at
* NOTE: This text is identical to that published in Bull.SVNS 35,
* pages XXV-XXVI (in the procès-verbaux for the April 5 meeting),
* including the table of numerical values.
* https://www.biodiversitylibrary.org//bibliography/5919#/summary
* Brief account of the full series (see C.R. paper, below, for details)
* This is in the section "Société Helvétique des Sciences Naturelles"
* and appears under the heading of "Physique, Mathématiques et
* Astronomie" on p. 367, where Forel's subject is given as "L'horizon du
* lac."
* [Note that Ch.-Ed. Guillaume attended this session, giving 2 papers.]
* Here it is "Une petite lunette astronomique établie sur un pilier
* de maçonnerie, dans un laboratoire à 2m5 au-dessus du lac . . . ."
* VARIABLE DIP with Table of values seen from 2 to 3 m above the water
* Now we have "une bonne lunette astronomique, établie sur un pilier de
* maçonnerie, . . . à 2m ou 3m au-dessus de la nappe du la, suivant la
* saison".
* "Les 607 observations valables dont je dispose, du 25 octobre 1898 au 30
* juin 1899, m'ont donné pour ha - hv les valeurs extrèmes +501" et -272",
* représentant une variation totale de 773", soit de près de 13' de
* degré."
* CALM AIR exaggerates effects:
* "L'erreur possible sur la position de l'horizon vrai, déduite de
* l'observation de l'horizon apparent, est plus grande quand l'air est calme
* que quand il est agité; . . . . L'erreur possible est plus forte quand la
* valeur ta - te est positive (quand l'air est plus chaud que l'eau) que
* quand elle est négative"
* Mentions (without citing) "professeur E. Kayser, de Dantzig, et . . .
* lieutenant K. Koss, de la Pola ".
* O'C #36
* FATA MORGANA paper in C.R.
* "En 1854, Charles Dufour a reconnu ce phénomène dans des apparitions
* que nous voyons chaque printemps sur notre Léman."
* ". . . la zone striée , mesure de 5 à 10 minutes de degré de
* hauteur. . . ."
* Forel's full paper on FM
* This contains his most detailed exposition and description of the
* fata-morgana. He is very specific: it never appears before 1 or 2 in
* the afternoon, never after 5 or 6 pm. The eye must be a few meters
* above the surface of the lake: 2 or 4 meters is the optimum height.
* See his 1899 papers for a little more detail about his telescope and
* the dip measurements that are mentioned here.
* NOTE: in his references, the Roman numerals sometimes refer to the
* number instead of the volume of Bull. Soc. Vaud. Sc. Nat.; e.g., on
* p. 472, the citation of Ch. Dufour's 1854 paper is to No.32 [but should
* be No.34], but that for Forel's own note in 1896 is to Vol. 32. This
* mixup confused the translator of the present paper, Prof. C. G. Knott.
* FATA MORGANA as transition between superior and inferior mirages:
* "I have seen the Fata Morgana . . . some four or five hundred times in all."
* "The best height would seem to be from two to four metres"
* (SEE ALSO Freiesleben, 1951, in DIP file)
* NOTE: This seems to be a slightly abridged translation into English
* of the previous item. The translation is rather insipid, and contains
* some errors in the references (e.g., the wrong page is given for Charles
* Dufour's 1854 paper on the mirages; it should be p. 129 in No.34, not
* p. 271 in No.32.)
* a summary of Forel's Edinburgh presentation -- cf. Abbe's 1896 MWR note
* Cited by Napier Shaw (1930, 1942).
* Helen Sawyer Hogg's account of Forel's book
* Available from ADS.
* Ian Halliday's mirage observation
* He cites Hogg and Forel, so it's filed here instead of with mirages.
* The mirage was seen over a frozen lake covered with snow, on a
* "comparatively mild day". Air was clearly warmer than snow.
* Available from ADS.
*
* Floor's first mirage paper
* Good photographs of inferior mirages taken with a Celestron 5 (1250mm);
* Floor comments that the altitude of the phenomenon is so small that
* pictures taken with ordinary lenses show little or nothing. Attention
* is drawn to the invisibility of the deck of the fishing boat in Fig. 2,
* and to the effects of turbulence: "In a brief exposure one sees these
* objects as if through a glass plate of inferior quality."
* Floor's second mirage paper
* A good, standard presentation of inferior-mirage theory for a flat Earth
* There appear to be good photographs illustrating the effects, but they
* are useless on my photocopy.
* Floor's third mirage paper
* Irregular and asymmetrical mirages.
* (I do not yet have a good copy of the photos, which are critical here.)
* A curious paper, comparing RIPPLES on water with those on inversions
* This is essentially an exposition of Fraser's (1975) "lifted-inversion"
* mechanism. But there are no references, and no mention of Fraser.
* Perhaps Fraser's idea had percolated around and reached Floor
* indirectly? There is no quantitative estimate of things as in Fraser's
* paper; this is all qualitative. He seems aware of White's (1979)
* point about oblique waves; yet he dismisses this notion and thinks that
* foreshortening near the horizon will make it all look as if the waves
* were seen face-on.
* Furthermore, though there is an extensive discussion in the last two
* paragraphs of the green rim, and green corners on the "tied-off" parts
* at the top of the Sun, there is no mention of green flashes.
* An English translation of parts of the previous note.
* Figs. 2 and 3 here are evidently the same photographs as Fig. 1 in the
* previous paper. Now Fraser is cited; perhaps this is due to the "Advice
* of Miss S. McNab"? The peculiar word "uitstulpingen" from the former
* paper is rendered here in English as "protrusions".
* Cites Feibelman's photos around 1960; but no mention of GF
* The "artificial distortion" is mainly the effect of jet-engine exhaust,
* though some smokestack effects are also shown.
* [Probably belongs in the "distorted sunsets" file.]
* May issue
* repeats Fraser's (and his own) canard about waves
* Fig. 5 nicely shows the difference between a miraged ship beyond the
* horizon, and another on the near side of the horizon.
* reprints 3 figures from his 1981 Zenit paper
* He does not realize that mirages are astigmatic, but does notice the
* problem for photography: ". . . the depth of field . . . does not always
* allow one to get both the optical horizon and the object in focus."
* cf. Touchet, 1925
*
* Hearsay accounts of IRISH FATA MORGANA stories (cf. Beauford, 1802)
* Near Rathlin she encounters "a clergyman of the place, by name Conolly,"
* with whom "I had a great deal of conversation on that extraordinary
* catoptric phænomenon the Fata Morgana , which is occasionally seen
* on this coast as well as the Straits of Reggio, to which it is so
* often compared. He said that he could not boast himself of ever having
* seen this beautiful delusion, but he had talked with persons of great
* credibility by whom it had been witnessed." Yeah, right. So we get
* stories about the usual Fata Morgana effects ("exactly resembling
* castles, ruins, tall spires, groves of trees, rocks . . . ") as well as
* "an enchanted island seen annually floating along the coast of Antrim,
* of which it is said a sod thrown on it from the terra-firma would fix it
* for ever. Attempts have been made at various times to throw this sod,
* but hitherto all have proved abortive. At Rathlin a belief prevails
* that a green island rises every seventh year out of the sea between their
* island and the promontory of Bengore. The inhabitants assert that many
* of them have distinctly seen it, and that it is crowded with people
* selling yarn and engaged in various other occupations common to a fair."
* MICEAL ROSS notices that some Irish folklore is mirage-connected.
* Lots of potentially useful references here, going back to 748 AD.
* -- see also Lehn & Rees (1990), and van der Werf (2017), in mirage file.
*
* NOTE: many of Lehn's papers are available at:
* https://home.cc.umanitoba.ca/~lehn/Papers.htm
*
* NOVAYA ZEMLYA EFFECT
*
* for the original, see the 1876 edition of de Veer's report, below
*
* See especially Bilberg (1697) in General Refraction file;
* see also MacMillan (1953), filed with MIRAGES
* see also Kramp (1799) in General Refraction file
* see also Borchgrevink in Mirage file.
*
* LE GENTIL argues from his observations in India
*
* Le Gentil was completely incredulous about the Dutch observations.
* His denunciation of them is concentrated in pp. 416-426; but there are
* little pot-shots at them starting on p. 395:
* ". . . elle est tout-à-fait contraire à ce qu'on sait de la
* réfraction horizontale; car quoiqu'elle varie beaucoup, on ne peut pas
* se figurer qu'elle soit si différente près du pôle de ce qu'elle est
* dans les autres climats.
* "Plusiers célèbres Auteurs ont cherché à expliquer ce singulier
* phénomène vu par les Hollandois, entr'autres Képler &
* Jacques-Dominique Cassini; ce dernier est celui de tous qui en donne la
* raison la plus vraisemblable, en supposant que ce que les Hollandois ont
* vu étoit une espèce de parhélie: on peut voir sur cela le Volume de
* l'Accadémie, année 1700 .
* "Pour moi je pense avec Scotto , que les Hollandois se sont
* trompés; & quoiqu'ils cherchent à prévenir l'objection qu'ils
* prévoyoient qu'on ne manqueroit pas de leur faire à leur retour, sur
* leur erreur, & qu'ils aient en conséquence écrit fort en détail leur
* observation. . . ." (p. 396)
* This gets mentioned again on p. 398, where he asserts that his
* observations were made at about the same height above the sea as theirs,
* as if this were all that was involved. Then on p. 407 he brings up
* the seasonal effects (whereby he finds the horizon high in winter), and,
* extrapolating to higher latitudes, says:
* ". . . un faux horizon au-dessus de celui de la mer; d'où j'ai conclu
* que loin de voir anticiper le lever du Soleil dans la nouvelle Zemble,
* on devroit au contraire le voir retarder. Cette observation m'a rendu
* très-suspecte celle des Hollandois dans ls nouvelle Zemble."
* On pp. 416-421 he quotes a French translation of the Dutch report;
* then: "Voici mes remarques.
* "Il me paroît, 1.° que ce Journal a été fait d'idée, & qu'il
* n'a point été écrit jour par jour."
* He goes on at great length to refute the conjunction of Jupiter and
* the Moon, etc., etc. But the best part (pp. 424-425) is the argument
* that they were mistaken about the date because the polar bears didn't
* show up for another 2 weeks after the Sun! He concludes (p. 426):
* "Bareints & ses compagnons d'infortune, ayant vu qu'ils s'étoient
* trompés, auront vraisemblement laissé subsister leur erreur, &
* d'après elle, ils auront bâti un roman : Bareints, dis-je, aura voulu
* donner aux Physiciens matière à exercer leur genie.
* "Mon opinion donc, est que le prodige que les Hollandois disent
* avoir vu dans la nouvelle Zemble, doit aller à côté de celui de la
* dent d'or, & mieux encore, avec celui du lever & du coucher
* extraordinaires du Soleil observé par les anciens Egyptiens, &
* rapporté par Hérodote."
* DAVID THOMPSON'S NARRATIVE
* (not a Novaya Zemlya observation, but strong refraction in polar regions)
* David Thompson wrote this between 1846 and 1851; but it was not edited
* and published until 1916. [Placed here, in order of composition.]
* "The first and most changeable Mirage is seen in the latter part of
* February and the month of March, the weather clear, the wind calm, or
* light; the Thermometer from ten above to twelve degrees below zero,
* the time about ten in the morning. On one occasion, going to an Isle
* where I had two traps for Foxes, when about one mile distant, the ice
* between me and the Isle appeared of a concave form, which, if I entered,
* I should slide into it's hollow, sensible of the illusion, it had the
* power to perplex me. I found my snow shoes, on a level, and advanced
* slowly, as afraid to slide into it; in about ten minutes this mirage
* ceased, the ice became [distinct] and showed a level surface, and with
* confidence I walked to my traps, in one of which I found a red Fox;
* this sort of Mirage is not frequent. That most common elevates and
* depresses objects, and sometimes makes them appear to change places :
* In the latter end of February at the Reed Lake, at it's west end, a
* Mirage took place in one of it's boldest forms; About three miles from
* me was the extreme shore of the Bay; the Lake was near three miles in
* width, in which was a steep Isle of rock, and another of tall Pines;
* on the other side a bold Point of steep rock. The Mirage began slowly
* to elevate all objects, then gently to lower them, until the Isles,
* and the Point appeared like black spots on the ice, and no higher than
* it's surface; the above bold Bay Shore, was a dark black curved line
* on the ice; in the time of three minutes, they all arose to their
* former height, and became elevated to twice their height, beyond the
* Bay, the rising grounds, distant eight miles, with all their woods
* appeared, and remained somewhat steady for a few minutes; the Isles
* and Point again disappeared; the Bay Shore with the distant Forests,
* came rolling forward, with an undulating motion, as if in a dance, the
* distant Forests became so near to me I could see their branches, then
* with the same motion retired to half distance; the Bay shore could not
* be distinguished, it was blended with the distant land; thus advancing
* and retiring with different elevations for about fifteen minutes, when
* the distant Forests vanished, the Isles took their place and the Lake
* shores their form; the whole wild scenery was a powerful illusion, too
* fleeting and changeful for any pencil. This was one of the clearest and
* most distinct Mirages I had ever seen. There can be no doubt it is the
* effect of a cause which, perhaps, was waves of the atmosphere loaded with
* vapours, though not perceptible to the eye, between the beholder and the
* objects on which the mirage acts, with the Sun in a certain position,
* when the objects were seen on the ridge of the wave, it gave them their
* elevation; when in the hollow of the wave, their greatest depression;
* and viewed obliquely to the direction of the wave, the objects appeared
* to change places. There may be a better theory to account for the Mirage.
* "While the Mirage is in full action, the scenery is so clear and vivid,
* the illusion so strong, as to perplex the Hunter and the Traveller;
* it appears more like the power of magic, than the play of nature."
* (pp.120-121)
* [Note observation of CONCAVE surface.]
* The concave appearance is also described by Forel (1895), p. 541.
* Available at Google Books. The typesetting in this book is oddly
* justified, with few words broken at the right margin, and unsettling
* padding before semicolons in some lines.
* Thanks to Mila Zinkova for pointing this out!
* Captain Middleton's sunsets delayed by 8 minutes
* "I also find the effects of cold occasion a great error in the time of
* the sun's rising and setting, making the refraction of the atmosphere much
* greater than in Europe.
* "I have observed the apparent time of the sun's central rising and
* setting for five or six months in the winter with a good level three or
* four days a week. I had a good second watch of Mr. George Graham's for
* the time; having computed the sun's true place, thence his declination,
* at the time when such appearance happened, and found his apparent rising
* sooner than the true time by near eight minutes, and his setting
* apparently so much later, so that the apparent day is longer than the
* real or astronomical day by almost sixteen minutes, and consequently
* the apparent night is so much shorter than the true night, making the
* horizontal refraction more than a degree.
* "N.B. I used a level, by reason these observations were taken upon a
* place forty feet above the surface of the ocean, and about seven or eight
* feet above all the land in the way of the sun's rising and setting in the
* middle of winter."
* A similar extract appears in Isham's Observations and Notes 1743-1749.
* This is No. XI of the Hakluyt Society's First Series.
* Full title:
* The Geography of Hudson's Bay: being the remarks of Captain W. Coats, in
* many voyages to that locality, between the years 1727 and 1751. With an
* Appendix, containing extracts from the log of Capt. Middleton on his
* voyage for the discovery of the North-West Passage, in H.M.S. "Furnace",
* in 1741-2. Edited by John Barrow, Esq., F.R.S., F.S.A.
* We have the 1964 reprint by Burt Franklin, New York.
* ABNORMALLY LARGE REFRACTION
* ". . . ganze Reihen von regelmässig am Meridiankreise beobachteten Sterne,
* die für Athen bis v i e r G r a d e u n t e r d e m
* H o r i z o n t e culminiren, wie ξ Lupi, ε1 Arae,
* ε2 Arae, β Arae, Capella U.C. und Kanopus, welcher letzte
* aber nur der Nachhülfe der Horizontalrefraction bedarf, um bei seiner
* Culmination den Athenienser Meeres-Horizont etwa zu tangieren."
* The prototypical display seen by Barents's men at Novaya Zemlya on
* 24 Jan. 1597.
* There is much discussion in Charles T. Beke's introduction to the first
* (1853) edition (printed here in the second edition on pp. cxliv - clvi),
* showing that de Veer's observations are reliable. He concludes that
* "We have therefore no alternative but to receive the facts recorded by
* de Veer as substantially true, and to believe that owing to the peculiar
* condition of the atmosphere, there existed an extraordinary refraction,
* not merely on the 25th of January, but continuously during fourteen days
* afterwards, at first amounting to nearly four degrees, but gradually
* decreasing to about one degree and a half."
* . . . "The problem is a curious, and, with our still insufficient
* knowledge of the laws of atmospheric refraction in high latitudes, a
* difficult one. Nevertheless we may confidently rely on the result being
* such as to establish the entire veracity of our Dutch historian."
* This is No.54 of the first series of works issued by the Hakluyt Society.
* First edition edited by Charles T. Beke, 1854;
* Second edition, with an introduction by Lieutenant Koolemans Beynen,
* (Royal Netherlands Navy)
* We have the 1964 reprint of the 1876 2nd Ed., by Burt Franklin, New York.
* Strong refraction causes SAUCER-shaped appearance (cf. Lehn, 1975)
* "Through an optical illusion, dependent on the mirage of the ice
* horizon, it appeared to us as if we were proceeding on the bottom of a
* shallow, saucer-shaped cavity. It was thus impossible to decide whether
* we walked up or down hill, which could only be decided by the heaviness of
* the sledges in the harness . . . ."
* [Note observation of CONCAVE surface.]
* NANSEN
* "The mirage was at first like a flattened-out glowing red streak of fire
* on the horizon; later there were two streaks, one above the other, with a
* dark space between; and from the main-top I could see four, or even five,
* such horizontal lines directly over one another, and all of equal length;
* as if one could only imagine a square dull-red sun with horizontal dark
* streaks across it. An astronomical observation we took in the afternoon
* showed that the sun must in reality have been 2° 22' below the horizon
* at noon; we cannot expect to see its disk above the ice before Tuesday at
* the earliest; it depends on the refraction, which is very strong in this
* cold air." (pp.394-395)
* NICE DRAWING of this, p. 394.
* O'C #96
* It turns out we have the *German* edition in our library:
* Here the drawing is on p.316, and the German text reads:
* "Die Luftspiegelung war anfänglich wie ein abgeplatteter glühend
* rother Feuerstreifen am Horizont; später wurden zwei Feuerstreifen
* daraus, einer über dem andern, mit einem dunklen Raume dazwischen. Vom
* Großmaste aus sah ich vier oder gar fünf solcher Horizontallinien
* übereinander und alle von derselben Länge, ungefähr wie man sich eine
* mattrothe viereckige Sonne mit dunkeln Horizontalstreifen darauf
* vorstellen könnte."
* "Eine astronomische Beobachtung, die wir nachmittags anstellten, bewies
* uns, daß die Sonne in Wirklichkeit um Mittag 2° 22' unter dem
* Horizont gestanden haben mußte. Wir können nicht erwarten, ihre Scheibe
* vor Dienstag über dem Eise zu sehen; es hängt mit der Strahlenbrechung
* zusammen, die in dieser kalten Luft sehr stark ist." (pp.315-316)
* Here the drawing appears on p. 316, and seems better reproduced than in
* the English edition. The date of the observation was 16.Jan., 1894.
* Summaries of 4 cases, three of them near 2.3 degrees
* Note: I have only 2 of the 4 cases here in this bibliography.
* Also note his use of the rare term "horizon géodésique".
* He seems to use it to mean the astronomical horizon, rather than the
* geometric one, with dip but not refraction taken into account.
* cf. Mercanton's note on refraction phenomena in Dec. 1920.
* in Compte rendu des séances de la Société suisse de géophysique,
* météorologie et astronomie (G.M.A.), assemblée générale
* à Neuchâtel, le 31 août 1920
* This appeared in the November-December issue.
* Cornelis names the "Novaya-Zemlya phenomenon":
* "That such reports are extremely rare I think must in the first place be
* ascribed to the modesty of the navigators. If they make an observation
* that gives strange results, they are inclined to think first of an error
* in their reckoning, and e.g. Shackleton's navigating officer became a
* laughing-stock (p.49). Likewise, Jacob van Heemskerck had to put up with
* being simply not trusted in the knowledge of navigation, because of his
* former teacher." (p.199) [cf. Koss's footnote!]
* "In case my explanation is regarded as acceptable, the obvious question
* is: `How is it possible that 300 years had to pass before an explanation
* was given?'
* "During more than two centuries, meteorology still became hardly
* recognized as science; then, when the study became caught up in
* knowledge, dedication, etc., we got that period, which still continues,
* of excessive specialization in the study of the sciences. With the
* division into all kinds of compartments and pigeon-holes, refraction has
* become lost in the crowd. The meteorologists leave the teaching to the
* astronomers, but these have by the nature of things an abhorrence of
* everything close to the ground, and only meddle with refraction when it
* has an inappreciable value. The meteorologists also are somewhat drawn
* away from the so-called terrestrial refraction, because it is consecrated
* by the compartmentalization to the area of geodesy, while the geodesists
* have not yet extended their activities to the polar seas. That the problem
* discussed has never before been taken in hand, I think must be ascribed to
* the far too complete specialization." (pp.200-201)
* Thanks to Denis Khotimsky for useful discussion of this paper!
* Cornelis's last paper (note his obituary on the preceding page)
* He argues that large horizontal refraction may occur in lower latitudes,
* but would go unnoticed, as "With an abnormally large refraction the
* Sun would only rise a few minutes too soon or set too late, and who
* would notice such a thing? One looks at the Sun then to enjoy the
* phenomenon, to see the green flash or surely to measure the dip of the
* horizon. Only in the last case could the result raise the suspicion of
* an abnormal refraction, but one would sooner think of having made an error,
* if the measurement were in obvious conflict with later azimuths." [cf.
* Koss & Thun-Hohenstein, 1901.]
* He suggests an interesting possible mechanism: if the wind moves faster
* over the wave crests than over the valleys, there should be a pressure
* and hence a density difference between them, thus causing some refraction
* effects. (I doubt that this can be appreciable quantitatively, though.)
* He then supposes that the resulting density gradients at the wave crests
* could produce a large horizontal refraction at sea.
* kindly supplied by C. de Jager!
* more papers by William Herbert HOBBS (see also "Mirage" file)
* (These are here as they were cited by Stefansson, below)
* Another review of the geographical implications of mirages;
* cf. his 1933 paper in Geografiska Ann. It cites some of his papers
* since then. This one is cited by Stefansson (below).
* Hobbs draws a useful distinction between "high" and "low" superior
* mirages (which he thinks are due to high and low inversions,
* respectively.) He remarks that "the object can be seen only from within
* a very limited area", because "Obviously at points nearer the object the
* curvature of the rays would not be sufficient to bring them down to the
* earth." (p. 232) -- cf. Lehn & Legal, below!
* FALSE HORIZONS and TRUNCATION of images:
* "It is characteristic of the high superior mirage, that above 1000
* meters, that there is usually a band which separates the raised image from
* the true horizon. In the case of the lower type, that near 200 meters, it
* may be the top of the object which is truncated in the image (Fig. 2)."
* At the end, he says that the examples given "do not, of course, by any
* means exhaust the many varieties of mirage which are peculiar to those
* regions. . . ."
* Another example of long-distance vision, updating the 1937 paper
* ". . . the air was calm and the sea smooth."
* "The Snaefells Jökull (4,715 feet) and other landmarks well known to
* the captain and the mate were seen as though at a distance of twenty-five
* or thirty nautical miles, though the position of the schooner showed that
* these features were actually at a distance of 335 to 350 statute miles."
* Here again is a "snow-covered summit" (cf. Korzenewsky, 1923).
* Hobbs again supposes that inversions of a few degrees "at elevations in
* excess of a thousand meters" can cause the mirages.
* VILHJALMUR STEFANSSON proposes island-hopping via mirages
* Cites Hobbs in AAG (1937) and Science (1939)
* Captain Middleton's EIGHT MINUTES again
* All in very antiquated spelling: ". . . making the Horizentall Refractions
* more than a Degree, and as the Refractions occation's an Error, in the
* time of the sun's Rising and Setting, so itt Likewise Vitiates the
* Amplitude; and this must be observ'd by marriners or they will never gaine
* the Declination of the magnitic Needle with any Certainty. . . ."
* This is in the Publications of the Champlain Society, Hudson's Bay
* Series, XII. Full title:
* James Isham's observations on Hudson's Bay, 1743, and notes and
* observations on a book entitled
* A Voyage to Hudson's Bay in the Dobbs Galley , 1749
* Edited with an introduction by E. E. Rich, M.A., Fellow of St, Catharine's
* College, Cambridge
* Assisted by A.M.Johnson, Archivist, Hudson's Bay Company
* with a joint letter from the chairman of the Champlain Society and the
* chairman of the Hudson's Bay Record Society
* NOVAYA ZEMLYA effect (he seems unaware of Cornelis's papers above)
* "The Novaya-Zemlya phenomenon is caused by repeated total reflection at
* the upper boundary of a ground inversion. . . . The conditions are most
* favorable in the arctics and the phenomenon must be confined to the polar
* regions."
* O'C #147
* A popular follow-up to Visser's technical paper, above
* Here he also reproduces Kepler's diagram, as well as explaining it
* quantitatively.
* Thanks to Albert Jansen for pointing this out!
* HORIZONTAL RED RAY accompanies the refracted Sun
* "Then a fraction of the sun's disc appeared again, flickered and
* disappeared. For some time it came and went. the greatest elevation
* revealing about one tenth of the orb. Sometimes as it reappeared a
* red flash seemed to shoot out and pulsate along the horizon. This was an
* exciting moment, not only because the sun had come back to us, but because
* it had returned by refraction four days earlier than expected." (Aug.14)
* This book was simultaneously published by Cassell, London.
* Thanks to Siebren van der Werf for this reference!
* Sir Ernest SHACKLETON's observations
* ". . . refraction, which amounted to 2° 37' at 1.20 p.m." (p.49)
* "Thin, wavering black lines close to the northern horizon were probably
* distant leads refracted into the sky." (p.54)
* NEGATIVE DIP:
* "Refraction generally results in too big an altitude when observing the
* sun for position, but to-day the horizon is thrown up so much that the
* altitude is about 12' too small." (p.64)
* [Note observation of CONCAVE surface.]
* NOTE: This book has been through many editions; the one cited is what
* I have seen. Earlier Macmillan editions were copyrighted 1947 and 1920.
* There were also 1919 and 1922 editions published by Heinemann in London.
* Thanks to Siebren van der Werf for pointing out the 1920 edition!
* Crude mirage calculations; many a re-invented wheel here.
* They start with the flat-Earth model and fudge in the curvature, instead
* of using the exact relations.
* ". . . the arctic mirage is fundamentally distinct from the fata morgana
* or desert mirage . . . ." (p. 120) [but the German version of the abstract
* translates "arctic mirage" as "arktische Fata Morgana"!]
* ". . . leaving the viewer with the distinct impression that the earth's
* surface is saucer-shaped." (p. 127) [cf. Wright & Upham, 1896]
* [Note observation of CONCAVE surface.]
* Stefansson's book is cited.
* The first hillingar and hafgerdingar paper
* hillingar = concave surface; hafgerdingar = miraged surface
* Popular account of the previous work, ``assembled for Scandinavian
* Review by Irmgard Schroeder, based on previous work by Lehn and
* Sawatzky.'' It contains the controversial assertion:
* "The first adequate analysis of atmospheric refraction was published in
* 1917." Via e-mail, Lehn tells me this refers to Nölke's paper in Phys.Z.
* Lehn discusses the hillingar and hafgerdingar again, with the
* Novaya Zemlya effect.
* hillingar = concave surface; hafgerdingar = miraged surface
* He attributes the darkness of Wegener's strip to "atmospheric absorption".
* He mentions the phase shift, but does not attribute it (or the dark
* strip) to Wegener, citing only Wegener's 1918 paper. Interestingly,
* he says the strip in Wegener's example is "blank".
* Lehn models the duct as uniform, with an abrupt (discontinuous) end;
* he admits the temperature profile is not uniquely determined.
* NOVAYA ZEMLYA EFFECT; SUNSET PICTURES
* Lehn & Schroeder's "merman" mirage paper in "Nature"
* Whether you believe the "merman" explanation or not, this contains a
* useful mirage photograph (their Fig. 5) taken 2 May over Lake Winnipeg
* due to a very low-lying inversion (about 2 m above the icy lake).
* "Such conditions occur almost every spring on Lake Winnipeg."
* Lehn inverts a superior mirage of a hill 20 km away
* The treatment is very straightforward, working up from the bottom
* of the image. But it is restricted to rays with a single vertex. All
* the ray tracing is done in closed form, with parabolic rays.
* This properly belongs in the regular mirage file, but is kept here.
* DARK STRIP IN SUPERIOR MIRAGE OF SUBMARINE
* Lehn & Friesen re-confirm the brightness theorem
* They cite, but oddly, do not refute, the Fraser & Mach paper.
* Lehn's "long-range" mirage paper
* This properly belongs in the regular mirage file, but is kept here.
* LOOMING and MIRAGES between Greenland and Iceland
* Footnote 29 gives the dictionary meaning of hillingar as "looming".
* Modelling of the Novaya Zemlya effect and some mirages
* Unfortunately the temperature profiles used are quite non-physical,
* so their inferior mirage contains a spurious 3rd image (cf. laminar
* sublayer in mural mirages -- this could be used as an example). Also,
* they use a quasi-isothermal atmosphere (using the height-mean temperature
* to find an effective scale height) instead of a proper polytropic model
* to calculate densities. So the results are really only qualitative
* and not very accurate. However, the leakiness of the duct required to
* produce the effect is demonstrated.
* And there is a good discussion of the ray curvature. Green flashes are
* demonstrated; and a new TERMINOLOGY for these mirages is introduced.
* Nice treatment of flattened sunsets at the end; but not citing Biot.
* Lehn & Schroeder's "Hafgerdingar" paper
* A nice analysis of the King's Mirror report. The only defect is
* the assumption that because the "foreground shows . . . no visible
* distortion, . . . [t]he atmosphere must therefore be relatively normal
* for the 3.7 km . . . between the observer and the point". (p. 215)
* (This is basically the same as O'Connell's error.) Also, the claim
* that "few sailors have survived to tell of them" has a logical flaw:
* we necessarily know of no sailors who went down in storms following
* such mirage displays; so there is really no valid reason to suppose
* that the mirages are a reliable precursor of violent storms. Rather,
* as the mirages are associated with high pressure, the natural
* alternation of highs and lows suffices to explain Wegener's (1926)
* Prognostische Bedeutung . Still, a nice piece of work.
* Cites Scoresby, and points out the concave appearance of the sea,
* referring to the appearance of "overhanging cliffs". See further
* discussion by Siebren van der Werf (2017) and Young & Frappa (2017).
* [Note observation of CONCAVE surface.]
* A Dutch "Novaya Zemlya" display (according to the authors; I doubt it)
* Siebren van der Werf, Ingrid Spendel, Hans Betlem, and Günther Können
* Seen on 23 May, 2018 (at the peak of superior-mirage season).
* Shows a nice series of 4 highly flattened sunset images, in color,
* with Siebren's attempt to explain the sunset with his old N.Z. model.
* (Looks to me like a typical San Diego sunset, looking up through a
* duct. At least we agree on the ducting.) Sunset delayed 5 to 7
* minutes. Some meteorological data, and times of pictures taken from
* 1.7m and 10m height (the latter not shown); Können observed from 15 m.
* The text draws attention to the "nearly complete flattening of the
* lower limb of the Sun, not at the horizon, but appreciably above it."
* Many thanks to Siebren for the PDF and extensive discussion!
* [This probably belongs in the "Distorted Sunsets" file; but I have put
* it here, in view of the title and the authors' opinion that it should
* be called an N.Z. display -- "the first time in the Netherlands".
* Michael Vollmer's 2020 paper on LOOMING and distant HORIZONS
* A good review of the "longest distance to the horizon" problem, with
* many good references.
* DOI: https://doi.org/10.1364/AO.390654
* Siebren's thorough analysis of the original Novaya Zemlya observation
* published online at
*
* https://comptes-rendus.academie-sciences.fr/physique/item/CRPHYS_2022__23_S1/
*
* or https://doi.org/10.5802/crphys.102
* DOI: doi : 10.5802/crphys.102
*
* FRANCIS HAUKSBEE discovers "Gladstone-Dale" relation
* A second, posthumous, edition appeared in 1719, published by J. Senex
* and W. Taylor; but the material of interest here is in both editions.
* P. 175 (p. 225 of 2nd ed.):
* "Experiments concerning the Refraction of the air"
* Hauksbee explains that John Lowthorp's 1699 demonstration of refraction
* could not be reproduced by the French Academy, so "I was order'd to make
* an Instrument for the purpose, by the direction of Dr. Halley . . . " (p.
* 176 of 1st ed.; p. 226 of the 2nd). He made a hollow brass prism fitted
* with plane glass windows at an angle of 64°, and a fitting to connect
* it to the air pump. Looking through a 10-foot telescope, he measured
* the apparent image deflection of a distant building, and found it
* proportional to the pressure.
* "By these Experiments it plainly appear'd, That the Refraction of
* the Air was, as far as the Eye could distinguish it, exactly
* proportional to its Density ; the Refraction being the same from the
* common Air to a Vacuum , as from a double Density to the common Air,
* and the Refraction from a treble Density to the common Air exactly
* double to that from the common Air to a Vacuum ." (pp. 178-179, 1st
* ed.; p. 229, 2nd ed.) [The precision given is half an inch in 10 1/2
* inches, or about 5%; more cannot be expected, because of dispersion.]
* (mentioned by Brook Taylor, 1715, and by Ivory, 1823).
* See Delisle (1719) for a comparable crude effort.
* BIOT and ARAGO did the job right (1806)
* This was written by Biot in the first person singular; but Arago
* protested (see his collected works) and had his name added. One
* should be aware that Arago was only 20 years old at this time.
* The approach is strictly Laplacian/Newtonian; the introductory
* paragraph says of gases: ". . . les particules qui les composent étant
* séparées par le calorique, et maintenues à des distances où leur
* attraction mutuelle n'a plus d'effet sensible, . . . les recherches que
* l'on peut faire sur les propriétés des gaz sont liées à presque
* toutes les branches des sciences naturelles. Celles que nous soumettons
* ajourd'hui à la classe, ont pour objet l'action que ces substances
* exercent sur la lumière; elles intéressent à la fois la physique,
* la chimie et l'astronomie : c'est sous ce triple point de vue que nous
* allons les considérer.
* ". . . Newton a prouvé qu'il résulte d'une attraction que les corps
* exercent sur les molécules de la lumière, attraction seulement sensible
* à des très - petites distances, et, en cela, tout - à - fait analogue
* auz affinités chimiques."
* On p. 303 is mentioned the work of "Hauksbée", whose experiments
* "prouvoient seulement que l'air a une force réfringente, et qu'elle
* est à peu près proportionnelle à sa densité."
* On p. 304, the influence of Laplace is evident; Biot says, "C'est
* ce travail que la classe, sur la proposition de M. Laplace, m'a chargé
* de reprendre en l'étendant à tous les fluides aériformes, . . . mais
* comme les expériences qu'il falloit faire étoient très-délicates,
* très-pénibles, et extrêmement multipliées, j'ai engagé M. Arago,
* secrétaire du bureau des longitudes, à s'en occuper avec moi.
* Nous avons fait ensemble toutes les expériences, tous les calculs dont
* je vais entretenir la classe, et par conséquent les résultats qui
* s'en déduisent doivent être considére's comme nous étant communs à
* tous deux. Nous devons dire aussi la part qu'ont prise à ces résultats
* deux personnes dont la participation nous est trop honorable pour ne
* pas nous en prévaloir; ce sont les auteurs de la Statique chimique
* et de la Mécanique céleste . Le sujet de toutes nos recherches
* étoit indiqué dans leurs ouvrages; leur conversation et leurs conseils
* nous ont fourni les moyens de les suivre et de les terminer."
* After a detailed consideration of experimental details, they come
* to the important conceptual contribution of the paper (p. 314): "Ce
* que l'on entend ici par pouvoir réfringent , n'est pas simplement la
* déviation produite sur le rayon lumineux; ce n'est pas non plus l'angle
* qui mesure cette déviation, mais c'est l'accroissement total du carré
* de la vîtesse ou de la force vive de la lumière après avoir éprouvé
* toute l'action du corps transparent." The table on the next page gives
* values of (n - 1) for air, and refers to the density dependence shown
* on p. 323. But their "refractive power" is clearly (n2 - 1).
* On p. 322, this matter is discussed: ". . . nous avons trouvé que,
* depuis le vide le plus parfait jusqu'au degré ordinaire de pression
* de l'atmosphère, la réfraction d'un même gaz quelconque est toujours
* rigoureusement proportionnelle à sa densité sans que cette règle ait
* besoin de la plus légère modification." The table on p. 322 shows
* extensive data for air; the next page gives less extensive values for
* oxygen, nitrogen, and hydrogen. So (pp. 323-324):
* "Nous pouvons donc en conclure avec certitude, comme nous venons de
* la faire, que la force réfringente de l'air et des gaz, depuis la plus
* grande raréfaction jusqu'à la pression ordinaire de l'atmosphère,
* est, pour un même gaz, rigoureusement proportionnelle à la densité
* . . . ; nous avons même condensé l'air dans notre prisme jusqu'à 0m80
* pour obtenir des densités plus fortes, et nous avons observé à de
* hautes températures pour voir si le même rapport y subsiste; nous
* n'avons pas pu y appercevoir la différence la plus légère."
* They were unable to find any difference between the refractivites of
* air and water vapor (pp. 324-325).
* On p. 331, they show they can predict the refractivity of air within
* half a per cent from the refractivities of its components. So they
* try to use what we would call molar refractivities to account for the
* refractivities of compounds, as well. This works well for ammonia
* (p. 332), but not so well for water (p. 334). They go on to try this
* method with carbon and its compounds (oils and alcohol) and diamond.
* The discrepancies are arm-waved away, and Biot concludes that the
* results are "extrêmement favorables au système de l'emission de la
* lumière, et paroissant contraires à celui des ondulations." (p. 344)
* There is an interesting remark about the dispersion of air on p. 346.
* On the next page they find excellent agreement with the refractivity of
* air deduced by Delambre from astronomical refraction.
* On p. 347 they return to the density dependence again. On p. 349,
* they emphasize that the determination of the density ratio of air and
* mercury gives the "height of the homogeneous atmosphere" that is needed
* in astronomical refraction theory.
* The main text ends on p. 353; then follow some detailed Notes on the
* experimental procedures. The first examines the prism angle. The second
* (p 363) deals with data reduction and analysis. The third (p. 379) deals
* with Laplace's barometric formula.
* This is now available from the BHL at
* https://ia600205.us.archive.org/25/items/mmoiresdelinst07inst/mmoiresdelinst07inst.pdf
* where the Histoire precedes the Mémoires (whose page numbering begins
* at 1, as usual). See also Delambre's comments on their work, on p. 9
* of the Histoire .
* Title page says "Semestre de 1806" and "Tome Septième, Première partie"
* GLADSTONE and DALE didn't even study gases!
* This paper is the origin of the "Gladstone-Dale Law" . . .
* "Every liquid has a specific refractive energy composed of the specific
* refractive energies of its component elements, modified by the manner
* of combination, and which is unaffected by change of temperature,
* and accompanies it when mixed with other liquids. The product of this
* specific refractive energy, and the density, at any given temperature,
* is, when added to unity, the refractive index." (p. 337)
* NOTE: their "refractive energy" is our "refractivity" (n-1).
* quote Newcomb and emphasize DISPERSION in astronomy
* "The practical difficulties involve . . . the necessary inattention to
* the dispersion of light. In practice the astronomer usually disregards
* all dependence of refractive index on color. This must involve errors
* in zenith-distance observations on stars whose colors are intrinsically
* different and especially in observations of stars near the horizon, where
* the short waves are largely absorbed and scattered by our atmosphere,
* causing the stars to be represented only by longer waves. Because of
* these difficulties tables of corrections for astronomical refraction
* are probably better determined from astronomical observations than from
* laboratory measures." (p. 60, following the Newcomb quote.)
* OBSOLETE data on dispersion of air and water vapor effects
* Barrell & Sears have a good discussion, but obsolete values
* (available from JSTOR; filed separately because of size)
* OLD EDLÉN formula (with 41 in second denominator)
* NEW EDLÉN FORMULA
* Effects of compressibility are about 10-4 at 245K and increase rapidly
* at lower T. (looks like 2 x 10-4 at 200K). Edlén (1966) is off by
* 7x10-8 at -30C, and by 4x10-7 at 45C, 100% RH.
* 4-parameter, 2-term Sellmeier dispersion formula
* simplified formulae for visible region, including WATER & CO2
* DEFINITIVE REFRACTIVITY FORMULAE:
* WATER-VAPOR PROBLEMS
*
* BIRCH-DOWNS CORRECTION CONFIRMED
* New high-accuracy data in the visibile re-confirm Birch & Downs
* Thanks to Ernie Lewis for pointing out this paper!
* INFRARED DISPERSION due to H2O
* Despite the title, this covers everything out to 25 microns.
* (see also Jacques Cassini, 1714)
*
* PEDER HORREBOW's Atrium Astronomiæ (1732)
* This shows how to separate the refraction, the solar parallax,
* the obliquity of the ecliptic, and the latitude from fundamental
* measurements of apparent altitudes, by determining the instrumental
* errors and correcting for them. It was written shortly after the
* great fire that destroyed Roemer's observatory and records.
* Of particular interest here is the report that a reliable man in
* Iceland had argued that the refraction of the Sun at the winter solstice
* there amounted to a whole degree [§.17, pp. 8-9]. Horrebow's comment
* on this is more nuanced than Mathieu's French version of this story in
* Delambre's Histoire (1827): Horrebow does express uncertainty about the
* veracity of this claim; but then he adds that "nevertheless, I easily
* believe that the refractions in Iceland are much larger than they are
* in Denmark." [Mathieu suppressed this qualification.] Note that this
* report is a decade before Captain Middleton's very reliable observations
* of large winter refractions at Hudson's bay (Coats, 1852; Rich & Johnson,
* 1949)).
* The Linda Hall library has a page on Horrebow:
*
* https://www.lindahall.org/peder-horrebow/
*
*
* The title page says:
*
*
* A T R I U M
* ASTRONOMIÆ,
* sive
* DE INVENIENDIS REFRACTIONIBUS
* OBLIQUITATE ECLIPTICÆ, ATQUE
* ELEVATIONE POLI TRACTATUS,
*
* cui subjungitur
* S C H E D I A S M A
* de
* A R T E I N T E R P O L A N D I
* ante annum seorsum editum
*
* AUTHORE
* P E T R O H O R R E B O W I O
*
* Philosophiæ & Medicinæ Doctore, atqve in Uni-
* versitate Regia Havniensi Astronomiæ
* Professore
*
*
* Pierre Charles le Monnier
* LE GENTIL's observations in India
*
* Contains many measurements of horizontal refraction, refraction at
* low altitudes, terrestrial refraction, etc., together with an assault on
* the integrity of the Dutch at Novaya Zemlya. See sections quoted in the
* Distorted Sunsets, Novaya Zemlya effect, and Mirage files.
*
* "Les Réfractions horizontales sont si sujette à varier, & d'une
* quantité si considérable, même d'un moment à l'autre, qu'on ne peut
* se flatter, quelqu'exactitude que l'on apporte à les bien observer,
* que d'avoir une quantité moyenne, souvent très-éloignée de la
* véritable, c'est-à-dire, des résultats très-différens les uns des
* autres. Cette inégalité est encore assez sensible à quelques degrés
* au-dessus de l'horizon, pour nuire aux observations ; & les Astronomes
* exacts ont une grande attention, dans les recherches délicates qu'ils
* font, de n'employer que des observations faites à d'assez grandes
* hauteurs pour n'avoir rien à craindre de l'inégalité des
* réfractions." (pp. 393-394)
* Le MONNIER's observations of variable refraction
* The uninformative abstract
* Actually published in 1784.
* Le MONNIER's full text
* His concern is to explain the divergent values of refraction reported by
* different authors. After rejecting Kepler's odd notion that refraction
* should increase with height above sea level -- which is refuted by
* Pascal's barometric observations -- he says:
* "Mais laissant à part cette digression, peu importante aux yeux
* des Modernes trop éclairés en ce siècle-ci pour s'y arrêter, il
* sembleroit néanmoins, d'après quelques essais intéressans, publiés
* dans nos Mémoires en 1749, par M. Bouguer, que ce seroit en vain, ou
* qu'on auroit tort d'expliquer par des différentes elévations du sol
* au-dessus du niveau de la Mer, les grandes différences qu'on trouve
* dans les Tables des réfractions de Picard, Cassini & de Flamstéed . . . .
* ". . . ces Tables ne paroissent avoir été construites que
* conditionnellement & pour un état de température moyenne, puisqu'on
* trouve . . . des preuves suffisantes qu'ils ne doutoient nullement qu'on
* n'eût besoin de Tables différentes pour les diverses saisons du froid &
* du chaud." So he looks for the extremes of refraction in extremely hot
* and cold conditions. Furthermore, the old results are faulty, as they
* do not allow for aberration, discovered only in 1728. (And no doubt
* the height effect is best investigated from the peak on Teneriffe.)
* ". . . réfractions qui conviennent à l'horizon . . . ne sont pas les
* mêmes l'hiver que l'été, j'en ai déjà publié les différences dans
* l'Histoire céleste & ailleurs, d'après mes propres observations . . . "
* (of which he cites a good number, as well as those of Picard). These
* examples show horizontal refractions of at least 40' for 2 Jan. 1675,
* and 45' for the next day, or 12 or 13' more than in summer. But on the
* same days, the refraction at 4° 30' and 5° was at most 2 minutes
* more than normal; ". . . d'où il est aisé de reconnoître que les
* différentes densités de l'air, . . . n'influe considérablement qu'aux
* approches de l'horizon . . . ." (p. 91)
* These conclusions from Picard's observations are confirmed by his own,
* which show more than 40' on Dec. 1 (p. 92).
* Picard's observations, "qui ont échappé à Flamstéed" show, for
* 20 Jan. 1675, a horizontal refraction of 46' 14''1/2 and 50' 33'' for
* the solar limbs, and the Sun's vertical diameter reduced to 19' 52''.
* (Actually published in 1784.)
* Bessel's original data (observations and reductions by Argelander)
* Here we have the individual measurements of the refractions that are
* discussed in Bessel's A.N. paper, immediately below. The tables are
* on pp. IX - XI, in order of date for each star. The solar refractions
* are on p.XII. "Diese Beobachtungen verglich Herr. Dr. Argelander
* mit den Tafeln in den Fundamentis astronomiae , wobey er aber die
* Fehler des Thermometers in Rechnung brachte und d i e Tafel für die
* Wärme-Aenderung anwandte, welche ich in der VII. Abtheilung gegeben habe;
* die Resultate dieser Vergleichung findet man in der folgenden Tafel,
* nach den Thermometer-Graden geordnet:" -- then comes the "Fehler der
* Strahlenbrechungs - Tafeln in den Fundamentis astronomiae p. a. 1755. "
* The tables of temperatures for the individual observations continue
* on the next page (XIII).
* On p. XIV is the first appearance of the table of arithmetic means of
* the table errors, sorted in bins of Z.D., with the number of observations
* and probable errors of both single observations and bin means. The errors
* of the means are reprinted in the A.N. discussion. The table is binned in
* half-degrees, and a separate table for the solar observations follows it.
* "Die Absicht bey diesen Beobachtungen war, die Strahlenbrechung für
* jeden halben Grad der Zenith-Distanz von 86° 30' bis zum Horizonte
* unter den verschiedensten Umständen zu bestimmen;. . . ."
* Note the mention of DISPERSION on p. XIV:
* ". . . es nothwendig war den beständigen Fehler zu bestimmen, welcher aus
* dem Unterschiede der absoluten Zeitangaben beyder Beobachter hervorgeht
* und wahrscheinlich noch verändert wird, durch die Verschiedenheit der
* Schätzung des Mittelpuncts des Farben-Spectrums, welches jeder Stern so
* nahe am Horizonte bildet."
* On p. XV the corrections to Fund. astr. P.50 are given again, taking
* into account the instrumental errors deduced from the corrected table
* of mean refractions. Here the solar data are omitted because of their
* smaller numbers. The probable errors of the stellar observations for
* single observations seem to be the values given by Bomford (1971).
* The famous comparisons of the eye-and-ear method with Maskelyne, and
* Maskelyne's unfortunate assistant Kinnebrook, are on pp. VII and VIII !
* NOTE: The details of the weather and exact times of the observations
* are in the previous (7th) volume.
* Available on the Web at
* http://reader.digitale-sammlungen.de/resolve/display/bsb10485006.html
* Thanks to Stephen McCluskey for pointing this out!
* Bessel discusses his own and Argelander's observations below 5°
* VARIATIONS near the HORIZON:
* "Bei meinen Bemühungen um diese Materie, habe ich die Refractionen
* nicht allein als Mittel, die beobachteten Zenitdistanzen zu reducieren,
* betrachtet, sondern geglaubt, dass ihre Festsetzung ein Interesse für
* sich besitzt. In dieser Ausdehnung genommen, erfordert die Auflösung
* der Aufgabe die Fortsetzung der Tafeln bis zum Horizonte; handelt es
* sich dagegen nur um die Reduction der Beobachtungen, so darf die Tafel
* nur bis zu den Höhen nöthig seyn, in welchen die Sterne noch ruhig und
* deutlich erscheinen; die nächsten 5 Grade bei dem Horizonte könnten
* dann füglich ganz unbekannt bleiben."
* He shows that his observations above 85° Z.D. agree with Bradley's
* within a few tenths of a per cent, and that the remaining discrepancy
* may be ascribed to uncertainties in Bradley's thermometric scale. "Weit
* weniger vollständig waren aber Bradleys Beobachtungen in der Nähe
* des Horizonts, und wenn sie auch keine Zweifel darüber übrig liessen,
* dass Delambrés Tafel hier zu kleine Refractionen giebt, so war eine
* weit zahlreichere Reihe von Beobachtungen doch desto wünschenswerther,
* da die zufälligen Störungen der Refraction, welche aus uns unbekannten
* Unregelmässigkeiten der unteren Luftschichten entstehen, das mittlere
* Resultat w e n i g e r Beobachtungen, sehr stark entstellen können.
* Diese Lücke füllte, auf meine bitte, Herr Dr. Argelander aus, . . . "
* These are his remarks on cols. 382-383. The table of probable errors
* and number of observations just after the above passage was shortened and
* copied by Bomford (1971) in his Table 4.1 on p. 301. At the end of col.
* 383 and the top of col. 384, he looks for the cause of the increasing
* errors near the horizon:
* Then if the agreement between observed and calculated refractions is
* poor, "so müssen entweder die astronomischen Beobachtungen, [oder] die
* Ausnahme über die specifische Elasticität, welche der Rechnung zum
* Grunde gelegt worden ist, irrig seyn. Welches von beiden das sicherere
* ist, darüber kann, nach der vollständigen hiesigen Beobachtungsreihe,
* wohl kaum ein Zweifel seyn, zumahl da die in 4 verschiedenen Jahren
* wiederholten Thermometerbeobachtungen des Herrn Zumstein auf dem
* Mont-Rosa, äusserst abweichende Resultate liefern und dadurch beweisen,
* dass die Wärmeabnahme der Atmosphäre nicht weniger als gleichförmig
* ist; -- man kann noch hinzufügen, dass die directen Beobachtungen der
* Wärmeabnahme immer am Tage, die der Refractionen stets in der Nacht
* gemacht sind und dass die Erwärmung der Erdoberfläche durch den
* Sonnenschein, wahrscheinlich die Wärmeabnahme vergrössert hat. --
* Meines Erachtens müsste man die Wärmeabnahme gerade aus den
* Beobachtungen der Strahlenbrechungen folgern, wobei aber die
* Unbekanntschaft mit dem mathematischen Gesetze derselben, noch eine
* Schwierigkeit erzeugen würde; es scheint mir wahrscheinlich, dass am Tage
* beobachtete Refractionen eine grössere Wärmeabnahme geben werden, als
* Nacht-Beobachtungen.
* "Auch dieses wird durch Herrn Argelanders Observationen bestätigt:
* ausser den Fixsternen bei Nacht, beobachtete er auch den Untergang der
* Sonne, und dieser ergibt durchgängig kleinere Strahlenbrechungen als die
* oben angeführten, auf die Fixsterne gegrundeten . . . ." [col. 384]
* Perhaps this is the FIRST determination of atmospheric structure from
* refraction observations?
* Anyhow, Bessel's awareness of DIURNAL VARIATIONS is remarkable, as is
* his awareness that the variations near the horizon reside in the lower
* atmosphere.
* Note that the letter is dated Nov. 10, but was published by the end of
* the year!
* Thomas Henderson's measures at the Cape
* Several observations of refraction from 87°.4 to 89°.1
* Ignazio Calandrelli was director of the observatory at the Pontifical
* University at Rome.
* He is surprised to find fair agreement with the tables of Carlini.
* In one case, there is a discrepancy of 5''.27, but the rest are off by
* only 2 to 3 seconds.
* He refers to the debate between Biot and Faye in C.R.
* This item ends on an unusual note. After thanking Pope Pius IX and
* the University officials, he expresses gratitude to his uncle Giuseppe
* Calandrelli "who had the honor of founding the first observatory in
* the College of Rome in 1787, thus promoting with his untiring zeal the
* study of astronomy, a study that raises the human mind to that highest
* knowledge from which it is forced to conclude: THERE EXISTS A GOD."
* N.B.: the pages are not numbered.
* ANDREW LANG's first paper comments on RARITY of clear horizons
* ". . . I have sometimes every morning, for six weeks running, watched,
* disappointed, to get an observation on his rising, in consequence of
* dense low clouds of cumuli at the horizon. To this day [July 11, 1862]
* I have not obtained a single observation this year. So it is not so
* easy a matter as may be imagined."
* (The 17 observations run from 1831 to 1857.)
* He finds the dip from 440 ft. in St. Croix to be between 20' 52" and
* 21', so adopts 20' 56"; then finds a mean refraction + parallax near
* 32' 18.8" (range: 31' 48.8" to 33' 8.5") at the mean apparent horizon.
* Here he is "A. Lang, Esq." Issue dated Dec.12, 1862.
* ANDREW LANG's second paper repeats his complaint
* "I could have wished to have made many more, but long intervals will
* occur before you can obtain a sight of the Sun rising from the horizon
* of the sea, from beds of cirri prevailing at the horizon, rendering it
* impossible." The mean of the 18 new observations gives 32' 14".
* (These run from 1860 to 1863.) Again the temperatures are all near 77 F.
* Now he is "Sir Andrew Lang". But it turns out his knighthood came from
* the King of Denmark much earlier. (St. Croix was part of the Danish
* West Indies from 1733–1801, 1802–1807, and 1815–1917, and the British
* Leeward Islands in between.)
* Andrew Lang was one of the earliest Fellows of the Royal Astronomical
* Society, having joined it only 2 years after its foundation. He provided
* time service to ships in the Caribbean from his observatory in St. Croix.
* He was born in Largs, Scotland, 28 September 1779, emigrated to St. Croix
* in 1800, and died there 17 May, 1870, aged 90.
* Thanks to John Gilchrist Lang of Melbourne, Victoria, Australia for
* providing information about his accomplished great-great-grandfather!
* E.C.Pickering's measures of astronomical refraction near the horizon
* [Part I was terrestrial refraction.]
* "The fact noticed by Argelander, that the refraction derived from the
* setting sun is less than that of a star is well shown in this table.
* The difference amounts to one or two minutes of arc."
* Note his use of "elevation" for height.
* Thanks to ADS full-text search for turning this up!
* Weidefeld confuses the apparent and astronomical horizons, but has some
* useful SUNSET TIMING data.
* from AJB, 1904:
* George C. COMSTOCK's sunset work -- theory
* To check Bowditch's assertion that altitudes below 10° should be
* avoided, Comstock got "an excellent series of observations of the times
* of sunset made at Key West, Fla." from the Hydrographic Office, and used
* "mechanical quadratures to compute directly from the differential
* expression for the refraction" for a range of conditions, based on
* meteorological data. Out to 75° ZD, the computed refractions "differ
* from the tabular values by amounts that rarely exceed a few hundredths of
* a second of arc.
* "At the horizon, however, the conditions are widely different and,
* for a given temperature and pressure, variations amounting to several
* minutes of arc may easily result from plausible changes in the
* distribution of temperature at different levels in the atmosphere."
* He used 3 models for the lowest 2 km:
* a. an unstable surface layer
* b. an average model
* c. a surface-based inversion "over a snowclad earth".
*
* "With one exception", the Key West sunsets fall within this range.
* "This result confirms that the mean refraction of the setting sun is
* "less than the tabular refraction based upon observations of stars."
* Calculated refraction for an altitude of 4° show "that the large
* variation of the horizontal refractions within the range of conditions
* a - c has almost completely disappeared at 4° altitude. The range
* of values in the refraction due to varying conditions in the lower two
* kilometers of the atmosphere is reduced from nine minutes at the horizon
* to less than one second of arc at 4° altitude."
* This originally appeared in Pop.Astr. 27, 529-530(1919).
* Strand's AAS abstract -- cf. the Smiley-Clemence argument
* Observations made at Dearborn Observatory (Evanston, Illinois).
* The "error is somewhat larger for the first 2° of altitude."
* Alexander Thom's very superficial effort: 3 sunsets measured
* The data extend below the astronomical horizon. "At these very low
* altitudes the Sun's disk often appears very distorted, and the
* horizontal projections from the limb on each side give the impression
* that it is passing through layers of varying density." "The observation
* of the upper limb as it vanished into the sea horizon may well be in
* error, as the Sun was by that time very faint." (So, no GF.)
* The paper is more useful for Fletcher's comments at the end.
* MARCEL TSCHUDIN's analysis, with some NEW OBSERVATIONS
* A very substantial piece of work. He reviews all the earlier
* observations, and re-reduces the work of Argelander & Bessel, as well
* as his own and other un-analyzed data.
* The diurnal and seasonal cycles of boundary-layer structure are taken
* into account, as well as the temperature and pressure at the observer.
* The radiosonde data used in computing ray-traced refractions are
* corrected for the time-lag in the temperature sensors. The remaining
* unexplained variations are about half a minute of arc.
* The discussion on pp. 40-41 nicely accounts for the difference between
* the temperature dependences of refraction used by astronomers and by
* surveyors. It is mainly due to the increasing importance of boundary-
* layer structure as one approaches the horizon: astronomers avoid the
* horizon, but surveyors work close to it, where the effect of lapse rate
* (which varies strongly between day and night, as well) exceeds the
* effect of temperature at the observer.
* The general impression is that the variations in boundary-layer
* thermal structure with time of day and year are very important near the
* horizon. The development of the nocturnal inversion increases refraction
* at the horizon by about 5 minutes of arc from sunset to sunrise.
*
* Cf. Fletcher (1952); also Oppolzer in Valentiner (1901); Emden
* (1923); Kolchinskii (1967); Saastamoinen (1972); and Radau (1882,1889).
* Helmert (1884) gave a general treatment for terrestrial refraction.
* Also, cf. the observations of Delambre (1814) and Brinkley (1815),
* and the Argelander/Bessel measurements.
*
* FUSS (1871) seems the first to conside TILT as an explanation for large
* refraction at low altitudes.
* "Lu le 9 février 1871"
* GLAZENAP on refraction anomalies and TILT
* Glazenap's interest here is in correcting systematic errors in
* parallax determinations inferred from *absolute* positions (this was
* before photographic parallaxes). His approach was primarily to use
* meteorological observations made north and south of the Observatory to
* estimate meridional density gradients, and hence the effective tilt of
* the isopycnic surfaces. He also tried to confirm, or at least check,
* the results, by observing circumpolar stars at both upper and lower
* culminations. Because of his interest in annual periodicities, the
* data are mostly grouped into monthly means.
* I am pleased to see that he cited Biot's work in the historical
* preface. In the conclusions, he admits the measurements are very
* difficult to make, and suggests improvements for the future. His final
* suggestion is to determine the refraction from well-observed stars near
* the horizon, and distributed evenly along the prime vertical: "It
* seems to me that this method of determining refraction gives more exact
* results than that followed by Peters in his Pulkovo observations and
* that usually employed." (His assumption of gradients only in the N-S
* direction must be the reason for choosing the prime vertical.)
* This was his doctoral dissertation; he was interested in the effects of
* refraction in azimuth.
* The copy ILL got from Columbia University turns out to be
* the presentation copy from Glazenap to "Otto Vasileevich Struve",
* whose publications are frequently cited in this work. ("Vasily" was
* F.G.W. Struve's Russianized name, according to the DSB.) Unfortunately,
* part of the presentation inscription and the marginal notes were trimmed
* when this paper-backed pamphlet was bound. Worse, the whole thing is
* on acid-bleached paper and is now crumbling; it will soon be lost.
* CLEVELAND ABBE mentions his work at Pulkovo
* Although Abbe does give the correction for gravity (assuming the local
* surface pressure was measured with a mercury barometer), our interest
* here is in his closing remarks:
* "Such differences, so far as they are due to refraction,
* must however also be caused by the observed irregularities
* in geographical distribution of pressure and temperature
* which produce effects equivalent to slight inclinations of
* the horizontal planes of equal density.
* "These irregularities are revealed by the daily weather
* map: their importance was urged by myself when at Pul-
* kowa in 1866 and in fact led me in 1869 to establish the
* weather bulletin of the Cincinnati observatory in order to
* study them.
* "The effect of geographical irregularity in distribution
* of pressure and temperature may amount to one or two
* seconds of arc in the refraction at small zenith distances
* and the systematic annual changes in this distribution must
* introduce an annual variation in refraction similar to that
* produced by parallax.
* "This cause also introduces an oft-times appreciable
* difference in the refractions on the north and south sides
* of the zenith.
* "Thus the daily weather maps may become an im-
* portant auxilliary in refined Astronomical work."
* Dated Washington 1886 August 16.
* CHANDLER WOBBLE sub-file
*
*
* This is not a refraction phenomenon, but is mentioned here because it
* was large enough to mask the tilt effect at small ZDs.
* Chandler announced the effect in November, 1891. His first paper
* mentioned that Küstner's data agreed so well with his own that he became
* convinced of the reality of the effect.
* Chandler's second paper:
* Here he gives the details of the complementary and overlapping data
* from Berlin, and the additional confirmation by the Pulkova observations
* made by Gyldén, Nyrén, and others; and by observations made by Newcomb
* and other observaers at the Naval Observatory in Washington.
* These two papers were followed by Chandler's many discussions of
* latitude data from many other observatories; see the ADS list of them.
* Review of Chandler's work
* Here we have a modern review of Chandler's polar-motion work.
* Unfortunately, the authors and/or editors seem so ignorant of both
* astronomical and German conventions that I have little confidence in their
* account: they print the AJ issue numbers as if they were volume numbers,
* and mistakenly call the numbered columns of A.N. "Bands" --- which is
* not a word in German. ["Band" means "volume"; its plural is "Bände".]
* It should be borne in mind that the Astronomical Journal had been
* defunct for 25 years, and had only been revived in 1886, five years
* before its publication of Chandler's diccovery. (See Comstock's
* 1922 biography of Benjamin Apthorp Gould, jr.)
* This is Vol.208 of the ASP Conference Series; IAU Colloquium 178.
* An early account is in Mascart's "Traité d'Optique", pp.296 ff.
* This is a peculiar work. Vol. I is largely concerned with the
* dispute between the emission and the undulatory theories, and states
* that the measurements of the propagation speed in dense media show that
* the emission theory was wrong. Yet in Vol. 3, we find astronomical
* refraction presented entirely in terms of the emission theory.
* Vol. 3 makes no mention of either Chandler's work or the measurements
* he used; but, considering that the A.J. had been suspended for 25 years
* and had only been resurrected 5 years before Chandler's announcement,
* Mascart's ignorance of it is not very surprising.
* Stellar photometry is treated on pp. 251-270. He begins by taking the
* airmass proportional to sec Z, and then reproduces Bouguer's results.
* Laplace's extinction result is on p. 254; Forbes and Langley are cited.
* The stellar magnitude scales of various observers are discussed on
* pp.269-270, but with no mention of Pogson, though Pickering's work
* is repeatedly cited.
* Astronomical refraction is treated in Chapter XVII, p.272. Dip of the
* horizon appears on p. 279. Astronomical refraction begins on p. 283,
* and the angle 1° 24' 12" is on p. 284, followed by Cassini's uniform model.
* Then the tangent-series method is introduced, but without mentioning
* its defects. Simpson is introduced on p. 286, and Bradley on 287.
* Laplace and the reduced height are on p. 288.
* Then he shows that Laplace's fudgy temperature profile would leave a
* finite density at infinity. This can be avoided by modifying the
* function; but this makes the lapse rate too big. Also, the atmosphere
* has a finite extent that is smaller than the heights shown by noctilucent
* clouds and aurorae (p. 292). "The two hypotheses of a constant
* temperature or an adiabatic variation appear equally improbable."
* The airmass function is briefly discussed on p. 294, where §714 ends
* with the statement that "On peut donc admettre, pour le calcul de
* absorption dans le voisinage de l’horizon, que la masse d’air
* traversée est proporuonnelle à la réfraction et en raison inverse
* du sinus de la distance zénithale, ou du cosinus de la hauteur de
* l’astre."
* After comparing various standard refraction tables (p. 294), he
* points out their increasing divergence with Z.D. "The different Tables
* used in Astronomy are very concordant up to 60° or even 80° from the
* zenith, where simple formulae . . . are still applicable, but the
* differences are exaggerated for directions closer to the horizon. . . .
* One sees that, for the horizontal refraction, the difference of the
* extreme values is about 4' and exceeds a tenth of their mean."
* He quotes Delambre's verdict that it's hard to believe that even
* the most complex theories suffice for the last 8 degrees. "This
* uncertainty is not surprising and the real variations should be much
* larger than the differences among the tables, as the assumed symmetry
* is no doubt not realized, because of the changes of pressure at a
* given height, and the irregular distribution of temperatures in the
* vertical.
* "In reality, the refraction of stars near the horizon cannot be
* evaluated just by knowing the state of the atmosphere in the immediate
* vicinity of the station. Observations of this kind are often illusory
* if one tries to find them from any other means than the relative
* separations of neighboring stars."
* He then cites the observations of Spole and Bidberg at Torneo, who saw
* the Sun completely separated while its upper limb, apart from atmospheric
* refraction, was still a considerable distance above the horizon. The
* calculated refraction was 58', almost twice the value given by the tables.
* On p. 300 he considers deviations of the vertical. "Here is the place
* to ask if the unequal distributions of pressures and temperatures in the
* atmosphere does not modify in an appreciable way the direction of the
* vertical, and consequently the latitude of the station."
* He then considers that the surfaces of equal density are symmetrical
* with respect to some vertical plane, with an inclination α to the horizon.
* Considering known pressure variations, he finds that this angle could
* reach a milliradian, or about 3 minutes; then the refraction at the
* zenith would be about 0.06 arcsec.
* He then shows that the effect increases with zenith distance, and
* derives the secant-squared correction term. (P. 302) But, given the
* observational difficulties and the inconsistant date from different
* observatories, he concludes that "a definitive opinion on this delicate
* question would be premature."
* This discussion is followed by his treatment of mirages. He connects
* the inferior mirage with increased dip of the horizon. He cites Monge
* and Wollaston, and then Minasi, Arago and Biot, etc.
* The section titled "COMPLEMENT" on pp. 665- 685 contains various
* additions to and comments on the earlier volumes. It is followed by a
* Table of Contents on pp. 687-692.
* Mascart became the first director of the Bureau Central Météorologique
* in 1878, so he had been familiar with atmospheric structure and gradients
* for more than a decade before this was written. But his interest in the
* atmosphere was mainly in atmospheric electricity, not dynamics.
* This 714-page book is not easily available, except from Gallica.
* COURVOISIER I
* Cites Oppolzer in Valentiner, p.580. "Eine e i n d e u t i g e
* Definition sollte sich nur auf die Storungen der normalen Refraktion
* infolge abweichender Form und Lagerung der brechenden Schichten, nicht
* aber auch noch auf einen Temperaturfehler erstrecken, der dadurch
* entsteht, daß -- wie bisher gewöhnlich zur Berechnung der Refraktion
* statt der »inneren« Temperatur die »äußere« gewählt wird."
* He develops the approximate theory by assuming the refraction is
* normally (µ - 1) tan z', which is good enough out to 80° Z.D. The
* correction term is proportional to Δtg z', which he says is good out
* to 87°, even neglecting the curvature of the Earth. He compares these
* values with Oppolzer's B-R values from Nyrén's observations at Pulkovo
* (1885). Eq.(2) is the sec2 relation.
* The whole idea here is to explain the room refraction as an effect
* of inclined constant-density surfaces.
* COURVOISIER II
* The analysis is extended, using Grossmann's observations. However,
* there's a lot of arm-waving. . . .
* Kienle's note endorsing Courvoisier's remarks is in cols. 189-192.
* PAUL HARZER's long paper
* This is what Comstock (1929) was referring to. Sugawa cites this, as
* well as an addendum in Pub. 14, p.1, which turns out to be the actual
* correction tables needed for conditions at Kiel.
* Harzer (1857-1932) was a student of C. C. Bruhns. He was an Adjunkt
* Astronom at Pulkovo in 1885-1887, after spending a year studying with
* Gyldén.
* This work is the first attempt to allow for changes of vertical
* structure with geographic position. Unfortunately, so little was known
* about atmospheric structure in Harzer's day that he assumed the gases
* would separate diffuseively in the stratosphere, and that the "optical
* surfaces" (i.e., isopycnics) would be surfaces of rotation about the
* Earth's axis. So the numerical results -- which Harzer says took him
* over 6 years to compute by mechanical quadrature -- are useless today.
* It's difficult to know how to cite this. Citations between sections
* of the text simply say "Publikation XIII"; ADS leaves that part out
* entirely, citing it as a book, and naming the publisher (C. Schaidt).
* Google Books call it "Veröffentlichungen der Universitäts-Sternwarte,
* Kiel. Nr. 1-23" (which contains Nr. 13.) Each "Publikation" is
* separately paginated, with its title page being p. 1. Pub. XIII
* begins on page 329 of the Google/HathiTrust PDF.
*
* The bound volume scanned by Google begins with "Publication der Sternwarte
* in Kiel. X." (so, number 10, not 1), which is dated 1899. But section
* II on p.9 suggests why Google thought this began with Publication I.
* (Section III begins near the end of p. 13.) Section VII, "Der Einfluss
* der astronomischen Strahlenbrechung", begins on p. 32. Extensive tables
* for individual stars begin on p. 57; section XIV, "Nachtrag", is pp. 68
* to 74, which is a complete revision of the foregoing material, and a few
* Errata. "Publication XI" (1901), printed by a different publisher,
* begins on the next page.
* These early Publications (with a "c") are printed in single-column
* format. Apparently the printer did not have any large Greek Σ type,
* so summations are indicated by a big boldface S (see p. 33.)
* On PDF page 233, we have the title page of "Publikation XII" (1910),
* which is still 1-column format. However, the sections now have Arabic
* rather than Roman numerals.
* Paul Harzer is listed on all title pages as "Herausgeber", and as
* "Director" of the observatory in nimbers X and XI; but as "Direktor"
* from XII on.
* Thanks to Marcel Tschudin for bringing this to my attention!
* Schubart considers the possible effect of diurnal temperature changes
* in producing an east-west TILT; the maximal tilts found are 10 arcsec
* at 100m elevation, and still less (2 or 3 sec) higher up. So he finds
* the result "praktisch ebenfalls bedeutungslos".
* Cited by Sugawa (1960).
* Available from ADS.
* Melchior's 1957 review
* This review explains Talcott's method, the importance of the
* micrometer calibration, and the Kimura term, which must be understood
* to follow Sugawa's papers (below). For a more thorough discussion,
* see Wako (1970).
* The local Kimura term is discussed on p. 221, where the "wind effect"
* appears. Here we see mentioned the "inclination of the surfaces of
* equal pressure and temperature" and local refraction "in the building".
* Chandler's work is reviewed on p.223.
* Astronomer Chikara Sugawa's initial paper on tilt, done analytically.
* "It has been shown by several researchers that the wind effect might
* be the principal factor in the zterm. Moreover, it may be thought almost
* equivalent to the effect of the anomalous refraction due to the tilting
* of air-strata of equal density. Then the room refraction in question
* may be nothing but a special case of the anomalous refraction due to
* the tilting of air-strata of equal density in the close neighbourhood
* of the observing room." As separating tilt from other instrumental
* temperature effects is difficult, he just finds empirical corrections by
* using 4 thermometers.
* Note that the principal factor turned out to be a nutation error in
* the star catalogs instead. See Wako (1970) for details.
* On p.131, he says: "As the room refraction is nothing but a special
* case of the anomalous refraction due to the tilting of air-strata of
* equal density, its effect will be expressed as follows according to our
* previous theory:" and shows the secant-squared correction term, citing
* Courvoisier.
* Available from ADS.
* Chikara Sugawa's initial paper on numerical integration of refr.
* [This paper really belongs in the "variable refraction" file, but is
* placed here because of his tilt papers (below).]
* He stops the integration at the top of the radiosonde profile (20 km),
* but fails to add in the atmosphere above it; so the results are useless.
* However, Table 2 gives monthly mean lapse rates at midnight, and may be
* useful for further work. Unfortunately, the boundary layer is not
* resolved; only integer kilometers are given.
* Available from ADS.
* CHIKARA SUGAWA's first paper on TILT effects
* A fairly thorough theoretical analysis, with preliminary climatic data.
* The monthly mean tilts in the lower atmosphere are typically on the
* order of 2 arcmin. Cites Radau, Harzer, Wünschmann, etc. but not the
* references cited by Oppolzer/Valentiner, or Kolchinskii.
* This paper makes a pretty convincing, though circumstantial, case for
* the importance of the tilt effect. Cites Varnum's 1922 AJ paper.
* Sugawa (1916-2013) was vice-President of IAU Commission 19 (Rotation
* of the Earth) from 1970 to 1973,and President of the Commission from 1973
* to '76.
* Available from ADS.
* CHIKARA SUGAWA's second paper on TILT effects
* This begins with a review of data on the wind effect. Correlations
* with other possible causes do not support some ideas about the physical
* cause of the effect, and support the tilt effect: "The principal
* meteorological factors of the non-polar variation of latitude consist
* probably of the anomalous refraction due to the tilting of the air-strata
* of equal density in the free atmosphere and the room refraction."
* Available from ADS.
* CHIKARA SUGAWA's third paper on TILT effects
* More extensive radiosonde data confirm the earlier results: tilts
* in the lower atmosphere are only 1 or 2 arcmin, on the average.
* Here the case for the tilt effect is made stronger. The Abstract says:
* ". . . the anomalous refraction due to the tilting of the air-strata of
* equal density might be a main physical cause of the wind effect on the
* latitude observations."
* This paper sums up the tilt investigations, and repeats (with many
* typos) the earlier results. The Summary says:
* "From a series of our study on the meteorological effect on the
* latitude observations, we have come to the conclusion that the local Z
* term may be mainly attributed to the effect of the anomalous refraction
* due to the tilting of the air-strata of equal density in the free
* atmosphere and the effects of the room refraction in the neighbourhood
* of the observing room.
* "The effect of the anomalous refraction due to the tilting of the
* air-strata of equal density in the free atmosphere has clearly a seasonal
* character giving its maximum in winter and its minimum in summer. The
* wind effect in the lower atmosphere indicates also a similar seasonal
* variation. Therefore, the wind effect may be regarded as a convenient
* indicator of the anomalous refraction in the free atmosphere. After an
* error of the micrometer value has been carefully examined, the annual
* component of the local Z term may be mostly explained by the effect of
* the anomalous refraction or the wind effect. The six-and four-monthly
* components of the local Z term are likely to be chiefly caused by the
* effect of the room refraction."
* Note that the tilt effect is related to just the "local" part of the
* z-term; Wako (1970) showed that the main part was due to an error in
* the star catalog, which used an incorrect nutation constant.
* See Sugawa & Kikuchi's 1979 paper for a later view of tilts.
* Available from ADS.
* Kurt Bretterbauer's estimated tilts
* He considers both large-scale pressure and temperature gradients as
* possible causes, and finds maximal tilts of 5 to 10 arcmin for pressure
* gradients corresponding the Föhn conditions (p. 116). These would
* produce refraction anomalies up to 1/3 arcsec at 45° ZD.
* For temperature differences, the problem "ist viel komplexer",
* because only local temperature differences are important, else the
* horizontal gradient would be too small to have an effect (p. 118).
* He points out that the northern slopes of mountains are much colder than
* the southern, especially when covered with snow. But these are subject
* to large diurnal changes. He assumes 2° C in 3 km over an air column
* 1500m high [probably an overestimate], which would produce tilts of
* 12.6 arc minutes, corresponding to 0.21 arcsec at the zenith, or 0.42 sec
* at 45° ZD.
* Karl Ramsayer's estimates
* This seems to be a section of a larger document; the heading reads
* B. Errors and Sources of Errors
* The English is a little awkward here; he uses the strange phrase
* "water steam" (an obvious literal translation of Wasserdampf ).
* He adds a term representing atmospheric structure to the usual 2-term
* tangent series, and concludes that for z < 60°, the influence of
* structure above the observer is "extremely small" (but not zero, even
* though his terms are still only the linear and cubed terms in tan z).
* He correctly concludes that the influence is only due to the curvature.
* Then, considering the tilt of the layers, he naturally finds the effect
* is proportional to sec2 z. On p. 264, he says "the main cause of the
* inclination of the optical layers is the horizontal gradient of
* temperature in the vertical of the observation." Here the coefficient
* at sea level is 1.7° of tilt per (° C/km) of gradient. So "in
* the neighbourhood of the ground", the tilt "may be several degrees.
* But on the other hand [it] will rapidly decrease with altitude because
* in higher altitudes the atmosphere will be better balanced."
* He then appeals to observations by Bauschinger and by Courvoisier to
* discover the magnitude of the secant-squared term, whose coefficient turns
* out to be 0.035 arcsec for Bauschinger, and 0.032 arcsec for Courvoisier.
* As he has included a tangent term to allow for the errors in the assumed
* refraction constants, this is probably a reasonable procedure.
* Additional Potsdam data taken with the Danjon astrolabe confirm that
* "the mean influence of refraction anomalies is only +/- 0.06".
* Likewise, the Diplomarbeit of R. Henn showed only a very small
* increase in error with ZD: "The influence of the inclinations of the
* optical layers is very small. This is very surprising because the
* observation station is situated amidst an extended slope where large
* inclinations of the lower optical layers are to be expected."
* Only the usual astronomical part of the sky (ZD < 82°) is considered,
* so of course he finds that Bessel's refractions are good, despite the
* unrealistic model.
* ??? Maybe this is a preprint of Ramsayer's volume of "Handbuch der
* Vermessungskunde" (10th edition, 1970) -- which cites F. Wünschmann's
* "Über die Konstitution der Atmosphäre und die astronomische Inflexion
* in ihr". Gerlands Beiträge zur Geophysik, Band 31, S. 83-118 (1931),
* on p. 865. Wünschmann is also cited on p. 132, where the tilt effect is
* discussed. [Sugawa's 1984 article cites that as "Aerosphäre", which is
* also in the title of Friedrich Wünschmann's thesis, according to the
* Mathematics Genealogy Project.]
* YASUJIRO WAKO shows that the main part of the z-term was catalog error
* Here is the detailed report. Note that the local part, which Sugawa
* had shown was caused by the tilt effect, is barely mentioned here.
* "The close relation between Kimura's annual z-term and the theoretical
* semi-annual solar nutation term based on the hypothesis of a liquid core of
* the Earth is suggested." [first sentence of Abstract]
* Notice the important distinction between the annual and local parts
* of Kimura's mysterious z term. By averaging over suitable intervals,
* and particularly by using only the "chain method", Wako separates these
* two parts. The annual part is shown to be produced by the viscosity of
* the Earth's liquid outer core, which lengthens the period of the polar
* motion and increases the coefficient of the solar nutation term (see
* p.526). Taking monthly means removes the lunar nutation terms, and
* combining 12 years of observations averages out most of the 19-year
* lunar cycle as well. (p. 532) This allows him to deal with just the
* semi-annual solar terms. The monthly means of the Talcott group errors
* are strongly correlated with the declination errors in the GC.
* Figure 4 (p. 532) "clearly shows that z , Δδ, and (GC-MD) vary in a
* very remarkably similar way. Thus it may be reasonable to consider that
* the constant parts in z should be attributed to the catalog errors of
* the latitude stars used."
* He then discusses the chain method in detail, and shows that the
* analysis of the amplitudes and phases of the evening and morning group
* differences determine the period and phase of the annual z term. He
* then shows how to separate the variations of this term common to all
* ILS stations from the local errors.
* On pp. 540-541, the theoretical corrections to several nutation terms
* for several Earth-core models are compared to the star-catalog errors
* inferred from the ILS data, as well as nutation corrections derived
* from observations of Earth tides. These numbers (except for one crude
* Earth-core model) agree that "the semi-annual solar nutation term for
* the actual Earth is to be corrected by 0."02 for the value calculated by
* the theory of rigid Earth." (p. 541)
* "Consequently, Kimura's annual z-term may be explained by erroneous
* values in the semi-annual solar nutation term and OPPOLZER's (1882)
* terms which are considered to be due to the difference between the
* perfect rigid Earth model and the actual Earth with liquid core."
* The 9th section of the text deals briefly with the differences among
* the stations. The residual defined in eq. (40) on p. 542 "is
* customarily called . . . the local Kimura term or local z term ."
* And in section 10, Conclusions , he says: "In this paper, we are not
* concerned with the origins of the local errors, because it is difficult
* to separate the effects of various sources from the observational
* materials." (p. 543)
* Sugawa et al. 1976 (IAU Comm. 19)
* Section 3 of this Report, "Research in Instrumentation and Astronomical
* Refraction", begins on p.106. The "wind effect" is briefly mentioned.
* Section 6, "Research in Problems Concerning the Rotation of the Earth"
* begins on p. 108 with Part A, "Chandler Wobble". This phrase is used
* several times on this page, and appears again on p. 109, under Part C,
* "Other Periodic Terms in Time and Latitude Observations", and p. 110,
* under Part D, "Secular Motion of the Mean Pole and Related Problems".
* As the BIH part of the report was written by Guinot, and the ILS
* section by S.Yumi, the parts mentioned above must be due to Sugawa,
* although ADS attributes the report to C.Sugawa, B.Guinot, and S.Yumi.
* Vasilenko gets results more like Sugawa's
* Typical slopes are around 2' in the lowest kilometer, decreasing to
* about half a minute above 4 or 5 km. He concludes that seasonal and
* daily variations are significant, based on radiosonde data.
* An interesting but little-known IAU Symposium
*
* The introductory front pages set the scene, in welcoming addresses by
* the heads of the relevant groups within the IAU (Teleki) and the IAG
* (Tengström). On p. xx of this volume, we see Newcomb's "wellknown"
* [I would have said "infamous"] statement about the state of astronomical
* refraction. Tatarski gets mentioned on p. xxiv, and elsewhere.
* The next several entries are contributions to the Symposium by
* many different authors. Many of them are followed by interesting
* discussions that illuminate the thinking about refraction by astronomers,
* meteorologists, geodesists and surveyors, both observational and
* theoretical, in 1979.
* I have commented on and quoted from these papers (and their
* discussions!) below. There are remarkably few references to them
* in the subsequent literature. However, there were several brief
* reviews of the volume. Today, it's hard to believe how ignorant the
* experts in these fields were of one anothers' work; but this was a decade
* before the first search engines appeared. Even now, we are hindered by
* the diverse nomenclature and conventions of astronomy, geodesy, and
* the atmospheric sciences.
* Available at ADS (including the Front Matter); IAU has the Copyright.
* Cover page says:
* Edited by
* ERIK TENGSTRÖM
* Geodetic Institute, Uppsala University, Sweden
*
* and
*
* GEORGE TELEKI
* Astronomical Observatory, Beograd, Yugoslavia
*
* with the cooperation of
* I. OHLSSON
*
* [Ingegerd Ohlsson was Tengström's secretary, who arranged the events.]
* Teleki's introductory survey paper in Symp.89
*
* "Refraction, though a unique phenomenon, has hitherto been investigated
* piecemeal as astronomical, terrestrial, photogrammetric, radio or some
* other. A synthesis of these partial knowledges recommends itself as well
* as a continual cooperation of the experts in these fields. Astrometry
* would immensely benefit by such cooperation as more information would
* be acquired, in the first place that related to the surface air layers,
* which in other fields is considerable more widely investigated."
* Here we see the consternation of astronomers at the point where space
* astrometry was about to overtake ground-based measurements of star
* positions. Almost everyone failed to see the transformation of the
* field: refraction would continue to be an enormous problem for surveyors,
* but the accurate star catalogs allowed much of the doubt about sources of
* error, as a big one was about to be removed. This solved the
* astronomers' problem, and allowed the geodesists and geophysicists to
* obtain reliable measurements of polar motion and deflection of the
* vertical.
* The list of references is a good collection of Teleki's own papers.
* Wilhelm J. Altenhoff's brief summary of radio refraction
* TILTs estimated for urban heat island: James A. Hughes (USNO)
* Models tilts of isopycnic surfaces near ground level as large as half a
* degree. The "heat island" is simplified but reasonable enough to show
* that "we do indeed have a problem." The calculated effects near the
* zenith are a few hundredths of an arc second, and are six times larger
* at ZDs near 60° or 70°. it is "evident that . . . the lower levels (say
* z<250m) are the major contributors to the effect,"
* The lapse rate in the model boundary layer changes sign at heights
* of few hundred meters because there are "two 'competing' effects,
* conduction and a gravity wave. The latter is responsible for the
* negative temperature perturbation which leads to the tilt reversals.
* Very small changes in the perturbation profile lead to sensible changes
* in the tilt angles, and hence the integrated anomalous refraction."
* "It appears to the author thst it is absolutely necessary to devise
* some means of determining these pernicious systematic effects observa-
* tionally. . . . this effort should be expanded to determine systematic
* isopycnic tilts . . . ."
* The abstract says "It is stressed that heat islands are not the only
* source of such systematic effects." (No reference to Sugawa's work.)
* PDF available from ADS.
* Haruo Yasuda and Rikinosuke Fukaya review "ANOMALOUS REFRACTION"
* These authors were at the Tokyo Observatory in Mitaka. Their Abstract is:
* "There exists an empirical relation between the anomalous refraction
* and the atmospheric density in the surface layer. From the relations
* the variations of scale height for each night can be determined by the
* temperature and pressure in the surface layer. A correction term to
* the refraction table is derived in an analytical expression,"
* They describe the Talcott method, without naming him. Unfortunately
* they refer to the unreliable 4th Ed. of the Pulkovo Tables, and the FK4
* catalog, and find "the differences between the stationary atmosphere
* adopted in the Refraction Table and the dynamical atmosphere at Mitaka."
* The comparison shows an annual cycle: the measured T and p in the
* observing pavilion, implying that "the measured temperatures are too
* high in winter and too low in summer, It coincides with an annual term
* of the grounding inversion of temperature, 1.39°C sin ( T + 295° ),
* at the Tateno Aerological Observatory."
* Densities are in "gr/little" (sic) -- probably grams/liter ? The
* systematic differences are correlated with the radiosonde data at 1 km
* but not at 5 km height. [No surprise there!] They try to use the
* analytical refraction theory from Newcomb (whom they give as "Newcomb, E.")
* The only other reference is to a paper by Teleki; no mention of Sugawa.
* Not very impressive.
* Available at ADS. There is no page numbered 26 in their scans.
* Metrologist SERGIENKO discusses ANOMALOUS REFRACTION
* "The existing refraction theories for a one-dimensional model
* atmosphere do not account for anomalous refraction. The latter can be
* calculated using a three-dimensional model atmosphere," (Abstract)
* A formal series expansion is presented, using the horizontal gradients
* as small parameters. These are to be determined from radiosonde data.
* Teleki comments that the basic problem is how to get real information
* on the variations with height of inclinations of the equal density layers.
* J. Dommanget's paper has a long abstract in English
* The topic is reduction of astrometric plates: the differential
* distortion due to refraction is to be corrected by using refracted
* positions of the reference stars in finding the plate constants.
* ". . . we give expressions for the refracted tangential coordinates . . . ".
* Basically, he absorbs the differential refraction in the plate constants.
* This works to astrometric accuracy as long as the center of the field is
* less than 75° from the zenith.
* Numerical examples were run on an IBM 1620. In the Discussion, Teleki
* asked if anomalous refraction could be corrected; Dommanget replied that
* he had used the normal refraction formulae. "Anyway, usually no observation
* at very great zenith distance." So this is basically useless.
* IVANOV's paper on turbulence and image motion
* An early application of Tatarski's work; his 1967 Russian book is cited.
* Unfortunately people were still thinking about a single turbulent layer
* at this time. "Using the differences of temperature and wind speed at
* the two levels 1 and 4 m" he finds the Richardson number and the {C n}2
* value. From measurements of image motion with apertures from 3 to 48 cm,
* "D=20 cm should be considered as the optimum objective diameter of
* astrometric instruments." The best integration time is 100 seconds."
* The random errors depend on the time spent, but their size depends on
* "astroclimatic conditions. One should search for places with minimum
* amplitude of image motion."
* J.Saastamoinen's paper on refraction calculation
* This largely continues his 3 papers of 1972, and is useful in showing
* his thinking more clearly. He continues to use the divergent tan z series,
* but fudges it to allow extension to 90° ZD. Another series is used for
* the region near the horizon. "Further applications include . . .
* photogrammetric and parallactic refractions, as well as range corrections
* in satellite geodesy."
* He begins well, with the integral of tan z d (ln n) but quickly switches
* to the old tangent series, which he writes using a binomial series that
* converges only if (y2 - 1)*(sec2 z) < 1, where y = (nr)/(nr at the
* observer). But he never shows where this condition is met. (Later, he
* fudges the terms to make his series work.) After many pages of analytic
* gymnastics, the text ends with "to be continued" -- followed by several
* pages of Appendices. Auer and Standish were about to blow all this away.
* A misguided mathematical exercise, ignoring the physics. No mention of
* Biot or Bemporad, of course.
* S. Mikkola's exercise with continued fractions
* At least here we have an admission that the series is asymptotic, and
* can be used only to some limiting ZD. Still no evidence that anyone
* at the meeting knew of Biot or Bemporad.
* Mikkola's full paper appeared in A&A in 1981.
* Sugawa & Kikuchi's 1979 paper
* They begin by approximating the troposphere as an exponential,
* beneath an isothermal stratosphere. This model, with tilted layers,
* is used for numerical experiments. Monthly means of sounding data were
* used for the temperature profiles. The 2-term tangent series is used to
* calulate refraction. The tilt effect is treated in §5 (p. 113).
* As refraction is only calculated to 45° ZD, it's hardly surprising
* that the refraction at the surface depends weakly on the atmospheric
* pressure. This gives a small zenith refraction of 3 mas, "corresponding
* to the pressure difference of 7 mb in 10° of latitude (about 1,110 km)."
* Unsurprisingly, their simulations are well fitted by a sec2 z form.
* "It may be possible to correct an anomalous refraction with an accuracy
* of 0."1 . . . .".
* TERMINOLOGY:
* "We have usually called astronomical refraction with the tilting of
* airstrata of equal density as an anomalous refraction. However, it
* actually appears to occur every time and everywhere. Therefore, it
* would be more exact and convenient to call it as apparent refraction."
* Shigetsugu TAKAGI and Yukio GOTO see the TILT effect
* They use radiosonde data to calculate refraction. ". . . the results
* show lager refraction [than] Radau's and Pulkovo Refraction Tables."
* Maybe not surprising, as they approximate the data as an exponential
* model. "Moreover, our results shows that the refraction is not symmetric
* around the zenith. For instance, the difference between the refractions for
* north star and south star with zenith distance 20° amounts to 0".13 and
* shows slight seasonal variation with about 0".01 amplitude."
* They interpolated profiles from nearby radiosonde stations, using 3
* layers: a boundary layer (0 to 1.5 km); troposphere (1.5 to tropopause);
* and stratosphere -- each with a log-linear profile.
* PULKOVO photographic vertical circle results
* The instrument is a 20 cm Maksutov telescope. FK4 stars were observed
* out to ZD 82°.5, with M.S.E of 0.".16 at the zenith and 0".30 at Z = 50°.
* Comparison with Pulkovo tables (1956) for 5753 Å showed chromatic
* effects. "Leningrad is situated to the north of the Pulkovo Observatory,
* so the northern part of the sky is more affected by the city lights
* and the atmosphere is less transparent. This circumstance seems to be
* the cause of the asymmetry of our results." Atmospheric reddening was
* included in calculating expected effects; see Fig. 2. [Results are
* preliminary.]
* Hughes et al., DISCUSSION
* Not terribly useful.
* Douglas G. Currie: 2-color technique and ANOMALOUS REFRACTION
* This is a rough analysis of the quadrant photosensor and its expected
* performance. I was surprised to see no consideration of magnetic field
* effects. At least atmospheric reddening problems are mentioned in the
* discussion.
* This was a very preliminary state of the general idea. In practice,
* it was not very useful. One problem not mentioned here is the effect of
* turbulence: because different colors pass through different parts of the
* atmosphere, the image motions are different in different colors of light
* -- cf. the old discussions of chromatic scintillation.
* For a modern example of the 2-color method in a more mature form, see
*
* Pabitro Ray, David Salido Monzú, Robert Presl, Jemil Avers Butt and
* Andreas Wieser
* Refractivity corrected distance measurement using the intermode beats
* derived from a supercontinuum
* Optics Express, vol. 32: no. 7, pp. 12667-12681, Optica, 2024.
* DOI: 10.1364/oe.514997
*
* Allen Joel Anderson: radio refraction
* Microwave Doppler used to determine very small changes in path length
* to spacecraft showed rapid variations in tropospheric refraction.
* Wilhelm J. Altenhoff: more radio refraction
* A brief account of published work (3 references).
* Peter Vincent Angus-Leppan's EXCELLENT REVIEW paper
* Abstract: ". . . atmospheric models of the temperature gradient and, for
* microwaves, the humidity gradient, are needed to represent the very
* significant variations. The models should take into account variations
* due to meteorological factors, surface conditions and the height above the
* surface. Many models for the vertical gradients have been produced. That
* of Brocks (1948) is very important and has been widely used and developed
* by researchers. More recently Monin and Obukhov, basing their work on the
* physics of the lower atmosphere and dimensional analysis, have included
* equations for the vertical gradients in their turbulence theory. The
* Turbulent Transfer Model, which embodies later results in this theory,
* is currently being refined and developed for geodetic applications."
* "The model must take into account the large number of factors
* which affect the gradients. No progress will come from trying to
* find the static, universal model, for example the best average value
* of the temperature gradient or the best value of the coefficient of
* refraction. The atmospheric model must be multi-factored to take into
* account the variations in the atmosphere, which are very large and
* real. For example, long term temperature measurements (BEST et al., 1952;
* FLOWER, 1937) show the average error due to observing temperature at 1.5
* m instead at the height of the line, say 50 m above the surface. In the
* month of April (spring) the error, in parts per million (ppm) varies from
* -3 in the day to +5 at night, at Rye, in Southern England. At Ismailia,
* Egypt, the average daily variation is -6 to +6 ppm. In mid-summer the
* errors are similar, but in winter they are quite different, with lower
* averages, but a far larger variation from day to day (ANGUS-LEPPAN, 1967).
* "The variations in k, the coefficient of refraction, are even more
* remarkable. Table I shows values at heights of 1.5, 7.5 and 75 m for
* the same month, April."
* There is a very clear explanation of the terminology and formulae used
* by optical surveyors and by those who use EDM (radio stadimetry).
* He uses the acronym TTM for the Monin-Obukhov model. It did not seem
* to have gained much traction in 1979, and still is not widely used.
* See pp. 172-173 for its discussion.
* This is a very sensible and useful review. It is followed by a
* very informative DISCUSSION section at p. 176. The treatment of lateral
* (i.e., azimuthal) variations in refraction near slopes and shores is
* particularly interesting. Note that Angus-Leppan says: "I do not
* recommend Brock's model any more. It was good at the time, but the
* turbulent transfer model is much better. [My own experience with it
* in studying inferior mirages agrees well with his recommendation.]
* Geodesists M.K. Szacherska and Z. Wiśniewski study error propagation
* They treat systematic errors as additional parameters to solve for in
* data reduction. But they treat the different errors as Gaussian and
* independent. This model has been used in reducing real survey data in
* Poland, and included refraction and deflection of the vertical. They
* assume systematic errors were linear in temperature and "circular" in
* time [of day?].
* Czech geodesist Ludvík Hradilek compares two ways to treat refraction
* He points out that the best method depends on the distribution of the
* points in the network, in both the vertical and horizontal directions.
* Cites the followeing paper as an example.
* Radim Blažek and Ludvík Hradilek show how to do it: by adding vertical
* angles and long (4 km) separations between stations to a levelling survey.
* "To obtain more information about refraction, trigonometric leveling
* traverses were designed as double traverses, i.e. two vertical angles
* were observed both foresight and backsight at most of the stations.
* . . . .Additional observations for vertical angles made it possible to
* calculate one coefficient of refraction for each station."
* Karl Ramsayer shows an experimental example.
* H. Kahmen splits refraction into daily and annual sine-waves
* "The central moments of these two components are used to estimate
* the covariance matrix of time series of refraction coefficients.
* Different functional and stochastic models are tested in connexion with
* time averaging of refraction coefficients."
* Not much connection with the real world; it's all based on simulations
* that use average conditions.
* Fritz K. Brunner uses MOST, citing Lawrence & Strohbehn (1970)
* Unfortunately, he uses the old Barrell & Sears refractivity formula.
* He also uses a constant value (9.8 K/km) for the adiabatic lapse rate.
* This is purely a theoretical study; no experimental data are offered.
* An Appendix derives the theory, and refers to Dyer's (1974) values
* for the function constants. Big N is used for the (scaled) refractivity
* of air, again referring to Barrel [sic] & Sears.
* D. C. Williams describes some test data
* ". . . in late May 1978, the effects of turbulence were particularly
* small. The refraction-corrected theodolite readings then agreed with the
* expected value to within one sexagesimal second. Other results obtained
* during the preceding two months indicate that increasing turbulence
* causes the dispersion angle to appear too large, the greatest error
* observed being about 3 seconds of refraction."
* "The performance of the instrument has also been evaluated on a 20
* km range near Uppsala during the present Symposium, by kind invitation
* of Prof. E. Tengstrdm. The principal difference from the 4 km range was
* that the intensity scintillations of the red and blue signals were no
* longer correlated when the refraction was large."
* Swedish geodesist S-G. Mårtensson
* "IDM measurements carried out in Uppsala sometimes show violent changes
* in refraction over short periods of time."
* ". . . it seems as if the refraction contains of two . . . essential
* spectral parts."
* "The high frequency spectrum is caused by the atmospheric turbulence and
* the low frequency spectrum corresponds to the refraction obtained, for
* instance by vertical angle measurements (or atmospheric models)."
* "This is, of course, nothing new. It is a wellknown phenomenon and has
* been mentioned in the literature by several authors, among others by
* G. Dietze (Dietze, G.: 1957) . . . ".
* "The new and interesting thing is that parts of the high frequency
* spectrum have been detected by IDM measurements in Uppsala, and the
* contents of this paper deal with certain properties of that spectrum."
* Refraction data are shown, measured in "cc", the abbreviation for
* "centesimal seconds". The new "high-freq." fluctuations are probably
* due to laser speckle.
* J. Milewski discusses Tengström's instrument, and possible improvements
* In the Discussion, there is much interesting info in Tengström's
* remarks about water vapor on pp. 264-265.
* R. Pazus describes the Polish survey in Iraq
* "During initial observations many interesting remarks about the
* refraction effects were made. In the evening receding of the horizontal
* line was being observed and objects on the horizon had shapes unnaturally
* elongated. This phenomenon occurs during the whole night and early in
* the morning later on the profile of objects diminishes and they conceal
* under the horizon. It happened that light of desert settlements situated
* at a distance of over 100 km was being observed at night.
* "A phenomenon of "picture division" is also interesting; the point
* is that during a very short time in the morning and in the evening,
* a picture being at a distance of several kilometers is seen double.
* At the beginning, in the evening a target picture elongates; later
* on it divides into two and, for example the target is seen distinctly
* at a higher level, and in less sharp outline, at a lower level. After
* several minutes this phenomenon disappears. However, very often during
* the day-time two horizon lines separated by a layer giving the optical
* illusion of water surface is being observed."
* The figures show the diurnal changes in refraction quite vividly.
* The large refraction at night was used to link widely separated
* stations. [cf. the Survey of India, where the same trick was used.]
* Geodesists Juhani Kakkuri and Ossi Ojanen calculate PARALLACTIC REFRACTION
* They use Oterma's (1960) tables and secant formula, which are useful
* only to 85° ZD.
* "The analyses show that parallactic refraction can be calculated using
* Oterma's theory with an accuracy of about ± 2 sec of arc for zenith
* distances from 70° to 75°, The accuracy of this order is also obtained
* for zenith distances from 75° to 80°, but from 80° to 85° the segment
* seems to become greater and correlated to the zenith distance, which
* may be an indication of unsatisfactory modelling of the atmosphere."
* [Most likely, the increasing errors and their sizes suggest that the
* neglected TILT EFFECT is the cause.]
* Chairman T.J. Kukkamäki, et al. discuss PARALLACTIC REFRACTION
* The discussion was introduced by Saastamoinen, who complained that
* "there is no model atmosphere that can be used for calculating it." His
* reason is that the part of the atmosphere above the balloon or light
* source is excluded, so one should know the refraction above the object.
* [I think this is not a big problem, as the missing part is usually small.]
* He also points out the neglect of tilt: "There is also the effect of
* uncompensated isopycnic tilts."
* Garfinkel disagreed: "If the model is good for infinity, it should be
* good for a distance which is less than that."
* Teleki supported Saastamoinen, but then said that Kakkuri's discrepancy
* "is a result of the tilting of the realistic atmosphere."
* Garfinkel then pointed out that Saastamoinen's "compensation" only
* applies to small ZDs, not near the horizon.
* [All these people seem to miss the point that the structure near the
* observed object is basically irrelevant.]
* I. Brook (chairman),D.G. Currie, A.H. Dodson, K. Poder
* Brook: "Very few instruments seem to advance beyond the prototype stage
* and I think it is a question of nonprogress in many ways."
* Currie and others then discussed the economic problem: very accurate
* instruments are very expensive. Why are such high accuracies needed?
* Several people mentioned the measurement of crustal movement as an
* important problem: relative motions are about 5 mm per year. Some kind
* of 2-color instrument seemed promising (this was 1979).
* Poder pointed out that "when you have a long range you get a
* separation between the red and the blue, which means what you are
* aiming at you do not really get, because the two waves will propagate
* in different atmospheric layers." To avoid this, he favored joining many
* short sections together to make a long line. But then Kukkamäki said:
* "How can we project these individual sections to the chord? We need
* very accurate break angles, which are hard to obtain."
* Later, Poder returned to this point, saying "The projection effect
* is such that for a typical line you will lose a maximum of about 10% of
* the accuracy on the projection. Normally, the loss will be only a few
* percent."
* Then the issue of absolute calibration came up.
* Brook: "How shall we calibrate these instruments? If we shall come
* down to 0.1 mm, we must have standards which are a power of ten better
* than the actual instrument."
* Dodson, speaking of his Mekometer experience, said: ". . . to get a
* calibration better than 0.5 ppm is certainly not easy."
* The Discussion is summarized on p. 292.
* T.J.Kukkamäki on levelling
* He initially found that image jitter was worst in mid-summer, so he
* proposed that levelling work must be interrupted fir 6 weeks from mid-
* summer to August.
* Then he found that the rod image was bad at noon, but got better later
* in the day. "Even when the sun was below the horizon this image seemed
* to be clear and unmovable. So I proposed that we should construct fitting
* instrumentation for observations in dark period, 1.e. some devices for
* lighting the rod scale and the levelling instrument itself. Before
* starting the practical measures in that direction, we made a lot of
* research into the microclimatic and also optical conditions in the
* first three meters of atmosphere above the ground, and I think, we got
* rather clear picture of the conditions there. As these details seem to
* be unclear to many scientists, even to those who have published about the
* levelling refraction, I should like tell something about our experience
* on the matter." [This was a nice way of saying that some people don't
* know what they are talking about.]
* He then outlines the diurnal cycle, and the fact that it's greater
* when the sky is clear. He also describes the slow motion of the sharp
* images under the nocturnal inversion. "The amplitude of the swaying . . .
* was with a temperature gradient of +0°.2/1m in average 1 mm for 75 m sight
* length."
* "So this result showed that the levelling in night, when the vertical
* gradient always is positive, is not possible with an accuracy requested
* for precise levelling."
* "Normal sight length in precise levelling is 40, 50 or 60 m. I cannot
* understand that e.g. in USA even 150 m sight length was accepted still
* in the instructions of 1929. When vibration makes observing difficult
* the sight length is to be shortened. When even 30 m is not short enough
* the observation is to be interrupted. I think that this understanding
* about the vibration is accepted generally."
* "Naturally the gradient is greater nearer to the ground. So the
* horizontal sight in levelling bends more in uphill sight where it comes
* nearer to the ground than in the downhill sight." Then he discusses the
* various (mostly wrong) formulae used for the temperature profile. To
* illustrate the general ignorance of refraction, he says:
* "Further we have noticed that in some cases rather strange apprehensions
* came in view. For instance one serious scientist said in discussion
* with me 40 years ago, that light is bending in morning upwards as the
* temperature is rising and in afternoon it is bending downwards as the
* temperature is going down. In an article of Bulletin godsique 20 years
* ago it is said that soon after the noon when the turbulent mixing reaches
* its maximum the temperature gradient is zero and no bending of light
* beam appears." So they decided to make their own temperature measurements.
* "At first we observed with thermocouple the temperature at 1/3, 1 and
* 3 meter, but we found soon that the second derivative of the temperature
* is not possible to determine from single set of temperature readings. One
* needs long recordings. Since that we have observed only one temperature
* difference between 0.5 and 2.5 meter." They adopted a weak
* negative-power (-0.1) law for the temperature, which roughly resembles
* the logarithmic term in MOST. [This was in the 1930s, long before M&O.]
* The figure shows the mean diurnal changes in refraction.
* Danish geodesist O. Remmer solves for a single refraction parameter in the
* least-squares adjustment, citing only his 1977 paper. His 1-page note
* is followed by 2 pages of Discussion, in which the Danes and the Finns
* took different points of view:
* Saastamoinen: "Maybe the Danish pessimism somehow depends upon the
* topography of Denmark. What is the height of the highest mountain in
* Denmark?"
* Remmer: "I am not going to speak about high mountains in flat Denmark.
* Our experiences are based on 20 m height differences."
* NOAA geodesist Sandford R. Holdahl
* "Refraction error is often regarded as the most serious problem with
* geodetic leveling. Its accumulation depends on the slope of the terrain
* being leveled, length of sight, and the vertical temperature gradient.
* Refraction error can be minimized by limiting and balancing sight lengths,
* and by not reading the portion of the level rod which is within 0.5 meter
* of the ground where air density changes most rapidly. The remaining
* refraction error should be removed by application of a correction to
* leveling data, otherwise heights and crustal motion may be determined so
* weakly that meaningful conclusions or interpretations cannot be inferred
* from the data by geophysicists."
* After noting that refraction corrections to levelling originated in
* Finland, he says:
* "Most countries have been reluctant to utilize the refraction correction.
* This is probably due to several factors: (1) extra instrumentation
* and computational effort are required, (2) disbelief in the idea
* that temperature in the lowest 3 meters can be represented by a single
* temperature function, and (3) belief that refraction error is small.
* The full effect of leveling refraction is normally not seen in misclosures
* between forward and backward levelings because it is usually common to
* both in approximately the same amount. Similarly, circuit misclosures
* do not reveal the total refraction error, consequently it is sometimes
* underestimated."
* He ran an experiment in California to check this, in December "when
* temperature gradients should be smallest. Observed vertical temperature
* differences averaged 4-10 times as large as those predicted by a table
* developed by A. C. Best (Best 1937)." (These were the data used by
* Remmer, in the previous paper.) "The high Δt values observed in
* California are alarming because they indicate, provided the existing
* refraction correction is valid, that refraction error in California and
* probably the remainder of the United States is much greater than was
* assumed previously.
* "A further objective of the experiment was to see whether vertical
* temperature gradients were larger on south slopes (i.e. slopes facing
* down to the south) than on north slopes (i.e. slopes facing down to the
* north). Simultaneous observations on north and south slopes revealed
* that south slopes gave vertical temperature differences, between
* heights of 50 cm and 250 cm, that averaged .89° C higher than north
* slopes. This result is disconcerting because it means that refraction
* error accumulated while leveling up the south slope of a topographical
* feature will generally not be canceled adequately by refraction error
* of the opposite sign accumulated while leveling down the north side.
* In mid-latitudes, refraction error will systematically accumulate in
* the north-south direction as each topographical feature is traversed
* by leveling." He later gives formulae to correct for this; they allow
* for heat conduction into the ground. "The described method is regarded
* as tentative. . . ".
* Swedish photogrammetrist J.Larsson
* He first explains photogrammetry, and then summarizes the (rather
* crude) methods used to correct for reraction.
* The Discussion is started by Saastamoinen, who seems well acquainted
* with photogrammetry. An interesting point is that if the camera in
* looking through a plane window in a pressurized airframe, the refraction
* at the window can cancel the atmospheric refraction seen from a height
* near 6 km.
* Dutch geodesist J. C. de Munck briefly reviews the various methods.
* Chairman: E. Tengström
* He asked if anything had been done to eliminate refraction "before
* Dr. Currie . . . . Or is this the first time the two-colour principle has
* been applied in astrometry?" Teleki said no; but Tengström mentioned
* Hertzsprung's 1912 paper. He added: ". . . it was the first time an
* astronomer tried to determine the actual atmospheric dispersion,"
* [This is absolutely not true! The green flash literature is full of
* previous qualitative (e.g., Delisle, Bouguer, Dollond, Minasi, Lee)
* and quantitative (W. Herschel, Biot & Arago, Rambaut, etc.) work.]
* After a brief digression into whether or not the refraction is really
* proportional to the refractivity, in which Garfinkel pointed out the
* reality of "higher order terms", and Currie dismissed them as
* unimportant, the discussion shifted to the dispersion of the atmosphere.
* Here Milewski said "The region 2000 Å to 7000 Å is without great
* resonance influences with the atomic and molecular structure of the
* atmosphere." He was evidently talking about the effects of absorptions
* on the dispersion of air -- which today we know is a significant effect
* -- let alone the ozone absorptions in this region! [Milewski said "down
* to about 2000 Å which is a very deep UV." and Currie agreed with this!
* Tengström then asserted that the 2-color method could be used to settle
* the tilt problem by observing refraction in the zenith, "or looking at
* star spectra with high resolution near the zenith," which again is
* nonsense. He then goes wrong the other way, saying that the tilt
* "would perhaps be possible to study also using greater zenith distances,
* though that is not yet proved."
* Thankfully, Ramsayer then pointed out that the tilt effects are
* "proportional to the square of the secant of the zenith distance and
* that they get smaller the more you come to the zenith."
* Dommanget said that "Astronomers are not really interested in the
* atmospheric refraction itself but only in the way of how to get rid
* of it." That, at least, is true.
* Swedish meteorologist G.H. Liljequist
* This is a rather superficial account of refraction phenomena, mostly
* mirages and looming. "In the winter, with strong cooling of the earth's
* surface, so-called surface inversions are common . . . in fine-weather
* situations, especially when the ground is snow-covered."
* "They are also found in late spring and early summer over the sea, i.e.
* at a time when the air is heated over the land, but the sea is still cold.
* "In summer - or in the warm zone - the heating of the ground in daytime
* gives rise to an abnormally strong temperature decrease with height in
* the layers close to the surface."
* The superior mirage is described (but not named): "The image of a
* dark object situated at a critical distance is seen like a vertical
* dark pillar. The "points" constituting the ground - or snow surface -
* are then drawn out vertically to present an image of the surface similar
* to a gigantic wall surrounding the observer at a distance of 1/2-5 km
* or more . . . . Objects at greater distance may disappear from view."
* Bad "seeing" is described as "scintillation". The Novaya Zemlya
* phenomenon is described. "Over an ice-covered sea a marked inversion
* can develop in the low layer and this inversion is not affected by any
* underlying topography - the surface is more or less flat."
* With only 3 references, this is a pretty slim effort. I was surprised
* at the responses to it in the following session (below).
* Chairman: G. Teleki
* Teleki: "After professor Liljequist's lecture I am more pessimistic
* than before. . . . Professor Liljequist's contribution today has
* emphasized the difficulties in treating the refractional problem without
* careful meteorological information."
* Garfinkel asked for observational tests of his model: ". . . the
* polytropic index . . . is not a constant, but it varies with the season
* of the year and possible also with the geographical location." He
* offered to provide his program on IBM cards, along with "corrected
* reprints of the paper, with removal of all misprints found so far."
* F.K. Brunner
* Brunner is plainly not a physicist. The distinction between phase and
* group velocity is involved here.
* The useful information here is that Angus-Leppan reported that his
* "TTM" model (basically MOST) cut the EDM errors in half, compared to the
* conventional method of reduction. (Of course, that has nothing to do
* with the "precursor" stuff.) ". . . we used the model for trigonometrical
* heighting ing over a fairly short line, but one which was grazing all
* the way, so it was a difficult case. The coefficient of refraction, which
* has a standard value of 0.13, varied by several units! But the prediction
* of that coefficient of refraction by our model was down to about 0.1 unit.
* So that it was able to model a very big variation rather accurately.
* What really impressed us, was the fact that the model was able to take
* into account some rapid changes, when shadow came over the line, and
* the agreement between the observed angles and the predicted ones was
* very good, even with the sudden changes."
* There are many more pages of discussion, mainly to do with the 2-color
* method and atmospheric dispersion. Mårtensson described night-time
* measurements in which "we have never been in the neighbourhood of
* what we call normal refraction. It seems more like we are measuring in
* periods where we have two times or even three times the normal refraction.
* With normal refraction I mean a k-value of 0.13 or 0.14. We have never
* been in that region." (p. 367) ". . . most of the times we had two to
* three times the normal refraction, and even just one week ago we had a
* k-factor equal to 1.04 at 2 o'clock in the night. For practical reasons
* we only measure during night-time, and our extreme results might be
* explained by our existing inversion layers."
* In the discussion of systematic errors, Kukkam&ki said: "When measuring
* our 900 km traverse with 25 legs, 30 km long, with geodimeter, we have
* found that there is some slight systematical difference between the
* observations before noon and after noon. And we have not been able to
* find out the reason for that. So, it means there are some systematical
* errors in these reduction formulas and reduction observations which we
* have used to reduce our observations to one and the same consistent
* system." (p. 368) [Probably the failure to use MOST was the cause.]
* TILT estimated: 36" on La Palma
* (cf. Fletcher, 1952)
* ". . . the layers are on average tilted towards north, i.e. making the
* angle betweenn [sic] the layers and the terrain surface at the La Palma
* site slightly smaller than if the layers were horizontal."
* [That is, the isopycnic surfaces tend to follow the terrain.]
* ". . . and a variation from night to night also of 36" rms . . . ."
* TILT measured: 1.3 arcmin
* The measurement is in an earlier paper by A.I.N. This one estimates
* tilts from meteorological data, and generally finds them less than a
* minute of arc [as we would expect from Fletcher (1952).]
* [translation of A.Zh.65,1322-1324(1988)]
* Summary of work at the Engelhardt Observatory
* Typical tilt is about 1 arcmin; refraction error can reach 0.1 arcsec
* at 70° Z.D., and more than 0.3" at 80°. Mean meteorological conditions
* are used in the models.
* The models used include the reversal of tilts in the lower stratosphere
* (above the isopycnic level), but even so the overall effect is dominated
* by the local lapse rate at the bottom. The model calculations extended
* only to 80° Z.D., so it is no surprise that the tilt corrections are well
* represented by a sec2 Z term.
* There is a good list of A.I.Nefedyeva's Russian papers -- mostly from
* Izvestya EAO. (No mention of Sugawa's very similar work decades earlier.)
* HIRT sub-file: GEODESY and deflection of the VERTICAL with TILTED LAYERS.
*
* Refraction anomalies measured with digital zenith camera
* Refraction at the zenith varies from 0.05 to 0.2 arcsec at periods of
* hours; slower systematic effects reach 0.04 arcsec. "The accuracy
* of the filtered data has been found to be about 0."05 to 0."08."
* The errors are "obviously not" due to errors in the star catalog.
* Cites mainly recent literature, starting with Sugawa's papers above.
* Also cites Ramsayer's work.
* DIURNAL cycle
*Christian Hirt,Sébastien Guillaume,Annemarie Wisbar,Beat Bürki,Harald Sternberg
* These geodesists measure the refraction coefficient (in the surveyors'
* sense); but give no meteorological info (no winds, even!) So we just
* get refraction measured over grassland.
* This seems to be just a feasibility study.
* doi:10.1029/2010JD014067
* Further work on deflection of the vertical with automated zenith cameras
* by: Derek van Westrum, Kevin Ahlgren, Christian Hirt, Sebastien Guillaume
* Here multiple instruments were used to get an accuracy of 0.04 arcsec
* in the direction of the vertical at 222 field stations along a 360 km
* line in the mountains of Colorado.
* doi: https://doi.org/10.1007/s00190-020-01463-8
*
* Let's start with several mentions of refraction in antiquity.
* Besides the reference to straight objects appearing bent when put in
* water in Plato's "Republic", there's the ``CATOPTRICS'' attributed to
* Euclid. Refraction is briefly mentioned in the last of the introductory
* propositions, perhaps best translated by A. Mark Smith in Trans. Am.
* Phil. Soc. 89, no.3, p. 127 (1999):
* "if some object is placed in a vessel at such a distance [from the
* viewpoint] that it can no longer be seen, and if water is poured in,
* then the object placed in the vessel will be seen."
* (Whether the author was really the EUCLID of geometry has been hotly
* debated; Smith briefly reviews the fight on p. 17 of his monograph.)
* This is the re-discussion of Smith's earlier work on Ptolemy (see
* below)
*
* In any case, that table-top demonstration of REFRACTION certainly
* has been known since antiquity. It is repeated by CLEOMEDES --
* about whom, nothing is known; authorities have claimed dates from the 1st
* Century B.C. to the 3rd A.D. His popular work on astronomy (a) tries to
* explain the Moon Illusion with refraction (!) [as does Ptolemy in the
* Almagest], and (b) seems to have the first suggestion that atmospheric
* refraction near the horizon might affect the Sun below the horizon:
* ". . . so that the Sun, when it has set and is below the horizon,
* presents its face to us as if it had not yet set . . . .
* For many such things appear in the air, and especially around the Sea.
* For it could happen that the ray leaving our eyes is bent on entering
* wet and humid air and reaches the Sun now hidden below the horizon.
* For besides, something similar is observed to happen among us. For if
* a gold ring is put into a cup or some similar vessel, if the vessel is
* empty, from a suitable distance the object lying on the bottom is not
* seen, to which vision would go in a straight path without the obstacle
* of the edge of the vessel. However, if it is filled to the brim with
* water, the ring in the vessel is seen from that same distance, while
* vision does not pass through the edge, but on striking the water at the
* edge of the filled vessel, vision is bent so that it descends into the
* vessel and falls on the ring. Now it could be that something similar
* happens in humid and watery air, so that the ray from the eye is bent
* below the horizon and slopes to meet the Sun when it has set, so that
* it appears to be above the horizon." [My rough re-translation of
* Ziegler's Latin translation on p. 225.]
* Evidently, Cleomedes thinks water is the essential element here.
* This appears in Book II of the "Circular Theory of the Heavens",
* Chapter 6, 124-125.
* Unfortunately, on pp. 121ff. he tries to explain the Moon Illusion the
* same way; speaking of the Sun, he says, "For it appears larger rising and
* setting, smaller in the middle of the sky. . . ." -- and then again tries
* to arm-wave his way to an explanation with "rather thick and humid air
* (for such is the air closest to the earth)," where the visual ray "is
* necessarily bent" [refracted]. And here again he says, "and besides,
* things which are under water appear differently shaped to us".
* [All from Book II, Ch. 1, 66.]
* See also the entry for Cleomedes in the DSB.
* A. MARK SMITH translates PTOLEMY's "Optics" (c. 170 A.D.)
* This is an English translation of the bad Latin translation made
* by a 12th-Century Byzantine functionary in Norman Sicily from the
* Arabic translation from the original Greek; so all bets are off.
* Still, the publication of a fudged -- or would you prefer "smoothed"?
* table showing the relation between angles of incidence and refraction
* for water/air and glass/air (in which the second differences are
* constant, so that the original data were forced to fit a simple parabola)
* seems to show Ptolemy's touch. So the attribution to Ptolemy is
* probably correct.
* On pp. 230-231, we have the classic demonstration -- perhaps the
* first time a coin is used: ". . . a coin that is placed in a vessel . . . .
* if the eye remains fixed so that the visual ray passing over the lip of
* the vessel passes above the coin, and if water is then poured slowly
* into the vessel until the ray that passes over the edge of the vessel
* is refracted toward the interior to fall on the coin, then objects that
* were invisible before are seen . . . ." The wording is so similar to that
* in Cleomedes that one must suppose one writer was (at best) merely
* paraphrasing the other -- especially after allowing for all the
* translations involved. But which really came first?
* Remarkably -- considering the complete ignorance of atmospheric
* refraction displayed in the Almagest -- there is a sensible discussion
* of astronomical refraction, apparently based on observation (pp. 238-239):
* "Furthermore, it is possible for us to realize that, at the surface
* between air and ether, there is a refraction of the visual ray according
* to the difference in density between these two media.
* "We notice that bodies that rise and set tend to incline toward the
* north when they are near the horizon and are measured by an instrument
* for measuring the stars. . . . and the more they approach the horizon,
* the more they are inclined to the north. . . . This is a result of the
* refraction of the visual flux at the surface that separates the air
* and the ether, a surface that must be spherical, its center being the
* common center of all the elements, which is the center of the earth."
* (cf. fig., p. 240)
* As the description is couched in terms of the diurnal circles,
* it appears that the instrument Ptolemy had in mind was the armillary,
* and not (as Smith supposes), an astrolabe.
* From the subsequent discussion, it's clear that Ptolemy supposed the
* effect to be inappreciable except close to the horizon; between the Pole
* and the zenith, "there is no difference, or only an imperceptible one,
* between apparent and true location." (p. 241)
* Also, in true Ptolemaic style, he does not consider determining
* refraction observationally, but thinks only of computing it "if the
* distance of the interface between the two media were known." But he
* knows only that it lies below the lunar sphere; so "it is impossible to
* provide a method for determining the size of the angles of deviation . . . ."
* Unfortunately, Smith cannot distinguish among ecliptic latitude,
* geographic latitude, altitude, and declination, calling them all
* "latitude". This garbles his "explanations" in the notes considerably.
* (See notes 15 and 16 on pp. 238-239, where he thinks an astrolabe
* measures "latitude"; and note 17, p.240; text, line 1, p.241.)
* The same errors are repeated verbatim in his rediscussion in Trans. Am.
* Phil. Soc. 89 (1999).
* On the other hand, Smith correctly notes the lack of discussion of
* astronomical refraction in the Almagest, and Ptolemy's confusing it
* there with the Moon Illusion. We must conclude that Ptolemy did
* eventually learn of astronomical refraction from observation.
* Smith's rediscussion, cited above for "Euclid".
* Here, the "latitude" confusion is on pp. 136-137, and the notes are on
* page 146, where Smith says "apparent latitude or orbit" when what is meant
* is a diurnal circle. In note 16, he says "the actual eye-to-object
* distance has virtually no effect on refractive displacement", which is
* true for stars, but not (today) even for the Moon, and closer objects.
* And of course his phrase "actual latitudinal distance" is nonsense.
* (See p. 127)
* Rome's edition of Theon's commentaries on the Almagest (c. 400 A.D.)
* On pp. 347-351 he discusses Theon's references to Archimedes's knowledge
* of refraction. The text is in Greek; the notes are in French. See his
* discussion of the Archimedes work on Catoptrics (1932) for details.
* More interesting here is his discussion of Ptolemy and the Almagest,
* which in fact says nothing about refraction. The odd thing is that
* the work on Optics attributed to Ptolemy says quite a lot about it;
* "Mais on ne connaît actuellement l'Optique (et même pas tout entière)
* que par la traduction latine d'une traduction arabe. L'arabe et le grec
* sont perdus. Ce passage-ci de Théon pose la question de l'authenticité
* de l'Optique, ou tout au moins la question des remaniements qu'elle a
* pu subir entre le IIe et le XIIe siècle." (p. 348)
* [cf. Smith's translation of Ptolemy's Optics, above.]
* In discussing the supposed "explanation" of the Moon illusion by
* "refraction" -- actually, by the arm-waving about "haze" at the horizon
* -- Rome says: "En réalité, comme nous l'avons déjà dit, Ptolémée
* n'a pas l'intention de donner ici une véritable explication. Il se
* contente de rattacher vaguement le phénomène à la réfraction."
*
* SCRIPTA CLARISSIMI MATHEMATICI is the works of Regiomontanus
* (Johannes Müller), Bernard Walther, and Georgius Purbach, edited
* and published by Johannes Schöner of Carolstadt.
*
* Title page reads:
*
* S C R I P T A C L A=
* R I S S I M I M A T H E M A T I-
* CI M. IOANNIS REGIOMONTANI, DE
* Torqueto, Astrolabio armillari, Regula magna Ptole-
* maica, Baculoque Astronomico, & observationi-
* bus cometarum, aucta necessariis, Ioannis
* Schoneri Carolostadij additionibus,
*
* Item.
* Observationes motuum Solis, ac Stel
* larum tam fixarum, quam erraticarum.
*
* Item.
* Libellus M. Georgij Purbachij de
* Quadrato Geometrico.
*
*
* The typography uses many obsolete glyphs that stand for common Latin
* syllables, like "pro" and "pre" and "que", made by adding crossbars
* and tildes and so on to the tails of p's and q's; see reference works
* on "paleography" to decode these.
*
* The type appears to be identical to that used in printing Copernicus's
* "De Revolutionibus" the year before. The text is full of Latin
* contractions and abbreviations, especially in the transcriptions of the
* observing records; I have the feeling it was just that way on the pages
* of the original observing logs. The folios, not the individual pages,
* are numbered (many of them incorrectly!)
*
* Walther, whose work we are interested in here, is not mentioned until
* fol. 27r, where his continuation of Regiomontanus's solar observations
* is noted in the chapter title:
*
* I O A N N I S D E
* M O N T E R E G I O E T B E R
* NARDI VVALTHERI EIVS DISCIPV
* li ad Solem obseruationes.
*
* On fol. 27v (the back of that title page) we find, after Regiomontanus's
* last observation (28 July 1475): "Obseruationes sumptæ per regulas
* Ptolemæi, de motu Solis, per Bernardum VValtherum Nurenbergæ
* discipulum M. Ioannis de Monteregio."
* In the succeeding pages, it's interesting to see Walther's care and
* skill developing. At first there are few remarks about the quality of
* the observations; as he goes on, there are more and more frequent
* notations like "Dubia", "Certa", or "Diligens".
* Walther's first observation of refraction is on fol. 52v/53r (the
* latter mis-numbered 57!), in the entry for the sunset of March 6, 1489.
* The cause of the discrepancy (refraction) and his investigation of it,
* are explained in the next day's entry; but there are further references
* to refraction on 12 Dec. 1490 (fol. 54r); 9 Sept., 1491 (fol. 55r,
* mis-numbered 59); and 12 Dec. 1503 (fol. 57v). There is a long list of
* ERRATA At the end of the volume.
* Fortunately, most of this has been translated into English by
* William H. Donahue (see next bibliography item).
* Images of the pages are available at
* https://digital.slub-dresden.de/werkansicht/dlf/14594/1
* and formerly at
* http://num-scd-ulp.u-strasbg.fr:8080/158/
* and on Google Books.
* DONAHUE's translation of JOHANNES KEPLER and WALTHER
* This is mostly a translation of Kepler's work on Optics; but as he has
* a whole muddle-headed chapter on refraction, in which he quotes
* extensively from Walther's observations, we get the Walther stuff
* translated along with Kepler (see pp. 162-167, in which Kepler adds a
* running commentary on Walther's rather terse account.) From Kepler's
* point of view, the reason for dragging in Walther is to demonstrate
* that refraction is measurable, and important.
*
* Original title: Ad Vitellionem paralipomena, quibus Astronomiae pars
* optica traditur (1604)
*
* This file deals mostly with the discovery of the sine law, etc.
* I have arranged the items more nearly in historical order than their
* order of publication; so Rashed's 1990 paper on Ibn Sahl comes first,
* then the papers on Harriot; then Snel, and finally Descartes, and Newton.
*
* Roshdi Rashed's discovery of the 10th Century Arab work (Ibn Sahl)
* ". . . a treatise on burning instruments written around 984 by a
* mathematician connected with the court of Baghdad . . . ."
* On p. 478, the law of refraction is invoked. A certain ratio (in
* modern terms, 1/n) is asserted to have a fixed value for all incident and
* refracted rays; but this condition is simply used to advance the geometric
* development. No values are given; no experimental evidence is offered.
* Beginning of HARRIOT sub-file
*
* THOMAS HARRIOT discovered the sine law first
* A second-hand account of a description of Harriot's method, but
* without establishing the date.
* The 1959 discovery that Harriot had known the sine law in 1602,
* based on his observations in 1597 and 1598.
* N.B.: there is an interesting aside here on Kircher (p. 114):
* "It is interesting to note that Kircher (Ars Magna 1646) adopted
* Kepler's formula, although Descartes had published the law of sines many
* years before. Kircher's own experimental values were poor."
* Johs. Lohne's 1963 paper, stating that Harriott had the law in 1601.
* (saved as Wiley's PDF only)
* Beginning of SNEL sub-file
*
* Cornelis de Waard's discovery of the Snellius outline
* Here we have (p. 68) prop. 47 of Liber 1: "The maximum refraction of
* the stars occurs at the horizon." Note that this occurs among
* propositions describing refraction in a sphere (props. 40-57).
* See also prop. 50, 52-55. Props. 53-55 deal with the relation between
* refraction and the height of the atmosphere.
* Note the 4 pages of the manuscript reproduced in Pl. I & II, from which
* we see that the transcription is not 100% correct. For example, Fig. 6
* shows that the manuscript has "remotior, et minor: contra in densiore",
* which de Waard transcribed as "remotior et minor, contra in densiore."
* Snel's notes
* This was prompted by de Waard's paper the previous year on Snel's
* outline, which Vollgraff calls "an index". On p. 722 the place of the
* image is discussed, showing that Snel doubted the idea that it lay on
* the perpendicular (a concept much discussed later in connection with
* Descartes).
* Note the typo of "1921" for "1621" on p. 723.
* "I venture . . . not to affirm, but to suggest, that at . . . December
* 1621, Snellius had already found the law of refraction." (p. 724)
* On p. 725 we have Snel's brief account of a distorted sunset, invoking
* "vapores crassos" as the cause of the flattening -- cf. Bouguer (1729).
* Klaus Hentschel discusses the Snellius outline
* This discusses the outline draft discovered in Amsterdam by de Waard.
* Of particular interest here are the references to astronomical and
* terrestrial refraction, both in Snel's outline and notes, and in Vossius's
* optics text. See p. 317 for Snel's discussion (in sections 47--55; Snel
* probably also was thinking of astronomical refraction in connection with
* section 56 (p. 318). It occurs again on p. 319.
* On p. 324, the references to Snel's book by Vossius give values for
* n for glass, air, and water; density is invoked. Chapter XVIII on the
* refractions of the Sun and distant mountains are of particular interest.
* The famous example of the coin at the bottom of a vessel filled with
* water recurs on p. 329.
* Odd that nobody caught the wrong values for the length of a degree
* of the meridian on p. 333, note 12.
* Beginning of DESCARTES sub-file
*
* RENÉ DESCARTES finally publishes the law in 1637
* This is a new translation by Paul J. Olscamp
* The "Optics" section begins on p. 65. Of light, he says (p.66):
* ". . . it will suffice that I make use of two or three comparisons which
* help to conceive it in the manner which to me seems the most convenient
* to explain all those of its properties that experience acquaints us
* with, and to deduce afterwards all the others which cannot be so easily
* observed; imitating in this the Astronomers, who, although their
* assumptions are almost all false or uncertain, nevertheless, because
* these assumptions refer to different observations which they have made,
* never cease to draw many very true and well-assured conclusions from
* them."
* On pp. 80-81, the sine law is presented as an exercise in proportion,
* without once mentioning sines of angles; no doubt because (p. 66) ". . .
* inasmuch as the execution of the things of which I shall speak must
* depend on the skill of artisans, who ordinarily have not studied, I
* shall attempt to make myself intelligible to everyone, and to omit
* nothing, nor to assume anything that might have been learned in the
* other sciences." (As Lohne (see above) shows, these diagrams go back
* to Ptolemy.)
* The model used is the corpuscular one usually attributed to
* Descartes's follower, Newton: ". . . inasmuch as the action of light
* follows in this respect the same laws as the movement of the ball. . . ."
* So he requires the light to move faster in the denser medium.
* There is an interesting discussion of "burning-glasses" on pp.146-147
* in which he considers the brightness of images, concluding that two
* lenses of the same form (and hence, focal ratio) but different sizes
* must produce equally hot images. "From this you can see that those who
* are only half informed in Optics allow themselves to be persuaded of
* many things which are impossible, and that those mirrors with which, it
* is said, Archimedes burned far-off ships must have been extremely large
* -- or rather, they are fabulous."
* Gorden Videen's opinion of Ibn Sahl is like mine.
* Antoni Malet's synopsis of Gregory's belated discovery parallels Ibn Sahl's
* This is about James Gregory's 1663 publication of the sine law, which
* he was able to discover by a process similar to that which Ibn Sahl
* apparently used. Gregory seems to have begun with Kepler's argument,
* but rejected Ptolemy's fudged "measurements" instead of believing them.
* He had used his understanding of conic sections to design the reflecting
* telescope named after him, published in 1657.
* ARAGO credits Descartes with the discovery
* After mentioning Ptolemy's work on optics, which includes a doctored
* laboratory (not astronomical) refraction table, he says:
* "Quant à la loi mathématique de ces déviations que l'Arabe Alhasen,
* que le Polonais Vitellio, que Kepler et d'autres physiciens avaient
* inutilement cherchée, c'est à Descartes qu'on la doit. Je dis
* Descartes, et Descartes seulement; car, si les réclamations tardives
* d'Huyghens en faveur de son compatriote Snellius étaient accueillies,
* il faudrait renoncer à jamais écrire l'histoire des sciences."
* Alas for Arago's prioritistic preferences, Snel today receives the
* honor; though, in accord with Stigler's Law of Eponymy, he was preceded
* by Harriot.
* As fair and even-handed assessment of the priority issue as any
* Scott thinks that "Descartes did not hear of Snell's work until the end
* of 1632, and it is not impossible that by this time his own researches
* were so far advanced that he had little to learn from Snell. . . .
* [Constantyn] Huygens met Descartes in Golius's house in 1632 and
* they discussed refraction at some considerable length. If, as seems
* not unlikely, Golius on this occasion mentioned Snell's discovery,
* and if, as seems equally likely, this was the first occasion on which
* he had announced it, Descartes has every claim to be regarded as an
* independent discoverer." (p. 38)
* A physicist's views on Descartes, refraction, and speed of light
* He seems to think Descartes's thought-experiments were real.
* Many useful references here.
* Discussion and partial translation of Descartes's work
* "Descartes' insightful derivation of Snell's law is . . . largely
* equivalent to the mechanical-particle or corpuscular derivation often
* attributed to Newton . . . ."
* [I would have said "implausible" rather than "insightful".]
* An incredibly muddle-headed discussion: he accepts Descartes's ignorant
* assumption that the position of the Sun was known independently of the
* Earth's shadow, and that ingress could be timed to a fraction of a second!
* (Huygens, who was an experienced observer, made a more realistic error
* estimate.)
* In addition, there's a spelling error in footnote 10.
* One of the more grotesque attempts to make sense of Descartes
* Beginning of NEWTON sub-file
*
* ISAAC NEWTON's first publication on prismatic dispersion
* This is the precursor to "Opticks": ". . . in the beginning of the Year
* 1666 . . . I procured me a Triangular glass-Prisme, to try therewith the
* celebrated Phænomena of Colours. " (p.3075)
* ". . . Light consists of Rays differently refrangible, . . . When
* I understood this, . . . I saw, that the perfection of Telescopes was
* hitherto limited, not so much for want of glasses truly figured . . . , as
* because that Light it self is a Heterogeneous mixture of differently
* frangible rays. " So Newton discovers chromatic aberration, and turns
* to reflecting telescopes.
* see also Fletcher's masterful review, in the "Variable Refraction" file.
*
* TYCHO BRAHE's REFRACTION TABLE (first publication)
* This work is reproduced in Dreyer's TBOO, Vol. 2; see
* I.L.E.Dreyer, ``Tychonis Brahe Dani Opera Omnia'' (Hauniæ, 1913).
* The solar refraction table is on p. 64 of TBOO, but on p. 79 of the
* 1969 reproduction by Culture et Civilisation (Bruxelles).
* The refraction table for stars is on p. 280 of the latter.
* (Comparison with page citations in "Kepler's Optics" shows that the
* 1969 reprint has the original pagination.)
* Note Tycho's comment next to the stellar refraction table saying
* that the stellar values are 4 1/2 minutes less than the solar ones.
* This is true for all the tabular values but the ones right at the horizon,
* which were apparently rounded off to the nearest minute.
* KEPLER's discussion of Tycho's refraction tables, etc. (1604)
* [See additional reference to this in the Distorted Sunsets file.]
* This is translated from Kepler's "Ad Vitellionem paralipomena" (p. 118/9)
* by William H. Donahue (p. 132 of his translation):
* Here Kepler sees the weakness in Cassini's model half a century before
* Cassini has invented it! He discusses the homogeneous atmosphere model
* in general terms -- not knowing the law of refraction -- and sees that
* the angles of incidence at 89 and 90 degrees' apparent ZD are too similar:
* "The increments of the refractions are in fact not large enough. . . .
* "In sum, it should be noted that the proportional refraction from
* 89° to 90° is going to be extremely small in the difference, because,
* while the inclination on earth varies by one degree, in air it varies
* by barely 13 minutes." So he sees that, whatever is the actual
* refraction law, the model can't produce a steep enough slope at the
* horizon; but, lacking the language of calculus, he can't pin things
* down well enough to see that the model itself is in error; instead of
* a general law, he has only a mass of discrepant numbers.
* He also points out that Tycho's numbers are rounded off at the
* horizon: "In fact, since the refractions presented by Tycho could
* not attain such precision from observation as is here required, you
* accordingly see them rounded off to exactly 34 minutes at altitude 0°
* and 26 minutes at altitude 1°." (Donahue p. 133)
* There are also some nice early examples of variable refraction near
* the horizon, cited on pp. 147 ff. of the translation (K. pp. 135 ff.)
* [See the reference to the Landgrave of Hesse on p. 149 (K. p. 136).]
* TYCHO BRAHE's refraction table, reprinted in Kepler's Rudolphine Tables
* This is the first table ever used to correct apparent positions for
* refraction. Because Tycho's observations were only good to a couple of
* minutes of arc, he could not detect refraction above 45° and thought
* there was none.
* Note that he gives separate tables for Sun, Moon, and stars. As
* pointed out by Owen Gingerich, in his paper with James R. Voelkel in
* JHA 29,1-34 (1998) on "Tycho Brahe's Copernican campaign", the odd
* result for the Sun is mostly (though not entirely) due to the assumed
* solar parallax of 3' of arc. His values for stars are mostly good to
* about 2' of arc, and the errors are about equally + and -.
* CASSINI's pre-refraction work on the solar position
* Here he reports a selection of results from the "heliometer" (a
* gigantic pin-hole camera) in the cathedral at San Petronio.
* Refraction is mentioned as a problem on p. 1, and gets considerable
* attention on p. 12. On p. 16 he points out that the refraction in
* Bologna is less than at Uraniburg. It is discussed in detail on p.18,
* where he accepts Tycho's table: no refraction above 45°. Finally,
* there are brief mentions on pp. 23 and 31.
* On p.30 he points out that the two hypotheses about the motion of the
* Sun predict a difference in its apparent diameter at perigee and apogee
* of only 1 minute of arc, which is why it was so diffucult to determine
* this observationally. And "nothing is more natural than that a closer
* object appears larger." But he finds from the daily motions that the
* physical motion is faster at perigee as well --- as, of course, Kepler's
* second law requires.
* This work shows how the refraction, the solar parallax, and the
* obliquity of the ecliptic are entangled in the observed altitudes.
* It sets the stage for Cassini's later work.
* Note the diagram of the Ricciolian system in the Figure at the back!
* The full title is "Specimen Observationum Bononiensium, quæ novissimè
* in D. Petronii templo ad astronomiæ novæ constitutionem haberi cœpere"
* CASSINI's refraction table (first publication)
* This is where Cassini's refraction table first appeared (p. 173).
* The nominal author is Malvasia; but the text is partly his and partly
* Cassini's. The preface (on unnumbered pages) is by Malvasia, and printed
* in italics. There are some dedicatory and introductory letters and poems
* (also unnumbered); the numbered pages begin with the Ephemeris itself;
* its frontispiece counts as page 1, and the first page with an actual
* number is p. 2, with the ephemeris for January, 1661. Each month gets
* a double-page spread; the page numbers are in the top margins at the
* outer corners.
*
* In Malvasia's preface, the general strategy for measuring and
* separating the refraction and the solar parallax is explained on the
* second and third pages: the observations reported in the Specimen
* showed that better corrections for refraction were needed. "So that
* he [Cassini] could distinguish the refractions of the Sun at all altitudes,
* he had to study the general refraction law in bodies in which they are
* more evident, like in glass, water, and other liquids; . . . ".
* There are also very interesting letters exchanged between Cassini
* and Count Malvasia, on the whole business of the solar ephemeris and
* parallax, and refraction, on pp. 152-156, and (after the Tables) again
* on pp. 174-186. This whole section is introduced with a large title
* sheet on p. 151, saying:
*
*
* N O V I S S I M AE
* MOTVVM SOLIS EPHÆMERIDES
* EX RECENTIORIBVS TABVLIS
* CLARISSIMI VIRI
* D. IOANNIS DOMINICI CASSINI
* IN BONONIENSI ARCHIGYMNASIO
* ASTRONOMIÆ PROFESSORIS
* A`
* MARCHIONE CORNELIO MALVASIA
* S V P P V T A T Æ
* Cum Epistolis Authoris ad eundem Cassinum , eiusdemque
* responsis.
*
*
* The correspondence begins in October, 1661, with a letter from Malvasia
* to Cassini (p. 152). It deals with the new solar ephemeris, and says
* nothing about refraction. Cassini's second letter (Nov., 1661) also
* deals with the coordinates of Modena and Bologna, not refraction.
* Then (p. 154) comes Malvasia's brief appeal to Cassini for help with
* the tables for the new Ephemerides (June, 1662).
* On p. 155, Cassini's letter of mid-June, 1662, first mentions the
* refraction problem.
* On p. 186, we see a parameter used by Cassini to calculate
* refraction:
* -7
* Height of the atmosphere in Earth radii: 6095 x 10
*
* The actual ephemerides are based on Philip Lansberge's elaboration
* of the Copernican model: heliocentric, but with epicycles, rather than
* Keplerian ellipses.
*
* This reader is surprised to see that many everyday astronomical terms
* used here are not in most Latin dictionaries: duratio, eclipticalis,
* eclipticus, libratio, parallaxis, refractio, semidiameter, . . .
*
* The title page of this folio volume is shown on the Web pages
* of the Astronomical and Geophysical Museum of Modena, at
* http://www.museoastrogeo.unimo.it ;
* [unfortunately, that website is now closed; but it was preserved on the
* Wayback Machine at
* https://web.archive.org/web/20081207063659/http://www.museoastrogeo.unimo.it/
* where you can find most of its pages]
* see http://155.185.1.56/lbo/img%5Clink50a.jpg for the image, which
* shows:
*
* E P H E M E R I D E S
* N O V I S S I M Æ
* MOTVVM COELESTIVM
* MARCHIONIS CORNELII MALVASIÆ
* . . .
* Additis Ephemeridibus Solis , & tabulis Refractionum , ex
* nouissimis hypothesibus
*
* DOCTORIS IOANNIS DOMINICI CASSINI,
* in Archigymnasio Bononiensi Astronomia Professoris Præstantissimi.
*
* MANY THANKS to Luca Lombroso for providing a photocopy of the relevant
* pages!
* JPEG images of all the pages are available at
* http://fermi.imss.fi.it/rd/bdv?/bdviewer/bid=000000930984
* A pretty readable copy is also available at Google Books, though their
* OCR is badly garbled (not only by the many ligatures and paleographic
* contractions, but even by rendering the long-s as "f").
* NOTE on typography: In addition to the common uses of "q;" for "que",
* the Italic font has several unusual items. The second page of the
* preface has "poße" for "posse" (line 12), and "aiÿs" for "aliis" (line
* 15). Evidently these glyphs were already in use in Latin as well as in
* German and Dutch. A colon is occasionally used as a "wild card" for any
* omitted letter or letters (e.g., "Io:' for "Ioannum".) The glyphs "ü
* and "v" are used rather indiscriminately; and there is a variant "v"
* (as well as a variant "u") with a more elaborate left hook. A tailed
* "e" is used for "æ"; and "ẽ" for "en".
* Also, notice the spelling in "Exemplum Quartum", p.179: "Vualterus"
* and "Mvtina" = Mutina was the Latin name of modern Modena.
* RICCIOLI's Astronomiæ Reformatæ
* This is needed to make sense of Cassini's letter responding to
* Riccioli's mixed-up misunderstanding of refraction and parallax, given on
* pp. 41-61 of the first Book here. His specific comments on Cassini's work
* in the Ephemerides are on p. 61; note also the discussion of trying to
* determine the solar parallax by Aristarchus's "dichotomy" method on p. 41.
* As he leans heavily on Tycho's empirical refraction table, that's
* probably what led him to call attention to the problem with Cassini's
* Table at the horizon.
*
* The Frontispiece page says:
*
* A S T R O N O M I A
* R E F O R M A T A
* A D
*
* Serenissimum D.
* FERDINANDUM MARIAM
* B A V A R I Æ E T C.
* D V C E M.
*
*
* Title page:
*
* A S T R O N O M I AE
* R E F O R M A T Æ
* T O M I D V O,
* QVORUM PRIOR OBSERVATIONES,
* H Y P O T H E S E S,
* ET FVNDAMENTA TABVLARVM,
*
* Posterior præcepta pro vsu Tabu=
* larum Astronomicarum,
* Et ipsas Tabulas Astronomi=
* cas CII. continet.
*
* Prioris tomi in decem libros divisi,
* Argumenta Pagina sequenti exponuntur.
*
* A U C T O R E
*
* P. IOANNE BAPTITSTA RICCIOLO
*
* S O C I E T A T I S I E S V.
*
* FERRARIENSI.
*
* BONONIÆ, MDCLXV.
*
* This accounts for the varying title in different lists.
* JPEG images of all the pages are available at
* http://fermi.imss.fi.it/rd/bdv?/bdviewer/bid=000000300871
* Cassini's letter responding to Riccioli.
* This is contained in Geminiano Montanari's:
* Ephemeris Lansbergiana ad annum 1666, item de solis hypothesibus et
* refractionibus siderum (Bononiae, 1666);
* this letter is also reprinted by Roberti in 1692 (q.v. for excerpts).
* Here, page 29 bears the heading:
*
* E P I S T O L Æ D V Æ
* ASTRONOMICÆ
* Altera Auctoris,
* Altera D.Io.Dominici Cassini.
* De Solis Hypothesibus, & de Refractionibus siderum
* ad dubia A.R.P.Io.Baptistæ Riccioli Soc.Iesu.
*
* and the first short letter is Montanari's, introducing Cassini's.
* Cassini describes the procedures for disentangling the solar parallax
* from refraction in considerable detail, along with many cross-checks to
* make sure everything was consistent. He discusses the peculiar run of
* the computed parallaxes near the horizon on pp. 47 and 48.
* Orthography: note the spelling "Vvaltherus".
* According to Pogg., this was first printed in Rome in 1665. But I find
* no trace of that version; Houzeau lists only this and the Roberti reprint.
* So does Giovanna Grassi's "Union Catalogue". I think it's likely that
* Pogg. got the "Epistolæ tres" mixed up with the 3 letters from Cassini
* to O. Falconieri, which were published in Rome in 1665, but deal with
* the Galilean satellites, not refraction. Grassi lists this letter as
* "Epistola a G. Montanarï.
* ENGLISH ABSTRACT of Cassini's 3 letters
* Summary of the contents of Cassini's 3 letters (above; and reprinted,
* below). This abstract is so useful that I quote it here in full:
* "The first Letter is in Latine,to Geminian Montanarius,
* publick professor of Mathematicks in Bononiensi Archigymnasio ;
* who was calculating Ephemerides of the Suns place, according to
* the latter Hypothesis of Cassinus. His former Hypothesis
* was grounded upon Observations of the Sun,from whose altitudes,when
* they were great,he made no Abatement; because,according to the common
* opinion, the Refraction is nothing,or,at least,inconsiderable.A specimen
* of it,was published about 16 years ago.But afterward he changed that
* Hypothesis, that it might agree with his observations as diligently
* made,but more artificially corrected. For,having ex meris stellæ
* Polaris altitudinibus exactissimis determined the height of the pole
* (and thereby of the Equinoctial,)at Bononia ; he observed also the Suns
* meridian height in both Solstices. And subtracting that winter height
* from that Equinoctials height ; and the said Equinoctials height from the
* Summer height, he alwaies found that former difference less,by above four
* minutes and an half, than the latter difference. Wherefore he attempted
* to order the Parallaxes and Refractions so, as that those Summer and
* Winter observations, being corrected according to that doctrine, might
* yield the Suns Southern greatest declination, equal to the Suns greatest
* declination Northward. In this Letter he sets down,What course he took
* to find the Refractions; What Experiments he made in glas and in water ;
* How he applied them to celestial Refractions ; His proceeding to determine
* the proportion of the height of the Air to the Semidiameter of the Earth;
* And at last to make Tables ad singulos gradus apparentis distantiæ
* à vertice. Those Tables make it evident, that Refractiones etiam in
* æstivis altitudinibus sunt sensibiles, &ad verticem usque conscendunt ;
* which hitherto hath alwaies been denyed.Not only his friends in Italy
* approve these Tables,but in France also. Petrus Petit in præclaro
* opere,quod DE NUPERIS COMETIS scripsit ediditque, saith, Cassini
* Tabulas (refractionum) &rationibus &Experimentis esse conformes.
* "But Ricciolus, in a late treatise Astronomiæ reformatæ, hath
* raised an Expectation of his new Tables of Refraction,and questions those
* Tables of Cassinus : Who,in this Letter, answereth his objections,and
* shews,how,by observations in Heliometro, we may try whose Tables
* are best.
* "The second Letter is in Italian, to Carlo Rinaldini Professor
* of Mathematicks in the University of Padua, dated August .7.1666.
* "In it, He shews some defect in the wayes of making Experiments of
* Refraction, prescribed by Vitello, Des-Cartes,Riccioli and Manzini. And
* then he describes an Instrument of his own invention for that purpose,
* &c .
* "The third letter is in Italian also,but without date:concerning
* a book of Dr.Mengoli ; wherein is a Table of Refractions for every
* degree of altitude. But Cassinus shews,that Table of Mengoli to
* be false;as being easily refuted by Experience,and grounded upon a wrong
* foundation.Most writers of Dioptricks since Des Cartes do agree with
* him,in acknowledging a constant Ratio in the Sines of the Angles
* considered in Refraction.But this Doctor Mengoli, mistaking those
* Angles, hath cast away a great deal of labour in calculating so many
* Refractions, and so making a Table full of false numbers.But Cassinus
* hopeth,that Signor Mengoli will review his Principles, and put true
* ones in their room,that so beginning anew he may reform the Conclusions,
* which he intended to demonstrate."
* Mengoli's screwball work on refraction is available at IMSS:
* http://fermi.imss.fi.it/rd/bdv?/bdviewer/bid=000000300759
* [No author is given for the abstract; I assume it was Oldenburg.]
* Reprint of CASSINI's "epistolæ tres" by GAUDENZIO ROBERTI
* According to Pogg., these letters were originally printed at Rome in 1665.
* I have copied only letters 1 and 3, as the second one has to do more
* with the law of refraction itself, and measuring instruments.
* EPISTOLA PRIMA Clarissimo Viro Geminiano Montanario
* In Bononiensi Archigymnasio Mathematicarum professori publico
* (pp. 283 - 314) is the most formal of the 3, with numbered notes
* in the margins, and the only one in Latin. In the section numbered 31
* is a brief explanation of "The method of construction of the refraction
* Tables":
* "In the whole study, I have tried to find the ratios of the
* semidiameter of the air to the semidiameter of the Earth, and of the
* sines of the inclination of the direct and of the refracted rays, that
* exactly reconcile the observed with the solsticial refractions, in which
* there is the least need of astronomical hypotheses. From these I have
* geometrically constructed the tables at single degrees of apparent zenith
* distance . . . " -- but no explanation of how those parameters were found.
* Note 74, p. 306, responds to Riccioli's suggestion that the peculiar
* behavior of the tables at the horizon might be a typographic error:
* "[Riccioli] writes that my table does not show the steep increase
* of refractions near the horizon that ought to occur, as he thinks, by
* proportion, because the difference of refractions from the first to the
* second degree is larger than from zero to the first, while the opposite
* should actually be required by the laws of astronomical refraction; hence
* he suspects a typographical error has crept into them. When I read this
* note, I have calculated the refractions again trigonometrically from the
* principles in the published letters for the same degrees of altitude,
* and likewise again came out those which are arranged in the table;
* hence there is no error, either typographical or trigonometrical, but it
* really follows from the laws of astronomical refractions published by me.
* The real reason why the difference of refractions from the first to the
* second degree is bigger than from the horizon to the first, is that at the
* first, up to an altitude of a degree, the inclination of the visual ray
* to the upper surface of the air is changed only 15 minutes, and from the
* first to the second degree of altitude is changed about five and thirty
* minutes, as is deduced geometrically by me by means of the ratio of the
* height of the air to the Earth's semidiameter, but so much variation
* of the inclination to the surface of the air in the second degree of
* altitude having been made produces a bigger ratio of the differences of
* the angles to the differences of the sines at a larger zenith distance,
* which produces the bigger difference of the refractions at the horizon, of
* course, as you will understand more clearly in my theory of refractions,
* which I am working on."
* -- cf. Kepler's explanation of this problem some 62 years earlier!
*
* The second letter, to "D Carolo Rinaldo", is in Italian. It bears
* the dateline "Bologna li 7. Agosto 1666".
*
* EPISTOLA TERTIA ad dominum A. P.
* In qua examinuntur fundamenta refractionum
* & parallaxium D. Doctoris Mengoli
* pp. 323-340. In Italian; no date.
* Mengoli's screwball work on refraction is available at IMSS:
* http://fermi.imss.fi.it/rd/bdv?/bdviewer/bid=000000300759
* PIETRO MENGOLI's crank work
* One of the more bizarre items in this collection. The frontispiece
* contains the diagram whose notations are explained on p. 9. A few
* excepts will suffice to explain why Cassini was so concerned about this:
* P. 8:
* CONCLUSIONS
* which are demonstrated in this work.
*
* 1 The horizontal refraction is 1' 58'' 6'''.
* 2 The summer horizontal parallax of the Sun is 38'' 49'''.
* . . .
* Well, there are 6 numbered items; maybe that's enough.
*
* P. 10:
* DEFINITIONS
* 1 Incidence , I shall call the obtuse angle which the ray from the
* luminous point to the point where refraction occurs at the surface of
* the atmosphere makes with the diameter of the atmosphere: and likewise
* I shall call Incidence the acute angle which the same ray prolonged makes.
* 2 Refraction , I shall call the acute angle which the ray by which
* the observer sees the luminous point makes at the surface of the
* atmosphere with the ray leading from the luminous point to where it is
* refracted, and prolonged: and likewise I call Refraction, the obtuse
* angle.
* 3 Difference , I shall call the acute angle which the refracted ray
* makes with the diameter of the atmosphere, at the point of refraction:
* that is, Difference between the Incidence and Refraction.
* . . .
*
* P. 11:
* SUPPOSITIONS
* 1 The refractions are angles not appreciably larger than two minutes.
* . . .
* PROPOSITIONS
* P. 14:
* 20 The refractions are proportional to the sines of the zenith
* distances.
*
* Even in Cassini's day this looked crazy. It's interesting that this
* was published in 1670, a year after Cassini (who had taken it apart
* for Mengoli's complete misunderstanding of the matter, in his "Epistola
* tertia" that was published already in 1665 and reprinted in 1666) had
* safely gone to Paris.
* The historians of mathematics seem to think Mengoli was an original
* and talented mathematician; but that isn't enough to make him competent
* at astronomy or physics -- as he clearly hasn't learned what the basic
* terminology of those fields means. (For that matter, consider the feeble
* efforts of Euler and Lambert in this area.) He was the last student of
* Cavalieri.
* Mengoli's screwball work on refraction is available at IMSS:
* http://fermi.imss.fi.it/rd/bdv?/bdviewer/bid=000000300759
* CHRISTIAAN HUYGENS's ``Traité de la Lumière'' (1690)
* (placed slightly out of order so as not to break up Cassini's works)
*
* He noticed the DIURNAL VARIATIONS in terrestrial refraction very early:
* "Mais il y a une experience qui rend cette refraction fort visible ;
* qui est qu'en fixant une lunette d'approche en quelqu'endroit , en
* sorte qu'elle regarde un objet éloigne de demi lieuë ou plus, comme
* un clocher ou une maison , si on y regarde à des heures differentes
* du jour , la laissant tousjours attachée de mesme , l'on verra que
* ce ne seront pas les mesmes endroits de l'objet qui se presenteront au
* milieu de l'ouverture de la lunette , mais que d'ordinaire le matin &
* le soir , lorsqu'il y a plus de vapeurs prés de la Terre , ces objets
* semblent monter plus haut , en sorte que la moitié ou d'avantage n'en
* sera plus visible ; & qu'ils baisseront vers le midy quand ces vapeurs
* seront dissipées." (pp. 42-43)
* Cf. Perrault (1674); that book is dedicated to Huygens, who clearly
* picked up this description from his friend Perrault. Huygens was
* well acquainted with the Perrault brothers, Claude and Pierre.
* See the English translation (below).
* Note that Huygens says he wrote the Treatise in 1678 and communicated
* it to the Royal Academy of Science then, intending to translate it into
* Latin ``in order to obtain greater attention to the thing. . . . But the
* pleasure of novelty being past, I have put off from time to time the
* execution of this design . . . .'' [in Thompson's translation.]
* Huygens in English translation by Sylvanus P. Thompson
* He says refractions in the air ``are very remarkable; for by them we
* often see objects which the rotundity of the Earth ought otherwise to
* hide; such as Islands, and the tops of mountains when one is at sea.''
* [p. 44]. Then come the standard remarks about astronomical refraction.
* But the best part is on p. 45: ``But there is one experiment which
* renders this refraction very evident; which is that of fixing a telescope
* on some spot so that it views an object, such as a steeple or a house,
* at a distance of half a league or more. If you then look through it
* at different hours of the day, leaving it always fixed in the same way,
* you will see that the same spots of the object will not always appear at
* the middle of the aperture of the telescope, but that generally in the
* morning and in the evening, when there are more vapours near the Earth,
* these objects seem to rise higher, so that the half or more of them will
* no longer be visible; and so that they seem lower toward mid-day when
* these vapours are dissipated.'' Huygens picked up this DIURNAL
* VARIATION in terrestrial refraction from Perrault (q.v.).
* To this he adds that the astronomical refractions ``are not altogether
* constant in all weathers, particularly at small elevations of 2 or 3
* degrees'' [p. 49]; so we may even say he noticed that the variations
* are confined to these small altitudes.
* This is a reprinted edition; the original publication was by Macmillan,
* London (1912).
* Jo. Jacobus HARTMAN's review article on refraction
* I'd count this as the first real review article on refraction, though
* Kepler's chapter in his Optics book might also be considered a review.
* This has copious references to the literature (more detailed than one
* usually finds), from Pliny's lunar-eclipse suggestion to an interesting
* discussion of the latest stuff: Cassini's reprinted letter, Huygens's
* treatise on light, etc. Interestingly, the reviewer thinks the air is
* so much more uniform than the discontinuity between air and æther that
* Huygens's suggested effect of refraction from one layer of air to the
* next is probably unimportant.
* Section XIII discusses the flattening of the Sun at the horizon.
* The pages are not numbered; this is hardly more than a pamphlet: the
* text of a public lecture.
* JOHANNES BILBERG and solar refraction
*
* Bilberg's paper begins with a dedication: "Serenissimo potentissimoque
* Principi ac Domino, D O M I N O C A R O L O X I . Suecorum,
* Gothorum, Vandalorumque Regi, Magno Principi Finlandiæ, Duci Scaniæ,
* Esthoniæ, Livoniæ, Careliæ, Bremæ, Verdæ, Stetini,
* Pomeraniæ, Cassubiæ, et Vandaliæ, Principi Rugiæ, Domino Ingriæ
* et Wismaræ, nec nos Comiti Palatino Rheni, Bavariæ, Juliaci,
* Cliviæ et Montium Duci, &c. &c." [This is Charles XI of Sweden, the
* illiterate father of Charles XII who conquered Poland a few years later.]
* Then, on pp. 6 and 7, there is a little poem about the work and its
* author (cf. Galileo's book on sunspots), introduced with the interesting
* phrase "in Tornea Urbe spectatum". [This is not Torun, but Tornio,
* Finland, at the northern end of the Gulf of Bothnia]. "Tornea" ia
* also the Swedish name.
* P. 8 is the table of contents; the most interesting items for us here
* are "Cap. III. Observationes solis diurnæ & nocturnæ" and "Cap. IV.
* Doctrina refractionum."
*
* The narrative describes his expedition to high latitudes to see the
* "never-setting Sun"; after being partly frustrated by clouds at Tornio,
* they went up-river nearly a degree, finally seeing the Sun 3 diameters
* above the horizon near midnight.
* The chapter on refraction begins with the coin-in-a-basin experiment,
* and says that an oar in the water appears broken for the same reason.
* "Just as a lead ball shot obliquely into water draws away from its
* original direction at the surface, losing some force in traversing the
* different media . . . ." [p. 33]
* Referring to the diagram facing p. 23, he says, "The ray SB is bent in
* passing from the æther into a denser medium, the atmosphere ABC, and
* the line BO represents the other part of the line; while otherwise the
* line would be extended to R, if it were the same medium, and not really
* to the eye O." [p. 34]
*
* Comments on NOVAYA ZEMLYA observations:
* Then he says the refraction is greater in regions near the Pole, "as
* can be confirmed by the experience of the Batavians" (i.e., the Dutch)
* "in nova Zembla". "For they saw the body of the Sun when it should have
* been 4 degrees below the horizon, which is surely a paradox; for by this
* reason the horizontal refraction grows excessively beyond the numbers
* in the refraction tables commonly computed.
* "Not unjustly, therefore, have many held these Batavian observations
* to be suspect." So he cites the supporting details: the clock, the
* conjunction of Jupiter and the Moon, etc. And he cannot agree with the
* doubters; "for in our observations something very similar occurred. For
* if the elevation of the pole of Torno is found to be 65° 43',
* subtracting this from a quadrant of 90° gives the complement of the
* elevation of the pole, 24° 17'. Now as the observed fact is around
* the solstice, the Sun is in the beginning of Cancer; if the declination
* of the Ecliptic, which is commonly taken to be 23° 30', is taken
* away, there remains 47' for the position of the Sun below the horizon."
* [This is demonstrated with the upper diagram facing p. 34.]
* Note that de la Hire (1700) re-reduced the observations, concluding
* that the refraction at Tornio was 58', and even more at Kangis.
*
* (cited still later by Le Gentil (1779), p. 394.)
*
* BIBLIOGRAPHIC COMPLICATIONS: This volume has several title pages,
* each with a slightly different title! The first says:
*
* Decuriæ
* Annorum Quartæ
* MISCELLANEORUM
* Medico-Physicorum
* Sive
* EPHEMERIDUM
* GERMANICARUM
* Annus Quartus
*
*
* The engraved frontispiece shows the motto:
*
* Cæsaro-Leopoldinæ Naturæ Curiosorum Academiæ
*
* below the imperial eagle, and below this the title:
*
* Ephemeridum Physico-Medicarum
* Decadis III
* Annus IV
*
*
* Then comes the title page proper:
*
* Miscellanea Curiosa
* sive
* EPHEMERIDUM
* Medico-Physicarum
* Germanicarum
* ACADEMIÆ
* CÆSAREO-LEOPOLDINÆ
* Naturæ Curiosorum
* Decuriæ III .
* ANNUS QUARTUS
* Anni M DC XCVI
* Continens
* Celeberrimorum Virorum
* Tum Medicorum tum aliorum Eruditorum in Germania
* &extra eam
* OBSERVATIONES
* Medico-Physico-Anatomico-Botanico-Mathematicas
* Cum
* APPENDICE
* &
* Privilegio Sac. Cæs. Majestatis.
* ----------------------------------------------
* Edita sumtibus Academiæ 1697.
* Francofurti & Lipsiæ,
* apud Johannem Michaelem Rüdiger, & Engelbertum Streck.
* Literis Christiani Sigismundi Frobergii.
*
* An English translation appeared the next year, with the title
* "A Voyage of the late King of Sweden. . . " (Edward Castle, London, 1698)
* -- see below.
* The English translation of the previous item.
* The translator has translated the given names of the various Swedes;
* so here Bilberg is "John Bilberg". The translated dedication reads:
*
* To the Most Serene, and Most Mighty Prince and Lord Charles XI.
* King of Sweden , Goths , and Vandals ; Great Prince of Finland ;
* Duke of Schonen, Estland, Lifland, Carelen, Bremen, Verden, Stetin,
* Pomerania, Cassuben, and Vandalia ; Prince of Rugen ; Lord of
* Ingria, and Wismar ; Palsgrave of the Rhine ; Duke of
* Bavaria, Juliers, Cleves, and Mons, &c. &c.
*
* Many of these place names are no longer used. Scania (Schonen) is the
* southernmost tip of Sweden; Estland (like "Schonen", a German place-name)
* is Estonia; Livonia (Lifland) is partly Latvia today; Karelia (Carelen)
* is now on the border between southern Finland and Russia; Verden is
* in Lower Saxony; Stetin is now Szczecin, Poland; Cassubia (Cassuben)
* spans the border between the German "Land" of Mecklenburg-Vorpommern
* and western Poland; the Vandals originally migrated from Scandinavia
* into Pomerania, but were long gone by the 17th Century, so it isn't
* clear what was meant by Vandalia here; Rugen is now Rügen, Germany's
* largest island, in the Baltic near Pomerania; Ingria (Ingermanland)
* is a region near St. Petersburg, Russia, and adjacent to Karelia;
* Wismar is a Hanseatic League town in Mecklenburg-Vorpommern, where
* Friedrich Wilhelm Murnau set his 1922 classic Nosferatu ; Juliacum
* or Juliers is now Jülich (it and Cleves were duchies, just west of
* Düsseldorf); Mons is in Belgium, a little west of them.
* The Royal Society's experiment to measure refractivity of air
* As can be seen from the failure of the French attempt to repeat the
* experiment (see below), maintaining the necessary hermetic seals was
* the tricky part. So he wisely says, "It is not (I think) an unnecessary
* trouble, that in this account of the Apparatus I have mention'd so many
* minute Circumstances, for we found it difficult enough to exclude the Air,
* and almost Impossible to discover the very little holes through which
* so subtil a fluid would freely enter and possess the spaces deserted by
* the subsiding Mercury."
* Both the raw and reduced measurements are given; the ratio of the
* sines of the angles was found to be 1.00036. The refractivity, which he
* calls the "refractive power", is "not always proportional to the Density
* (at least not to the Gravity) of the Refracting Medium . . . . And there
* are some fluids which tho lighter than Water yet have a Greater Power
* of Refraction . . . . But the Refractive Powers of Air and Water seem to
* observe the simple Proportion of their Gravities . . . .
* "And if this should be confirm'd by succeeding Experiments . . . it
* would be more than probable that the Refractive Powers of the Atmosphere
* are every where, at all heights above the Earth, proportional to it's
* Densities and Expansions. And here it would be no difficult matter
* to trace the Light through it, thereby to terminate the shadow of the
* Earth; and . . . to Examin at what distances the Moon must be for the
* Earth to suffer Eclipses of the Observ'd Duration. This Limitation is
* considerable enough in Astronomy, abundantly to recompense the trouble
* of Prosecuting such a New Experiment."
* [For Hauksbee's confirmation of this, see his 1709 paper in the
* Refractivity file.]
*
* General discussion of refraction, and Homberg's faulty experiment
* "Les refractions qui changent le lieu apparent de tous les Astres,
* ont trompé jusqu'à ces derniers tems tous les Astronomes . . . .
* Quand on commenc,a à s'en défier & à les connoître, on crut qu'elles
* n'agissoient que jusqu'au 45 degré d'élévation, au-delà duquel on
* croyoit en être de;livré. Mais M. Cassini fit voir qu'elles alloient
* jusqu'au Zénit, quoiqu'en diminuant extrêmement, & mit par-là une
* nouvelle précision dans les Calculs Astronomiques."
* Then there is discussion of the supposed large variation with
* latitude, mentioning Bilberg's "Livre nouveau" (1695), asserting that
* the King of Sweden had actually seen the Sun did not set on the summer
* solstice. "Ces grandes Réfractions du Septentrion sont fort utiles à
* des Peuples prive's du Soleil pendant plusieurs mois . . . ."
* Some speculation about possible differences in density and thickness
* of the air at high latitudes follows, with de la Hire's remark "que le
* Barométre de Stokolm est comme celui de Paris."
* Finally, the laboratory experiment made by the Royal Society comes up,
* and Homberg's attempt to reproduce it (with negative results). This
* worries them: "It paroît presque incompréhensible . . . . Mais . . .
* peut-être n'est-il pas impossible que les réfractions célestes
* se fassent, non pas dans le passage de la Matiére Ethérée à
* notre Atmosphére, mais dans le passage d'une couche supérieure de
* l'Atmosphére à une inférieure plus épaisse."
* [NOTE: Hauksbee's 1709 experiment was made in response to this failure.]
* Bibliographic note: the proceedings of the pre-revolutionary Royal
* Academy of Sciences in Paris appear in two parts, usually bound together
* but separately paginated. The year usually given is that when the
* meetings took place; the actual date of publication is some years later.
* The first part is the meeting notes and abstracts of papers, entitled
* (typically) "Histoire de l'Académie Royale des Sciences, Année 17xx".
* This is usually abbreviated "Hist. Acad. Roy. Sci."
* The second part is the full text of the papers read, entitled
* something like "Mémoires de Mathématique et de Physique, tirés des
* registres de l'Académie Royale des Sciences" and again with the year
* of the meetings appended.
* This is usually abbreviated "Mem. Acad. Roy. Sci."
* The official title, according to the "Gallica" website from which
* this copy came, is "Histoire de l'Académie royale des sciences avec
* les mémoires de mathématique et de physique tirés des registres de
* cette Académie".
* Their scan is from the "Seconde Edition, revûë, corrigée &
* augmentée," printed in 1761.
* de la Hire's commentary on Bilberg's observations
* Here the story is a little different: "Le Roi de Suéde fit un voyage
* à Torneo, ville située dans la partie Septentrionale de la Suéde,
* vers le Solstice d'Eté de l'année 1694, mais comme il n'arriva dans ce
* lieu que quelques jours après le Solstice, il donna ordre à l'Auteur
* de ce Livre . . . ."
* He cites the facts of the case, and concludes that the refraction was
* 58' at Torneo, and still more at Kangis. Then comes his remark about
* the barometer, quoted in the meeting summary.
* J. D. CASSINI's commentary on Bilberg's observations
* "Je calculai des ces Observations, les Refractions du Soleil à ma
* maniére, & je les trouvai un peu plus grandes qu'elles n'avoient été
* calculées par les Observateurs."
* He re-reduces the Swedes' observations, using his refraction model
* and a solar parallax of 10''.
* I have a poor copy, as well as a much more readable one from
* "Gallica", which uses the second edition (1761). Both copies appear
* to be typographically identical.
* Philippe de la Hire's botched attempt
* He deserves credit for having made the first attempt to study the path
* of the refracted ray, taking account of the compression of the lower
* layers of the air by the weight of the upper ones --- the basic idea
* of hydrostatic equilibrium. But, not having the gas law, he supposes
* the thicknesses of successive layers of equal mass to be in arithmetic
* progression. Worse, he then mis-formulates the problem so as to obtain a
* cycloid for the shape of the ray path (in the flat-Earth approximation),
* or an epicycloid (allowing for sphericity). Why did no one notice that
* this would make the Sun and stars invisible, as every ray returns to the
* Earth's surface?
* This was read on 25 Feb. 1702, but not published until 1743.
* Continuation of de la Hire's epicycloidal theory
* This was read on 5 Aug. 1702, but not published until 1743.
* very early DIP VARIATIONS
* Pere Laval, reported by Cassini
* Dip varied from 13.5 minutes to 15
* ``. . . la diversité de la hauteur apparente de l'horizon se devroit
* attributer plutôt aux divers temperamens de l'air qui causent les
* refractions.''
* Cassini reports double images of the Sun at sunrise several times;
* Laval has seen the Sun set ``en forme de bonet detaché de tout l'horizon
* apparent''
* SEEING: ``Dans le plus grands instrumens on appercoit dans le Soleil &
* dans les autres astres un petit tremblement qu'on peut attributer aux
* divers degrés de la temperature de l'air par où ses rayons passent. . . ''
* ``Les observations proches de l'horizon sont sujettes à des variations
* par les diverses temperatures de l'air comme il paroît par l'usage des
* Lunetes, qui dans les grandes chaleurs sont voir une apparence de
* boüillonnement dans les objets éloignez.'' [first use of BOILING?]
*
* Bibliographic note: the proceedings of the pre-revolutionary Royal
* Academy of Sciences in Paris appear in two parts, usually bound together
* but separately paginated. The year usually given is that when the
* meetings took place; the actual date of publication is a few years later.
* The first part is the meeting notes and abstracts of papers, entitled
* (typically) "Histoire de l'Académie Royale des Sciences, Année 17xx".
* This is usually abbreviated "Hist. Acad. Roy. Sci."
* The second part is the full text of the papers read, entitled
* something like "Mémoires de Mathématique et de Physique, tirés des
* registres de l'Académie Royale des Sciences" and again with the year
* of the meetings appended.
* This is usually abbreviated "Mem. Acad. Roy. Sci." or sometimes
* "Anc. Mem. Acad. Sci." or ". . . depuis son établissement," to
* distinguish it from the later volumes (for years after 1699).
* According to the title page, this volume was printed in 1731!
* There was a still later edition, reprinted in Amsterdam, with different
* pagination. Reuss (Repertorium Commentationum ) gives its page as 98.
* very early DIP VARIATIONS
* Pere Antoin François Laval, reported by Cassini
* DIP varied from 11'46" to 14'30" from 144 feet height
* I have 2 copies of this. The one from the Gallica website has
* this item on pp. 89-91 (though p. 89 is mis-numbered 79). The Gallica
* copy has the long-tailed Q, and sets the names in Roman face; the other
* has a more modern Q, and sets the names in italics. Probably Gallica
* has the original, and I have the reprint, edition.
* Cassini's discussion of Laval's observations
* He calculates that the height of 144 (Paris) feet would produce a dip
* of 13' 14"; but the observed dip is only 11' 46"; "la difference entre
* cette hauteur & celle du rayon direct seroit d'une minute 28 secondes,
* que l'on pourroit attribuer à la plus grande refraction du rayon visuel
* qui rasoit la surface de la mer.
* "Mais le plus grand abbaissement apparent de l'horizon de la mer a
* été observé de 14' 30", qui est plus grand que celui du rayon direct
* d'une minute & 16 secondes; ce qui est contre les regles de la refraction
* qui devoit diminuer cette inclinaison . . . .
* "Nous avons déja remarqué par diverses autres observations, qu'une
* partie de la surface de la mer contiguë à l'horizon sensible, se confond
* à la vûë avec le Ciel, & que pour lors la circonference apparente de
* l'horizon sensible tombe dans la mer exposée à notre vûë." This
* must refer to some earlier observation of an inferior mirage at sea?
* "Comme nous avions communiqué cette reflexion au P. Laval sans
* qu'il ait eu aucune occasion de distinguer par quelque signe sensible
* cette difference, l'on voit combien il est difficile de la distinguer,
* & à quelle erreur est exposée la methode de chercher la grandeur du
* diametre de la Terre par l'observation de la tangente de la mer sans
* cette circonspection." (p. 196)
* ". . . la variation des hauteurs apparentes de la mer n'a aucun
* rapport regulier avec la variation qui s'observe en même temps dans le
* Thermometre & dans le Barometre; ce qui semble confirmer ce que nous avons
* remarqué plusiers fois, qu la partie de l'air qui cause la refraction
* est d'une nature differente de la partie à laquelle on attribuë la
* pesanteur qui équilibre la hauteur des liqueurs dans le vuide." (p. 197)
* [copy downloaded from Gallica.bnf.fr]
* Pere Laval, reported by Cassini
* According to Reuss, the copy I have is from the reprint edition; the
* original first page was 105.
* Pere Antoin François Laval
* JACQUES CASSINI's refraction theory and observations
* This is the abstract of Jacques Cassini's talk to the Academy on Feb.28,
* 1714. He reviews his father's theory, and explains how it was worked out.
* He explicitly says, "Afin que la difference de la hauteur veritable & de
* l'apparente soit plus sensible, & par consequent la quantité de la
* refraction plus exacte, il est bon d'observer le Soleil à une petite
* hauteur." [p. 80]
* On p. 83 occurs a typo that has been widely propagated: he first says
* the "seconde refraction" (i.e., in addition to that at the horizon) is
* 5' 28'' at 19 degrees above the horizon; but everywhere else, this is
* given as 10°. Then the method of approximation appears:
* ". . . il cherche en tâtonnant, ou estime à peu-près quelle doit être
* la hauteur de la matiere refractive qui les donne, & comme il trouve
* que cette hauteur étant supposée de 2000 Toises , les deux refractions
* viennent juste, il en conclut que la hauteur de la matiere refractive est
* de 2000 Toises , après quoi on peut calculer les angles d'incidence &
* de refraction pour tous les degrés , & par consequent les refractions
* qui leur conviennent.
* "Cette hauteur de 2000 Toises , qui n'est pas d'une Lieuë , est
* beaucoup plus petite que celle de 6 lieuës ; que donnent à l'Atmosphere
* ceux qui lui donnent le moins, comme Mrs. Cassini & Maraldi , car
* il y en a d'autres qui vont jusqu'à 18 ou 20. L'Atmosphere ne seroit
* donc refractive que dan une petite partie de son étenduë , & dans son
* couches les plus basses, ou, si l'on veut, la matiere refractive seroit
* differente de l'Atmosphere.
* "Mais l'hypothese d'où l'on tire cette hauteur de 2000 Toises est
* que le rayon rompu vienne à l'œil en ligne droite, & l'hypothese peut
* fort bien n'être pas vraye." [p. 84]
* ". . . M. Cassini fait l'hypothese la plus simple qu'il soit
* possible, c'est que la densité croisse toûjours également à chaque
* couche infiniment peu épaisse de la matiere , c'est-à-dire , comme
* les nombres naturels 1, 2, 3, &c. De-là il suit que le rayon rompu se
* détourne toûjours également, & comme à chaque pas infiniment petit
* qu'il fait il est le côté de la Courbe qui se décrit , cette Courbe
* est toute composée de côtés qui se détournent également, ou qui sont
* des angles de contingence égaux, & par consequent elle est Circulaire,
* puisque le Cercle seul a cette uniformité de Courbure." [p. 85]
* [Manifestly this is not true, as the local zenith distance varies.]
* On p. 86 is the first mention of greater refraction in winter; it
* is attributed to "vapeurs grossieres". But (p. 87)
* "Il faudroit donc differentes Tables de refraction pour les
* differentes saisons, & même pour les differentes temperatures de l'air,
* comme nous avons dit ailleurs qu'il en faudroit pour les differens
* climats." So SEASONAL EFFECTS are asserted.
* This is (of course) available at Gallica, and at the BHL.
* Its original title page shows a publication date of 1717, and cover
* pp. 61-67. But I have a photocopy of the Amsterdam reprint, whose
* title page shows it was actually published in 1719; its pages are 79-87.
* The page numbers above refer to the reprint, not the original.
* JACQUES CASSINI's full paper
* Here the details of the theory are worked out. More important, a
* considerable number of OBSERVATIONS of large refraction at the horizon
* in winter are given in detail.
* Some interesting quotes:
* "Ces refractions . . . diminuënt à mesure que les Astres s'elevent,
* & ne cessent entierement qu'au Zenith, comme mon Pere l'a démontré,
* quoique tous les Astronomes avant lui ayent été persuade's qu'elles
* étoient insensibles à la hauteur de 45 degrés." [p. 43]
* "Par la regle des refractions reçuë de tous les Philosophes, les
* sinus d'incidence sont toûjours proportionels au sinus des refractions,
* . . . ." [p. 45]
* In describing his father's method, he says:
* "Si cette refraction avoit été trouvée plus grande ou plus petite
* que celle qui avoit été déterminée par observation, il auroit fallu
* diminuer ou augmenter la hauteur AP de la surface refractive, jusqu'à
* ce qu'on l'eut trouvée de la quantité requise." [p. 46]
* His circular-arc ray moves the top of the atmosphere up about 3 1/2
* times higher than the uniform or "rectilinear" model. But: "Cette
* hauteur . . . est encore beaucoup plus petite que celle qu'on attribue
* à l'Atmosphere, ce qui sembleroit confirmer le sentiment de ceux qui
* croyent que les refractions sont causées par une matiere particuliere
* dont l'étenduë n'est pas si grande à beaucoup près que celle dont
* l'Atmosphere est composée." [p. 49]
* And of course he finds ". . . que les differences entre les refractions
* calculées pour la même hauteur par les deux methodes diminuent ensuite à
* mesure qu'on s'eloigne de l'horizon jusqu'à la hauteur de 15 degrés où
* les deux hypotheses donnent la même refraction . . . ." [p. 57]
* The OBSERVATIONS begin on p. 58. On 11 Jan. 1711, he found the Sun's
* upper limb refracted by 49' 48" at an altitude of 3' 5". The refraction
* near the horizon remained 7 or 8 minutes high (compared to the Table)
* on 30 and 31 Jan. and 7 Feb., "ce que j'attribuai aux vapeurs épaisses
* dont l'horizon est chargé en Hiver." On 1 Dec. 1712, the refraction
* was 41' 7" at 16' 50" altitude. The biggest was 51' 4" at 2' 40"
* altitude on Dec. 1, 1712. He has "toûjours trouvé la refraction
* horizontale en Hiver plus grande de quelques minutes qu'on ne la suppose
* ordinairement". [p. 60] Other large values were 46' 0" at 4' 50" on
* 7 Feb. 1713 and 43' 54" at 5' 0" on 24 Feb. 1713. [p. 61]
* Of course the refractions at altitudes of a few degrees fit his new
* model better than his father's. The daily variations die out at 3°
* or so. He concludes that ". . . vers l'horizon les refractions sont plus
* grandes en Hiver qu'en Eté, & qu'il faut employer des Tables differentes
* pour avoir la hauteur des Etoiles dans ces differentes Saisons."
* The figures are on a gatefold (p. 66) that can be laid out to the
* right of the bound volume while one reads the text. The Table (p. 67)
* is also a foldout. [These page numbers are for the Amsterdam edition,
* actually published in 1719. The 1717 original is available at the BHL
* and Gallica, where the pages are 33-52, the foldout figures are on p. 53,
* and the Table on p. 54.]
* JOHN FLAMSTEED's observed refraction table
* Filed slightly out of order here; it really belongs just after the
* Flamsteed-Newton file, but was published posthumously in 1725. But
* the refraction table was deduced in 1698 from observations made in the
* 1680s. And, as an empirical table, it logically goes with Kepler's
* Rudolphine tables -- whose arrangement it resembles, with the table of
* refractions at the very end of the volume. Used by Euler.
* The actual refraction table appears at the end of both Vol. I and Vol.
* II of this 3-volume work. The table at the end of Vol. I is headed:
* "Refractionum TABULA â præcedentibus Observationibus deducta &
* composita ab J. F. 1698", which means it was done after the exchanges
* with Newton about refraction theory. The table at the end of Vol. II
* simply says "Refractionum TABULA, per J. F. " The values in both are
* the same; but the seconds column in Vol. I always has 2 digits, with a
* leading 0 if the value is less than 10.
*
* The title page of Vol. I reads:
*
* HISTORIÆ COELESTIS
* B R I T A N N I C Æ
* VOLUMEN Primum.
*
* Complectens
* STELLARUM FIXARUM
* Nec non
* PLANETARUM OMNIUM
* O B S E R V A T I O N E S
* Sextante, Micrometro, &c.peractas .
*
* Quibus subjuncta sunt
* P L A N E T A R U M L O C A
* ab iisdem Observationibus deducta
*
* Observante JOANNE FLAMSTEEDIO, A.R.
* In Observatorio Regio
* G R E N O V I C E N S I
* CONTINUA SERIE
* Ab Anno 1675, ad Annum 1689.
*
*
* This faces a fine engraving of "JOHANNES FLAMSTEEDIUS Derbiensis
* Astronomiæ Professor Regius, Anno Ætatis 74 "
*
* BROOK TAYLOR
* Yes, this is the Taylor of "Taylor's Series". The final section of the
* book deals with refraction. He derives the exponential atmosphere, and
* the differential equation for the refraction, but then says (p. 110)
* it's necessary to resort to series expansions. No actual refraction
* is computed. The most interesting result is that the curvature of the
* ray is 1/5 that of the Earth (see p. 118 -- the last page of the book.)
* The notation is excessively awkward, using both dots and primes, both
* above and below the letters.
* Typographical note: Taylor often uses "q;" for "que". (Cf. Walther.)
* LENORE FEIGENBAUM's English translation of Taylor's "Methodus Incrementorum"
* See also Thomas Young's 1825 translation.
* Thanks to Lenore Feigenbaum for providing a copy of the refraction part!
* JACQUES CASSINI thinks he has found annual parallax of Sirius
* But he worries about annual variations in refraction: ". . . les
* refractions sont inégales en differentes saisons de l'année, plus
* grandes ordinairement en Hiver qu'en Eté." [p. 65]
* Details of Jacques Cassini's "parallax" and seasonal refraction work
* An interesting sidelight is the remark on p. 260 about "l'hypothese
* de Copernic, laquelle est la plus generalement rec,ûe" des Philosophes à
* cause de sa merveilleuse simplicité."
* Note also the paragraph at the top of p. 263 on daytime observations
* of Sirius transits, even when it passes the meridian at the same time
* as the Sun.
* But our interest here is in the SEASONAL VARIATION of refraction.
* On p. 264, he explicitly mentions the coldest day of the winter; on
* p. 266: "Il reste presentement à considerer si ces variations que nous
* venons de trouver . . . ne peuvent point être attribuées à l'effet des
* refractions, & l'on remarquera pour cela que s'il y a quelque inégalité
* dans les refractions d'une saison de l'année à l'autre, elles doivent
* être plus grandes en Hiver où l'air est plus condensé qu'en Eté où
* ce même air est plus dilaté.
* "Nous en avons même un exemple dans l'Observation de Sirius
* du 18 Janvier 1715, où le froid étant le plus frand de l'année,
* la hauteur Meridienne de cette Etoile fut observée plus grande qu'à
* la fin de Decembre de l'année précedente, ce qui ne peut attribué
* qu'à l'effet d'une refraction extraordinaire."
* See Halley (1720) for a strangely off-base comment.
* EDMUND [sic] HALLEY criticizes Jacques Cassini's "parallax" of Sirius
* (on the grounds that the variations are due to refraction changes)
* NOTE: filed slightly out of order here, because of the publication delay
* of the French Academie; but it logically follows Cassini (above).
* Citing Hauksbee's lab demo, Halley argues that the refraction changes in
* proportion to the pressure; as the barometer changes by over two inches
* out of 30, the refraction will likewise change by 1/15 of the 1' 55'',
* i.e., 7 or 8'' at the 25° meridian altitude of Sirius at Paris.
* Remarkably, the issue of seasonally varying refraction was already
* raised in the Histoire account of Cassini's paper! And in the Memoir he
* discusses this on p. 266, correctly attributing the seasonal variations
* in refraction to the expansion of the air (i.e., temperature) rather
* than Halley's implausible pressure variation.
* Referred to, but not cited, by Bruhns -- who mistakenly thinks the
* observations are Halley's rather than Cassini's.
* The second attempt by the French to measure refraction (air vs. vacuum)
* The work was done by Delisle; "l'experience qu'on avoit faite ici est
* fausse, & celle de Londres est vraie." (This must have been painful.)
* Delisle found that the French apparatus had leaked, so that the "vacuum"
* was actually air -- hence, the null result. He found a deflection of
* 45" at the window inclined 45°; but recognized that not all the air
* had been pumped out. "Si le Vuide du Tuyau de M. Delisle . . . a été le
* plus parfait, . . . il s'ensuite que le rayon . . . a dû en passant dans
* nôtre air souffrir une refraction sensiblement égale à la refraction
* astronomique . . . ."
* [published in 1721; the Academy is starting to catch up.]
* de Mairan shows how literally the "surface" of the air was understood
* The argument of interest here begins on p. 108: "Aux deux causes
* précedentes de la diminution de la chaleur en Hiver, . . . il en faut
* necessairement ajoûter une troisieme, qui est celle de leur obliquité
* par rapport à l'Atmosphere.
* "Il y a eu de grandes Physiciens qui . . . ont eu recours à
* l'obliquité des rayons sur l'Atmosphere, comme à la principale &
* presque unique cause du froid de l'Hiver." He then quote from Rohault's
* physics text: "L'air . . . s'élevant au dessus de la Terre jusqu'à
* la hauteur d'environ deux ou trois lieuës, ou les vents ni les nuages
* n'arrivent jamais, sa surface doit être fort unie, de même que celle
* de toutes les liqueurs qui ne sont pas agitées ; & comme c'est une
* proprieté des rayons de lumiere qui se presentent pour passer d'un
* milieu dans un autre, de n'y pas entrer tous, mais de se reflechir
* d'autant plus que leur chûte est plus oblique . . . ." Enough said.
* On p. 110 he talks about total internal reflection, and gives the
* critical angle for water: ". . . si la lumiere . . . passoit de l'eau dans
* l'air, du Milieu le plus dense dans le moins dense, elle ne se romproit
* plus du tout, de's que l'angle d'incidence seroit parvenu à n'être
* que de 41° 25' ; & que depuis cette obliquité jusqu'au parallelisme,
* tous ses rayons seroient absolument reflechis à la rencontre du nouveau
* Milieu."
* P. 111: "Chaque rayon prêt à entrer dans l'Atmosphere, peut être
* consideré comme une balle de Mousquet tirée contre la surface de l'eau
* d'un Bassin, laquelle aura d'autant plus de chemin à faire dans l'eau,
* avant que d'en toucher le fond, qu'elle y sera tirée plus obliquement.
* "Il semble donc, en supposant la surface particuliere de l'Atmosphere
* d'un Pays parallele au terrain, & de la même obliquité que l'Horison
* par rapport aux rayons du Soleil . . . ." (p. 112) -- but, as he has also
* vaguely alluded to scattering, maybe that's what he has in mind?
* On p. 113, he considers "l'Atmosphere chargée de vapeurs &
* d'exhalaisons, telle qu'elle est ordinairement dans toute sa partie
* inferieure, lorsque le Soleil est proche de l'Horison," and then says,
* "je ne pense pas que la surface de cette seconde Atmosphere, non plus
* que celle de la premiere, puisse être aussi unie que la surface d'une
* eau tranquille," which allows him to fudge, or at least arm-wave, about
* the calculation of the resulting attenuation.
* On p. 129 is an interesting reference to "les Hollandois, qui
* passerent l'Hiver dans la Nouvelle Zemble en 1597," and observed a
* refraction of 4 degrees: "sept à huit fois aussi grande qu'à Paris.
* De sorte que pour peu qu'elle augmentât encore à proportion en
* approchant du Pole, elle pourroit devenir suffisante, ou même plus que
* suffisant, pour y procurer un jour ou un crepuscule perpetuel."
* DELISLE's details of the air-refraction experiment
* "Par M. Delisle le Cadet". He modified the apparatus used by Homberg
* to ensure evacuation. The later English experiments agree closely
* with Flamsteed's measures of astronomical refraction; and the measures
* made with compressed air (evidently referring to Hauksbee's work)
* confirm that the refraction is proportional to the density of the air.
* "J'ai trouvé la même chose par mes Experiences," he says. But he
* can't reproduce the right absolute value; so (p. 334) "il paroît que
* la regle du rapport direct des Refractions avec les hauteurs de Mercure
* n'est pas toûjours vraye . . . ." On the last page, he offers several
* suggestions for improving the experiment, one of which indicates part of
* the source of his trouble: the glass covers of the tube ends need not be
* inclined so much; "il est vrai qu'en les inclinant moins, on diminué la
* quantité de la Refraction, ce qui la rend plus difficile à mesurer, mais
* aussi on voit moins distinctement au travers des Verres fort inclinés;"
* so it appears the problem is with the bad optical quality of these plates.
* So it was a very marginal technical accomplishment, which the English
* managed to do better than the French.
* NEWTON's refraction table, published by Halley
* [actually filed in the NEWTON file.]
* As Kramp (1799) and Biot (1836) showed much later, this is calculated
* from an exponential (i.e., isothermal -- because the gas laws weren't
* known to Newton) model atmosphere.
* JACQUES CASSINI's textbook
* Jacques ("Cassini II" or "Cassini fils") was the son of the original
* Giovanni Domenico Cassini, who became Jean Dominique Cassini when he
* moved to Paris. He claims this was the first textbook of astronomy in
* French: "Comme on n'avoit point encore d'Elémens d'Astronomie écrite
* en françois, & que le public sembloit le désirer . . . ." [p. xj]
* On the same page, he explains his approach: "La méthode que j'ai
* suivie, a été de ne supposer, autant qu'il a été possible, que ce
* qui étoit parfaitement connu, & de passer des notions les plus simples,
* à celles qui paroissent les plus composées."
* Of interest here is the explanation of his father's refraction model,
* which is on pp. 12 - 17. It is all done geometrically, in words; there
* are no equations. [See his Fig. 6 for the diagram.]
* "On peut déterminer les réfractions en deux manieres différents,
* ou par des observations immédiates des Astres, faites à tous les degrés
* de hauteur, ou bien par deux seules observations faites à deux degrés
* différens de hauteur, par le moyen desquelles on trouve la hauteur
* de la matiere qui rompt les rayons, & la réfraction qui convient à
* tous les autres degrés jusqu'au Zénit.
* "La premiere méthode paroît la plus naturelle, & on s'en sert
* ordinairement pour déterminer les réfractions des Astres lorsqu'ils
* sont peu éleve's sur l'horison: mais on est obligé d'avoir recours à
* la seconde dans les plus grandes hauteurs, lorsque la différence d'un
* degré à l'autre n'est pas assez sensible pour être apperc,ûe par des
* observations immédiates." [pp. 12-13]
* After explaining the direct method first, he arrives at the
* theoretical one, on p. 15:
* "Soit S (Fig. 6. ) le Soleil ou une Etoile, dont le rayon SH ,
* rencontrant la surface réfractive EGH en H , se rompt & vient à
* notre œil en A ; en sorte que HA soit perpendiculaire au
* demi-diametre AC de la Terre.
* "Cette Etoile sera vûe suivant le ligne AHI , & l'angle IHS
* mesurera la réfraction horisontale que l'on a trouvée par observation,
* de 32' 20'', de même qu'elle est marquée dans la Connoissance des Temps.
* "L'Etoile étant parvenue de S en F , soit un autre rayon FG ,
* qui rencontre en G la surface réfractive EGH , et vienne en A ;
* en sorte que l'angle HAG ou IAT , qui mesure la hauteur apparente de
* cette Etoile sur l'horison, soit de 10 degrés. L'angle TGF mesurera
* la réfraction qui convient à la hauteur de 10 degrés, que l'on a
* trouvée par observations, de 5' 28''.
* "Suivant la regle des réfractions . . . il s'agit de déterminer quelle
* doit être la hauteur AE de la surface réfractive EHL au-dessus de la
* surface de la Terre ABD , pour que le sinus de l'angle d'incidence PGF
* du rayon FG , soit au sinus de l'angle PGT ou AGC de réfraction
* de ce même rayon, comme le sinus de l'angle d'incidence OHS du rayon
* SH , est au sinus de l'angle de réfraction OHI ou AHC de ce rayon;
* et que l'angle TGF , qui mesure la réfraction à la hauteur de TGF ,
* qui mesure la réfraction à la hauteur de 10 degrés ,soit à l'angle
* IHS , qui mesure la réfraction horisontale, comme 5' 28'' à 32' 20''.
* "Soit supposée AE , hauteur de la surface réfractive, de 2000
* toises; le semi-diametre AC de la Terre étant, suivant la mesure de
* la Terre, de 3271600 toises, on aura CE , CG & CH de 3273600 toises;
* & dans le triangle rectangle CAH , dont les côtés CA , CH sont
* connus, on trouvera l'angle CHA ou OHI de 87d 59' 50'', auquel si
* l'on ajoûte l'angle IHS de 32' 20'', on aura l'angle OHS de
* 88d 32' 10''.
* "Maintenant dans le triangle CAG , dont les côtés CA , CG
* sont connus, de même que l'angle CAG de 100 degrés, qui est égal
* à l'angle droit CAH , plus l'angle HAG de 10 degrés, hauteur
* apparente de l'Astre sur l'horison; on trouvera l'angle AGC ou PGT
* de 79d 48' 12'', & l'on fera, comme le sinus de l'angle CHA de
* réfraction, lorsque l'Astre paroît à l'horison, que l'on a trouvé
* de 87d 59' 50'' est au sinus de l'angle OHS d'incidence, qui est de
* 88d 32' 10''; ainsi le sinus de l'angle AGC de réfraction, lorsque
* est élevé de 10 degrés sur l'horison, qui est de 79d 48' 12'', est
* au sinus de l'angle PGF d'incidence qui lui répond, que l'on trouvera
* de 79d 53' 40'', dont retranchant l'angle PGF de 79d 48' 12'',
* reste l'angle TGF de 5' 28'', qui mesure la réfraction qui convient
* à la hauteur de 10 degrés." [pp. 15-16.] Now comes the revealing part:
* "Si cette réfraction avoit été trouvée plus grande ou plus petite
* que celle qui avoit été déterminée par observation, il auroit été
* nécessaire de diminuer ou augmenter la hauteur AE de la surface
* réfractive, jusqu'à ce qu'on l'eût trouvée de la quantité requise.
* "La hauteur de la surface réfractive étant une fois établie,
* on peut trouver de la même maniere, la réfraction qui convient à
* tous les degrés de hauteur apparente d'un Astre sur l'horison,
* comme lorsqu'il est en K ; car dans le triangle AKC , les côtés CA
* & CK étant connus, aussi-bien que l'angle CAK , qui est égal à
* la hauteur donnée plus 90 degrés, on trouve l'angle CKA ou RKN ,
* que ce rayon fait avec la perpendiculaire, & l'on fera, comme le sinus
* de l'angle CHA de 87d 59' 50'' est au sinus de l'angle OHS de
* 88d 32' 10''; ainsi le sinus de l'angle CKA ou RKN est au sinus
* l'angle RKM , dont retranchant l'angle RKN , reste l'angle MKN ,
* qui mesure la réfraction qui convient à la hauteur apparente de
* l'Astre sur l'horison.
* "Suivant cette hypothese, qui représente assez exactement
* les réfractions que l'on a déterminées par observation, pour les
* diverses hauteurs des Astres sur l'horison, la substance qui cause les
* réfractions s'étend au-dessus de nous à une distance beaucoup plus
* petite que celle qui compose l'Atmosphere, puisque l'on trouve qu'elle
* ne monte qu'a 2000 toises, au lieu que l'Atmosphere doit surpasser de
* beaucoup la hauteur des montagnes de la Terre les plus élevées, dont
* il y en a plusiers qui excedent cette étendue.
* "Il est vrai que l'on a supposé dans cette recherche, que les rayons,
* après avoir rencontré la surface réfractive qui les détourne de leur
* premier direction, viennent droit à notre œil sans souffrir d'autre
* réfraction, au lieu qu'il y a beaucoup d'apparence, qu'en traversant
* l'Atmosphere, ils passent continuellement d'un milieu plus rare dans
* un milieu plus dense, & forment une ligne courbe suivant la tangente de
* laquelle nous appercevons les Astres. Mais comme il seroit nécessaire,
* pour déterminer cette courbe, de connoître les diverses dilatations
* de la matiere réfractive, à différents hauteurs au-dessus de la
* surface de la Terre, ce que l'on ignore jusqu'à présent; nous nous
* sommes contentés de rapporter cette méthode simple, par le moyen de
* laquelle on trouve avec facilité les réfractions, à peu-près de la
* même quantité que par les observations immédiates." [p. 17]
* We have this only on P-10 microprint cards!
* CASSINI III examines seasonal (temperature) effects
* He still has doubts that the refraction is due to air itself:
* ". . . de supposer que puisque la matière réfractive est plus dense
* en hiver qu'en été, & que cette densité a un certain rapport à
* la constitution de l'air . . . ."
* But he is mainly concerned with seasonal effects due to temperature
* variations: "Le grand froid qu'il a fait cette année qui a plus
* approché de celui de 1709 . . . , nous a fourni une occasion de
* déterminer le maximum de l'effet de ces variations en hiver."
* He is careful to check for instrumental effects; ". . . l'instrument
* que l'on a employé pour ces observations, avoit six pieds de rayon,
* & . . . on ne peut guère se tromper de plus de 5 secondes dans l'estime
* des divisions." [The observations were all made at altitudes from 18
* to 20 degrees, so they show only refractivity effects, not gradients.]
* On p. 211, he explains that "Avant que l'on connût les règles de
* l'Aberration, on ne sçavoit à quoi attribuer les différences que l'on
* remarquoit dans les hauteurs de certaines Étoiles, ou plûtôt on les
* rejetoit sur les erreurs de l'observation, & c'est une des principales
* raisons pourquoi on a ignoré si long-temps la cause d'un phénomène
* qui paroissoit si singulier, mais qui s'explique parfaitement dans
* l'hypothèse de M. Bradley."
* There follows a short section on observations of terrestrial
* refraction, which "On a toûjours négligé d'y avoir égard, soit
* parce qu'on les croyoit trop petites ou trop irrégulières, soit qu'on
* n'eût pas assez approfondi les règles de cette variation, ou formé
* des hypothèses suffisantes pour y avoir égard . . . ." On p. 214 there
* is further discussion of the variations in dip of the sea horizon.
* He thinks these variations are partly due to the humidity of the sea
* air, and partly due to the sea breeze, "qui repousse les eaux vers
* les côtes" [!]
* Actually printed in 1745.
*
* Report of Bouguer's observations in Peru
* The news here is that Bouguer has found the refraction less at higher
* elevations of the eye, contrary to Cassini's model: ". . . il a découvert
* un autre fait formellement contraire à ce qui paroissoit bien établi."
* At Pichincha, 527 toises above Quito, "On y respiroit à peine à
* cause de la grande subtilité de l'Air à cette hauteur, & le froid y
* étoit extrême . . . ." Tables are announced, citing the Mémoire.
* Details of Bouguer's observations in Peru
* This is a letter, datelined Quito, sent by Bouguer 24 Juillet 1737.
* He reserves for a later time the individual observations, and the
* method of constructing tables. Even so, a number of individual
* observations are given. The tables are constructed "en suivant en
* partie la méthode que j'ai expliquée dans la Piéce que je publiai en
* l'année 1729, sur la maniére d'observer en Mer la hauteur des Astres."
* [i.e, his prize essay.]
* From the smallness of the refractions observed at Quito, he concludes
* that Cassini's model merely assigns the refraction to a mean height
* (pp. 412-413). Interestingly, he recognizes that, at great heights,
* ". . . le froid, . . . en condensant l'air, peut faire une espece de
* compensation, & rendre l'inégalité moins considérable." (p. 414)
* He concentrated his attention around 15° altitude, because
* "Au-dessous, les Réfractions sont trop variables, & au-dessus trop
* petites, pour pouvoir être saisies avec précision."
* He thinks the refractivity falls with the 7th power of the distance
* from the center of the Earth (p. 420).
* BOUGUER'S SECOND MEMOIRE, 10 years later
* Here is promised "tout le géométrique & toute la théorie qui l'ont
* guidé dans cette occasion." From Chimborazo, he saw the Sun more
* than a degree below the astronomical horizon; but he claims a sudden
* jump in refraction at the astronomical horizon. Bouguer calls the
* part of the refraction on the ascending branch of the ray "de son
* véritable nom de Réfraction astronomique ; & la seconde, eu égard au
* trajet qu'il fait depuis l'œil . . . c'est ce que M. Bouguer nomme
* Réfraction terrestre . . . ." (p. 153)
* The limit of the refractive atmosphere (p. 154) he puts at 5158 toises.
* There is an interesting philosophical remark on p. 155 about the use
* of approximations to simplify the calculation: "Il y a peut-être un peu
* à perdre sur la précision géométrique, mais la véritable élégance
* d'une solution est d'être simple ; l'Astronomie offre assez de
* difficultés réelles, sans en aller chercher d'imaginaires, & qui
* n'auroient pour but qu'une exactitude inutile." Bouguer finds that
* the refraction is proportional to the angle at the center of the Earth
* between the observer and the point where the line of sight reaches the
* top of the atmosphere. (p. 156)
* He looked for diurnal variations, and found the refraction at night
* 1/6 or 1/7 greater than in the daytime, though this is only appreciable
* below 7 or 8 degrees. (p. 156) "Les variations diurnes des réfractions
* ne sont probablement dûes qu'à la dilatation des couches le plus basses
* de l'atmosphère . . . ."
* There is a curious remark about the effect of the supposed elongation
* of the Earth at the poles, and its effect on refraction, on p. 157.
* Finally, regarding his revisions of the earlier tables: "Combien de
* choses inconnues sur une matière aussi importante, & qui avoit été
* déjà traitée tant de fois!"
* BOUGUER's second memoir (1749) -- an amazing piece of work!
* He starts out: "On étoit persuadé en Europe, lorsque nous partîmes
* pour le Pérou, que les Réfractions astronomiques devenoient plus grandes
* à mesure que l'Observateur s'élevoit au dessus du niveau de la mer :
* ce ne seroit pas assez de dire que ce sentiment étoit presque général,
* car il n'y avoit sur ce sujet qu'un seul avis, & personne ne pensoit à
* en douter. C'est ce qui m'invita à ne pas abandonner si tôt l'examen
* des réfractions, après que j'eus reconnu qu'elles changeoient dans un
* sens contraire à celui qu'on avoit cru . . . ." -- and continues:
* ". . . je proposerai des expédiens aussi exacts que commodes pour
* construire les Tables anaclastiques . . . & de développer davantage tous
* les moyens de calcul que m'a fourni la solution analytique que j'avois
* déjà donnée de ce problème dans une pièce publiée en 1729" --
* i.e., the prize essay on measuring altitudes at sea.
* There is a nice description of the path of a ray from a star seen
* below the astronomical horizon, with the double path through the
* atmosphere below the observer (p. 80 and Fig. 1). He even has (p. 81)
* an early description of parallactic refraction: "il faudroit donc, dans
* la rigueur, augmenter la parallaxe de cette planète vers l'horizon,
* puisque c'est à peu près la même chose que si le semi-diamètre de la
* terre étoit un peu plus grand." [Note also his distinction between
* "l'atmosphère" and "la matière réfractive."] He explicitly points
* out the symmetry of the ray about its lowest point. Here (p. 82) he
* denotes the terrestrial refraction as the whole part below eye level.
* In discussing the theory (p. 84), he refers to "la matière qui cause
* la réfraction & qui est répandue dans l'air" -- clearly distinguishing
* between "air" and "the refractive medium". He then refers to his 1729
* theorem involving a power of the distance from the center of the Earth,
* and offers a more direct and elegant proof of it. (pp. 85-90 & Fig. 2)
* There is a nice line on p. 85: "Toutes les fois qu'on parvient par
* de longs circuits à des propositions très-simples, il doit y avoir
* d'autres chemins qui y conduisent : il n'est pas possible qu'une vérité
* qui se réduit à des rapports peu complique's, ne soit pas susceptible
* d'une démonstration très-courte."
* Note that his "dilatations" are the reciprocals of the refractive
* index as a function of radial distance from the center of the Earth; so
* if we would say n is inversely proportional to Rm, this gives his
* exponent m .
* On p. 86, he discusses explicitly the question of the "refractive
* material": "Il se pourroit fort bien qu'il n'y eût point de matière
* réfractive, & que les réfractions répondissent, non pas aux dilatations
* de l'air grossier, mais à une certaine fonction de ces dilatations . . . .
* Ce seroit toûjours la même chose pour nous : nous serions même tentés
* d'admettre cette seconde hypothèse, mais nous continuerons néanmoins
* à designer sous le nom de matière réfractive cette fonction . . . le
* rapport de sinus d'incidence & du sinus de réfraction . . . ."
* He then uses the geometric impact parameters at two neighboring points
* along the curved ray to relate them to the ratio of sines (i.e., the index
* of refraction). The ordinates of his curve BGI plot the reciprocal of
* our index of refraction. The argument proceeds in very geometric terms;
* the analytic relations are expressed in terms of ratios and proportions.
* On pp. 89-90 he effectively derives the refractive invariant.
* On p. 93, he points out that if the refractive index were inversely
* proportional to radial distance, the ray would keep a constant inclination
* to the local vertical, and be exactly a logarithmic spiral. Thus a
* horizontal ray would circle the Earth: "elle s'étendroit circulairement
* tout autour de la Terre, & elle ne seroit bornée que par l'Observateur
* même, qui se verroit de dos." [Thus beating Kummer by over a century!]
* He also sees that a stronger rate of decrease of refractive density will
* cut off the sky near the horizon -- thus pre-empting Bravais (1853) and
* Hasse's Kimmfläche (1960).
* On p. 95, he says that the radius of curvature of the ray must be 7
* or 8 times that of the Earth. Then, as the ray is so nearly straight,
* its length can nearly be replaced by that of its tangent or its chord.
* This leads to the conclusion that, if the refraction is proportional to
* the projection of the curved part onto the Earth's surface, it is also
* proportional to the projection of the line of sight from the observer to
* the upper surface of the atmosphere -- which he found from his Peruvian
* observations to be at a height of 5158 toises (about 10 km). He adds
* (p. 96) that for more accuracy, the apparent ZD should be decreased by
* about half the refraction, in doing this calculation. [The similarity
* to Bradley's rule is obvious.] "Ainsi il suffira de connoître m , ou
* de connoître une des réfractions, pour avoir toutes les autres, & cela
* par un calcul extrêmement simple ; il faudra seulement être attentif
* à ne pas conclurre les grandes réfractions par les petites, mais à
* inférer au contraire les petites de l'observation des grandes." (p. 97)
* He concludes that m is about 7 5/8.
* [Notice that all this scaling of refractions in proportion to the
* horizontal lengths, or the length from the observer to the "top of the
* refractive material," is a result of assuming a linear decrease in
* refractivity from the ground to the top of the atmosphere.]
* Then he considers the refraction at the edge of the Earth's shadow
* in lunar eclipses. He also (pp. 98-99) invokes terrestrial refraction
* observations made from both ends of a long line of sight to estimate m
* independently, which gives him 7 22/25 from his observations in Peru.
* A further check comes from the observed "terrestrial" refraction
* observed at a depression of 1 degree from Chimborazo; this gives 7 and
* 431/967 for (m - 1). On pp. 100-101, he tries another check, this time
* searching for the m that fits 2 refractions at different altitudes by
* successive approximations; this gives m = 9 1/8.
* Section III (p. 102) considers DIURNAL VARIATIONS. He finds (p. 105)
* that the nocturnal refraction is greater than the diurnal by 1 part in 6
* or 7. [Of course, some of this must be due to temperature, which he did
* not record.] This applies at apparent altitudes below 7 or 8 degrees.
* "Sans doute qu'elles ne sont jamais portées plus loin que quelque temps
* avant le lever du Soleil : c'est alors que le froid est le plus grand;
* l'atmosphère plus condensée doit avoir perdu le plus de sa hauteur,
* au moins par sa partie inférieure, & il n'est guère vrai-semble que
* la matière réfractive ne participe aussi un peu à cette altération."
* He then shows (p. 106) that the horizontal refraction should change
* inversely as the square root of m , if m changes [of course, assuming
* the same refractivity at the surface!] -- cf. Ivory's later comment
* on Mayer's formula. He notes that "Hauksbée . . . en Angleterre" had
* found a much smaller change in the volume of air with seasonal change
* in temperature than needed to account for the observed diurnal changes
* in refraction. So (p. 108) he invokes de Mairan's 1721 remarks about
* "vapeurs". But he makes a good argument that the diurnal effects must
* reside in the lowest layers of the atmosphere: "l'air est trop diaphane
* pour contracter beaucoup de chaleur par l'action immédiate des rayons du
* soleil qui le traversent; il s'échauffe par le voisinage de la terre &
* par celui des corps qu'il touche : la chaleur qu'il a acquise doit ensuite
* se transmettre peu à peu aux couches supérieures; mais elle doit le
* faire toûjours assez lentement . . . : les plus grandes changemens se
* font donc toûjours en bas . . . ."
* On p. 109, he mentions the effect of the shape of the Earth: the
* radius of curvature depends on azimuth. He has the sense of the effect
* correct: "La courbure de la circonférence de la Terre se trouvant plus
* grande dans le sens du méridien que dans celui du premier vertical,"
* so the refraction should be larger in the latter. But the effect is
* negligible for ordinary purposes.
* The paper concludes with a revised table of refractions for Quito,
* superseding that of 1739.
*
* THOMAS SIMPSON's work -- a lead-in to Bradley and Oriani
* This is the origin of "Bradley's formula" -- Bradley found better
* values for the constants.
* P. 54: ". . . let the Law of Density of the Atmosphere be what it
* will, the Refractions of the Sun , Moon and Stars, at all Altitudes
* except very small ones, will be nearly as the Tangents of their apparent
* Zenith Distances drawn into the respective Density of the Atmosphere, at
* the Places and Times, for which such Refractions are to be determined ;
* and therefore if the Density be the same, are simply as the Tangents
* of their Zenith Distances." On p. 55, he investigates the accuracy of
* this rule, by dividing the atmosphere into two parts at the level where
* the density is half that at the surface. "Now the Height of this Surface
* . . . cannot be more than about 5 Miles, or 1/800 of the Earth's Radius."
* So, on p. 56, he finds that the refractions above 20° altitude can be
* inferred from that at this limit, regardless of the "Law of Density".
* P. 57: "If the Density of the Atmosphere, in going from the Earth,
* be supposed to decrease uniformly (which Law will be found to answer
* better to Experiment than the commonly received one, founded on the
* Elasticity of Air) . . . " [Of course, Mayer re-did this model better
* in 1755, but failed to publish his work.]
* Simpson adopts the uniform decrease of density with height, but worries
* about its conflict with the exponential decrease of pressure with height.
* On the other hand, the exponential model predicts too large a horizontal
* refraction.
* P. 61: ". . . the refraction in high altitudes, it has been proved,
* will be but little affected by different Laws of Density, and therefore
* come out very near the same, compute them according to what Hypothesis
* you will; even so near, that if the Refraction at any Altitude not less
* than about 7 Degrees be truly given from Experiment, the Refractions,
* computed from thence, for any higher Altitude, will never differ from
* one another by more than about 2 Seconds." [cf. Oriani]
* Available from Google Books.
* TOBIAS MAYER's unpublished (until recently!) letters, translated by
* Eric Forbes, who gives the chronology on p. 8; see p. 25 for its notes.
* Mayer's formula first appears on p. 50; the derivation is discussed rather
* sketchily on p. 46. Both cover his letter to Euler dated 6 Jan. 1752,
* which is why I place this reference here instead of 219 years later.
* Forbes notes that Mayer's formula is too small near the horizon, but
* apparently does not understand why.
* Here is Forbes's translation of Mayer's explanation [the notes to these
* pages are on pp. 102-103.]:
* ". . . the most worthwhile result that I got out of it was when I took
* the curve of density to be a straight line . . . . Then, in this case,
* the formula for the refraction may be integrated by simple logarithms,
* or even algebraically by means of a suitable approximation. . . . Now,
* although this hypothesis is an open contradiction of the truth, the
* resulting formula for the refraction nevertheless agrees very closely
* with observations, and this makes me think that it would not really help
* much if one were to choose straightaway another and better expression
* for the density of the air. I have already seen Mr. Bouguer's treatise
* ten years ago . . . ." [Note: Mayer uses ρ for the refraction, and
* α for the zenith distance. And, according to Delambre's Histoire ,
* the Bouguer works cited by Euler on p.44 and Mayer on p. 46 must be his
* crowned essay "Méthode d'observer exactement sur mer la hauteur des
* astres"; Forbes's references to B.'s papers in Mem. Acad. Roy. Sci.
* make no sense, as those contain only observations, not theory.]
* It appears from Mayer's remarks on p. 47 that he found it useful to
* fudge the height of the atmosphere to agree well with the refraction data:
* ". . . where 36,000 is the number" of Paris feet in the model atmosphere's
* height. "According to Mr. Bernoulli one must assume for it 22,000 which,
* however, is contrary to experience; and if the densities decrease in
* exactly the same ratio as the elasticities" [i.e., if the atmosphere
* were isothermal], "the same divisor would be 27,000."
* LEONHARD EULER's paper
* See Kramp (1799) for trenchant criticism of Euler's work -- although
* Plana (1828) showed that Kramp himself made many serious errors.
* Of interest here is his matter-of-fact acceptance of atmospheric
* dispersion (p. 131): ". . . comme les rayons, qui sont de diverses couleurs,
* souffrent des réfractions differentes, je considère ici seulement
* les rayons d'une telle nature moyenne, qui est également eloignée de
* ceux, qui subissent ou la plus grande, ou la plus petite réfraction :
* car c'est par rapport à ces rayons moyens, que les Astronomes sont
* accoutume's de dresser leurs tables de réfraction."
* Euler calls the refractive index 1/α . However, he then says
* that the refraction is the same in passing from air of density c to
* density 2c as in passing into the first from a vacuum, thus making
* α, or the refractive index, a power-law function of the density.
* [This is of minor practical consequence, however.] (p. 132)
* This might be the first paper where ζ is the local zenith distance
* at the observer; ω is the local ZD along the ray (p. 133).
* His constant C (p. 134) is the refractive invariant. The equations here
* show an interesting transition from the pure proportions used earlier
* toward the purely algebraic notation of later writers.
* Euler works largely geometrically; so he thinks the way to discover
* the refraction is to have the path of the ray first (p. 135). But
* one good consequence is that he sees immediately that the perpendicular
* to the ray's tangent at infinity is the impact parameter of the ray's
* asymptote in air (p. 136); he calls this perpendicular length p .
* He then (p. 137) considers the hydrostatic equation, and realizes that
* the density is proportional to the pressure only at constant temperature
* (p. 138). And he imagines a thermometer graduated on an absolute scale,
* so that at constant pressure this temperature is inversely proportional
* to the density. (p.139)
* The cumbersome rational exponents on p. 139 show the typographical
* disadvantage of using a fixed size of type, instead of a smaller font for
* superscripts and exponents. Although the printer finally resorted to a
* smaller exponent face on p. 141, the equations there too are hard to read,
* due to (a) extra-long equality and minus signs, (b) a refusal to break
* equations across lines, and (c) placing the LHS on the line above the RHS.
* The lack of space before and after equations also impairs legibility.
* On p. 142, Euler assumes the ray has the form of a negative power-law
* with exponent m . This is far from the truth, so the rest of his
* development is not very useful. The familiar number 206265 appears on
* p. 148. Then complete speculation is introduced about the height at
* which the (absolute) temperature would be half that at the surface; he
* guesses it would "surpasse de beaucoup une mile d'Allemagne." So he
* tries 2 German miles [about 15 km]. (Later he tries 3 miles.)
* Another typographical note: he uses an S turned sideways for an
* infinity sign (pp. 150-152).
* On p. 158, he comes up with the first 2 terms in the tan Z expansion,
* when 10 μ tan2 ζ is small; another expansion when it is large;
* and yet a third expression for the intermediate values. There is an
* interesting Freudian slip on p. 159, where he says "parallaxe horizontale"
* for horizontal refraction. He proposes a horizontal refraction that
* varies with the barometer and thermometer. Perhaps these considerations
* influenced Mayer.
* On pp. 161-164, he compares his theories with the observational table
* of Flamsteed, and the theoretical one of Cassini. Finding Cassini's
* values more consistent with his model with a temperature gradient, and
* Flamsteed's closer to the isothermal one, he concludes: "D'où il semble
* qu'en Angleterre le degré de chaleur de l'atmosphère en montant diminuë
* moins qu'à Paris." Only a theoretician could do such a thing!
* On p. 168, he decides that the tangent approximation is good enough
* out to 70° ZD; and that "qu'à moins que l'astre ne soit trop proche
* de l'horizon, la réfraction est assés exactement proportionnelle
* à la hauteur du barometre; & réciproquement proportionnelle à
* la hauteur du thermometre, ou plutôt au degré de chaleur. Mais,
* pour les hauteurs de l'astre fort petites, le changement causé par le
* barometre & le thermometre devient plus grand que selon lesdites raisons,
* & cela surtout à l'égard des changemens de la chaleur."
* He then summarizes his results, dividing them into 3 cases as before
* (near zenith, near horizon, and intermediate). Interestingly, he
* notes that when the zenith distance exceeds 90°, which can occur
* when the observer is quite high, the refraction becomes greater than
* the horizontal; but of course this was already seen by Bouguer in Peru.
* The Supplement on p. 171 refines his earlier derivations somewhat,
* and again recognizes that the tan Z approximation is good near the
* zenith, and does not depend on atmospheric structure.
* Note: the Plate with Figs. 1 and 2 follows p. 346.
* This paper is in the section called: Mémoires de l'Académie
* Royale des Sciences et Belles-Lettres, Classe de Mathématique
* and is available at
*
* http://bibliothek.bbaw.de/bibliothek-digital/digitalequellen/schriften/#A2
* JOHANN HEINRICH LAMBERT's refraction monograph (1758 and 1759 editions)
* Note the extended references to Bouguer's work on photometry in
* the Avant-Propos (pp. 5-7): "La Photométrie n'est pas un païs
* entierement inculte. Des savans fort célebres y ont travaillé. Mr.
* Bouguer en a donné un tres bel Essai sur la Graduation de la lumiere.
* Il la fait pasier par plusieurs vitres, par l'eau, par l'athmosphere. Il
* en cherche l'affoiblissement. Il s'en sert pour la célebre expérience
* sur la comparaison de la Clarté du Soleil & de la Pleine-Lune." And
* this passage is *quoted* in the introduction to Lambert's Photometria
* -- so how can people say he did everything independently from Bouguer?
* Lambert's orientation as a theoretiker shows in the presentation:
* he begins with many geometric theorems, and only later gets to the
* matter of refraction. According to Houzeau, Lambert introduced
* the notorious series-expansion approach; and here it is, on p. 45:
* "\section. 76. Exprimer les refractions par une suite." He expands
* the square root in the denominator using the binomial theorem, first
* obtaining a slowly-convergent series in sin z (which he calls γ),
* ". . . dont les termes croissant suivant les puissances impair . . . "; then,
* transforming the terms into a faster-converging series in the tangents.
* So on p. 47, section 78: "On poura donc exprimer les refractions par la
* suite . . . ", which is the usual one with alternating signs.
* On p. 70, section 103, is an application to terrestrial refraction.
* "Mr. Cassini a observé au pied du clocher a Massanne la dépression
* apparente de la surface de la mer, & la trouva de 50',20''. & la hauteur
* de la Tour au-dessus du niveau de la mer de 408 1/2 toises. . . . Ces
* valeurs etant substituées dans la formule . . . [p. 71] on trouve
*
* x = 7,06 = R.
*
* De sorte que la raïon horisontal etoit sept-fois plus grand que celui
* de la terre." [A second example gave 7.02; he adopts 7.]
* pp. 75-76: He shows that the terrestrial refraction is half the
* reciprocal of this number, times the angle at the center of the Earth,
* so that 1/14 of that angle is the terrestrial refraction.
* A curious feature (and one typical of Lambert) is his "proof", on
* p. 77, that refraction cannot alter the apparent size of an object:
* having established (given certain assumptions and approximations!) that
* the terrestrial refraction depends only on this central angle, he derives
* as a corollary that it can only displace objects vertically, not alter
* their apparent size. [So mirages would be impossible!] -- another
* example of Arthur Searle's comment [Obs.22, 310-311 (1899)] that
* "In particular, Lambert's theory, developed in his `Photometria,'
* had been regarded as almost demonstrably true, while, in fact, it
* consisted of an ingenious mathematical superstructure on a very
* insecure foundation."
* Full title is:
* "Les proprietés remarquables de la route de la lumière, par les
* airs et en general par plusieurs milieux refringens spheriques et
* concentriques, avec la solution des problèmes, qui y ont du rapport,
* comme sont les refractions astronomiques et terrestres, et ce qui en
* depend"
* N.B.: This seems to be a reprint on the Readex cards. The NUC lists
* the 1758 edition, published by "Chez H. Scheurleer, F.Z. & Compagnie",
* also at La Haye -- a photocopy of which is now available at
*
* http://www.kuttaka.org/~JHL/L1758a.pdf
*
* The body type of the two editions is identical, even including the same
* list of "Fautes á corriger" at the end of p. 116. Only the title
* page appears to have been reset for the 1759 edition. The Dutch
* typesetters seem to have had some difficulty with the French: the
* left-hand running head varies from "Les Propriétés Remarquables" (pp.
* 10 - 16) to "Les Propriétes Remarquables" (p. 18) to "La Propriétes
* Remarquables" (p. 20) to "Propriétes Remarquables" (pp. 22 - 26) and
* back again.
* [cited by Kramp]
* NEVIL MASKELYNE publishes BRADLEY's rule (1763)
* Bradley's rule is described on pp. 120-121: ". . . a rule formerly
* communicated to me by the late Dr. Bradley, and deduced by him from his
* observations, according to the principles contained in a paper of the
* late Dr. Simpson's, in his Mathematical Dissertations." And the whole
* procedure then follows, including the corrections for temperature and
* pressure.
* On pp. 86 ff. are directions for observing lunar eclipses. I was
* surprised to read: "if any telescope is used, it must be one that has a
* great deal of light . . . . Those called night glasses may be very
* conveniently used . . . ." I was not aware that term was in use this early.
* This is the first edition of many; it seems to be a sort of precursor
* to the old Nautical Almanacs, with tables of the Sun and Moon, star
* positions, etc. The years covered are 1760 to 1780. These tables are
* given capital Roman numerals, and are at the back of the book. The
* refraction table is on p. I.
* The title page says "Printed for the author; and sold by. . . " (listing
* several London booksellers). I list only the first.
* Available at the Gale website
* MASKELYNE publishes BRADLEY's rule
* [For proof that it comes from Simpson, see Rigaud's Supplement, 1833.]
* On the first page, he says, "The two rules for the correction of
* refraction and parallax I have also . . . communicated to the public in
* my British Mariner's Guide" [published in 1763].
* P. 265: "This rule is founded upon an hypothesis that the refraction
* in altitude is as the tangent of the zenith distance . . . . This rule
* is exact enough for the purpose of the calculation of the longitude
* from observations of the distance of the Moon from stars at sea as
* low down as the altitude of 10°, for there the error is only 10''
* from the truth. But, if the altitude of the Moon or star be less than
* 10°, the rule may be still made to answer sufficiently, by only first
* correcting the observed zenith distances by subtracting from them three
* times the refraction corresponding to them taken out of any common table
* of refraction, and making the computation with the zenith distances
* thus corrected. This correction depends upon Dr. Bradley's rule for
* refraction, which he found to answer, in a manner exactly, from the
* zenith quite down to the horison, namely that the refraction is = 57''
* × tangent of the apparent zenith distance lessened by three times
* the corresponding refraction taken out of any common table."
* [See Maskelyne's further comments in 1787. Bradley died in 1762.]
* TOBIAS MAYER's refraction formula, published posthumously by Maskelyne
* An amazingly important work in the history of astronomy, for it contains
* the "lunar distance" method of finding longitude that won Mayer's widow
* a share of the Board of Longitude prize, as well as testimonials from
* navigators about the practicality of the method. However, our interest
* here is merely in the formula for refraction.
* The text is given in both Latin and English. The refraction formula
* appears on pp.64 (Latin) and 117 (English). On the next page, we read
* that the formula is "deduced from theory", without further explanation.
* (The origin of Mayer's theory was debated for years -- cf. Delambre,
* Plana, etc. -- until the Euler-Mayer correspondence was discovered, and
* published by Eric Forbes in 1971.)
* Lambert's crazy paper about the atmosphere
* Having essentially repeated Newton's calculation for the speed of sound,
* assuming the isothermal compressibility of air (Mem. 1768, p. 70-79),
* which gives a result about 15% too small, Lambert thought he could
* fudge up the right answer by increasing (!) the density by some 30%,
* attributing this to foreign matter suspended in the air.
* Here he extends this idea to refraction. He distinguishes between
* a supposed "air pur" and "air naturel" that contains the suspended
* matter, starting from the discrepancy in calculated refraction at the
* horizon found by Simpson, who "trouve qu'en supposant l'air naturel,
* la réfraction horizontale iroit à plus de 50', tandis qu'elle n'est
* que de 32 ou 33 minutes. Cela le porte à supposer une matiere
* réfractive, qui décroisse uniformément en montant. Cette hypothese
* emporteroit la conséquence, que la matiere réfractive ne s'étend
* qu'à une certaine hauteur, puisqu'au-dessus de cette hauteur elle
* devendroit négative. Mr. Bouguer paroit admettre une supposition
* assez semblable, puisqu'il prétend qu'a une hauteur qui va au-dessus de
* 5118 toises sur la mer, le réfractions sont nulles." " (p. 104) This
* somewhat misrepresents Bouguer's actual point of view; but it provides
* an interesting hint as to why the French supposed the "refractive matter"
* did not coincide with the air itself.
* On the next page, he argues that the "particules étrangeres" affect
* only the weight of the air, not its refractivity. On p. 106, he notes
* that "On sait qu'en pompant l'air il paroit d'abord un brouillard" -- an
* early observation of the cloud-chamber effect! -- "& qu'à mesure qu'on
* continue d'exténuer l'air ces particules commencent à tomber peu à
* peu dans le fond du verre, l'air exténué n'ayant plus assez de force
* pour les soutenir toutes dans ses interstices." So far, so good.
* But then: "Mais comme avec tout cela le brouillard qu'on voit dans le
* cloche après les premiers coups de piston, tombe peu à peu au fond de
* la cloche, il semble que la densité des particules étrangeres diminue
* plus fortement & plus vite que la densité de l'air."
* The real sloppiness begins on p. 107, where he has AEC for AEB
* (second line of section 9). On p. 108, the second equation in section
* 10 is missing an R on the RHS. Then in section 11, he supposes the
* density proportional to the log of the refractive index, instead of
* the refractivity. Naturally, this leads to a contradiction (p. 109) --
* but he attributes the discrepancy to a deviation of the refractivity
* from being proportional to the density of air (despite having cited
* "Hawksbee" on p. 106); and then attributes this difference to the effect
* of the foreign matter.
* On p. 110, the ever-popular "vapeurs" take a share of the blame.
* He contrives to fudge the compensating effects of the vapors and
* the suspended particles so as to maintain Mariotte's law. But then
* (p. 112) he acknowledges that he has to take account of the decrease in
* temperature with height; and now it gets really arm-wavy. In section 24
* (p. 114) we have: ". . . le feu est spécifiquement plus léger que l'air.
* En conséquence les particules de feu doivent monter avec une vitesse
* accélérée, la vitesse initiale étant celle avec laquelle elles
* s'élancent par leur propre élasticité. La force accélératrice est
* cette même légéreté spécifique." We are off into far left field;
* this is practically a crank work from here on -- especially as he then
* has many pages of mathematics purporting to describe the equations of
* motion of the "particles of fire". This is indeed "an ingenious
* mathematical superstructure on a very insecure foundation," to quote
* Searle again.
* On p. 118, he decides that "la densité des vapeurs décroit comme le
* quarré du poids de l'atmosphere," and affirms that "Cette conséquence
* paroit être assez vraie par elle-même." But on p. 120, there is
* some weasel-wording: "il faut observer que l'air peut être extremement
* chargé de particules aqueuses, sans qu'il paroisse être humide" --
* whatever that is supposed to mean. By p. 128 he has worked out his
* elaborate theory for the air, giving a table of the adopted components
* as functions of height. On p. 131 is more weasel-wording to explain
* away situations in which his model doesn't work.
* Then he returns to the speed of sound, taking into account his
* elaborate model -- again (p. 132) cautioning that it doesn't work
* "pour les anomalies journalieres ou acidentalles." In other words,
* when his theory agrees with observations, it proves the theory is right;
* when it doesn't, the atmosphere is "abnormal" so it doesn't matter.
* Classic crank reasoning. Discrepancies with observation are also
* blamed on the wind (section 52).
* He returns to refraction on p. 138; on the next page, he gives the
* differential equation for refraction in his theory, but does not solve it
* (section 58). In the final section, he refers briefly to his earlier
* result about terrestrial refraction.
* In sum: Lambert at his worst. Note that Bruhns missed this one.
* (Available at the Berlin Academy website, bibliothek.bbaw.de/bbaw/ )
* JOSEPH-LOUIS LAGRANGE's paper on refraction
* Lagrange cites de Luc's (1772) experiments on the density of air, and
* assumes a linear lapse rate. He denotes the natural log function by "l",
* and common ("tabulaire") logs by "L"; so his conversion modulus m
* is 1/l10 = 0.4342945. The first part is devoted to the barometric
* law, and determining the heights of mountains. Only on p. 270 does he
* start to deal with refraction at last, citing "Hawksbee"'s experiments.
* He calls the refractive index (i.e., the ratio of sines) "raison de
* réfraction"; then his n is what we would call the refractivity [our
* (n-1)], The refraction he calls ρ.
* His temperatures are all Réaumur degrees above or below de Luc's
* reference temperature of 16°¾; so his absolute zero for thermal
* expansion is 215°R below that point. This makes his correction
* factor (1 + t /215). [Oriani adopts this value also.]
* On pp. 278-279, he shows that "la réfraction est généralement
* proportionelle à la hauteur du baromêtre, & à la tangente de la
* distance apparente de l'astre au zénith, lorsque cette distance est
* assez différente de 90° pour que 2α/cos Z soit une quantité
* très petite vis à vis de 1." [His α is essentially H/R.]
* Then he shows that the refraction can be integrated if one assumes
* the radial distance is a power of the refractive index. But (p. 281)
* Simpson's values of the constants disagree with de Luc's measurements
* [in our terms, Simpson's linear model requires the wrong lapse rate.]
* He then examines Bradley's formula, and shows how it corresponds to his
* power-law relation. "Ainsi la regle de Mr. Bradley est nécessairement
* sujette aux mêmes difficultés que celle de Mr. Simpson, à laquelle
* elle revient dans le fond."
* He concludes by saying that Mayer's formula disagrees with the tangent
* rule below 70° Z.D. (p. 282)
* The Berlin Academy was modelled after the Paris one, including the use
* of French as its official language. These pages are available as *.jpg
* images at http://www.bbaw.de/bibliothek/digital/ now. Note that
* they appeared 2 years after the year of the meetings; so this is
* usually cited as "1772". Plate V follows p. 140 (Lambert's paper).
* Cited by Delambre/Mathieu, and mentioned without citation by Bruin;
* reprinted in Serret's Oeuvres de Lagrange, v. III (Paris, 1869),
* pp. 519-545. Oriani's 1787 work is based on this paper.
* LE GENTIL's refraction observations below 14° altitude, and table
* Here he criticizes Bouguer's measures in Peru as being too small.
* Le Gentil's observations were all made in 1769 (not 1796 as printed
* on p. 431).
* In the discussion, he prefers Cassini's model of a uniform
* atmosphere. To fit his own data at 10° and 14°, he requires the
* height to be 1750 toises, not 2000 as Cassini had it for Paris.
* [NOTE: He correctly describes Cassini's procedure (p.441), namely
* that he assumed a height, calculated a table from the horizontal
* refraction, and adopted the result that agreed best with observations.
* The calculations on pp. 442-443 show in detail how Cassini's model
* is worked out.]
* The adjoined Table (pp. 446-447), calculated by Duvaucel, of course
* shows the parabolic behavior near the horizon, being tabulated at 15'
* intervals there, the (tabulated!) differences being very nearly in the
* ratios of 1 : 3 : 5: 9 for the first degree.
*
* Ch. I, Art. IV. Observations sur les réfractions, à différentes
* hauteurs au-dessus du niveau de la Mer, toujours à 46 pieds environ
* au-dessus de son niveau.
* The footnote says:
* "Ces Observations ont été lûes à l'Académie royale des Sciences,
* dans son assemblée du 27 Novembre 1774."
* Note that p. 439 is incorrectly marked 349.
* MASKELYNE's further reminiscences of Bradley's work
* Maskelyne's aim is to correct Cassini III's notion that the separation
* between Paris and Greenwich was uncertain by 15 seconds or so. To do
* so, he exposes the details of the determination of Greenwich's place by
* Bradley, and this brings up his refraction rule.
* "Had Dr. Bradley lived longer, for the benefit of astronomy, to
* publish his valuable observations . . . .
* "However, having formerly been apprised by Dr. Bradley himself of
* several particulars . . . particularly of the method which he used for
* settling his latitude and refractions, . . . and being assisted with some
* of his manuscript calculations, I flatter myself I can throw the light
* wanted on the question . . . ." (p. 153)
* "He afterwards, from the consideration that the refractions at the
* pole and equator [i.e., the celestial ones, as seen from Greenwich]
* may be taken without sensible error as the tangents of the zenith
* distances, according to Mr. Thomas Simpson's theory of refractions in his
* Mathematical Dissertations . . . found . . . the mean refraction at 45° 3'
* to be 57'', the barometer standing at 29,6 inches, and the thermometer
* of Fahrenheit's scale at 50°." (p. 155)
* ". . . and thus at length he inferred his elegant rule for determining
* the refraction in all circumstances, that it is to 57'', in the direct
* compound ratio of the tangent of the apparent zenith distance lessened
* by 3 times the refraction to the radius . . . .
* "But it may be proper to confirm this rule for refractions also from
* the same manuscript of Dr. Bradley . . . ." (p. 156)
* "This valuable rule was first communicated by myself to the public
* in vol. LIV. of the Philosophical Transactions, p. 265. and in p. 49. and
* 129. of the first edition of Tables requisite to be used with the Nautical
* Almanac, together with a Table of the mean Refractions deduced from it,
* with the first Nautical Almanac, that of 1767, published by order of
* the Commissioners of Longitude in 1766; and again, at page the 5th of
* the Explanation and Use of the Astronomical Tables . . . . The words in
* page the 5th of the said Preface are as follows. `The astronomical
* refractions . . . were settled with the greatest accuracy by Dr. Bradley
* . . . . The following elegant rule was the result of his observations,
* that the refraction at any altitude is 57 seconds, in the direct compound
* ratio of the tangent of the apparent zenith distance lessened by 3 times
* the refraction to the radius . . . .' " (pp. 157-158)
* Note: Bradley's pressure and temperature corrections have been elided.
* He adopted 29.6 inches of mercury as the standard pressure, and "the
* degree of height of Fahrenheit's thermometer increased by 350 to 400"
* as the temperature correction, relative to 50° F.
* Maskelyne goes on to point out that Bradley's refractions were
* slightly too large, owing to the adoption of a solar parallax also
* too large. His corrected reduction of Bradley's work then gives
* "the refraction at the apparent zenith distance of 45° 3' = 55'',8,
* which is 1'',2 less than Dr. Bradley's determination, and 1'',2 greater
* than deduced from Mr. Hawksbee's experiment of the refraction of air
* hereafter cited." (p. 168; see p. 173 for Hawksbee.)
* "Mayer's refractions agree almost exactly with Dr. Bradley's, and
* are entitled to much weight, having been determined by a 6-feet mural
* arc constructed by Mr. Bird." (p. 172)
* There is then a long section in which he shows that La Caille's
* refractions were too large, owing to a systematic error in his circle;
* but that the errors compensate if La Caille's refractions are applied
* to just his own measurements. (This systematic error is the source of
* Cassini de Thury's impression of an uncertainty of 15 seconds or so.)
* There are many contemporary references to Bird, Short, Dollond,
* and other great instrument makers, as well as an appeal to measurements
* made by Messier in Paris to confirm the longitude there. On p. 186,
* "M. Mechain, the learned editor of the Connoissance des Temps ,
* informs me . . . ." A fascinating work, in many ways.
* BARNABA ORIANI's work: ``Oriani's Theorem.''
* For summary, see the next entry.
* The typography is hard to read: the Greek font is much smaller than
* the Latin body type, and oddly shaped. The Italic font used for
* variables has some peculiarities: an obliquely tailed z ; and the
* Italic lower-case h is nearly indistinguishable from b . Oriani
* uses L to denote the common logarithm: "L A/b " means "log(A/b)"
* in modern notation. Likewise, he uses a period (.) rather than a
* centered dot to denote multiplication, and a comma as a decimal point.
* So his "1649.0,9739" means 1649×0.9739 in our notation. But he writes
* common logs as "L " and natural logs as "l. " before their arguments.
* So his "l.10" is the familiar modulus 2.302585. . . Blessedly, he writes
* the base of natural logs as e ; but all the exponentials are written
* out as e raised to some (often complicated) power. Breaking equations
* in the text across lines does not help, either. There is a long list
* of Errata on the page after the title page.
* A much more readable account of Oriani's work is the summary given
* by Bruhns (1861), p. 69, which boils it down in modern typography, showing
* how closely Oriani followed Lagrange's 1774 notation and development.
* The 2-term result appears at the bottom of p. 217. Remember that the
* temperatures are on the Réaumur scale.
* This is now available from Google Books. As usual, they have made
* the figures impossible to read.
* BARNABA ORIANI's work: ``Oriani's Theorem.'' [reprinted]
* NOTE: The page numbers here are exactly 120 less than in the original
* Ephemerides. The reprint also corrects 3 Errata on pp. 60, 80, and 94
* of the reprint (= 180, 200, and 214 of the original). The typeface
* and framing are exactly those of the original, so the original type must
* have been used, changing only the page numbers.
* Oriani's work begins with a discussion of the barometric law and the
* expansion of gases, complicated by the different thermometric scales of
* Réaumur, Fahrenheit, and Hauksbee. On p. 70, he has adopted a law of
* density vs. height in the atmosphere, and begins with the refraction
* problem. The refractive invariant appears (in rather obscure notation)
* in the middle of p. 78. After a lengthy discussion of the refractivity
* of air under standard conditions, he expands the differential of the
* refraction as a power series in x/r [x = height, r = radius of Earth]
* on p. 86. Expressing the tangent in terms of the sine, he then can
* write out the series in terms of integrals of powers of x times the
* differential of the density [rho]. He can't integrate exp(-x2) and
* so has recourse to numerical quadrature of his density table (Tab. II)
* to evaluate the coefficients (pp. 89, 90). The isothermal atmosphere
* (p. 93) presents no difficulties.
* He concludes that for Z.D. not exceeding 50 degrees, the refraction
* can be taken proportional to tan Z, with 57 seconds as the constant at
* 28 inches on the barometer and 0 deg. Reaumur (p. 97). For greater
* values of Z up to 65 or 70 degrees, the first 2 terms of the series
* suffice (p. 98): "This expression depends on no hypothesis about
* either the law of heat in the atmosphere or about the density of the
* air at various distances from the surface of the Earth." Up to
* Z = 80 or 85 degrees, the third- and fourth-power terms must be
* included; but his expansion diverges at 86 deg.
* Comments on usage and notation: Oriani uses "L." for common, and
* "l." for natural logarithms. He sometimes writes "x x" for x2.
* His "French fathoms" (hexapedia gallicia) are toises. He uses the
* abbreviation "D." for "Dominus" as an honorific title; it may be simply
* translated as "Mr." We also have "Cl." = Clarissimus.
* MANY THANKS to Brenda Corbin for supplying a photocopy!! (with many
* helpful marginal comments in Latin handwriting.)
* CHRISTIAN KRAMP's monograph
* This is heavily concerned with the gamma function, which was invented
* by Euler in 1729; the Γ notation was introduced in 1809 by Legendre; see
* https://www.csie.ntu.edu.tw/~b89089/link/gammaFunction.pdf for a readable
* history and account of its properties. Kramp introduces it here as the
* integral over an exponential atmosphere of various powers of the height.
* [He later introduced the modern ! notation for factorials; but in this
* work, he is still using a very awkward notation. To confuse things more,
* he has a "Gamma" function; but it is more like the modern log-gamma
* than the usual factorial version. Here he calls them "facultés"
* instead of "factorielles".]
* The old terminology makes this difficult reading: the scale height
* is called a "soutangente" (i.e., the intercept of the tangent at the
* origin.) Angles are sometimes given in centesimal seconds [as
* when he cites the result of ``citoyen Laplace'' that the refractivity
* of air corresponds to an angle of "183 sec " (p. 120)]. He also uses
* "horison" for both "sea level" and "astronomical horizon". Furthermore,
* he seems to use "temperature" to mean "weather conditions," as in ". . . à
* la température de 28 pouces de hauteur barométrique, et à 0 dégrés
* du thermometre." (Those are Réaumur degrees, of course.)
* The first chapter is mostly arm-waving about possible atmospheric
* models. He claims that the "specific elasticity" of the air might be
* a negative exponential function of height (to allow for the known
* temperature gradient in the atmosphere, and possible composition
* gradients). This gives him what he wants: an exponential density law.
* Though Lavoisier (who had been guillotined just 5 years before) had
* discovered oxygen a few years earlier, its abundance was still not well
* known; in discussing the properties and composition of air, Kramp cites
* Kirwan's Essay on phlogiston , and refers to "l'air commun, composé,
* comme on sait, de 27 parties de gas oxygène, et de 73 de gas azote."
* In comparing various published refractions with his own (anticipating
* the results of later chapters), he says (p.19):
* "Prenons pour dernier exemple, la table de réfractions que nous a
* laissé le plus grand de tous les géomètres, et le plus habile de
* tous les observateurs qui aient jamais existé; l'homme sans lequel notre
* astronomie mériteroit à peine le nom de science, parce que c'est à
* lui seul que nous devons la connoissance des éternelles loix de la
* nature, et l'application de l'analyse à ces mêmes loix, en un mot,
* l'immortel NEWTON." [Poor Flamsteed must be spinning in his grave!]
* But Kramp also notices (well before Biot) that Newton's table must
* have been calculated for an exponential atmosphere with a scale height
* of 4377 toises:
* "La table de Newton . . . indique une température de 18 dégrés
* et deux tiers au-dessus de la glace. Et réciproquement, l'air se
* trouvant à la température de 18 dégrés et deux tiers, la réfraction
* horizontale de Newton est exactement ce qu'elle doit être dans la
* supposition d'une élasticité spécifique constante. Est-ce
* l'observation ou l'analyse qui a fourni cette table au géomètre anglois?
* Dans le premier cas, l'exemple d'un pareil accord seroit unique peut-etre
* dans toute l'histoire de la physique . . . ." [p.19]
* So, although he can't understand how Newton could have calculated it,
* he decides the table must be a theoretical one: "Comme il paroît
* cependant que la table de Newton est beaucoup plutôt le résultat de
* l'analyse que celui de l'observation, nous la mettrons de côté, quelque
* favorable qu'elle soit d'ailleurs à la supposition d'une élasticité
* spécifique constante . . . ." [p. 20]
* The second chapter introduces refraction; by p. 35, he has the
* refractive invariant. He calls the refractivity little omega.
* There is also the usual "deduction" of the sine law of refraction
* from the supposed "attraction of the luminous particles" by the air.
* His series expansion is like Oriani's, and breaks down at 84° Z.D.
* Chapter 3 is a lengthy discussion of the mathematical properties of
* factorials (i.e., the Gamma fcn.). On p. 64, the integral form is
* introduced. This allows him to show (p.65) that the integral of
* exp(-t2) dt is (1/2)sqrt(pi) -- or, as he is fond of saying,
* "L'intégrale . . . revient à la quadrature du cercle." The chapter
* ends on p. 112 with the remark: "Tels sont les principes analytiques,
* dont nous aurons besoin dans le chapitre qui suit, ayant pour objet
* les réfractions approchantes de l'horison." (all in italics!)
* Chapter 4 picks up where Chapter 2 left off. The divergent series
* encountered near the horizon can now be transformed into convergent
* ones, using the results of Ch. 3. By p. 119 he has put it all
* together, and on p. 120 offers as an example the case already
* mentioned by "Le citoyen Laplace" (but without proof of the method
* used) in l'Exposition du système du monde ; Kramp shows that his
* method agrees numerically with Laplace's result for the horizontal
* refraction, within 1 part in 1000. [It's interesting that he
* anticipates that Laplace's derivation will be given in detail in the
* forthcoming Méchanique Céleste , which is mentioned here explicitly
* -- though it was not to be published yet for several years!]
* On p. 122 there is mentioned a fourth table at the end of the volume,
* which does not exist in the copy I have seen (which ends on p. 210).
* Was there such a table, or did it fail to get published?
* On pp. 127-132, there is a discussion of observations of very large
* refraction, mainly based on observations by le Monnier, but also
* mentioning the Dutch observations at Novaya Zemlya. He shows that
* if the scale height shrinks to 1880 toises (p. 130), the curvature of
* the ray equals that of the Earth, and the refraction becomes infinite
* at the horizon. He adds that "souvent nous en aurions dans nos
* climats, si les vapeurs dont l'air est chargé, ne nous empêchoient
* pas alors de discerner les objects éloignés." (i.e., LOOMING)
* On p. 133, he shows that the refraction problem requires the error
* function, which he then tabulates (explaining how the tables were
* constructed). Then, p. 138, he has the complete solution of the
* refraction problem near the horizon in terms of the error function.
* On p. 141, he derives the refraction gradient at the horizon (or,
* effectively, the magnification). Comparison with the available
* observations shows a systematic discrepancy. [In fact, it is due to
* the temperature gradient in the troposphere; but Kramp doesn't know
* that.] Of course, Newton's table nearly fits; but this discrepancy
* was the reason why Flamsteed was unhappy with Newton's results.
* Kramp tries to explain away Bouguer's discrepant values as due to
* "une interpolation défecteuse." He also criticizes Bradley's rule,
* which does not fit his theory (p. 144).
* On p. 150, he gives his calculated refraction table, compared to the
* results of Bradley's rule, which is off by more than a minute of arc
* between 1 and 2 degrees' altitude. (He also gives a table in the
* units of the "new division".)
* The 5th Chapter, p. 159, compares his theory with earlier ones, and
* Bradley's rule in particular. His criticisms of Euler and Bradley are
* generally just; but some of his points assume that his own model is
* faultless. Euler's error was to assume a power-law form for the ray
* (a sort of hyperbola), which caused his results to be quite poor even
* near the zenith; "Il paroît au reste que le jugement que nous venons
* de porter, n'appartient pas à nous seuls; car d'un côté, l'on ne voit
* pas que les formules d'Euler aient été suivies par aucune astronome;
* de l'autre, nous ne voyons pas non plus qu'Euler y soit jamais revenu
* dans aucun de ses ouvrages postérieurs."
* Bradley's rule is based on the supposition that the refraction
* is proportional to the angle subtended at the center of the Earth,
* which Kramp readily shows leads to all sorts of contradictions and
* inconsistencies. From this false assumption, Bradley deduced the rule
* that the refraction is the tangent of the apparent Z.D. diminished by
* a certain multiple of the refraction.
* Mayer's method is to apply some fudging to equations arising in the
* theories of Euler and Bradley, allowing some extra adjustable parameters
* in an attempt to get a better representation of the data; but his results
* differ negligibly from Bradley's, and so accomplish nothing.
* Lambert assumes a certain locus arising in the theory is an arc of a
* circle; it is not, so his theory is inconsistent -- though, remarkably,
* not all that far from the truth.
* The 6th Chapter (pp. 175 - 192), on terrestrial refraction, finally
* deals with the actual ray curvature ("rayon osculateur"). Where the
* ray is horizontal, this "est nommé rayon horizontal par quelques
* auteurs, et nommément par Lambert . Ce rayon est donc égal à
* s/ω ou a/n; il est donc au rayon de la terre comme c : ω ou
* comme 1 : n." As he assumes a constant temperature, he finds this
* cannot exceed 6.652 even for 30° Réaumur, and is less for lower
* temperatures (e.g., 5.54 at 10°). "Il ne pourra donc jamais être
* égal à sept fois le rayon de la terre, valeur que Lambert lui avoit
* assigné d'après quelques observations de Cassini . . . ." [Here he
* is of course too sure of himself.] He goes on to consider dip of the
* horizon, distance to the horizon, and related questions. Here, he
* shows that Bradley's rule works, provided the heights are small
* [pp. 182-184]. Finally (pp. 188 ff.) he considers the effects of
* refraction in lunar eclipses.
*
* Even a cursory reading reveals several typos and lapses:
* The missing Table IV, cited on p. 122, has already been mentioned.
* Ch. IV, section 14 (p.117) is missing a minus sign in the denominator.
* Ch. IV has 2 sections numbered 57, none numbered 58 (to which he refers
* in sections 91 and 92, p. 146).
* More serious errors in Kramp's analysis were found by Plana (1828),
* who showed that Euler's analysis was actually pretty good.
* These lapses seem incongruous, considering Kramp's frequent claims of
* superiority to everything that has gone before.
*
* NOTE: Some of this is translated by Thomas Young (1825).
* There is a brief commentary on Kramp's paper by A. Mason Du Pré, Jr.,
* Isis 29, 43-48 (1938); but as it is written from the point of view
* of a mathematician who explicitly excludes the refraction theory from
* consideration, it is of little interest to us here.
*
* The title page says "Par le citoyen KRAMP"; the Strasbourg publisher
* is Philippe Jacques Dannbach; the date, "l'an de la République VII "
* LAPLACE's REFRACTION & AIRMASS theorem
* [duplicate entry, repeated here for the sake of logic.]
* BOWDITCH's annotated translation of Laplace
* This is a modern reprint edition. Bowditch's translation and commentary
* originally appeared under the title:
* "Méchanique Céleste. By the Marquis de La Place . . . "
* (Hillard, Gray, Little, and Wilkins; Boston; 1829-39)
* DELAMBRE again (cf. his entry in the "Distorted Sunsets" file)
* Delambre's textbook might be listed with the later ones; but I have
* him here for two reasons: first, his discussion of Cassini's model,
* and second, his observations of VARIABLE REFRACTION.
* NOTE: It is essential to consult the long list of "Additions et
* Corrections" that follows the Preface. The pages correcting the
* material mentioned here are xxxij and xxxiij.
* Of Cassini, he says (p. 294):
* "Dominique Cassini est le premier qui ait proposé une hypothèse
* propre à calculer les réfractions pour toutes les hauteurs; et la
* table qu'il en dressa était déjà d'une exactitude très-remarquable."
* Delambre is fond of the tangent-series approach, and develops it for
* the plane-parallel case. (pp. 295-296)
* Of Tycho's table, he says (p. 297): "Cette table, qui lui avait
* coûté beaucoup de travail, est extrêmement défectueuse, et il était
* difficile qu'elle fût meilleure, puisque le plus souvent l'erreur de
* l'observation surpassait la réfraction cherchée." Then he continues:
* "Cassini supposa l'atmosphère sphérique ainsi que la terre, et
* voici à peu près comme il raisonna : nous donnerons seulement une
* forme plus analytique à ses calculs." But this is nonsense; Cassini
* lacked the analytic ideas Delambre uses. So Delambre introduces
* cosines and tangents where Cassini had only sines. However, he does
* at least start out where Cassini did; and he says (p. 298) that
* "Cassini détermine par des essais successifs la valeur de h . . . ".
* He plugs in modern values for (n - 1), and adopts the example used by
* Jacques Cassini, using 5' 28'' for the refraction at 10° altitude.
* From an exact solution, he finds n = 1.0002924339; "mais si nous
* donnons au rayon de la terre sa valeur 3271200T, nous aurons
* h = 2000T,4;. . . ." [But Jacques Cassini's value is 3271600 toises!]
* "Rien de plus simple que le calcul des formules" involving the
* difference of the inverse sines; "mais quand y approche de 90°,
* les tables donnent peu de précision, et l'on pourrait se tromper de 2
* ou 3''."
*
* This part could as well go under the "Variable Refraction" file;
* it's here only because of Biot's reference to it. The discussion begins
* with CHAPITRE XIII (p.291): "Petites irrégularités dans les hauteurs
* des Étoiles."
* ". . . passé 82° les réfractions varient d'un jour à l'autre et
* dans des circonstances en apparence toutes pareilles de quantités qui
* passent ces différences." (p. 305)
* Sections 50 and 51 are devoted to the variable refraction at low
* altitudes: "J'ai déjà parlé de l'incertitude des observations de
* réfraction dans le voisinage de l'horizon. J'ai remarqué que d'un
* jour à l'autre, et dans des circonstances qui étaient les mêmes en
* apparence, la réfraction variait de 15 à 20" sans qu'on pût en
* soupçonner la cause; mais les variations sont encore bien plus
* sensibles à l'horizon, on en jugera par le tableau suivant:"
* which, for example, shows two days with the same T and p but horizontal
* refraction differing some 4'. (Sunrise observations 4 days apart in
* June.)
* In section 51, he gives the range of observed variations: 6 or 7" at 75
* degrees' Z.D.; 10 or 11 at 77; 15" at 79; over 30 from 82 to 86 degrees;
* 35" at 88°; 45" at 89. "Les tables de Bradley et Mayer donnaient
* des erreurs plus fortes encore, ensorte qu'il me paraît impossible de
* faire aucune bonne table pour ces derniers degrés. Mais du zénit à
* 82°, on peut avoir nombre de tables à peu près également bonnes."
* He then adds that Piazzi's refractions have differences "au moins égales
* à celles qui se trouvent dans mes observations."
* In § 52, he says he has seen Z.D.s of terrestrial objects at sunset
* increase from 2 to 2½ minutes, "ensorte que des objets cachés pendant
* tout le jour devenaient visibles le soir." [LOOMING]
* N.B.: Biot (Addititons to the CdT.,1836) says that the values at 75°
* are impossible.
* (But Brinkley (1815) observed similar "irregularities" at low altitudes.)
* Text available at Google; but as usual they lost the figures.
* GROOMBRIDGE, and DELAMBRE's comments (1814)
* Stephen Groombridge's refraction measurements
* Groombridge's text is about as opaquely written as possible; it's amazing
* that Ivory was able to make use of these data. His previous measurements
* were restricted to Z.D.s less than 78°10'. Here he reports observations
* made in 1811 and 1812, "as near to the horizon, as the trees in Greenwich
* Park would permit", which turns out to have been about 87°.
* "With a view to assist me in ascertaining whether the refractions were
* affected by local vapours, D r. B r i n k l e y has kindly communicated
* to me some observations of low stars;" which got him to 88°. So he was
* still above the low zone where the refraction becomes wildly variable
* due to (at least) variations in lapse rate.
* There is much discussion of which thermometer to use (i.e., that
* "within" or "without" the telecope room). Of more interest is the
* commentary by Delambre, who translated this into French for the CdT.
* Thanks to Luc Dettwiller for calling my attention to this!
* The Royal Society's website would have you believe this was published
* Jan. 1; but the date on the paper says "Read March 31, 1814".
* DELAMBRE translates and comments on Groombridge (and others)
* The translation begins on p. 219.
* Delambre's comments actually begin on p. 224; and the footnotes inserted
* in the translated text and denoted by (a) through (h) begin on p. 220.
* There is much information of historical interest here, in addition to
* the technical details of refraction measurements. In the long historical
* note (a), Delambre says of his own observations: "les variations extrêmes
* que j'y remarquai, malgré l'état stationnaire du baromètre et du
* thermomètre , me faisaient désespérer qu'on pût jamais avoir une Table
* conforme aux observations de 89 à 90° principalement ; mais même à 78
* et 80°, je trouvais, d'un jour à l'autre, des variations de plusieurs
* secondes, qu'il me paraissait difficile de rejeter en entier sur les
* observations. Je remarquais des différences aussi irrégulières dans celles
* qu'a publiées M. Piazzi, qui avait pris le parti de regarder comme la
* réfraction moyenne qui convient à un certain degré de distance au zénit, le
* milieu entre toutes celles qu'il avait observées à ce degré. M. Groombridge
* a suivi cet exemple, mais il ne nous a pas mis à même de juger de la
* précision avec laquelle s'accordaient les observations entre lesquelles il
* a pris un milieu. On pourrait juger, par les distances solsticiales d'été,
* qu'il a pu trouver des anomalies semblables à celles qui se rencontrent
* dans les étoiles de M. Piazzi; il est vraisemblable aussi que ces irrégu-
* larités augmentent avec les distances, ce qui pourrait nous faire douter
* qu'on puisse jamais représenter des variations qui ne paraissent dépendre
* ni de l'état du baromètre, ni de celui du thermomètre." (p. 230)
* "La formule de Bradley est sans doute fort simple, ou du moins
* fort aisée à retenir;" well put. And on the next page, he discusses the
* deficiencies of any one-parameter "law" for refraction, because the
* parameter has to change with the atmospheric state. But once the
* horizontal refraction is given, everything in between can be found.
* Delambre then (p. 236) shows how a few slightly different formulae of
* Bradley's type can represent the "mean" refraction in a satisfactory way
* from the zenith to 87°; "mais au-delà, les réfractions calculées seraient
* toutes plus faibles que les réfractions observées." [Of course, we now
* understand that this is just the region where the local lapse rate comes
* to dominate the refraction.] ". . . il est donc bien évident que la
* formule de Simpson est insuffisante" (p. 237). (He shows several
* numerical examples.) [Of course the Simpson-Bradley model fails in this
* region, because it is based on a model with an impossible lapse rate!]
* On p. 240, Delambre goes back to consider Groombridge's previous
* refraction measurements (Phil. Trans., 1810), and compares the various
* sets of Tables (i.e., interpolation formulae used in making them.)
* He concludes that the errors can be attributed to the observations out to
* 88°, but that at 89 and 90 degrees, the disagreements are due to errors
* in the formulae used to construct Tables.
* Note: For more details of Groombridge's work, with comments by
* Delambre, see the 1819 item below.
*
* His discussion of Groombridge is followed by a summary and discussion
* of the 3 volumes of Mudge and Dalby work, which had remained unknown in
* Paris due to "the difficulty of communications" between 1799 and 1811
* -- i.e., the chaos that followed the French Revolution. On pp. 255-256,
* he discusses their observations of variable terrestrial refraction, and
* adds an account of his own experiences, one of which he saw in "fog".
* Thanks to Luc Dettwiller for providing a PDF of this!
* John Brinkley (Andrews Prof. of astronomy at U. of Dublin) pays
* particular attention to the "irregular refraction" beyond 80°.
* "It is shewn that at 80° 45' the error of the formula deduced cannot
* amount to half a second, whatever be the variation of density in the
* atmosphere." (p.79) Did Biot read this? His method is similar.
* "But the quantity of refraction varies so much from some unexplained
* cause, the heights of the barometer and thermometer remaining the same,
* that observations below 80° can be of little use. This irregularity
* is very manifest at 80° 45' in the observed refractions of Capella
* below the pole." (p. 81) [These observations are reported in detail
* on p. 110.]
* "It has been shewn . . . that above 80° the refraction will not be
* sensibly changed by any law of variation of density . . . ." (p. 105)
* "It is well known to those conversant in observations made with good
* instruments that near the horizon an irregularity in refraction hitherto
* unexplained shews itself. This commencing even at less zenith distances
* than 80°, is at first very small, but increases to a very considerable
* irregularity as we approach the horizon." (p. 108) [cf. Delambre, above.]
* [Note that p. 109 is numbered 104.] On that mis-numbered page, he has
* a footnote pointing out that "The hypothesis upon which refractions are
* computed is that the different strata of air are concentrical with the
* earth's surface, circumstances may be easily imagined to affect this
* hypothesis, with respect to low stars."
* His observations of Vega below the Pole, at Z.D. 87° 42', are given
* to the nearest tenth of a second of arc, but show variations from +26 to
* -17 seconds; so he concludes that "It is not likely the irregularities
* will ever be submitted to any law, and investigations respecting formulae
* for refractions for zenith distances greater than about 80° may be
* considered more curious than useful." (p. 117) [The individual Vega
* observations are on pp. 115 and 116.]
* Available from JSTOR at https://www.jstor.org/stable/30078777
* Unfortunately, that copy is full of typos and garbled glyphs, so that a
* 3 often looks like an S, and the base of natural logs is written 2.7128
* instead of 2.7182. . . .
* I lack the figure, as does the JSTOR copy. However, the BHL gives
* access to a copy at the Natural History Museum, London, which shows the
* figure following p. 32, and facing p. 33, which is Brinkley's paper
* "Read May 9, 1814" describing how the observations were made, and
* tentatively suggesting he had detected parallaxes on the order of a
* second of arc in a few bright stars.
* Its URL is:
* https://www.biodiversitylibrary.org/page/2428795
*
* Unfortunately there is an error in the page numbering: Brinkley's paper
* follows Vince's (on a waterspout) that ends at a page numbered 40.
* So the numbers from 33 to 40 inclusive appear twice in this volume,
* first in signature F and then again in signature G.
* Brinkley's semi-empirical corrections to the "French Tables" (Delambre)
* He distinguishes between "regular" and "irregular" refraction.
* Referring to his 1815 paper, he says, "It is admitted, that the true
* refraction is always less than that computed on the hypothesis of an
* uniform temperature, and greater than that obtained by supposing the
* density to decrease uniformly; that, as far as 80° from the zenith,
* these limits approach each other very closely; and that, till very near
* the horizon, they do not widely recede from each other." (p. 166)
* SCALED REFRACTION IS INCORRECT: "When however it is required to
* compute the refraction for other states of the Barometer and
* Thermometer, the results by my tables and the French differ for low
* altitudes. This is occasioned from it being supposed in the French
* Tables that the refraction is proportional to the density, which is by
* no means sufficiently exact in very low altitudes." (p. 170)
* Note that the paper itself cites Young's work in 1819, and was "read,
* January 17, 1820" -- so the date on the title page is not right.
* Discussion of VARIABLE REFRACTION near the horizon, between GROOMBRIDGE
* and DELAMBRE (addendum to the 1815/1818 item)
* This contains additional details of Groombridge's measurements. Delambre
* writes it in the first person, and refers to Groombridge in the third,
* but credits Groombridge as author, so I list them both here.
* Referring to the earlier item, Delambre says that he had expressed
* regret at finding only the mean values in Groombridge's Memoir. "It
* appeared to us impossible that he had not noticed the frequent anomalies,
* as we had. . . . M. Groombridge has responded to our remarks, and made us
* aware of the extreme deviations that he had found in each of the stars
* that pass between 81°40' and 88°42' from the zenith."
* Delambre explains that the format of this volume (i.e., narrow pages)
* prevent him from reproducing Groombridge's data in the form provided,
* "so we are limited to giving the names of the stars, their zenith
* distances, the height of the barometer, that of the thermometer (interior
* and exterior). the excess of the calculated refraction over that
* observed, in using the interior and exterior thermometer successively."
* In fact, the two tables here (on pp. 350 and 351) contain the same
* stars, in the same order, as Tables I and II, respectively, on p. 345
* of Groombridge's 1814 paper in Phil. Trans., and should be read in
* conjunction with it. There, only the mean values are given; here,
* only the extremes.
* [Notice that the tabulated residuals are C-O, not the usual O-C. So
* the excess of negative resids. means that the observed refractions were
* on average larger than the calculated ones -- hardly surprising, as the
* model was the old Simpson-Bradley one.]
* Delambre points out several outstanding examples of large refraction
* changes with no, or very small, change in T and p. "Fortunately these
* variations only occur at altitudes where one never observes the Sun or
* the planets. We see this in Groombridge's solstitial observations,
* which agree as well as one could wish. The deviations of several
* seconds, which one notices mainly in summer, should be attributed to
* the difficulty of putting the edge of the Sun in contact with the wire
* of the telescope."
*
* The ADDITIONS begin on p. 217 of this volume; this is near the end of the
* volume.
* Available at Gallica.
* Thanks to Luc Dettwiller for bringing this item to my attention!
* THOMAS YOUNG's first Postscript
* The main paper is about error analysis, as the title shows; the
* refraction part is an addendum, paginated separately from 1-4.
* He starts out by quoting Brinkley out of context.
* Interesting for an early guess at the existence of a STRATOSPHERE:
* "The variation of t can only be determined from conjecture; but
* supposing the alteration of temperature to cease at the height of about
* 4 miles . . . ." [which would place the tropopause near 6.4 km]
* The variation of lapse rate "in the lower regions of the atmosphere
* . . . appears to be amply sufficient to explain the irregularities of
* terrestrial refraction, as well as the uncommon increase of horizontal
* refraction in very cold countries . . . ." -- that is, he assumes a
* constant temperature for the upper air, and infers the tropospheric
* lapse rate from this, and the variations at the surface.
* Young published a slightly corrected version of the Postscript in
* Quart. J. (1821), q.v.
* DELAMBRE's "Histoire moderne" comments on Cassini's model
* Here Delambre translates snatches of Cassini's remarks in Malvasia's
* Ephemerides into French, and adds some comments.
* P. 724: "En supposant les réfractions du Soleil les mêmes pour toute
* l'année, et telles qu'il les a données pour l'été, la parallaxe du
* Soleil sera nulle ou tout au plus de 15'' . . . . Au reste, la parallaxe
* de Képler, qui est de 59'' 36''', comparée à l'excentricité qu'il
* vient de trouver, lui donne une symmétrie for élégante entre les
* orbes ; car il en résulte 3460 diamètres de la Terre pour la
* moyenne distance du Soleil, dont la fraction 0,017 vaut 58,822 pour
* l'excentricité du Soleil, ce qui est précisément la distance moyenne
* de la Terre à la Lune. Ainsi le centre de la route annuelle du Soleil
* est un point de la circonférence de l'orbe lunaire, et ce point est celui
* qu'occupe la Lune quand elle est à l'apogée du Soleil, c'est-à-dire au
* 7e degré du Cancer. D'où il suit que la plus grande équation simple
* du Soleil, la parallaxe horizontale de la Lune, qui est le demi-diamètre
* de la Terre, vu de la Lune, et le demi-diamètre de l'orbite lunaire,
* vu du Soleil, sont également exprimées par le nombre 58' 26'' 20'''.
* [NOTE: the sine of this angle is 0.016998. . . , or 0.017 very nearly.]
* Cassini développe encore avec plus de détails ces conséquences, qui
* sont un peu [!] dan le goût du Mystère cosmographique de Képler,
* et malgré le doute que nous avons énoncé ci-dessus, il nous est
* clairement démontré qu'il avait bien lu et bien médité Képler,
* auquel il a fait plus d'un emprunt." . . .
* "Il conclut de ses observations, qu'un rayon quelconque tombant
* obliquement sur la surface extérieure de l'atmosphère, est accoursi de
* 0,0002841, et que la hauteur de l'atmosphère est de 0,0006095 du rayon
* terrestre pris pour unité; c'est-à-dire apparemment que le sinus de
* l'angle est diminué de 0,0002841, ou qu'il faut multiplier le sinus de
* l'angle d'incidence par la constante 0,9997159, c'est-à-dire ajouter
* au log. sin. de l'angle le log. constant 9,9998666. En effet, ayant
* calculée la table d'été, j'ai retrouvé les quantités ci-jointes, qui
* prouvent que la formule est exacte, au moins jusqu'à 74°. Cassini ne
* donne pas d'autre explication. Nous trouverons sa théorie dans les
* Élémens publiés par son fils en 1740, et nous l'avons mise en formules
* (Astronomie , t.I, p. 297); mais nous n'avons pu deviner comment il a
* trouvé les deux réfractions fondamentales. Il a l'air de les prendre
* dans la Connaissance des Tems, pour donner un exemple de calcul."
* [This discussion, which ends on p. 725, does not quite do Cassini fils
* justice; his discussion is clearly a ``textbook example'' in which the
* numbers are chosen arbitrarily for convenience, so as to obtain the
* desired result. Delambre seems to have missed the "Epistolae Tres" that
* reveal a bit more about how Cassini proceeded.]
* [We have this only on P-10 microprint cards!]
* Young's RADIUS OF CURVATURE paper
* He derives the radius of curvature via the lapse rate required to
* counteract the density change due to pressure: ". . . at 50°, with the
* barometer at 30 [inches] . . . the height of the homogeneous atmosphere . . .
* is 27,000 feet; and the temperature descends about 1° for every 300
* feet that we ascend." So, as the refractivity is about 1 part in 3540,
* it "varies 1/3540 * 1/27000 in every foot, as far as the diminution of
* pressure is concerned, amd 1/3540 * 1/300 * 1/494 is to be deducted for
* every foot, on account of the diminution of temperature, or as much more
* or less as this diminution of temperature is more or less rapid; so that
* if the change were 1° in 27000/494 = 55 feet, the refraction would
* be annihilated, and, if still more sudden, there would be a depression
* or looming, instead of an elevation. But in ordinary circumstances,
* supposing Professor Leslie's estimate of 1° in 300 to be correct,
* we have 1/3540 (1/27000 - 1/148200) = 1/116873000 for the variation in
* a foot, and consequently, 116873000 feet for the radius of curvature
* of the ray; which is to the Earth's radius, or 20900000 feet, as 5.6
* to 1; consequently, the elevation of a distant object must be 1/11.2
* of the angle subtended at the earth's centre, since the angle contained
* between an arc and its chord is always equal to half the angular extent
* of the arc."
* Note: 1° F in 300 ft = 6.1 K/km; 1° F in 55 ft = 33° C/km.
* JAMES IVORY's first paper on refraction
* Is he the FIRST to notice that "The simple hypothesis of Cassini seems
* hardly to have met from astronomers with the attention it deserves;
* for, if we use accurate elementary quantities in the computation, it will
* determine the refractions to the extent of 74° from the zenith with
* the same degree of exactness as any of the other methods, without even
* excepting the formula of Laplace." (p. 322) He also notes that in
* Cassini's model, "the depression of 1° of the centigrade thermometer
* will correspond to an elevation of nearly 4343/250, or about 17½
* fathoms." [He effectively assumes absolute zero is -250° C.]
* He then goes on to consider what we would call POLYTROPIC models:
* "Between the two extreme cases just described" [i.e., Cassini's model
* and the isothermal one] "we may consider that an infinite number of
* intermediate ones are interposed, while the total height of the atmosphere
* increases from its least limit of 4343 fathoms to be infinitely great;
* the heat in each particular atmosphere decreasing uniformly as the
* elevation increases, which is the law most conformable to experience.
* We have thus an infinite number of different hypotheses, in all of which
* the refractions will be the same to the extent of 74° from the zenith;
* coinciding in every case with the formula of Laplace, the exactness of
* which is indisputably established by observation. But beyond the limit
* mentioned, the refractions will diverge from one another, and each
* particular case will have a horizontal refraction peculiar to itself.
* ". . . The hypothesis advanced by Thomas Simson [sic], of a density
* decreasing uniformly with the elevation, is also contained in the series
* of atmospheres above mentioned . . . ." [p. 323]
* On p. 324, he decides that the observed horizontal refraction
* corresponds to an atmosphere 4 times the height of Cassini's, with a
* lapse rate of one degree C in 70 fathoms [128 m], or about 7.8°/km.
* He notes that this differs from the observed rate of 1° in 90 fathoms
* [165 m] -- about 6°/km -- which corresponds to an atmosphere 5 times
* the height of Cassini's, and a horizontal refraction of 2164'' which is
* too much. [Apparently the problem here is the error in the "elasticity
* of air" (i.e., the zero of the absolute temperature scale).] But he
* attributes the discrepancy to a non-uniform decrease of temperature:
* ". . . hence we may infer that the supposition of a uniform decrease of
* heat in the atmosphere, cannot be reconciled with the astronomical
* refractions. But, although this be strictly true, yet the refractions
* are so nearly represented by the law mentioned, that the actual deviation
* from it must be very inconsiderable."
* So his best estimate is a polytrope of index 3, or perhaps 4.
* (May issue)
* JAMES IVORY's first paper, continued
* Here he discusses the horizontal refraction more, finding that "there
* are good grounds for thinking that the horizontal refraction in the
* French Tables is rather too small." He cites "the observations of
* Mr. Brinkly" [sic] and the table based on Groombridge's observations,
* and [p. 406] notices that "the refractions at the horizon depend not
* only upon the initial rate of the decrease of heat, but also, although
* in a very small degree, upon the acceleration." So he comes close to
* seeing Biot's result, but misses.
* (June issue)
* Young's Postscript reprinted, corrected, and augmented
* The "parenthetical correction" restores some of Brinkley's wording,
* as well as considerable correction and simplification of the math.
* We now find: "It is not possible, in the present state of our knowledge
* of the subject, to determine, from observation, either the refraction
* with sufficient accuracy to enable us to compute from it the law of the
* variation of temperature, or the variation of temperature with sufficient
* accuracy for computing the refraction." [Section 8.]
* Ivory's comments on Young's "Postscript"
* Here begins the feud between the two. "The principal point we have to
* inquire into will therefore relate to the convergency of the new
* series for low altitudes, and more particularly in the extreme case of
* the horizontal refraction." (p. 161) But there are also plenty of
* snide remarks about "the pretensions held out" and "the numerical
* computations . . . are so inaccurate that no conclusion can be drawn from
* them in which confidence can be placed." (p. 162)
* Here is where he calls Young's Table on the 1822 Nautical Almanac
* "empirical". (p. 167) What he means is that the Table is just a
* fudge-fit to the French Tables, not based on a separate physical theory.
* (Sept. issue; dated Sept. 4)
* This volume of Phil.Mag. is available at JSTOR.
* Ivory, on Mayer's formula
* Ivory explains that if the density is proportional to p/T, the
* refraction near the zenith is proportional to the density; but at the
* horizon, to T to the -3/2 power. He applies this to Cassini's model
* (of which he says, "As is apt to be the case in some more complicated
* suppositions, the attention is not here so absorbed by intricate
* combinations of the quantities concerned, as to overlook the manner in
* which the phænomenon is produced by its real causes, which are the
* alterations in the refracting power of the medium and in the extent of
* the homogeneous atmosphere." (p. 345) "We must, therefore, conclude
* that the rule of Mayer is true, not only in the hypothesis of Cassini,
* or in that of Mayer whatever it was, but absolutely in every supposition
* that can possibly be formed with regard to the constitution of the
* atmosphere." And he notes that near the zenith, "the variation in
* refraction is very nearly proportional to β, that is to the density
* of the air, according to the usual practice of astronomers. But when
* the zenith distance is great . . . another mode of calculation must be
* pursued . . . which necessarily leads to the rule of Mayer."
* So (p. 347) "At the horizon . . . the correction for heat, according
* to Mayer, is quite different from the common rule." [i.e., the
* assumption that the refraction is proportional to the refractivity.]
* [This behavior at the horizon might be regarded as prefiguring Biot's
* theorem.]
* The frequent references to the September issue, p. 167, refer to
* Ivory's previous paper; this one is in the Nov. issue.
* Ivory's Postscript on Cassini's model
* This is an addendum to Ivory's paper "On the Rolling Pendulum" on
* pages 417-420. The Postscript refers to the previous paper, on Mayer's
* formula, in which he made an application to Cassini's model.
* Here, he derives an approximation for Cassini's refraction, and points
* out that it differs from Laplace's result by only 0."074 at 70° ZD, and
* 0."154 at 80°. "We are therefore warranted in saying that, when the
* same elementary quantities are used, there is, practically speaking, no
* difference in point of accuracy between the formula derived from the first
* and most simple hypothesis relating to the constitution of the atmosphere,
* and that obtained by the last effort of scientific skill ; and this is
* a coincidence which it is surely both curious and instructive to mark."
* Ivory's note on horizontal refraction
* He refers again to his "Sept." paper. Here the method is to expand
* the exponentials in series; note the use of c rather than e as the
* base of natural logs. "Both these series were found in Kramp and
* Laplace; but these geometers proceeded in an inverse order to that
* followed here. . . . But the analysis given here seems to have the advantage
* of greater simplicity." (pp. 92-93)
* "Although the case of the horizontal refraction has alone been
* considered, yet the same analysis will apply to the general state of
* the problem; but, as this is attended with no difficulty, and further
* explanation will be unnecessary." (p.93)
* Dated Feb. 4, 1822.
* Young replies to Ivory's comments . . .
* Sarcastic sniping at Ivory for having called the Nautical Almanac
* formula "empirical". He proposes to extend the series expansion by
* extrapolating the terms, using their logs as the basis of the
* extrapolation, and assuming the series to be convergent. This
* dubious procedure, not surprisingly, leads him to extrapolate a
* horizontal refraction at variance with Laplace's result; "so that there
* must probably be some numerical error in one of the computations; at
* any rate the difference does not arise from the want of convergence of
* the series."
* [N.B.: Not signed; but the authorship is hardly in question.]
* More of the same. Here Young claims that the atmospheric structure
* can be inferred from the refraction data. The argument leads him to
* an expression for a barometric formula, which gives the height of Quito
* (from the pressure there) of "8740 feet, instead of 9377; or if we augment
* the 8740 in the proportion of the expansion of air from 50° to 80°,
* it will become 9264; but it is well known that in computations of this
* kind it is necessary to introduce a variety of subsidiary corrections."
* [In other words, he gets the wrong answer, and arm-waves it away.]
* "But it is at present impossible to expect any thing like perfect
* accuracy in a determination so liable to uncertainties of various kinds."
* [N.B.: Not signed; but the authorship is hardly in question.]
* Thomas Young's anonymous "Inverse Series" paper
* Much detailed mathematical churning, which Ivory (1824) shows is
* equivalent to his own (Phil. Trans., 1823) results.
* There is much arm-waving here, as well as posturing; all potential
* difficulties are waved aside.
* There are a few interesting historical remarks; on p. 144:
* ". . . Taylor, who first applied to the problem of atmospherical
* refraction his very useful theorem for `integration by parts,' as the
* process is sometimes now called, . . . ."
* [issue no. 31, dated October, 1823.]
* JAMES IVORY's important paper [N.B.: FILED separately, due to length]
* This paper begins with a clear historical review; develops the theory
* for a temperature profile that fits the atmospheric data near the
* ground and the astronomical data near the horizon, and concludes with
* informative comparisons of earlier tables, explaining that the "French
* Table" of 1806 is (deliberately) slightly in error, and that Bessel's
* table is soundly based on observation only to 86° Z.D. and quickly
* fails beyond that.
* The whole derivation is strictly Newtonian; but there are numerous
* trenchant remarks here:
* "Perhaps it is owing to its great simplicity, that the method of
* Cassini seems not to have met from astronomers with the attention it
* deserves." (p. 410)
* "If we reflect that all these atmospheres will agree in giving the
* refractions actually observed by astronomers as far as 70° or
* 80° from the zenith, it is natural to think that the one which
* likewise coincides with nature at the horizon, will deviate but little
* from the truth in the intermediate 10°." (p. 411)
* [From Gay-Lussac's balloon ascent] "the elevation for depressing the
* thermometer one degree will come out equal to 95 fathoms: and if we
* suppose that the same rate prevails in all parts of the atmosphere, the
* whole height will be . . . nearly 29 miles. The observations of twilight
* show that this is less than the true altitude; and hence we must infer,
* that the thermometer falls at a slower rate in the higher, than in the
* lower, parts of the atmosphere." Ivory took this decrease to be
* gradual; but today we know it is due to the stratosphere -- which this
* comment might be seen as predicting! (p. 416)
* "Hauksbee first determined by experiment, that air refracts light in
* proportion to its density . . . ." (p. 417) -- What about Gladstone &
* Dale? Stigler's Law of Eponymy again!
* ". . . it much be observed that the French table was originally
* constructed for 32° of Fahrenheit, and was reduced to the mean
* temperature of 50°, on the supposition that the refractions vary in
* the same proportion with the density of the air . . . ." (p. 448)
* -- but Ivory is aware this SCALING is an error. (Cf. p. 479 also)
* On p. 449, Ivory introduces his parameter f that determines how
* rapidly the lapse rate changes with height. This allows him to have
* a mixed model that has one polytropic index near the surface, and a
* gradually increasing one higher up. "f = 0, when m = 4 . . . ; and
* f = 1/4, when m is infinitely great." This allows him to make the
* height of the atmosphere big enough to agree with twilight, while having
* the observed lapse rate at the surface, and the observed horizontal
* refraction. (p. 450)
* "It appears that, although the refractions near the zenith are
* affected in a degree hardly perceptible by the peculiar constitution of
* the atmosphere, yet, near the horizon, they depend entirely on the same
* arrangement of the strata of air indicated by terrestrial experiments."
* That is, the horizontal refraction depends on the lapse rate near the
* ground, and the observed average lapse rate agrees with the horizontal
* refraction. (p. 456)
* "With regard to altitudes less than 2°, it is not clear that the
* astronomical refractions do not participate of the extreme irregularity
* that attends the terrestrial refractions . . . ." (p. 472)
* Laplace, Delambre, and Brinkley are heavily referred to. Note that
* the "base of hyperbolic logarithms" is called c here; his e is a
* different quantity.
* On p. 467, Ivory points out that the usual (i.e., Lambert's) series
* expansion is only semi-convergent. This remark seems to have been
* generally overlooked; evidently the term was fairly new, and unfamiliar
* to the English astronomers. It seems to have been invented by Legendre;
* according to Morris Kline's "Mathematical Thought from Ancient to Modern
* Times" (Oxford, 1972), pp. 1097-1098, it first appeared in Legendre's
* "Essai de la théorie des nombres", p. 13 (1798); but I don't see it
* there. However, Giovanni Ferraro points out that Legendre's "Exercices
* de Calcul Intégral, sur divers ordres de Transcendantes et sur les
* quadratures" (Paris : Courcier, 1811-1817) p. 294, discusses series
* "which he termed semiconvergent (demi-convergent) because they first
* decrease (converge, in his language) and then increase (diverge))."
* This wording is so similar to that used by Ivory that I think it likely
* this is where he learned the term. [However, this book is not among
* Ivory's surviving library, preserved at Dundee, at:
*
* http://www.leisureandculturedundee.com/localhistory/ivory
*
* where it's necessary to click on "The Collection"; Ivory's books are then
* listed alphabetically by author. Thanks to librarian Erin Farley for the
* URL!]
* On the other hand, Legendre's "Essai de la théorie des nombres" is
* in Ivory's library. Can someone find the passage in it where the term
* "semi-convergent" or "demi-convergent" (or something of the sort) occurs?
* Thanks to Craig Fraser, via Jed Buchwald and Richard F. Lyon, for
* helping uncover these references! In addition, I find that Josef Lense
* discusses this issue in his "Reihenentwicklungen in der mathematischen
* Physik" (Walter de Gruyter & Co., Berlin, 1953). On p. 16 he says:
* "Solche Reihen nannte Legendre semikonvergent oder halbkonvergent,
* weil sie sich für zahlenmäßige Berechnungen fast wie konvergente
* Reihen verhalten. Jetzt pflegt man sie nach H. Poincaré asymptotisch
* zu nennen . . . ".
* Lense cites v.1, p. 267 of Legendre's "Exercices"; and, indeed, on
* that page one finds: ". . . la suite . . . deviendra nécessairement divergent
* après un certain nombre de termes. Mais ce qui est fort remarquable,
* c'est que cette formule n'en est pas moins propre à donner la valeur
* . . . avec tout le degré d'approximation qu'on peut desirer.
* ". . . on aura . . . une suite d'abord très-convergent, mais dont la
* convergence diminuera de plus en plus, jusqu'à un certain terme où
* elle deviendra divergente, et cette divergence augmenterait de plus en
* plus à l'infini.
* "Nous donnerons cì-après un exemple du calcul de ces sortes de
* suites qu'on peut appeler suites demi-convergentes ."
* The passage on p. 294 cited by Giovanni Ferraro gives the promised
* example of
* ". . . suites demi convergentes , c'est-à-dire des suites qui sont
* convergentes dans les premiers termes, et qui deviennent ensuite
* divergentes."
*
* Ivory suffered from persistent delusions of persecution throughout
* his life, but never seems to have accused anyone of actually conspiring
* against him -- see de Morgan's "Budget of Paradoxes" on this.
* N.B.: from 1792 to 1852 the volumes were not numbered; this would be 113.
* G. PLANA's first paper on refraction
* There is much review of the works of Gay-Lussac, Leslie, etc. in the
* early pages. In discussing the barometric law, he points out (p. 176)
* that Oriani discovered the independence of the refraction at ZDs less
* than 74° before Laplace.
* Unfortunately, Plana plunges into the details of the math before
* trying to understand things; so there is a lot of useless thrashing.
* (See, e.g., the futility of the numerical trials on pp. 242-243.)
* However, there is some merit in his view (p. 256) that one can regard
* the true atmosphere as a perturbation from a simple exponential.
* Starting on p. 300 is an interesting quibble about the history of
* the differential of refraction. He thinks Laplace's derivation is
* the only valid one, picking holes in Young's work.
* Henry ATKINSON's long paper
* He begins with a long study of observed refractions, looking for "the"
* law that determines the (supposedly fixed) structure of the atmosphere;
* but of course finds there is none. ". . . for the fluctuations of
* the atmosphere are so frequent and so great, that on a superficial
* view, they would seem to set at defiance any attempt to subject them
* to calculation. This difficulty, however, I hope to show is not
* insurmountable. In the prosecution of this subject, it is intended,
* first, to show how to calculate, to any required degree of accuracy,
* the quantity by which a ray of light is deflected from its rectilinear
* course in its passage through any given horizontal stratum of air ;
* on the supposition that the density of the air, not only at the top and
* bottom of the stratum, but at any intermediate point, can be accurately
* caleulated :---secondly, to ascertain as far as possible, from a great
* number of the best observations that can be got, not only the mean state
* of the atmosphere at the surface, but the law by which its temperature
* varies as we ascend:---how this change of temperature modifies its density
* :---whether the same laws obtain in cold as in warm climates :---what
* fluctuations these laws are liable to, and to what height they extend
* :---and lastly, to apply the knowledge thus obtained to the calculation
* of tables of refraction, both celestial and terrestrial." (p. 140)
* There is an elegant derivation of Bradley's rule on p. 145; cf. Delambre.
* On p. 150, he cites General Roy's measurements of temperature and
* pressure, published in 1777, as a reliable source of atmospheric data.
* On p. 157, the finds the mean lapse rate to be 6.4°F in 1666 feet, or
* 3.56°C in 508 m, which is 7°C/km -- not bad for 1826. He goes on to
* investigate geographic variations in temperature, and investigates data
* for various mountains in Europe, which provide seasonal mean values.
* These data lead him to conclude that the general rule is that the lapse
* rate is approximately constant with height, rather than the linear
* density decrease assumed by Simpson et al.
* On p. 171, he uses Humboldt's observations to estimate lapse rates for
* the tropics. Combining those data with mean temperatures from places
* at greater latirudes, he then fits a formula involvoing both height and
* latitude by "Legendre's method of minimum squares " (p. 174) After
* some further analysis of widespread temperature measurements, he finds
* that "the law of the gradation of heat, as we ascend in the atmosphere,
* is the very same for the temperate and torrid zones". (p. 191)
* He seems not to have heard of Charles's law, but fits General Roy's lab
* results to an empirical formula, and so calculates densities for the
* refraction calculations (pp.197 ff.) As he approached the horizon, he
* found it necessary to divide the lower atmosphere into more and more
* parts. A single layer sufficed from the zenith to 44°Z.D.; then two
* layers, from 45° to 60°; then 4 layers to 75°, 8 to 81°; 16 to 86°;
* 32 to 88°; and 64, to 89° 40'. In these later calculations, only the
* lower atmosphere had to be so finely subdivided. "In computing the
* refractions for 89° 40' and 90° of zenith distance, it was found
* necessary to make the strata in the lower part of the atmosphere
* very thin." The table on p. 203 gives the details. The resulting
* refraction table is on p. 205, and is compared with Brinkley's and
* Groombridge's observed refractions..
* He then discusses the corrections for pressure and temperature. This
* brings him to the seasonal variations, which he finds do not vary with
* height below about 21,000 feet. And he notices that changes in thermal
* structure above that height have very little effect on even the horizontal
* refraction.
* On p.220, he appeals to General Roy's observations of temperatures at
* the tops and bottoms of hills to show that "there are occasionally very
* great deviations from the mean state of the atmosphere, but that such
* fluctuations occur at all seasons of the year. . . . But it does not always
* turn colder as we ascend." On p. 221, he tries to find how far upward
* these anomalies extend. Even at heights of 2400-3600 feet, they are
* "not greater than at the height of 600 or 700 feet." So the limited data
* available "seem to indicate that those fluctuations do not extend to any
* great height." Still, "The irregularity, or deviation from the mean
* state, amounts to something considerable at low altitudes, and therefore
* ought not to be neglected Where accuracy is required." (p. 222)
* Pages 223-227 contain a discussion of extinction, and the visibility
* of faint stars near the horizon: ". . . at 85° of zenith distance very
* little more than one-tenth of the light of the star arrives at the eye;
* and at 89°, only .003. It is therefore quite plain that no star can
* be seen at 89° of zenith distance, unless the air possess a degree of
* transparency far, very far, beyond what it possesses in its mean state.
* Indeed, I believe, experience shows that at 85° or 86° of zenith
* distance small stars frequently cannot be observed . . . ." So there is
* a selection effect in measured "mean" refractions: the numerous faint
* circumpolar stars can't be seen at low altitudes on murky nights with
* humid air, so the means are biased toward high-pressure systems when
* the air is clear: ". . . whenever . . . the degree of cold must either
* increase more slowly than it commonly does, or else that it must diminish,
* and the air become warmer . . . either of these states of the atmosphere
* gives a refraction greater than the mean. A correction must therefore
* be applied on this account, when we compare a Table of mean refractions
* with observations very near the horizon." (pp.224-225). He constructs
* a table of this correction, based on the statement that "at about
* 85° of zenith distance, stars of the second, and perhaps of the third,
* magnitude may generally be seen with a good telescope, whenever the air
* at greater altitudes is fit for observations." (p. 227) The table of
* corrections for this bias below 5° altitude is on p.229.
* Then he worries about the air in the observing room being a couple of
* degrees warmer than the outside air.
* On p.233, he turns to terrestrial refraction, and soon cites the paper
* by Williams, Mudge, and Dalby (1795). Of course he quickly finds that
* the radii of curvature of the rays depend on the lapse rates (which he
* calls "the gradation of heat".) He checks his refraction formula with
* General Roy's observations. (p. 241) Of course, that confirms that
* the terrestrial refraction depends mainly on the lapse rate. "We
* know that the change of temperature . . . is much more rapid near the
* ground than it is a little above it".
* Text available from ADS; but their PDF copy of Plate III is nearly as
* useless as the ones Google Books usually produces.
* NOTE: This paper was used as the basis for refraction corrections in
* the Great Trigonometrical Survey of India; see
*
* An Account of the Measurement of two sections of
* the Meridional Arc of India, bounded by the
* parallels of 18° 3' 15"; 24° 7' 11"; & 29° 30' 48".
* conducted under the orders of the Honourable East-India Company
* by Lieut.-Colonel Everest, F.R.S
* late Surveyor-General of India
* (London, 1847)
* Thomas Young tries to out-do Ivory
* This is supposed to be a closed-form solution for what we would
* now call the polytrope of index 2 -- and hence, an atmosphere with a
* super-adiabatic lapse rate. He loses the minus sign before the final
* result.
* But when I try to evaluate his expression -- correcting for the missing
* minus sign -- I get numbers that agree with his at the horizon, and at
* 5° 44', but are off by more than a minute of arc higher up!
* Ivory's reply to Young's comments
* The dispute here is about the temperature to be used in correcting the
* Table entries. Ivory also points out that Young's model is a
* special case of his own more general one, and so feels his work has
* been appropriated. More sniping at the table in the N.A., which "may
* be withdrawn, and another of a less mysterious construction substituted
* in its place, as it appears that a new method for the refractions was
* read before the Royal Society at their meeting on the 5th February last."
* [That would be Young's note in Phil. Trans., above.]
* April issue.
* Ivory continues his dispute with Young
* "The Table in the N.A. is one of no authority. No astronomer in Europe,
* except the author, can tell how it was constructed. Its character rests
* upon a dictum . We know that there is no correct theory." (p. 419)
* "I have also ascertained, by sound principles as I shall show below,
* that no confidence can be placed in my Table, nor in any other at present
* in existence, passing 88½° of zenith distance. Nearer the horizon
* the errors of every Table increase at a prodigious rate." (p. 419)
* Interestingly, he returns to POLYTROPES again (pp. 420-421); Ivory's
* m is the polytropic index. He now finds m = 4 to be best.
* "But the foregoing hypothesis, although it agrees sufficiently
* with the observed refractions, is opposed to Nature in another respect.
* It limits the extent of the atmosphere above the earth's surface to 25
* miles, which is probably less than half the real height." (p. 422)
* And the really interesting feature is the mention of Dalton's study of
* what we would call ADIABATIC atmospheres, on pp. 423-424: he cites lab
* measurements that give the exponent as 1.3492 or 1.3748 rather than 4/3
* -- but then concludes that the discrepancy indicates that this is just
* a first approximation, and that unknown higher-oder terms will account
* for the difference: "It thus appears that the other terms of the
* development beside the first have a sensible influence on the refractions
* at very low altitudes." However, he correctly notes that the speed of
* sound is connected with the adiabatic exponent (p. 426).
* cites his April paper (above).
* June issue; letter is dated June 14.
* Young's "Historical sketch"
* Notable for English translations of Taylor's work, and some of Kramp's.
* Unfortunately, he continues to make snide remarks about Ivory --
* whose "ridiculous accusations" he attributes to "an unfortunate
* enthusiast, whose imprudence seems almost to have impaired his reason"
* [pp. 369-370] -- though he has to eat crow a bit on p. 373, where
* he admits that Ivory had observed "with some truth that Dr. Young's
* inverse series was not in all cases so convergent as could be desired,
* or even as the author appeared to believe it . . . ."
* Here is yet another attempt to divine how Newton came to construct
* his refraction table: naturally, Young assumes Newton did it his way
* (which, in this case, is by using Taylor's work.)
* Young's "history" is very lopsided and uneven, being largely taken
* from second-hand sources. So he slights Lambert, without giving him
* credit for establishing the binomial-series expansion method.
* And there is no mention of Oriani at all! So we get:
* "For the mathematical theory of refraction it may be said that nothing
* of immediate importance was done from the time of Newton and Taylor, to
* that of Laplace and Kramp." (p. 363)
* [published anonymously, but clearly by Young.]
* Ivory's swift response to Young's "Historical Sketch"
* More sniping at Young; and (effectively) an accusation of plagiarism:
* "What Dr. Young calls his latest solution of the problem, published
* in the Philosophical Transactions 1824, and another particular solution
* mentioned at the end of the XIVth Number of the Astronomical Collections
* in the Journal of Science, are both taken from my paper." (p. 34)
* "I made no observation on the infinite series, except that it does not
* converge; and I proved the want of convergency in a particular instance.
* This brought upon me a torrent of vehement writing not confined within
* the limits of bienseance ." (p. 36)
* "The table of refractions in the Nautical Almanack is a singular
* instance of a set of practical calculations seemingly deduced from a deep
* theory; and yet, when we fully reach into the truth, having a slight,
* or even no, connexion with the theory. For it is not the formula which
* produces the table; it is the table, after the choice is made to make it
* consist of number from the tables of M. Bessel and the French astronomers,
* which determines the formula." (p. 37)
* So much for a "torrent of vehement writing"!
* Jan. issue; dated Jan. 14.
* Ivory's comparison with Bradley's observations
* Ivory agrees with Bessel to about 87° ZD, within a second or two.
* Beginning at 87° 23' Ivory is increasingly below, and Bessel
* increasingly above Bradley; their errors are nearly 40" at 89° 27'.
* Around 88°, Ivory is closer than Bessel to the observations.
* Dated Feb. 8, 1825.
* Ivory's essays on adiabatic atmospheres
* There are some mentions of refraction here, but mostly in passing.
* On p. 84, he notices that the actual lapse rate is smaller than the
* adiabat inferred in the laboratory "by one part in four". The
* "dilatation for one degree of the centigrade thermometer" is now 3/800,
* making absolute zero -267° C -- certainly an improvement over his
* earlier value of 250. (p. 85)
* Again, on p. 88, he notes that the actual lapse rate is slower than
* adiabatic; on the next page, he finds the sound speed in agreement with
* the lab data on adiabatic expansion. On pp. 89-90, he notes that the
* adiabatic atmosphere would correspond to m = 3 [polytropic index 3]
* "and the horizontal refraction will be found equal to 33' 7" at the
* mean temperature of 50° of Fahrenheit, and the barometric pressure
* of 30 inches." For the isothermal one, he gets 37' 34" at the horizon.
* ". . . they are the limits between which the real atmosphere is contained."
* P. 243: ". . . the arbitrary number m . . . may vary from zero to
* infinity." But in Dalton's adiabatic model m =3; so "m cannot be
* less than 3." And "So long as m has a finite value, the total height
* of the atmosphere is limited, and equal to l × (m + 1) . . . ."
* From his adopted lapse rate of 1° C in 90 fathoms, he gets m = 13/3
* or "in round numbers", 4.
* P. 247: Here he worries about the inadequate total height of the
* polytropic models: "If instead of taking m = 4, we make it 5, which
* is a supposition not inconsistent with observations, the objection will
* still remain . . . ." So he introduces his variety of fudge-factor to
* extend the upper atmosphere.
* P. 249: "Even the horizontal refractions are not much different in
* the several cases, and approach nearly to the quantity found by
* observation, -- if indeed we can affirm any thing of an element hitherto
* ascertained with so little precision."
* P. 250: "Now if we . . . make make the initial graduation of heat the
* same in the two atmospheres, the refractions in both will very nearly
* coincide, the difference amounting to only a few seconds at the horizon."
* So again he nearly sees Biot's result, but misses it. He concludes that
* the horizontal refraction is between 34' and 35' at 50° F, making the
* lapse rate between one degree in 84 fathoms [corresponding to 6.5 C/km]
* and 120 fathoms [4.6 C/km]. "The true atmosphere is undoubtedly
* contained between these limits."
* The first installment is in the Aug. issue; the second, in Oct.
* Ivory compares observations with Brinkley's table, and his own
* The emphasis here is on the unreliability of *any* table at low
* altitudes; and on the claim that Brinkley's table is superior.
* "We may therefore conclude that no table of refractions hitherto
* published can safely be trusted to at altitudes less than 2°. And this
* conclusion is corroborated by the parallel instance of the terrestrial
* refractions, which are found to vary from a certain limit through all
* degrees of magnitude, and even to change from positive to negative.
* . . . The boundary which separates the refractions irreducible to any
* degree of regularity, from those that can be theoretically computed, at
* least with tolerable regularity, . . . seems to be placed at an altitude
* of 2° or 1° ½ above the horizon."
* NOTE: "the New Table" evidently is Ivory's from 1823, though he says
* 1824 in this paper.
* This volume is the last in the first series of Phil.Mag.
* DELAMBRE's posthumous work, edited by Claude Louis MATHIEU
* I include this here because of its coverage of refraction, and
* especially because of Claude-Louis Mathieu's footnote on p. 696.
* Of Le Gentil's miraged sunrises, he says: "Ces apparences singulières
* ne sont pas rares dans nos climats; car, pendent l'hiver de 1808,
* je me trouvais à Dunkerque avec M. Biot, et nous avons eu occasion de
* voir des effets très varie's de réfraction extraordinaire." He then
* mentions Biot's book on mirages, and says of Biot, "il a rassemblé,
* dans des planches, tous les dessins que je faisais sur les lieux."
* So it is his drawings that appear in Biot's book, and have been
* reprinted so many times!
* N.B. This is *not* the Mathieu of the Mathieu functions; that is
* Émile Léonard Mathieu.
* Alas, we have this only on Readex Microprint cards; but Gallica has it.
* RIGAUD's Supplement: Bradley; Harriot and Greaves
* The first 16 pages puzzle out Bradley's reasoning from his notes.
* His "rule" turns out to have come from Simpson's paper. Notable
* for the demonstration that Bradley discovered empirically that the tan2
* term is negligible, so that refraction should involve tan z and tan3 z.
* The observations were made in 1750 and 1751, so I suppose Bradley's
* analysis followed shortly thereafter.
* There is also much interesting stuff on Harriot, including the
* information (p. 33) that Lalande is responsible for the legend that
* the blindness of Galileo and Cassini was due to their solar observing.
* Ivory compares his table with Bessel's tables
* He finds a systematic error in the Fundamenta Astronomiae beyond
* 85° Z.D. For the Tabulae Regiomontanae the agreement is better,
* but those (observed) values are still larger than Ivory's theory
* beyond 88°. But Plana's mean observed value at 88° 24' is only
* about a second of arc greater than Ivory's table -- though with a range
* of some 31''. "The discrepancies of the individual values . . . have
* not been explained . . . ." Note that he assumes the two tables can be
* harmonized by a constant factor at all Z.D.
* There are tantalizing hints here that Ivory has some insight into
* refraction at last: "The quantity f used in the construction of the
* Table in the Phil. Trans. seems to be determined with considerable
* exactness: for a small variation of its value would materially alter
* the refractions at low altitudes." (col. 112)
* "If attention be paid to the construction of the Table in the Phil.
* Trans. it will appear that it determines the refractions only so far as
* they depend upon two principles, namely, the refraction power of the air,
* and the rate, expressed by (1 - f ), at which the density decreases in
* ascending at the surface of the earth." (col. 114)
* The table at the bottom of col. 112 starts with 84°, but this is
* obviously a typo for 88° (as is correctly given at the end).
* He refers to his 1824 Phil. Trans. comparison with the Fund. Astr.;
* this is a typo for 1823.
* Note that the discrepancies at 89 and 89.5° with Bessel's [i.e.,
* Argelander's] observed values could be used to estimate a typical
* nocturnal inversion at Königsberg. [Marcel Tschudin (2019) has finally
* done so!]
* This letter was communicated 15. Decbr. 1834, says the editor.
* Note: Ivory had been knighted in 1831.
* The NEWTON-FLAMSTEED correspondence [FILED separately]
* An appalling tale of growing mistrust and enmity, in which there is
* more than enough blame on all sides (including, apparently, Halley).
* Fortunately, we need only concern ourselves with the refraction
* discussion, before the atmosphere became completely poisoned. It
* begins with Flamsteed's letter No. 17 to Newton, dated Oct. 11, 1694,
* in which he mentions finding the horizontal refraction to be 33',
* decreasing to 23' a degree above the horizon; whereas the existing
* theories (based on a uniform atmosphere) would make this difference
* only about 5' instead of 10. "It seems only the medium, in which the
* refractions are made, is not equable as supposed by those who build
* their tables upon theories. This subject deserves your consideration:
* I desire your thoughts of it at your leisure." Newton's reply (No. 18,
* October 24, 1694) says, "The reason of the different refractions, near
* the horizon, in the same altitude, I take to be the different heat of
* the air in the lower region. For, when the air is rarefied by heat, it
* refracts less: when condensed by cold, it refracts more. And this
* difference must be most sensible when the rays run along in the lower
* region of the air for a great many miles together; because 'tis this
* region only which is rarefied and condensed by heat and cold: the middle
* and upper region of the air being always cold. I am of opinion also
* that the refraction in all greater altitudes is varied a little by the
* different weight of the air discovered by the baroscope. For, when the
* air is heavier, and by consequence denser, it must refract something
* more than when 'tis lighter and rarer."
* On Nov. 17, 1694, Newton sent Flamsteed a preliminary table of
* refractions, based on a linear decrease of refractivity with height (see
* p.141). Below 30° altitude, it has separate entries for the seasons,
* based on Newton's estimate of "the rarefaction of the air in winter and
* summer; which I found some time ago, by certain experiments, to be as 8
* to 9, or thereabouts." On Dec. 4, Newton wrote again: "The table of
* refractions I sent you I do not design to publish. 'Tis not so accurate
* as it may be made . . . . There being a certain circumstance omitted in
* computing it, I intend to examine it with allowance for that
* circumstance, and when I have set it right I will send you a new copy of
* it."
* On Dec. 20, Newton sends the diagram and explanation (see p.145): "Let
* A K L represent the globe of the earth, and suppose this globe is covered
* with an atmosphere of air whose density decreases uniformly from the
* earth upwards to the top . . . ."
* No. 24, Jan. 15, 1694-5; Newton to Flamsteed: "The theorem of
* refractions I sent you has this fault, that it makes the refracting power
* [i.e., the refractivity gradient] of the atmosphere as great at the top as
* at the bottom. This has put me upon thinking on a new theorem . . . . But
* the calculation is intricate.
* "I thank you for your observations about the morning and evening
* refractions. The reason why the former are greater in summer than the
* latter, I take to be nothing but the different heat and coldness of the
* air. For the air cools all night, and is coldest at sunrise: and heats
* all day, and is hottest about 12 hours after sunrise. The cold condenses
* the air, and makes its refraction greatest at sunrise; and the heat
* rarefies it, and thereby diminishes its refractive power in the evening."
* Flamsteed's notes on this summarize his reply: "I grant the heat and
* cold of the air is the chief cause of the change of its refractive power,
* but not all: for other days were as hot as that, yet had less refractions.
* "The sun rose then over the Thames and adjacent marshes. Set over a
* dry hill on the west end of London. It was a misty morning, and a great
* fog over the meadows."
* Newton to Flamsteed, Jan.26, 1694-5 (No.25): "I agree with you that the
* dense vapors, which always stagnate upon the surface of the sea and often
* upon fenny places, cause a strong refraction. And it's probable that
* those, which rise to a greater height, may increase the refraction of the
* horizontal sun. But can you tell whether the refraction of the sea-vapors
* or fen-vapors be greater in hot weather or in cold? at morning or at
* night?
* "To make a new table of refractions has taken up almost all my time
* ever since the holidays: and I have hitherto lost my pains in fruitless
* calculations, by reason of the difficulty of the work. For considering
* that such a table is the foundation of astronomy, and very necessary for
* your great work, and that you have taken so great pains in providing
* materials for it, I was desirous to complete it . . . ."
* No. 26, Newton to F., Feb. 16, 1694-5: "I have been, ever since I wrote
* to you last, upon making a new table of refractions and have not yet
* finished it: 'tis a very intricate and laborious piece of work; yet
* something I have done towards it. For, supposing the atmosphere to be of
* such a constitution as is described in the 22nd proposition of my second
* book (which certainly is the truth) I have found that, if the horizontal
* refraction be 34', the refraction in the apparent altitude of 3gr. will be
* 13' 3": and if the refraction in the apparent altitude of 3gr. be 14', the
* horizontal refraction will be something more than 37'." [But 14' and 33'
* are Flamsteed's observed values, which he asserted were "incontestable".]
* "So that, instead of increasing the horizontal refraction by vapors, we
* must find some other cause to decrease it. And I cannot think of any
* other cause besides the rarefaction of the lower region of the atmosphere
* by heat."
* Newton then goes on to speculate about the effects of "sea-vapors and
* fen-vapors" as being in fact due to "condensation of the air by cold. For
* in travelling we find it always colder upon the water than upon the land
* . . . and therefore the water doth cool the air to the height of some fathoms
* above it, and by cooling condenses it and increases its refractive power.
* . . . And, were the air upon the sea overloaded with vapors, it would scarce
* be so transparent as to let Calais with its buildings and church steeples
* be seen through it cross the Channel."
* On p. 152, the footnote gives Flamsteed's comment: "He adds a great
* many words to persuade me that to have the theory of the moon published
* with my observations, would be a great proof of their accuracy : whereas,
* theories do not commend observations ; but are to be tried by them :
* and theories are then only probable, when they agree with exact and
* indubitable observations ."
* Finally, No. 27, March 15, 1694-5, Newton to Flamsteed: "I have now
* finished the table of refractions, and send you enclosed a copy of it."
* To which is footnoted: "This table is not found. F.B." The only value
* mentioned is 13' 20" at 3° altitude; which agrees with Newton's table
* published by Halley (1721).
* Available at Google Books.
* BIOT finds refraction gradient at horizon while reading NEWTON's letters
* to FLAMSTEED, published by Baily the previous year. He finds that
* Newton assumed a simple exponential (i.e., const.-T) atmosphere.
* Of more interest to us here is his discovery of a theorem about the
* horizontal refraction. He first mentions the well-known result that the
* refraction depends only on local conditions, out to about 74° Z.D.
* "Mais, ce qu'on n'avait pas remarqué, il existe près de l'horizon, ou
* plutôt à l'horizon même, un théorème analogue, qui a, de plus, la
* singularité de s'y réaliser toujours, dans toutes les constitutions
* possibles d'atmosphères, non pas approximativement, comme celui que nous
* venons de rappeler, mais d'une manière absolue et rigoureuse." (p. 241)
* He calls the derivative of the refraction with respect to the apparent
* zenith distance the " coefficient varié de la refraction."
* "Mais, tandis que, près du zénith, le coefficient varié dépend
* seulement du pouvoir réfringent observable dans la couche où
* l'observateur se trouve, sa valeur à l'horizon dépend à la fois de
* ce pouvoir et de son décroissement immédiat, à mesure qu'on s'élève
* au-dessus de l'observateur; de sorte que l'action des couches lointaines
* n'y influe absolument pour rien." (p. 242)
* "Outre la singularité inattendue de trouver un élément de la
* réfraction horizontale, indépendant de l'état des couches lointaines,
* et s'obtenant, dans tous les cas possibles, sans intégration; outre la
* liaison qui en résulte entre l'accroissement de la réfraction près de
* l'horizon et les variations également observables du pouvoir réfringent
* à partir de la couche inférieure, le théorème que je viens d'énoncer
* aura encore d'autres applications utiles." (p. 243)
* Of course the latter connection immediately lets one obtain the
* magnification at the horizon from the local lapse rate, though Biot does
* not say so explicitly. Thus, we may fairly attribute the MAGNIFICATION
* theorem to him -- especially in view of his calculation of the
* flattening of the Moon at the horizon in his 1810 Physical Astronomy
* textbook, which shows a long-standing interest in the subject.
*
* The details are given in his Connaissance des Tems addendum (see
* below)
* Biot thinks DUCTS improbable on Earth
* Concerning his theorem about horizontal refraction, he says:
* "En revoyant depuis ma démonstration j'ai reconnu que ce théorème
* n'aurait pas lieu dans des atmosphères qui donneraient des trajectoires
* horizontales rentrantes sur elles-mêmes. Quoique ce cas d'exception
* soit purement idéal, je crois devoir le signaler, pour que les
* géomètres qui chercheraient à démontrer le théorème dont il s'agit,
* ne se trouvent pas embarrassés par cette difficulté inutile."
* This is the detailed analysis corresponding to the C.R. summaries
* A very nice piece of work! Biot mentions the possibility of ducting
* (p.42), but does not think it can occur in our atmosphere. Here
* (pp.95-108) he explains how he figured out what Newton did. The
* writing is all very clear and easy to read throughout. There are
* frequent references to Ivory and Delambre, as well as Kramp (and, of
* course, to ``the author of the Mécanique Céleste .'')
*
* Much of the following also appears in the two C.R. notes above:
*
* Of most interest to us here is his discovery of a theorem about the
* horizontal refraction. He first mentions the well-known result that the
* refraction depends only on local conditions, out to about 74° Z.D.
* "Mais, ce qu'on n'avait pas remarqué, il existe près de l'horizon, ou
* plutôt à l'horizon même, un théorème analogue, qui a, de plus, la
* singularité de s'y réaliser toujours, dans toutes les constitutions
* possibles d'atmosphères, non pas approximativement, comme celui que nous
* venons de rappeler, mais d'une manière absolue et rigoureuse." (p. 6)
* He calls the derivative of the refraction with respect to the apparent
* zenith distance the " coefficient varié de la refraction."
* "Mais, tandis que, près du zénith, le coefficient varié dépend
* seulement du pouvoir réfringent observable dans la couche où
* l'observateur se trouve, sa valeur à l'horizon dépend à la fois de
* ce pouvoir et de son décroissement immédiat, à mesure qu'on s'élève
* au-dessus de l'observateur; de sorte que l'action des couches lointaines
* n'y influe absolument pour rien." (p. 7)
* "Outre la singularité inattendue de trouver un élément de la
* réfraction horizontale, indépendant de l'état des couches lointaines,
* et s'obtenant, dans tous les cas possibles, sans intégration; outre la
* liaison qui en résulte entre l'accroissement de la réfraction près de
* l'horizon et les variations également observables du pouvoir réfringent
* à partir de la couche inférieure, le théorème que je viens d'énoncer
* aura encore d'autres applications utiles." (p. 8)
* Of course the latter connection immediately lets one obtain the
* magnification at the horizon from the local lapse rate, though Biot does
* not say so explicitly. Thus, we may fairly attribute the MAGNIFICATION
* theorem to him.
*
* Considers (but rejects) the possibility of a DUCT (p. 42):
* "On peut concevoir, et constituer théoriquement des atmosphères où
* la condition dont il s'agit serait satisfaite en plus d'un point pour
* certaines valeurs données du second membre. Alors les trajectoires
* jouissant de cette propriété seraient rentrantes sur elles-mêmes, et
* comprises dans l'intérieur de l'atmosphère réfringent; de sorte que la
* vision des objects extérieurs ne serait pas généralement possible par
* une trajectoire horizontale." [This predicts Wegener's BLANK STRIP !]
* But "Dans l'atmosphère terrestre, les trajectoires étant toujours
* très peu courbes, leur horizontalité n'a lieu qu'en un point."
*
* In considering the effects of water vapor, he remarks that they are
* insufficient to account for the variations of refraction near the
* horizon, citing DELAMBRE, p. 321: "Néanmoins, . . . on se convaincra
* aisément qu'elles ne peuvent pas produire des variations accidentelles
* de 5" et 6" à 75° de distance zénithale, comme Delambre assure en
* avoir observées." (p. 71) (So he is aware of VARIATIONS.)
*
* As the rays are no longer nearly horizontal in the upper atmosphere, the
* simple tangent formula applies there. Thus he can "expliquer un
* résultat de calcul obtenu par M. Ivory, et dont il a signalé la
* singularité. Il consiste en ce que les valeurs calculées des
* réfractions se trouvent presque exactement les mêmes dans des
* atmosphères de hauteur très inégale, différant, par exemple, depuis
* 1/62 du rayon terrestre, pourvu seulement qu'elles s'accordent avec
* l'atmosphère réelle dans les températures et les pressions de la couche
* inférieure, ainsi que pour les premiers décroissements qu'elles leur
* assignent; les décroissements ultérieurs pouvant d'ailleurs se trouver
* très divers l'une à l'autre, et devant même l'être, pour leur donner
* de si inégales extensions." (p. 73) (So the upper air is unimportant.)
*
* On p. 76 begins the 3rd section: "Calcul des réfractions, par
* quadratures numériques à toute distance du zénith, et dans une
* constitution quelconque d'atmosphère." Here is where he changes
* the variable of integration to "l'angle continuellement formé par la
* tangente de la trajectoire, avec son rayon vecteur mené du centre
* des couches." (This is exactly the local zenith distance of the ray;
* so his integrand V is, apart from notation, identical to that of Auer and
* Standish.) He uses a 13-point quadrature, done with a piecewise-parabolic
* fit through these 13 points (i.e., basically the same kind of iterated
* Simpson's rule used by Auer & Standish.) On p. 81 he gives the numerical
* values at the 13 nodes, and shows that this method reproduces Ivory's
* result at the horizon to 1.247 arcsec. [He uses the 2-term tangent
* approximation for the top 1% of the atmosphere.] He makes the following
* interesting comment on this small difference:
* "Il se peut que cette petite différence vienne de ce que
* l'interpolation n'aurait pas été tout-à-fait assez serrée dans ses
* premiers termes; mais je n'oserais pas non plus répondre qu'elle ne soit
* pas due à quelques petites erreurs dans l'appréciation des dernières
* décimales des nombres que ces calculs nécessitent." (p. 81)
* He then applies his method to the isothermal model, and to the
* polytrope of index 1, and discusses Bradley's formula. He also shows
* that his method works for zenith distances exceeding 90° (i.e.,
* below the astronomical horizon.)
*
* In the 4th section (p. 95), he shows in detail that Newton's table
* is for an isothermal atmosphere.
* In the 5th (p. 108), he compares Ivory's model atmosphere with that
* used by Laplace.
* The lack of sensitivity to atmospheric structure, particularly at
* great heights, is discussed on pp. 74 and 112.
*
* NOTE: the development is all in terms of the emission theory.
*
* Full title is "Connaissance des Tems ou des Mouvemens Célestes,
* a l'Usage des Astronomes et des Navigateurs, pour l'An 1839" and this
* is the part called "Additions a la Connaissance des Tems".
* -- note the use of the spelling "tems" throughout.
* "(Lu à l'Académie des Sciences, le 5 septembre 1836.)"
* Note the Erratum at the end of Biot's paper. As usual, Google's scan
* lacks the essential figures. As the Additions are paginated separately
* from the ephemerides, Biot's paper begins at Google's image 427.
* Thanks a million to Brenda Corbin at USNO for a copy of the figures !!!
* LUC DETTWILLER's review of Biot's refraction work, centered on the
* magnification theorem, and so put here out of chronological order.
* This is a nice review of Biot's works on refraction, boiled down to
* the main points, with extensive quotations from the original papers.
* (His comments on Biot's verbosity remind me of Glaisher's comments on
* Flammarion's loquacity.) The introduction briefly reviews Biot's
* wide-ranging accomplishments; the rest of the paper illuminates Biot's
* path to the magnification theorem with detailed derivations.
* Part of the special issue: Astronomy, Atmospheres and Refraction
* Available at https://doi.org/10.5802/crphys.117
* DOI: doi:10.5802/crphys.117
* CHALLIS comments on Biot
* Cites Brinkley (1815) and Ivory (1823): "The fact is, astronomical
* refractions are very little influenced by the higher parts of the
* atmosphere, so that supposititious [sic] atmospheres agreeing with the
* existing atmosphere in the lower strata, and widely differing in the
* upper, may yet produce the same amount of refraction." (p. 233) Here
* he cites Biot: "The memoir of M. Biot on astronomical refractions, read
* before the Paris Academy, Sept. 5, 1836, and printed in the additions
* to the Connaissance des Tems for 1839, treats the problem with all
* the generality and precision that may be hoped for on a subject of
* this nature."
* Google's scan, of the U. of Michigan library copy, is missing
* pp. 228 and 229.
* A further fine paper by Biot on refraction and atmospheric models
* The "hook" here is that, as Laplace's work on the oblateness of the
* Earth has allowed it to be inferred from observations of the Moon more
* readily than from direct measurements, one might also suppose that his
* work on refraction would equally well allow the structure of the upper
* atmosphere to be inferred indirectly from refraction observations.
* ". . . les intégrales analytiques que l'on en déduisait embrassant toute
* l'étendue de l'atmosphère supposée, ne laissaient pas discerner la part
* que les couches supérieures seules prenaient dans la réfraction totale
* obtenue, ni surtout celles qu'il fallait leur attribuer nécessairement."
* He again asserts that "la petitesse absolue des réfractions à toute
* distance du zénith exclut la possibilité des trajectoires lumineuses
* rentrantes sur elles-mêmes," despite his work on mirages. [p. 598]
* "Puis, dans les hauteurs qui nous sont accessibles, on trouve
* expérimentalement que le pouvoir réfringent décroit à mesure qu'on
* s'elève, et que la dépression de l'horizon apparent augmente; d'où
* l'on conclut qu'en s'éloignant de la surface terrestre, les éléments
* de chaque trajectoire forment des angles graduellement moindres avec
* leur rayon vecteur central." -- a nice argument based on DIP!
* P. 599: an interesting remark about the thinness of the atmosphere,
* argued from twilight. But Arago objects, in a note saying that this
* argument is based on single scattering, while polarimetric observations
* have shown that skylight involves multiple scattering. Biot then says
* this shows the atmosphere is even thinner than the single-scattering
* argument suggests, which makes his own argument stronger!
* P. 600: He again points out that any reasonable atmospheric model
* must give nearly the same refraction out to large Z.D., the uncertainty
* being less than 0".001 at 45°, 0".277 at 74°, and 2".243 at 80°.
* This restriction becomes tighter at greater heights, so that the
* sea-level horizon ray receives a contribution uncertain by less than 0".15
* above 5/1000 of the Earth's radius. "Les couches supérieures, d'où
* cette portion résulte, pourraient donc être constituées de toutes les
* manières imaginables, quant à leurs densités, leurs températures,
* et jusqu'à un certain point leur nature physique même, sans que nous
* apercevions jamais aucun effet appréciable de ces différences dans les
* réfractions totales que nous observons; et ainsi, par réciprocité,
* les réfractions observées ne peuvent nous fournir aucune notion sur
* ces régions élevées de l'atmosphère." [p. 601] Here are his two
* limiting models for calculating refraction: ". . . si on les [réfractions]
* calcule en supposant les pressions proportionnelles à la première
* puissance des densités. on les trouve plus fortes que la réalité;
* et avec la seconde puissance de ces mêmes densités on les trouve trop
* faibles. La vraie loi est donc intermédiaire entre des deux-là; . . . "
* -- that is, between these two POLYTROPES: the isothermal one and the
* polytrope of index n = 1, corresponding to a lapse rate of 17°/km
* (nearly twice the adiabatic lapse rate).
* P. 603: "Si les considérations précédentes détruisent la
* possibilité d'inductions qui eussent été précieuses pour la physique
* du globe, elles nous montrent comment on pourra rendre les tables de
* réfractions plus parfaites, et surtout plus générales qu'elles ne
* le sont aujourd'hui. . . . Car, par exemple, le décroissement de la
* température près de la surface terrestre paraît très variable dans
* un même lieu, aux différentes saisons; et il est peu probable que sa
* quantité absolue soit la même dans toutes les localités. Or, cet
* élément influe sur une des constantes les plus importantes des tables;
* et, d'après un théorème que j'ai démontré, c'est de lui surtout
* que dépendent les différences des réfractions entre elles près de
* l'horizon. Il faut donc déterminer expérimentalement ses variations,
* . . . et l'en affecter dans le calcul des tables, au lieu de l'y supposer
* constant et partout le même, comme on l'a fait jusqu'ici." And:
* ". . . on pourrait . . . observer régulièrement les constantes de ces
* régions de trouble, au moyen de petits ballons captifs qui porteraient
* des instruments à indicateurs, dont les résultats s'appliqueraient
* comme correctifs à des tables permanentes, construites pour la région
* non troublée." [p. 604] ". . . et alors l'analyse aurait fait pour
* la théorie des réfractions astronomiques tout ce qu'il est permis
* d'espérer."
* BIOT's series in J.Savants, reviewing the Newton-Flamsteed correspondence
* Of the 3 parts, the last deals with the refraction question.
* This volume is now available at Gallica, under the old "Sçavans"
* name, at
* https://gallica.bnf.fr/ark:/12148/bpt6k110181v#
*
* Biot's installments are in the March, April, and November issues.
* Biot's more detailed analysis of Newton's refraction table
* This evidently was extracted from the CdT article (above) and expanded.
* It must be read after the previous item, as several things otherwise
* unexplained would not make sense.
* Décembre issue
* KRYLOV's attempt to read Newton's mind retroactively . . . .
* Another stab at unravelling Newton's refraction table.
* Already on p. 15 he is expanding the refraction in powers of sec z or
* tan z; on p. 18 he finds that Newton's table agrees [as it must!] with
* the one-term approximation out to about 55° ZD. . . . So [p. 20] he
* even supposes it possible that Newton used the first 2 terms in the
* series expansion! Worse, he assumes [p. 25] that beyond 87° ZD,
* Newton's table is based on Flamsteed's observations rather than on
* calculation.
* Whiteside's transcription of Newton's working papers
* As Biot conjectured, these turned up in the Portsmouth collection of
* Newtoniana. The refraction discussion is mainly in the enormous
* footnotes on these pages.
* On p. 432, he calls Biot's analysis "brilliant", and adds, "We are
* heavily indebted to his pioneering lead."
* N.B.: filed here out of order, for its clarification of Newton's table.
* Whiteside's refraction paper
* I find the rather arch tone of this paper a bit unpleasant; but the
* worst part is his bizarre final paragraph (p.308), where he wrongly
* claims that "working astronomers still find computational advantage
* in maintaining the fiction of a Newtonian emission theory" -- which
* is sheer nonsense! Apparently he has no understanding of what
* geometrical optics is all about: as it depends only on Snel's law,
* which long predates Newton's emission theory, the latter is irrelevant.
* Furthermore, he doesn't understand the statement (which he attributes
* to Woolard & Clemence, but which was extensively discussed by Biot in
* his CdT paper) that the refraction within 80° of the zenith is nearly
* independent of the atmospheric model used. Had he understood
* Biot's 1836 CdT paper (which he even cites!), he would have understood
* this fact. Unfortunately, this wrong-headed final paragraph seriously
* undermines the good parts of the paper, and reveals that Whiteside was
* as much an "armchair astronomer" as Newton.
* Again filed out of order for relevance here.
* PETER ANDREAS HANSEN's papers on PARALLACTIC REFRACTION
* This is a long, detailed analysis of the geometrical circumstances of
* solar and lunar eclipses, as seen from an arbitrary point on the Earth.
* The term "parallax" appears several times; but there is no explicit
* treatment of parallactic refraction.
* A "Zusatz" begins in the middle of col. 100. "Refraction" appears
* briefly in cols. 101 and 102. The bulk of the paper assumes a spherical
* Earth; in Col. 102, the flattening is introduced, and the astronomical
* latitude is distinguished from the geocentric latitude of the observer.
* The issue is dated 7 December 1837.
* This is an addition to the paper above. Here, refraction is included:
* "In der Theorie der Verfinsterungen hat man nie die Einwirkung der
* Strahlenhrechung entwickelt. Man hat entweder gradezu gesagt, dass
* diese keine Wirkung auf die Verfinsterungen äussere, oder man hat
* dieses wenigstens stillschweigend angenommen. Dieses ist aber nicht
* richtig, denn die Strahlenbrechung ist nicht ohne Einfluss auf die Zeit,
* Dauer und die Oerter des Anfanges oder Endes einer Verfinsterung oder
* Sternbedeckung, wenn gleich in den méhrsten Fällen diese Wirkung
* unbeträchtlich ist." (first paragraph.)
* Now for the PARALLACTIC REFR.:
* ". . . in der That die Strahlenhrechung nicht nur von der scheinbaren
* Zenithdistanz, sondern auch von der Entfernung des Himmelskörpers
* abhängt." (col. 184) He then distinguishes between the total ray
* bending (the ordinary astronomical refraction) and the angle between the
* ray at the observer and the direction to an object at a finite distance
* (the Moon): "in allen Fällen, wo die Entfernung des Himmelskörpers
* endlich ist, ist die wahre Zenithdistanz kleiner, als die durch unsere
* Strahlenhrechung verbesserte scheinbare Zenithdistanz."
* His derivation follows the Cél. Mech. notation (i.e., the emission
* theory) and (like Biot) he follows Laplace's awkward notation. From this
* he derives the size of the correction needed when the nearby object is
* near the horizon.
* As the effect is just as if the observer were raised to some height
* and the atmosphere were removed, he then derives the height required
* to move the observer up to the extension of the ray's path outside
* the atmosphere.
* Note the corrections in col. 192 of printer's errors in Nr.339-342.
* Friedrich Wilhelm Barfuss's paper
* An interesting piece of work. Barfuss starts out expounding basic
* refraction theory like a student's term paper; but he carries it on to
* remarkable lengths. In col. 139, he suggests that, despite the continual
* decrease of temperature in the region explored by balloons, "Daß indeß
* diese Progression durch die ganze Atmosphäre gelten sollte, ist nicht
* wahrscheinlich, vielmehr ist es glaublich, daß in einer gewissen Höhe
* die Temperaturdifferenzen wieder abnehmen, oder wohl gar die Temperatur
* constant bleibt." -- a guess at the stratosphere matched only by Young's.
* At the foot of col. 141, he derives the 2-term series expansion
* in nearly as good a form as Green's version; at the end of the section
* (col.143) he comes up with Stone's criterion: "Wenn nun bei der Berechnung
* der Refraction ein Fehler von 0"05 für nichts geachtet wird, so setze
* man obigen Ausdruck = 0"05, . . . woraus tg z = 3,04 gefunden wird, wozu
* eine Zenithdistanz > 70° gehört. Also lassen sich durch obige Formel
* für r die Refractionen aller Zenithdistanzen bis 70° genauer als
* bis 0"05 berechnen.
* ". . . Aber für größere Zenithdistanzen wird die Sache weit
* schwieriger, weil nun das Gesetz der Abnahme der Brechungen immer stärker
* zu wirken anfängt, und seinen Einfluß nicht bloß in einzelnen Secunden,
* sondern sogar in Minuten äußert. . . . In den untersten Luftschichten
* walten diejenigen Ursachen von welchen . . . die Dichtigkeit der Luft
* abhängt . . . so gut wie ohne Regel, und diese Regellosigkeit in der
* Luft, muß auch eine Regellosigkeit in der Strahlenbrechung bewirken,
* welche um so stärker wird, je größer die Zenithdistanzen werden.
* Diese Betrachtungen leiten uns zu dem Entschlusse, die Refractionen
* größerer Zenithdistanzen, als etwa 86° aus den Tafeln, welche für
* die practische Astronomie bestimmt sind, gänzlich auszuschließen, und
* noch fehlenden Refractionen der Zenithdistanzen von 70° bis 86 Grad
* weniger durch ein hypothetisches Gesetz der Abnahme der Brechungen,
* sondern mehr auf einem empirischen, durch die Theorie gehörig
* unterstützten Wege zu bestimmen." [col. 144] He suggests that the
* slowly-converging series in sin z can be used to find an approximation
* in this region with only one free parameter to be found from observation,
* if the theoretical expressions for the others are used. (col. 145)
* Note that the paper is introduced by a brief endorsement by Bessel!
* Published as "BEILAGE zu No. 344. der Astronomischen Nachrichten"
* dated 25 Jan. 1838.
* Typographical note: the ß is printed here as a long-s/short-s
* kerned pair or logotype, not joined as a ligature.
* IVORY's Bakerian lecture on refraction
* Chiefly useful today for its historical introduction. From the start,
* he appears uncertain about the relative importance of upper and lower
* atmosphere, mentioning "The limit of the atmosphere . . . " on p. 170, but
* ". . . a great share of that part of the astronomical refraction which
* depends upon the constitution of the atmosphere, must be ascribed to
* the initial rate at which the density decreases." (p. 171).
* Newton's table (published by Halley) is treated on pp. 178-183.
* Ivory emphasizes (pp.181-182) that the refractions at altitudes above
* 16° depend only on the refractivity of air and not on the vertical
* structure (or, as he says, the "constitution") of the atmosphere.
* So a table of mean refractions above this altitude "gives no intimation
* with respect to the particular constitution of the atmosphere".
* On p. 185, he again emphasizes that "as far as 74° from the zenith
* . . . all tables of refraction may be computed by CASSINI's method."
* On the next page, he describes Laplace's method of mixing "the two
* atmospheres with densities decreasing in arithmetical and geometrical
* progression," namely, a weighted product of their density profiles.
* He compares the result with Bessel's measured refractions, but warns
* that "With respect to the two degrees of altitude next the horizon, no
* accurate judgement can be formed, for want of observed refractions
* that can be depended on." (p.186)
* He seems to go out of his way to pick a fight with Biot (pp. 189-190);
* and his procedure is just as arbitrary as that of Biot, or Laplace
* (whom he criticizes). [No mention of Oriani.]
* He comes closest to the truth on p. 190: ". . . we are now acquainted
* with three things . . . that have an influence on the mean refractions.
* These are, the refractive power of the air, the spherical figure
* of the atmosphere, and the mean rate at which the density of the air
* decreases . . . ."
* Ivory then tries "to complete the solution of the problem by
* estimating the effect of all the quantities on which the density at any
* height depends." (p. 191)
* On p. 196, he says that the lapse rate is so difficult to measure that
* some mean value must be adopted. On the next page, he discusses the
* available data, and adopts a value that increases the horizontal
* refraction by only 19" from his 1823 result for dry air. He then works
* out the effect of water vapor, and concludes that the refraction is the
* same as for dry air at the same T and p. (p. 209)
* In searching for the next-order term in his series expansion, he says
* "In the present state of our knowledge of the phenomena of the atmosphere,
* it seems impossible to determnine f' by experiments. " (p. 215)
* On the next page, he notes that the unknown terms are "of no account
* whatever, except the apparent altitude be equal to 2° or less", and on
* p. 219 finds that the contribution from the part that depends on the
* height of the atmosphere "will be a minute fraction of a second" even at
* the horizon. He ends by concluding that finding the unknown small
* corrections to the mean refraction would require "many good observed
* refractions at altitudes less than 5°. If such values were found, our
* knowledge of the decrease of heat in ascending in the atmosphere would
* be improved. . . ."
* Ivory, like Biot, speaks of "the molecule of light" and uses the
* emission theory to "derive" Snel's law. (pp. 174-175)
* His frequent references to the "Principia", as well as his religious
* training, suggest that he knew Latin; but he never seems to have read
* Oriani's work,
* BIOT's argument with POISSON begins
* Biot takes as his point of departure the discussion at the 7th meeting
* of the British Association, Mathematical division, where apparently
* Poisson's idea that the upper limit of the atmosphere might be liquid
* was discussed, with its supposed consequences for refraction
* calculations. Referring to his Connaissance des Tems memoir, he
* points out that the uppermost layers must have negligible effects. He
* also comments on Atkinson's paper in Mem. RAS, vol. 2, pointing out that
* his own method is greatly superior for actual calculations, and that
* Atkinson falls back on Bradley's rule for the top layer. ``En cela
* donc, le calcul de M. Atkinson, analysé avec exactitude dans ses
* éléments physiques, prêterait à la même illusion que les autres
* lois continues de décroissement employées par tous les géomètres qui
* l'ont précédé; illusion qui consiste à supposer qu'en pliant ces
* lois aux mesures de température faite dan les couches inférieurs, et
* tirant de leur emploi analytique des réfractions conformes à celles
* qui s'observent, on peut inférer de cette coïncidence, que les
* mêmes lois s'étendent, même approximativement, aux couches
* supérieures par lesquelles l'atmosphère est terminée. Car lorsque
* l'on maintenant ainsi, jusque dans ces couches, l'état et les
* propriétés habituelles des gaz, la portion de la réfraction totale
* qu'elles produisent, a toujours une valeur sensiblement égale dans
* tous les modes de superposition qu'on peut leur attribuer. Donc,
* inversement, on ne doit pas alors chercher des indices de leur
* température dans les valeurs des réfractions observables.''
* Poisson's objection is attributed to a report printed in the Atheneum
* No. 519, p. 743, from which Biot gives a short translated excerpt.
* Biot on atmospheric structure
* He points out that both the refraction and the barometric formulae in
* use are based on an empirical mixture of isothermal and what we would
* now call polytropic models, and looks for a more exact solution.
* The pressure, temperature, and density at each height are connected by
* the gas law and the requirement for hydrostatic equilibrium; so only
* one more relation is needed to solve the problem. Poisson has given
* a fictitious example; but one can also use empirical data, obtained by
* balloon ascents. He tries this with Gay-Lussac's balloon data, finding
* that the pressures and densities are almost linearly related, and show
* only a slight curvature in the lower atmosphere. A linear extrapolation
* of the uppermost data would make the density finite when the pressure
* vanishes; but this would make the atmosphere end at 23 km, which he
* knows is too low. But drawing a line from the last point to the origin
* gives an error of the opposite kind; so the truth must lie between them.
* So he finds that the temperatures must continue to decrease in the
* upper half of the atmosphere. He thinks it is impossible for the
* pressure and density to go to zero together at the top of the
* atmosphere, and so adopts a parabolic extrapolation that gives a finite
* density, and a reasonable height for the top of the atmosphere. With
* better balloon data, one could apply his methods from the CdT for 1839
* and thus obtain realistic refraction to the horizon; "et l'on
* appliquerait aux couches inférieurs les corrections variables que
* leur état nécessite; corrections qui seules peuvent faire
* connaître la vraie valeur de la réfraction qui s'y produit."
* More of the same
* BIOT's monograph on atmospheric structure and refraction
* The sub-title says "Lu à l'Académie des Sciences les 2, 16 et 30 avril
* 1838" -- so the preceding items are the abstracts.
* There is an interesting historical note on pp. 3 -- 5, in which he
* extols the work of Laplace, but then remarkably says that Ivory's work
* is still better. Also on p. 4, he says (of inferring atmospheric
* structure from refraction observations):
* "Et enfin j'ai montré que cette induction cesse même totalement
* d'exister pour les régions supérieures de l'atmosphère, parce que
* les réfractions observables ici-bas sont sensiblement indépendantes
* du mode de superposition qu'on peut leur attribuer."
* Astronomical refraction is briefly considered on pp. 89-90.
* Note that the fling with spelling reform has passed!
* A minor follow-up to Biot
* Dieu spends most of his effort reviewing the subject, with emphasis
* on Biot's work. At the end, he tries a pressure proportional to a
* quadratic function of the densities (i.e., a linear plus a quadratic
* term).
* This is a "Thèse d'Astronomie" and Dieu is listed as "Professeur de
* Mathématiques supérieures au Lycée de Dijon".
* BIOT's 1854-55 series of papers
*
* These were initiated by a paper by Hervé Faye, suggesting that
* astronomical refraction could be improved by using measurements of
* terrestrial refraction. Faye seems to have had a black thumb: Miss
* Clerke reports that he believed the solar prominences were appendages
* of the Moon; that he maintained the "cyclone" theory of sunspots; had
* a strange theory for the formation of the planets, etc.
*
* Here is Faye's initial paper:
* He starts out well enough, in pointing out that the tables of mean
* refraction are based on some particular model atmosphere; "Mais s'il en
* était ainsi, je veux dire, si la loi de succession des indices de
* réfraction était fixe, les réfractions terrestres ou géodesiques
* seraient fixes aussi. On sait au contraire qu'elles sont éminemment
* variables . . . . Par conséquent, . . . l'hypothèse des astronomes est en
* désaccord avec ces faits:" -- so far, so good -- "en d'autres termes,
* les réfractions moyennes ne peuvent pas être constantes, sauf dans la
* partie où l'effet de la rondeur de la Terre est négligeable." Whoops!
* Worse, he assumes the approximation used in geodesy, that the refraction
* is proportional to the angle at the center of the Earth, is exact.
* This leads him to Bradley's formula, which he seems to regard as
* reliable. Then, citing the large daytime variations in terrestrial
* refraction, he derives a predicted variation (for fixed p and T at the
* observer) of 0."07 at 45° and 2."97 at 75° Z.D.
* Finally he says that all the unresolved disagreements, between
* catalogues, between Sun and stars, obliquities in summer and winter,
* latitudes measured at different times, etc., etc., "toutes ces
* discordances proviennent d'une seule et même cause, et cette cause
* serait la partie de la réfraction dont les astronomes n'ont pas tenu
* compte." --- all depending on "le coefficient de la réfraction
* géodésique." Talk about overplaying your hand!
* Among all his other misunderstandings, he refers to Hossard's measures
* of diurnal changes in terrestrial refraction; but fails to understand
* that these changes are due to near-surface lapse rate changes.
* NOTE: This is the 28 Aug. meeting.
* Biot basically says Faye is all wet
* He refers to Faye's Note, "dans laquelle notre confrère nous apprend,
* que la théorie de ces phénomènes, telle que a été établie par
* Newton, Laplace, Ivori [sic] et la généralité des géomètres,
* présente une contradiction qui l'a toujours frappé . Il spécifie en
* quoi elle consiste; et il indique les moyens qu'il a imaginés, pour la
* faire disparaître.
* "Mon nom étant rappelé deux fois dans cette Note, à propos de
* recherches relatives à ce grand problème physique, dont je me suis en
* effet longtemps occupé, je me trouve dans la nécessité de déclarer
* ici mon complet dissentiment avec M. Faye, tant sur l'essence de la
* faute qu'il signale dans les théories adoptées, que sur la valeur du
* procédé qu'il propose pour y porter remède."
* He points out that all the theories give "presque identiquement les
* mêmes indications" up to 60 or 70° from the zenith, and that the
* large variations of terrestrial refraction are more likely to introduce
* noise than a useful correction, as they are "si capricieusement
* variables". (Did Willard Fisher ever read this?)
* Finally, "Je n'aurais ni le temps, ni la volonté, de prolonger sur
* ce sujet une polémique qui me semblait superflue . . . ."
* NOTE: This is the 4 Sept. meeting.
* But Faye won't take NO for an answer:
* ". . . j'y ai cherché quelque argument décisif, mais, je dois le dire,
* je n'ai trouvé qu'une fin de non-recevoir."
* Regarding the first point (that refraction is independent of model up
* to 70°), he re-asserts his numbers for 45 and (now) 65°. He makes
* the valid point that at Greenwich the Sun barely reaches 75° on the
* meridian in winter, and that Airy's observations for the theory of the
* Moon extend even to 85° Z.D.
* Regarding Biot's assertion that only the part of the trajectory
* where the local Z.D. exceeds 70° is affected by structure, he says
* that the whole path meets this criterion at an observed Z.D. of 72° 10'.
* Regarding Biot's objection that the large variations would produce
* wildly varying corrections, he asserts that his corrections are small.
*
* The note is followed by comments by Mathieu (pp. 486-487) and Regnault
* (pp.487-488). Mathieu says Biot is right, and astronomers will
* never adopt Faye's proposal. Regnault points out the need to measure
* temperature profiles directly, and the difficulty of measuring air
* temperatures at any height, but especially in a balloon, because of
* environmental radiation: "Tout le monde sait combien il est difficile avec
* certitude, à terre, la température de l'air, même à l'ombre, parce
* que le thermomètre est influencé simultanément par le rayonnement des
* corps ambiants. La difficulté est bien autrement grande dans un ballon
* . . . ."
* NOTE: This is the 11 Sept. meeting.
* Biot tries to spread oil on troubled water . . .
* "Lorsqu'une discussion scientifique s'elève dans une Académie telle
* que la notre, et acquiert un développement qui amène plusiers de ses
* Membres à y prendre part, en attirant l'intérêt de tous, ce peut
* être une excellente occasion de faire concourir au perfectionnement des
* théories controversées, les connaissances spéciales que chaque
* individu possède,et qui s'adapteraient à leurs détails avec moins
* d'entente, par le manque d'une direction commune, si elles y étaient
* appliquées isolément. Cela peut offrir aussi l'avantage de répandre
* dans un plus grand nombre d'esprits éminents, des doctrines que leurs
* études propres ne leur ont pas donné lieu d'approfondir, quoiqu'ils
* pussent y apporter des améliorations importantes, si on les décidait
* à y pénétrer. Supposant donc de telles discussions, suives et
* soutenues, dans la seule intention de fortifier, d'accroître, la somme
* des vérités déjà acquises, sans y mêler de misérables sentiments
* d'aigreur ou d'animosités personnelles, la science ne saurait que
* gagner à ce qu'elles se produisent . . . .
* ". . . il faut que chacun soit rec,u à dire complétement sa pensée
* sans qu'on s'en offense; à exposer librement ce qu'il croit vrai, ce
* qu'il croit faux, en accordant à ses contradicteurs la même patience,
* la même indulgence, dont il aura presque infailliblement besoin, à son
* tour, pour peu que la controverse se prolonge, et s'étende aux régions
* de l'inconnu."
* But then comes the punch line:
* ". . . ceci exige que j'établisse préalablement la proposition suivante:
* "Remonter de la réfraction opérée entre deux signaux terrestres,
* à la réfraction astronomique, par des résultats transportés de la
* première à la seconde, c'est un mode de déduction, qui, bien que
* théoriquement admissible, au point de vue mathématique, conduirait à
* des conséquences vicieuses dans l'application."
* "Cette proposition sera l'objet d'une Note . . . dans la séance
* prochaine."
* NOTE: This is the 18 Sept. meeting.
* . . . but Faye is hardly mollified:
* "Puisque M. Biot annonce qu'il va reprendre ses recherches sur les
* réfractions atmosphériques, je crois devoir signaler de nouveau à
* son attention, malgré la dernière phrase de la Note dont nous venons
* d'entendre la lecture, le fait fondamental que j'ai pris moi-même pour
* point de départ. Ce fait consiste en ce que les variations
* périodiques des réfractions ne sont pas toutes accusées par le
* thermomètre et encore moins par le baromètre place's dans la couche
* où se trouve l'observateur."
* ". . . j'ai rencontré une opposition décidée, parce que, dans
* l'esprit de mes contradicteurs, la réfraction terrestre s'est aussitôt
* présentée avec in cortége de mirages et d'anomalies énormes."
* "Il est facile de montrer, en effet, que les réfractions terrestres
* convenablement étudiées, ne sont pas des phénomènes capricieux,
* désordonne's, mais des phénomènes réguliers, en général . . . ."
* ". . . je me crois en droit d'affirmer que M. Biot se trouvera conduit,
* par ses nouvelles recherches, à des conclusions équivalentes aux
* miennes . . . ."
* NOTE: This is also the 18 Sept. meeting.
* Laugier shows that Faye's result makes no sense
* He enumerates 5 problems: I. Bradley's formula does not represent the
* mean refraction well unless the correction term depends on Z.
* II. While the daytime terrestrial refraction gives the term a value
* in fair agreement with nocturnal refraction, the terrestrial refraction
* is much larger at night; so there is an inconsistency.
* III. Bradley's form causes the correction term to be flat when the
* terrestrial refraction is large, and steep when it is small:
* "Ainsi, plus la réfraction terrestre sera faible, plus ses effets
* seront à craindre . . . ; au contraire, lorsque la réfraction terrestre
* sera très-forte, son influence totale sera sans doute très-grande,
* mais elle pourra varier beaucoup, les réfractions astronomiques ne
* changeront presque pas."
* IV. Faye takes as rigorous the geodesists' formula, which is known to
* be an approximation: "or cette formule, suffisamment approchée pour le
* calcul des petites corrections qu'on applique aux distances zénithales
* des objets terrestres, n'est pas mathématiquement rigoureuse" and its
* consequence "ne me paraît pas acceptable."
* V. Faye thinks he has obtained Bradley's formula "sans avoir consulté
* le ciel," but it is a necessary consequence of his having used the
* ordinary differential equation of astronomical refraction and proves
* nothing.
* "En résumé, la formule proposée par M. Faye . . . ne saurait, dans
* aucune cas, expliquer les incertitudes des réfractions qui ont lieu à
* des petites hauteurs."
* NOTE: This is still the 18 Sept. meeting.
* Mathieu's verbal comments on all this so far:
* "M. Faye vient de parler longuement de la réfraction terrestre et
* de ses capricieuses variations, mais il n'a rien dit pour justifier
* l'emploi qu'il en fait dans sa formule de la réfraction et pour
* répondre aux graves objections présentées par M. Laugier."
* He then points out that the reverse transfer (from astronomical to
* terrestrial refraction) was done "par l'auteur de la Mécanique
* Celeste . Comme la réfraction terrestre n'est que la partie de la
* réfraction astronomique comprise entre l'observateur et le point où la
* trajectoire lumineuse rencontre l'objet terrestre," he was able to apply
* simplifications leading to the relation for terrestrial refraction that
* Faye has used as his starting point. "Laplace ne considère donc pas
* son coefficient n comme l'expression complète, rigoureuse, du rapport
* entre la réfraction terrestre et l'angle au centre . . . . Eh bien, M.
* Faye déduit de la formule approchée . . . une loi . . . entachée de
* l'erreur qui existe . . . et il arrive à la formule . . . . M. Faye porte
* dans la formule des réfractions une loi défectueuse de constitution
* atmosphérique; il n'est donc pas étonnant qu'il en tire une formule
* qui conduit aux étranges résultats que M. Laugier a signale's tout à
* l'heure.
* "Il est permis de conclure de cette discussion que la formule de
* Bradley ne peut pas être employée dans le calcul des réfractions
* astronomiques avec le coefficient (1 - 2n)/4n , variable seulement comme
* l'entend M. Faye."
* NOTE: This is STILL the 18 Sept. meeting!
* Biot's first installment, followed by several heated comments
* NOTE: This is the 25 Sept. meeting that went on for 5¾ hours !!
* (See p.938 of the 7 Oct. issue of "l'Athenaeum Française" for a summary!)
* Here, Biot starts to lay out the theory of atmospheric refraction for
* the Academy. He begins with the Proposition that ended his previous
* note. Then, pointing out that the terrestrial refraction depends only
* on the lowest layers, and that their properties cannot be extrapolated
* to the higher ones that affect the astronomical refraction, he comments
* that "Cette impossibilité, dont on verra ci-après la preuve, rend mon
* dissentiment avec M. Faye encore plus complet que je ne l'avais
* témoigné d'abord.
* "Ces dénominations, de réfraction terrestre et de réfraction
* astronomique, sone impropres. La première n'est que la petite partie
* de la seconde, qui s'opère dans les couches d'air les plus basses et
* les plus rapprochées de l'observateur . . . ."
* Then, getting in a dig at Faye, he says that the mathematical details
* of refraction "sont énoncées et fixées, dans le livre X de la
* Mécanique céleste , avec un détail et une rigueur de démonstration
* qui ne laissent rien à désirer. Je les ai tirées de là, en
* conservant scrupuleusement les mêmes notations symboliques avec
* les-quelles l'illustre auteur les a exprimées, et qui doivent être
* familières à tous ceux qui ont voulu étudier, après lui, ce
* problème, où il faut faire concourir des considérations de
* mécanique, de physique, d'astronomie, si délicates et si multiplées."
* -- adding that he hopes to summarize the experimental side as well,
* "sans y chercher le futile intérêt d'une polémique individuelle qui
* ne conviendrait ni à mon âge ni à mes goûts, mais en conservant
* toutefois l'entière liberté de discussion que l'indépendance
* académique autorise, et qui est indispensable pour séparer l'erreur de
* la vérité."
* After presenting the outline of the general theory, he mentions his
* work with Arago and the sighting of 4 images of the signal at Campvey as
* seen from Desierto de las Palmas in Spain. "Le lendemain le temps
* était encore calme, mais la mer était couverte au loin de masses de
* brouillard, arrondies, détachées les unes des autres, représentant
* des montagnes. Nous pensâmes que des courants d'air locaux avaient
* pu refroidir certaines parties de la surface de la mer, entre l'île
* d'Yviça, où était le signal, et la côte de Valence, où nous étions."
* (He takes this as evidence that the terrestrial refraction is not to be
* trusted.) (p. 571)
* Then there is a numerical example, to show that the same model
* atmosphere (based on Gay-Lussac's sounding) gives different
* terrestrial coefficients of refraction for targets at different
* distances. Furthermore, the observations give only the sum but not
* the difference of the refractions at the two ends of the sight line; the
* latter is also required to obtain the true difference in level of the
* stations. "On y supplée en les supposant égales, ce que nos tableaux
* . . . montrent devoir être peu en erreur, aux distances restreintes où
* la convexité de la Terre oblige de placer les signaux géodésiques.
* Cela revient à considérer comme circulaire la portion de la
* trajectoire lumineuse . . . . Mais cette hypothèse, suffisante pour la
* pratique de l'ingénieur, n'est pas théoriquement acceptable comme
* réalité." (p. 575)
* Then he discusses the coefficient of terrestrial refraction, which he
* characterizes as an average over the layers involved. If the density
* is a power of the radius -- an hypothesis introduced by Laplace to make
* the integration possible -- we get the same form as Bradley's law.
* But there are no degrees of freedom to allow the model to conform to
* physical reality; in fact, the model at STP gives a value of the
* refraction coefficient quite different from what is observed, and too
* low a refraction at the horizon (30' 24."12), corresponding to a lapse
* of 1 degree C in 63.8 m or about 3 times what is observed.
* He gets in another dig at Faye by referring to "la nouvelle notation
* que M. Faye a substituée à celle de Laplace." (p. 579)
* Laugier attacks Faye . . .
* This is a rather vicious attack on Faye, turning his own words against
* him, and even accusing him of plagiarism:
* "L'idée d'emprunter au coefficient de la réfraction terrestre un
* élément de correction pour les réfractions astronomiques, est sans
* doute venue à l'esprit de plusiers personnes. Je l'ai rencontrée dans
* un ouvrage publiée récemment, et l'on sera bien étonné d'apprendre
* que cet ouvrage est précisément le tome IX du Mémorial du Dépôt
* de la Guerre , si souvent cité par M. Faye dans cette discussion."
* He quotes extensively from it, adding: "Cette idée est exactement
* celle que M. Faye expose et développe dans les différentes Notes qu'il
* a présentées à l'Académie, et après la lecture de ce passage si net
* et si précis, on ne comprend pas comment il a cru pouvoir se dispenser
* de citer M. Hossard au commencement du Mémoire qu'il a lu dans la
* séance du 28 août . . . ."
* and Faye counters Laugier: "je demande la permission de repousser une
* accusation que M. Laugier vient de produire avec un certain éclat.
* . . . il me serait bien facile d'établir, s'il était sérieusement
* contesté, car je me suis publiquement occupé de ces sujets dans le
* sens que j'y attache encore aujourd'hui, longtemps avant que le tome IX
* du Mémorial ait paru, et j'en montrerais au besoin la preuve dans des
* feuilles lithographiées, authentiques, qui datent de 1852 ou même de
* 1851."
* Faye's formal reply to the earlier criticisms
* He compares his formula to Laplace's table, with differences of 0."1
* or more from 40° Z.D. onward; 0."7 at 75°, 7" at 86°, -35" at
* 89°, and -2' 26" at the horizon. He cites, from the Greenwich
* observations, discordances from day to day of nearly 4" at 75° and
* 10" at 85° 39'. He objects that the derivative used in Laugier's
* item III is not a fair comparison, as "les variations absolues de n
* sont d'autant moindres que n est lui-même plus petit . . . ."
* He also objects that it is unfair to attack his assumption as not
* rigorous: "Ce raisonnement serait parfaitement juste si la loi de
* Laplace était elle-même rigoureuse. Or on sait bien que cette loi
* n'est nullement rigoureuse; on sait que Laplace l'a adoptée après en
* avoir essayé deux autres, dont l'une donnait une réfraction
* horizontale trop grande, l'autre une réfraction horizontale trop
* petite, du moins il croyait ainsi. Il en a conclu naturellement que
* la vraie loi devait se trouver entre les deux; mais, dans l'ignorance
* où il était et où nous sommes encore de cette vraie loi, il s'est
* borné à combiner analytiquement les deux premières, de manière à
* obtenir pour l'équation différentielle de la réfraction la
* possibilité d'une intégration élégante."
* But he criticises Biot, claiming that daytime convection can vitiate
* "les lois d'équilibre, telles que M.Biot les formule d'après les
* pages si connues de la Mécanique céleste ".
* ". . . les objections . . . ont laissé intact le fond même de la question
* principale: Doit-on tenir compte, oui ou non, des variations
* atmosphériques que ni le baromètre ni le thermomètre ne font
* connaître, quand on se borne à les consulter dans une seule couche,
* mais que la réfraction terrestre indique parfaitement?"
* Legrand shows that Faye's "correction" is due to wrong pressure
* ". . . si la formule de M. Faye ne concorde pas numériquement avec
* celle de Laplace, ce n'est pas à cause de l'ordre de densité qu'elle
* suppose, mais à cause qu'elle ne satisfait pas à la pression
* barométrique que suppose celle de Laplace. L'ordre de densité des
* couches est indifférent, mais le poids de l'atmosphère ne l'est pas.
* Que M. Faye détermine la constante de sa formule de façon à
* reproduire la pression atmosphérique, et il verra disparaître le
* désaccord qu'il dénonce. Qu'il suppose même à l'atmosphère une
* densité constante, pourvu qu'elle exerce la même pression, et à 79
* degrés du zénith (ancienne division) elle lui donnera à 1 seconde
* près la même réfraction que la formule sur laquelle les Tables sont
* construites; Laplace donne (art. 4) la formule qu'il faut employer à ce
* calcul, et je l'ai fait."
* In this paper, Biot discusses the agreement of all theories up to 80°
* from the zenith.
* "On donne à ce système un arrangement intérieur, qui . . . s'assimile
* aussi approximativement qu'il est possible à l'état moyen de
* l'atmosphère réelle, sans être compliqué par ses perturbations, dont
* l'analyse mathématique de notre temps ne saurait pas calculer les
* effets accidentels." (p. 708)
* "La parité presque exacte de résultats numériques conclus
* d'hypothèses si diverses, présente déjà un mystère mathématique,
* qu'il faut nécessairement éclaircir, avant de chercher à découvrir
* pourquoi ces résultats se trouvent si approximativement conformes aux
* réalités." (p. 711)
* "Si donc, les hypothèses . . . conduisent, par le calcul, à des
* réfractions peu différentes entre elles, et qui ne s'écartent pas
* excessivement de la réalité, cela tient à ce que, au delà d'un
* certain degré de raréfaction de l'air, tout le reste de l'atmosphère
* fictive ne contribue à la réfraction totale que pour une part
* insensible ou à peine appréciable, qui, en outre, devient
* indépendante du mode de stratification que l'hypothèse employée lui
* attribue." (p. 717)
* Then (p. 720) he quotes the table from his CdT paper showing that the
* maximum limit of error of any atmosphere in hydrostatic equilibrium
* cannot exceed 0.277 arcsec at 74° and 2.24 sec at 80° Z.D.
* This installment considers the irregularities of refraction.
* Biot cites his own experiences with the effects of the Bora near Fiume:
* the oscillations of Polaris were regular, with amplitudes of a few
* seconds of arc (8 or 9 max.). He shows that the horizontal ray enters
* the atmosphere (supposed 51 km high) some 7.5° from the observer's
* location; but the ray at 80° from the zenith enters only a little
* over 2° from the observer, and is quite close by in the lower
* atmosphere. So the rays closer to the zenith experience essentially the
* local conditions.
* Biot attempts to explain why the assumptions of hydrostatic equilibrium
* and concentric spherical layering are justified in the real atmosphere.
* To my mind, this is a weak paper, based on only semi-quantitative
* arguments. He makes a plausible but not rigorous case that these
* assumptions are very nearly correct up to 80° Z.D.
* Biot prepares to discuss the Tables
* This is largely a review of the introductory parts of his CdT paper.
* Here he takes Delambre to task for having fitted Laplace's small-Z
* approximation with data extending to 90° 20' Z.D.
* He points out that the only differences among the tables of Bessel,
* Ivory, etc. are their assumptions about the atmospheric model.
* (He discusses each model in a separate paper later.)
* He is careful to define the refractivity in terms of T, P, latitude,
* etc. He also notes the radius-of-curvature condition: ". . . il
* représente le rayon de la sphère qui serait osculatrice à la couche
* d'air de la station, suivant le plan vertical où la réfraction
* s'opère." But, as he points out, this makes the equatorial or polar
* refraction differ from that at 45° by only 0."377 at 80° Z.D.
* Biot's summary of the series: a brief historical reprise
* Biot is rather hard on Flamsteed, Bessel and Ivory. He says, of the
* refractions near the horizon: ". . . échappent inévitablement à
* toute théorie . . . dans l'impossibilité où l'on est de prévoir leurs
* caprices . . . ", thus anticipating Fisher's characterization. He also
* points out that empirical tables furnish information about the lowest
* layers of the atmosphere.
*
* This ENDs the Biot-Faye debate.
*
* Count Paul de Saint-Robert cites Ivory and Biot
* The Count's name was Paolo Ballada; he spent 45 years in the Army, having
* entered the Military Academy of Turin as a boy. He quickly became a
* Professor of Ballistics at the School of Artillery and Engineers,
* eventually retiring to devote himself to mountaineering and entomology.
* He was well known for his work on the thermodynamics of gunpowder. His
* interest in mountaineering evidently led to his interest in Glaisher's
* studies of the atmosphere ar great heights, and this paper.
* He begins by showing that Glaisher's balloon observations support a
* uniform decrease in density with height. Then "the trajectory described
* by a ray of light passing through an atmosphere so constituted is an
* arc of hyperbola." Already on p. 408 he notes that "refraction . . . is
* for the most part dependent on the first envelope of air not extending
* very far from the earth's surface."
* However, his main interest is in using pressures to determine heights.
* So he develops hypsometry, starting with Simpson's model atmosphere.
* He immediately grants that this would have the atmosphere only 10 or
* 11 miles high, "which height is no doubt too small, it having been
* estimated by means of the duration of the twilight to be between forty
* and fifty miles." (p. 409) He also admits that his model makes the
* density go to zero before the pressure, "which is physically impossible."
* But for hypsometry and refraction, "it is quite sufficient that the law
* adopted represents the constitution of the atmosphere in the first
* envelope of air near the earth's surface, and that it is useless to
* consider the higher strata, which do not materially affect the inquiries
* we are about." He finds that "the height necessary to ascend to
* have a fall of one degree in the temperature . . . increases while the
* elevation increases".
* The treatment of refraction begins on p. 412. He points out that the
* height is so small compared to the radius of curvature that the plane-
* parallel model is good enough so that "astronomical refraction, down to
* about 74° zenith-distance, is hardly affected in a perceptible degree
* by the peculiar constitution of the atmosphere.
* "Near the horizon the same ray of light encounters the several
* concentric strata of air in parts which are far from being parallel;
* hence we cannot determine the deflections caused by them without knowing
* the arrangement of their density. But happily refraction depends almost
* entirely upon the lower portion of the atmosphere (which is accessible
* to exploration), and is not sensibly affected by the higher regions."
* He then brings up Ivory's 1823 paper, quoting the line "the
* refractions undergo hardly any change in all the atmospheres comprehended
* in the formula" from Ivory. He then says, "The physical cause of this
* fact was afterwards shown by Blot," citing the CdT for 1839, and
* explaining that "As we recede from the earth's surface, the angle
* between the curve and the radius-vector, directed to the centre of the
* earth, will progressively decrease. It is obvious that in continuing to
* ascend we must come to an altitude where this angle will not be greater
* than 74°, or whatever other zenith-distance beyond which refraction is
* no longer influenced by the superincumbent atmosphere, and depends only
* upon the density at such altitude." (p. 413)
* He immediately grants that "to reach the angle of 74°, it is
* necessary to ascend to a very great elevation." What he failed to grasp
* is that we need not reach 74° Z.D.; we merely need to reach a height
* above which the additional ray bending is negligible. He nearly gets
* this when he says "the extreme tenuity of air renders the amount of
* refraction so small that it may be well supposed to depend only on the
* density of the air at that place, though the angle of incidence should
* not yet be reduced to the limit of 74°." And he illustrates this with
* the Z.D. of the horizontal ray (at sea level) at the greatest height
* reached by Glaisher, 30,000 feet: 87° 8' 25". (p. 414)
* "When the law of equable decrease of density upwards from the
* sea-level is admitted, the path followed by a ray of light is an arc of
* an hyperbola whose interior focus occupies the centre of the strata,"
* as he shows on the next pages. On p. 418, he finds a horizontal
* refraction of 33' 37", which he calls "a very satisfactory value."
* "It is often repeated that the refraction computed on the hypothesis
* of uniformly decreasing density is less than the truth. But I may observe
* that this happens only when the rate of the decrease of density is taken
* too small." He goes on to point out that what counts is the density
* gradient at the bottom: "What we want is the rate of decrease of the
* density in the inferior portion of the atmosphere". He reproduces a
* result from Biot's work, and says: "Biot's three memoirs . . . are the
* most complete writings that have hitherto appeared on the subject."
* He then turns to the terrestrial refraction, and discusses the
* surveyors' "refraction coefficient" (i.e., the ratio of curvatures.)
* On p. 422, he argues that the terrestrial refraction coefficient is
* quite variable, and should be inferred from "direct meteorological
* observations." There is an interesting footnote on this page that
* says: "A series of observations for determining the hourly variations
* was carried out by M. Hossard, at Angoulême, during the months of May
* and June 1844. The observations were made half-hourly, from daybreak
* till twilight ; and the object observed was at a distance of about
* thirteen miles. The conclusions to which they led are the following:---
* The refraction is greatest about daybreak; from 5 or 6 A.M. until 8 A.M.
* it diminishes very rapidly; from 8 A.M. until 10 A.M. the diminution is
* slow; from 10 A.M. to 4 P.M. the refraction is nearly constant; from 4
* P,M. the refraction commences to increase."
* DOI: 10.1080/14786446408643693
* CARL MAX BAUERNFEIND does the POLYTROPE of index 5 . . .
* An extreme example of the 19th-Century habit of representing everything
* analytically. Bauernfeind's series expansions go to the 28th power of
* sec z (see col.222)! However, he finds not all are appreciable; so his
* final expansion for z < 83° only goes to the 19th power. . . .(col.226)
* Note that his parameter m is 6 times the usual (h/R) parameter, as his
* height is the *total* height of the atmosphere, not the uniform height.
* He derives a lapse rate of 5.77° C/km [Emden gives 5.69 for n = 5].
* His model atmosphere ends at 47.25 km, corresponding to a uniform
* height of 7875 m.
* However, he does show reasonable agreement with "Bessel" (i.e.,
* Argelander) between 85 and 90° ZD. Another interesting bit is the
* attempt to calculate refraction below the astronomical horizon; he tries
* to compare with Bouguer's observations at Chimborazo.
* Full title of these 2 works is "Die atmosphärische Strahlenbrechung
* auf Grund einer neuen Aufstellung über die physikalische Constitution
* der Atmosphäre." This is AN Nr. 1478-1480.
* Bauernfeind's treatment of terrestrial refraction, summarized.
* (This is his meeting abstract.)
* On p.314 he says density but means density gradient. He also claims
* to have discovered the minimal ratio of 5 for the radii of curvature,
* ignoring T. Young (and many others). On p. 321, he notices that the
* terrestrial refraction -- i.e., the ray curvature -- "nahezu dem
* Quadrat der Luftdichtigkeit proportional ist." So he seems unaware
* of Ivory's paper on Mayer's result.
* Bauernfeind's detailed treatment of terrestrial refraction.
* In view of his excessively mathematical treatment, and my lesser
* interest in terrestrial refraction, I have only copied the first page.
* One good line: "Hiernach unterliegt es keinem Zweifel, dass beide
* Refractionen aus einer und derselben Differentialgleichung . . . hervorgehen
* und ihr Unterschied nur aus den Integrationsgrenzen entspringt . . . . so
* ist offenbar die Bestimmung der terrestrischen Refraction r aus der
* Differentialgleichung der atmosphärischen Strahlenbrechung der allgemeine
* und die der astronomischen Refraction der besondere Fall . . . ." (col.34)
* AN Nr. 1587-1590.
* THEODOR von OPPOLZER's preliminary note
* The error-function formula briefly announced, with a comparison to
* Bessel's table.
* Note: there were two Oppolzers. This is the father; Egon was his son.
* Oppolzer, on neglecting small terms
* "Es ist übrigens klar, dass . . . bei der Darstellung der Beobachtungen
* keinen wesentlichen Fehler aus dieser Uebergehung entstehen; es erscheint
* nur die Konstante um Etwas fehlerhaft bestimmt."
* [cf. Bauernfeind's (1864) discussion in his section 9, cols. 231 ff.]
* Bauernfeind's first big report of results
* See his 1888 and 1892 papers for corrections of some serious errors.
* The big fold-out color lithograph, "Steindrucktafel II", shows the
* DIURNAL VARIATIONS in the terrestrial refraction very plainly. The
* actual numerical data are given as well, in the very extensive tables
* beginning on p. 267. (Cf. Hossard, 1853)
* Also notable for the extensive discussion of attempts to detect
* LATERAL REFRACTION, without success (pp. 226-243): the random noise
* in Tafel Nr. 8 (pp. 230-234) is typically 2 or 3 arcsec, and the
* systematic effects cannot exceed a few tenths of a second. However,
* the sight-lines lay an average of 200 m above the ground, so no effects
* were to be expected (pp. 264-265).
* Full title is "Abhandlungen der mathematisch-physikalischen Classe
* der königlich bayerischen Akademie der Wissenschaften. Dreizehnten
* Bandes. In der Reihe der Denkschriften der XLVIII Band." So this
* may also be cited as Münchener Denkschr. vol. 48. Also, each number
* in the volume is separately paginated, starting at p. 1; this is the
* III. Abtheilung.
* Note that B. has another big paper in the same issue: the 5th in his
* reports on "Das Bayerische Präcisions-Nivellement." (pp. 49-136)
* JEAN-CHARLES HOUZEAU's VADE-MECUM
* This is an annotated bibliography of all of astronomy. The refraction
* sections are in Chapitre VI (pp. 299-310, 318-320).
* The selections are limited to the most important papers. See Houzeau's
* Bibliographie Générale for a more complete listing.
* Luc Dettwiller tells me this is available at
* https://archive.org/details/in.ernet.dli.2015.377029
* HOUZEAU and LANCASTER's BIBLIOGRAPHIE GÉNÉRALE
* This is a chronological listing, by subject categories, of references.
* By resorting to cryptic abbreviations (like those used later in ADS), the
* authors managed to compress the bare listing of citations to only about
* 1300 pages; the internal references are by column numberss. Our main
* interests are in Section III (Astronomie Sphérique):
* § 18. Refraction theory cols. 370 -- 1597
* § 19. Refraction measures and tables cols. 377 -- 1597
* § 20. Refraction near the horizon cols. 385 -- 1598
* Dispersion is put under "Astronomie physique" (Section VI):
* § 34. Diffraction & "effets optiques" cols. 787 -- 1643
*
* Notice that the Russian literature is largely excluded; its titles were
* translated into French, in some cases. "Nous avons fait usage du
* français, notre langue maternelle , qui est généralement compris par
* le plus grand nombre des hommes de science." (p.XLIX)
* The rules for encoding the names of publications are given on pp. L ff.
* More complicated rules were needed for the names of authors, where German
* umlauts were dropped, Hungarian accents and Russian letters were made
* French in some way, and honorific titles were removed.
* The Key to the abbreviations begins on p. 1 (PDF image 95). But the
* main part of the volume is the numbered columns , which begin at image
* 182 of the Google PDF. So column C is on image (2*C + 181) of the PDF.
*
* Available at Google Books.
* RADAU's review paper compares previous theories
* Biot's form of the integral is given on p.6, without further use.
* Has closed formulae for Cassini and Mayer on p. 7. On p. 10, he
* chooses the nice phrase "reduced height" for the uniform atmosphere.
* The series-expansion coefficients are discussed on pp. 13 - 14.
* On pp. 30 - 31, he shows (in effect) that Bauernfeind's k is the
* polytropic index (note the discussion of the ratio of specific heats).
* Polytropic models are discussed in detail on pp. 46 - 55; k is the
* polytropic index. Detailed numerical results are given for k = 4, 5,
* and 6. The table on p. 55 shows that Bessel's [i.e., Argelander's]
* observed refractions exceed those calculated, even for k = 6, below
* 2° altitude.
* On p.53, having cited large variations at low altitudes in the
* observations of Fuss (1871) and Kowalski on p.52, he says: "Il n’est
* pas probable que ces différences extraordinaires viennent toujours des
* irrégularités du décroissement; elles peuvent être dues, dans beaucoup
* de cas, au dénivellement des couches réfringentes." He then refers to
* the theory he had developed in his earlier Mḿoire (p.104 et seq.) and
* gives his table of the small effects produced by a 1-arcmin tilt. On
* the next page, he describes a different derivation, which produces the
* 1/cos2 correction that would later be derived by mny other people.
* The correction term is then proportional to sec2 z in eq. (59). So
* a tilt of a degree would change the refraction by 0.1 arcsec near the
* zenith, and 0.2 sec at 45° Z.D. Even assuming the tilt extended to
* the whole atmosphere, he gets only 13 or 14 seconds at the horizon.
* Diurnal and seasonal effects appear on p. 57. Ducts, p. 58 - 60.
* He seems to think the infinite refraction in ducts is merely a
* mathematical problem!
* Bruhns is cited on p. 62; perhaps he misled Radau as well as Newcomb.
* The major models are compared on p. 64. Radau notices that the
* model with the smallest initial lapse rate (Bessel's Fundamenta )
* gives the largest refraction near the horizon (p. 63), and that the
* one with the largest initial lapse rate (Kowalski) gives the smallest
* refractions. P. 65 tabulates refractions for initial lapse rates of 4,
* 5, 6, and 7° per km.
* Finally, non-spherical models are considered in §XVIII, pp. 99 ff.,
* though the main emphasis is on TILTed layers. He thinks (p. 112) that the
* variations in refraction are due to such tilts, although his calculation
* in p.111 gave only 10" of arc change in refraction at the horizon for
* a tilt of 1'.
* To calculate the tilt effect, he starts with a plane-parallel model
* (p.101). The invariant gives him the limiting angle (88°36'). He
* concludes that the plane-parallel model is OK to ZD < 60° or 70°.
* Then adopting λ as the tilt angle, he tilts all the layers through this
* angle. (This notation was also used by Sugawa and Courvoisier.)
* On p. B.103, he finds that the maximum refraction error is inversely
* proportional to cos2 z (which of course is sec2 z). "In sum, the
* irregular deviation is always in the sense of the tilt of the layers,
* which is to say, probably, in the direction of the wind." (p. 104)
* "A south wind should raise, and a north wind, lower, stars that pass
* south of the zenith, etc." Then he cautions that the effect would be
* smaller if the tilt is not the same throughout the whole atmosphere.
* For example, he supposes that the layers become horizontal above 1100 m.
* Then the correction is not more than 1/10 as big. (This is why he finds
* such small effects in his final results on p. 112.)
* He also shows that tilting all the plane layers by λ produces the same
* effect as displacing the centers of spherical layers by this angle,
* instead of having their centers at the center of the Earth. On p.106,
* he reproduces the formula of Gyldén cited by Fuss.
*
* This is evidently the basis for Newcomb's treatment.
* Note that Contre-Amiral Mouchez was the Directeur de l'Observatoire.
* The (previously defective) ADS copy is now complete.
* Bauernfeind's second big report
* See his 1888 and 1892 papers for corrections of some serious errors.
* The big fold-out color lithograph, "Steindrucktafel I", shows the
* DIURNAL VARIATIONS in the terrestrial refraction very plainly.
* Full title is "Abhandlungen der mathematisch-physikalischen Classe
* der königlich bayerischen Akademie der Wissenschaften. Fünfzehnter
* Band. In der Reihe der Denkschriften der LIII Band." So this
* may also be cited as Münchener Denkschr. vol. 53. Now, the numbers
* are continuously paginated, so the Abtheilung Nr. is no longer required.
* Hofrath Prof. Theodor Ritter v. OPPOLZER's big paper
* He neglects water vapor. On pp. 2-3, he points out the need to use
* temperatures measured inside the observing room, not outside.
* At the bottom of p. 9, he cautions against the use of Taylor series,
* "besonders wenn durch die Natur des Problems die assymptotische
* Annäherung an einen Grenzwerth erwartet werden darf," and then goes on
* to consider a parabolic temperature formula (p. 10). Its difficulties
* lead him to assume a temperature gradient proportional to the density
* gradient. This (effectively) exponential form then leads to Gamma
* functions for the refraction integral (pp. 15-18); he recognizes that
* his series expansion is semi-convergent (p. 18); cf. p. 27.
* At the bottom of p. 28, he discusses briefly the Oriani theorem (which
* he attributes to Laplace). He thinks the peculiarities of refraction
* near the horizon are due to "local disturbances" (by which he evidently
* means the temperature difference between the observing room and outdoors).
* Finally he determines the correction terms to be added to his "main
* term" and presents tables for everything. See Bemporad's encyclopedia
* article for further comments. [Not a very useful paper.]
* BAUERNFEIND's big summary paper
* Here he corrects the errors of the 1866 and later papers: "Dieser Fehler
* fiel mir erst im Sommer des Jahres 1883 auf . . . ."
* This contains a useful review of his past papers; but it's so
* defensive, and so full of priority disputes, as to be offensive.
* However, he does review the history of his efforts (see mostly the
* introductory section A, pp. 519-524; and section E, pp. 547ff.)
* The corrected plots on Tafel V at the end of the paper clearly show
* the DIURNAL VARIATIONS in refraction.
* The references to "mein leider so früh gestorbener Freund und Kollege,
* Prof. Theodor v. Oppolzer," (p. 550) are particularly interesting.
* He objects to Oppolzer's (1886) criticisms; yet he ends the text
* (p. 561) with a complementary quotation from Oppolzer's paper.
* On p. 559 there is a serious slip, in which he says that a constant
* temperature means the ray path is a straight line!
* He also has the curious habit of referring to "meine Beobachtungen"
* when it's clear that they were all made by underlings -- whom he at one
* point accuses of reading the wrong thermometers! [p. 558]
* See his 1892 paper for further corrections.
*
* Marcel Tschudin tells me this is available on the Web, starting at
* https://archive.org/stream/abhandlungenderk16kn#page/518/mode/2up
* RADAU's big paper with refraction tables and comparison with observations
* He calls the lapse rate Δ (defined on p. G.5.)
* Notes that temperature inversions increase the horizontal refr. (G.7)
* TILTS of a few minutes are to be expected from typical pressure and
* temperature gradients horizontally. (G.8) ". . . il est évident que la
* température est la cause principale des dénivellements des surfaces
* réfringentes. Comme ces dénivellements troublent l'équilibre, ils sont
* accompagnés de courants atmosphériques, et l’on peut admettre que ces
* courants suivent en général les pentes des couches de niveau."
* He then takes up the lapse rate. His symbol k is the polytropic
* index; he gives the values for k = 4, 5, 6, and 7, and notes that
* Newton used an isothermal model. The heights of several models are
* on p.10. On p.11 he says that ". . . la température des couches très
* élevées n’a aucune importance . . . ", and notes that the infinite height
* of an isothermal model is "une fiction mathémalique qui à pour excuse
* le fait que la densité théorique devient insensible à partir d'une
* hauteur modérée (60{km} ou 70{km})."
* He then considers more complicated analytical models, which are quite
* unrealistic, and goes on to include humidity, citing the works of Fizeau
* and Jamin. (p. 15) On p.17, he considers tilted layers by assuming
* the ray path is a brachystochrone. But then he says that it's usually
* enough to consider concentric spheres, and so treats the refractive
* invariant (p. 20).
* Dispersion is briefly treated on p. 24; symmetry, on p. 27.
* The problem of convergence of the series expansion appears on p.36,
* but semi-convergence is never explicitly mentioned. A table there
* gives numerical values of the series-expansion coeffs.
* The refraction near the horizon is vaguely related to the lapse
* rate in the lower atmosphere (pp. 47 ff.); but the connection is never
* made clearly. He notes that an inversion can greatly increase refraction
* near the horizon, and that such excesses are often observed (p. 52);
* here he cites the observations of Fuss (1871) and Kowalski (????).
* But he is more inclined to attribute them to TILT than to lapse rate
* (pp. 53-59), as in his 1882 paper --- much of which he repeats here.
* An anonymous 1-page summary in English appears in MN 50, 237 (1890).
* HEINRICH BRUNS
* A unique piece of work! Bruns says he used this approach for his
* lecture series at the Geodetic Institute in Berlin in 1879/80; one
* wonders what his students must have thought of it, as the mathematical
* development becomes quite complicated. (However, his 1891 student
* Felix Hausdorff went on to become a famous topologist. Bruns himself
* was a student of Kummer's, having obtained his own doctorate in 1871.
* Bruns was the second director of the Leipzig observatory, succeding Carl
* Christian Bruhns, q.v.)
* According to Helmert (Geodäsie, vol. 2, p.552 (1884)), Bruns hoped to
* obtain a better determination of the geoid from measured zenith distances
* by means of this improvement in refraction theory; Helmert cites Bruns's
* Figur der Erde (1878), pp. 45-49.
* Biog.: http://www-history.mcs.st-andrews.ac.uk/Printonly/Bruns.html
*
* Note the footnote on p. 169, about the proportionality between
* density and (μ - 1): "Die gewöhnlich benutzte Formel, die statt μ
* das Quadrat von μ enthält, entspricht den Beobachtungen nicht besser
* als die obige, bringt dagegen in die Entwickelungen eine überflüssige
* Complication hinein."
* p. 171: "Ferner lehrt ein Blick auf die Formeln . . . dass dann die
* zweckmässigste Variable für die Integration nicht, wie es bisher
* geschah, der Kugelradius r , sondern die Grösse ν = μ r ist,
* denn in diesem Falle tritt das . . . noch unbekannter Element . . . nur als
* einfacher Factor unter dem Integralzeichen."
* Now comes an important point: "Die vorstehenden Bemerkungen enthalten
* bereits die Lösung der Aufgabe, Refractionstafeln auf Grund einer
* gegebenen Reihe von Refractionsbeobachtungen zu construieren, ohne dass
* man über die Constitution der Atmosphäre mehr weiss, als von vornherein
* allgemein feststeht." So he proposes to find differential corrections
* to the model parameters by using the observed errors of a provisional
* table to adjust the parameters used to construct the table; "d. h. es
* ist möglich, unter Umkehrung des bisher immer befolgten Weges,
* von den Refractionsbeobachtungen ausgehend das Gesetz der verticalen
* Temperaturänderung in freier Luft numerisch so weit fest zu legen,
* als dies die Natur der Sache eben zulässt." [Of course, this last
* phrase is the tricky part, as Biot showed; but Bruns seems not to have
* read Biot.] Still (p. 174): ". . . [die] höheren Schichten . . . welche
* zu dem Werthe von R überhaupt nur einen kleinen Beitrag liefern."
* He points out that the series expansion in odd powers of tan z is only
* semiconvergent (p. 180). But, applying it to Oppolzer's formula, he
* shows that reasonable results can be obtained -- but only if the height
* of the atmosphere is about 31 km. "Wenn . . . zwei Refractionsformeln,
* die den Beobachtungen gegenüber als gleichberechtigt anzusehen
* sind, erheblich verschiedene Höhen der Atmosphäre voraussetzen, so
* ist zu erwarten, dass die daraus abgeleiteten Temperaturen . . . zwar in
* geringen Erhebungen übereinstimmen, in grösseren Höhen dagegen rasch
* auseinandergehen werden." [Here is an indication of the unimportance
* of the upper atmosphere, though he does not say so explicitly.] (p. 183)
* Now comes the really interesting part (p. 184): expanding the
* refraction R as a sum of rational functions of ξ = cot z (which is
* equivalent to rational terms in tan z). So R is expressed as a sum
* of partial fractions. The development is limited to one or two terms.
* (Note the remark on p. 190: "Rechnet man . . . mit den Constanten . . .
* welche von einem meiner Schüler, Herrn Hausdorff abgeleitet sind . . . .)
* A one-term fit is moderately satisfactory: comparison with Gyldén's
* table shows "dass man mit einer mässigen Aenderung von H bereits durch
* die eingliedrige Formel einen besseren Anschluss erzielen kann, als ihn
* viele der bisher aufgestellten Refractionstheorien besitzen." (p. 196)
* [Here H is the value of R at the horizon.] It is interesting that
* the auxiliary angle φ is near 5° -- i.e., about where the zenith
* behavior goes over into the near-horizon behavior of the refraction.
* He has trouble fitting Bessel's mixture of theory and observation.
* Imposing a least-squares fit (p. 199), he find poor agreement between
* 85° and 86° ZD. He thinks (p. 201) this is due to remaining
* observational errors that have not been smoothed out.
* All these fits lead to model atmospheres that end around 30 or 40 km.
* Nevertheless, he concludes "dass die Partialbruchformel bereits mit
* zwei Gliedern eine Biegsamkeit besitzt, welche allen Anforderungen
* genügt". (p. 202) From the discussion on p. 208, it's clear that
* his model atmosphere has p = 0 and T = 0 at the upper boundary; and
* ". . . man aus Refractionsbeobachtungen keinen Schluss auf die
* Constitution desjenigen Theiles der Atmosphäre ziehen kann, der zu
* der Refraction nur einen unmerklichen Beitrag liefert . . . ." The table
* on p. 209 gives the temperature decreases for his models at heights up
* to 10 km.
* Furthermore, the strategy of forcing the approximation to fit near the
* zenith and then at a few well-chosen large ZDs is a good one.
* See Bemporad's encyclopedia article (1913) for further discussion.
* According to Julius Bauschinger's obituary notice in AN 252, No.6026,
* pp.29-32 (1934), Bauschinger succeeded Bruns in Leipzig about 1920.
* FELIX HAUSDORFF's thesis on refraction theory (part I)
* (not yet in my files)
* RUDOLF WOLF's fine review of refraction -- lots of historical references
* (Yes, this is the Wolf of the sunspot numbers.)
* The refraction section is on pp. 259 - 278, sections 453 - 459. He is
* influenced by Carl Christian Bruhns's history, and so misses Biot's 1836
* accomplishment; but he understands the importance of Oriani's theorem.
* Very helpful and illuminating comments throughout. This is a much
* fuller account than the brief one in his 1877 Bd. 16 of "Geschichte
* der Wissenschaften in Deutschland" that was reprinted in 1965.
* Note that the P-10 version calls this "Volume 2, half-volume 3".
* The first volume appeared in 1890; the last, in 1893.
* Thanks to Sharron Huling, for providing photocopies of these pages!
* Bauernfeind again
* Here he finds fault with his assistants again for making errors:
* "Einige solche Fehler kamen leider bei dem im Jahre 1881 von zwei
* tüchtigen Assistenten ausgeführten Präzisionsnivellement zwischen
* Höhensteig und Kampenwand (H-K) vor . . . . Nach dem Berichte des
* Assistenten Oertel war von Höhensteig bis zum Fixpunkte Nr. 1629 bei
* Hohenaschau Alles in Ordnung; von da ab . . . stellten sich alsbald einige
* erhebliche Abweichungen ein." So the results have to be corrected
* again.
* FELIX HAUSDORFF's continuation of his refraction theory (part II)
* This is a continuation of his thesis, done under Heinrich Bruns
* -- who presented it to the academy here. It begins (after an
* introductory pargraph) with section 10.
* He develops beautiful mathematical properties of the refraction
* integral here (see pp. 135-136), mostly by means of clever changes of
* variable.
* NOTE: This volume is available at Google Books.
* FELIX HAUSDORFF's continuation of his refraction theory (part III)
* Here he considers the effects of ellipticity of the geoid, which of
* course turn out to be quite small.
* When one looks at other titles in the same volume (Sophus Lie and
* Elie Cartan on group theory, for example), it's clear why Hausdorff
* quickly gave up on his dead-end work in refraction and moved into math.
* NOTE: This volume is available at Google Books.
* EGON von OPPOLZER (Theodor's son) goes in the wrong direction
* Remarkably, he accepts Hann's (1875) idea that nitrogen and oxygen
* are diffusively separated in the *troposphere*! So the upper atmosphere
* is supposed to be mostly nitrogen. In any case, his supposed "correction"
* amounts to 0".1 at 75 or 80°, and only a second at the horizon --
* another example of the UNimportance of the upper atmosphere.
* GEORGE COMSTOCK's first paper introducing an effective wavelength
* A very meticulous investigation. He arranged mirrors in front of the
* telescope objective, so that pairs of stars nearly 120° apart could
* be seen together in the micrometer eyepiece. Closure was achieved
* by using sets of 3 stars near the equator. (see pp. 50, 55-56)
* P.188: ". . . if we assume the D line as corresponding to the wave
* length of the light of an average yellow star . . . ", he finds the
* wavelength for an average red star is 621.5 nm and for an average
* white star, 558.0. "As a control . . . , I have submitted to four
* different persons the Stern-Spectraltafel of H. C. Vogel with a request
* to identify upon it the colors: yellow, ruddy yellow, yellowish red and
* the superior limit of red. I have also had similar determinations made
* directly from the prismatic solar spectrum by two persons. The mean
* wave lengths corresponding to the color symbols as thus determined are"
* (and he gives a short table).
* Comstock here assumes that the effective wavelength for refraction
* corresponds to what a color scientist would now call the "dominant
* wavelength" corresponding to the visual color of each star. But:
* "It is obviously impossible to determine in this manner the wave lengths
* to associate with any of the symbols involving the letter W, white."
* On p. 189 he adopts the mean wavelength for the stars observed as
* 562.0 nm; but this depends heavily on his assumed D-line for yellow
* stars.
* On p. 192 he correctly takes account of the radius of curvature
* and its dependence on azimuth. He also takes account of the influence
* of water vapor on the refractivity; and concludes (p. 194) that the
* visual refractivity of dry air for the conditions of the Pulkovo Tables
* (0° C, 760 mm Hg, standard gravity at 45° latitude, and the D line)
* is 0.00029209 for stars 69° from the zenith, which agrees with lab
* data. Corrections to Bessel's mean refractions are discussed on
* pp. 193-195.
* On pp. 195-196 he discusses possible TILT of the layers, noting
* that a tilt of 1' at 75° Z.D. would change the refraction by 0.24".
* "The practical conclusion is that the computed refractions in zenith
* distance may be made considerably more precise by taking into account
* the inclination of the strata, i. e. the barometric and thermometric
* gradients. This will be most conveniently done by using as the argument
* of the tables the zenith distance of the star reckoned from the normal
* to the strata instead of from the vertical." (p. 196)
* JULIUS BAUSCHINGER's observations near the horizon
* Julius Bauschinger (1860-1934) was the son of the Munich engineer
* Johann Bauschinger. He got his Ph.D. in Munich in 1883, having studied
* under Hugo von Seeliger, and been a member of the Venus-transit expedition
* to Hartford, Conn., in 1882. He became an assistant, then Observator
* in Munich. Shortly after this was published, he went to Berlin as
* Professor at the University, and became the Director of the Astronomisches
* Rechen-Institut, and publisher of the Berliner Astronomisches Jahrbuch.
* He was co-author of Peters' 8-stellige Tafeln, and published many works
* on orbit determinations, eventually directing the Leipzig Observatory,
* where he succeeded Bruns in 1920.
* An interesting piece of work. He observed to just past 88° ZD.
* His discussion of the expansion coefficient of air is spoiled by his
* assumption that the refraction is proportional to the density at all
* zenith distances; but at least all the data are published here.
* He considers (pp. 212 ff.) the lapse rate, and even a nocturnal
* inversion of 2° C at 200 m height. Using a procedure much like
* Wegener's [did Weg. read this?], he numerically integrates the lower
* region, divided into layers 10 m thick, and then adds the refraction
* of the atmosphere above from tables. The effect of the inversion is
* inappreciable to 80° ZD, but reaches 16" near 88° . [p. 218]
* From his failure to distinguish between Ivory's and Gyldén's
* theories, he concludes that ". . . der Einfluss der obersten Schichten bis
* zu Zenitdistanzen von 88° ein nahezu verschwindender ist; für sie
* sind lediglich die unteren Schichten massgebend und in diesen genügt
* die Ivory'sche Formel." [p. 217]
* He uses Kayser & Runge's dispersion curve for air to find the
* effective wavelength of observation from the refraction constant (p. 222)
* and finds about 600 nm, "etwa auf die Mitte zwischen den Linien C und D,
* die an der Grenze von gelb und roth liegt. Ob die Ursache hievon in der
* selectiven Extinction des Lichtes in der Atmosphäre zu suchen ist, wonach
* besonders bei starkem Wasserdampfgehalt der Luft die blauen Theile des
* Spectrums stärker absorbirt werden als die rothen, muss bei dem Mangel
* an exacten Messungen hierüber dahin gestellt bleiben. Die hiesigen
* Wahrnehmungen würden dafür sprechen, denn das Spectrum der Sterne
* zeigte stets nur gelb und roth, und nur ein einziges Mal . . . auch blau."
*
* Full title:
*
* Beobachtungsergebnisse des Repsold'schen Meridiankreises der
* K. Sternwarte zu München
* I. Theil
*
*
* Untersuchungen
* über die
*
* astronomische Refraction
*
* mit einer Bestimmung der Polhöhe von München und ihrer Schwankungen
* vom November 1891 bis October 1893 und einem Katalog der absoluten
* Declinationen von 116 Fundamental-Sternen
*
* The manuscript is dated "April 1895"; Roy. Soc. Cat. gives "[1896]".
* Comstock's second paper
* NOTE: This is the earliest mention of the term "effective wavelength"
* in the ADS lists.
* Here, after citing the first paper, he grants that "since the colors
* . . . will usually be quite different from the pure spectral colors, the
* average wave-length of the light of a given star must not be assumed to
* be even approximately determined by matching its color . . . with that
* of a definite part of the solar spectrum, and the same holds true,
* a fortiori for the effective wave-length, if we understand by that
* term the wave-length of that part of the stellar spectrum which the
* observer adopts as determining the position of the star and upon which
* his attention is concentrated in the observing." (This definition is
* quoted by Cherubim.) Comstock now says his previous conclusion that
* the color effect corresponded to dominant wavelengths was erroneous.
* Note BRIGHTEST PART criterion: "The term effective wave—length as
* above defined is nearly equivalent to the wave-length of the (visually)
* brightest part of the star’s spectrum, it being assumed that in
* ordinary visual observations the observer’s attention is concentrated
* upon this part of the spectrum into which the atmosphere transforms the
* stellar image." (p. 27)
* Citing Schwarzschild's paper, he applies the interference method,
* but with two slits instead of a grating, and choosing their widths to
* suppress the even-numbered orders. (pp. 28-29)
* On p. 29, he again emphasizes that ". . . for those parts of the pattern
* in which the fringes are indistinguishable in appearance from faint stars,
* e. g. , of the tenth magnitude, . . . the total amount of light here present
* is so small that only the brightest part of the spectrum is visible,"
* so that ". . . the value of \lambda corresponding to the point of maximum
* brightness in the spectrum, i. e. , the effective wave-length" can
* be determined.
* LEO DE BALL sub-file
*
* L. de Ball wrote a series of papers on refraction in 1902-1906.
*
* The 1904 paper is a simplification of the earlier one with the same
* title in A.N. 158,Nr.3774 (1902). This is just a study of differential
* refraction due to the differennt ZDs of the two stars.
* Our only interest here is the use of the derivative of the tangent
* of the zenith distance; he derives the sec4 relation. Mentions, but
* does not cite, Hansen's refraction formula.
* His 1905 papers are identical, except for language; the first (dated
* Mai 25.) is in A.N.; its English translation is dated June 15. This
* is all about the seasonal systematic errors caused by ignoring the
* small but significant effect of ignoring the effect of water vapor
* on both the mean molecular weight (and hence the scale height) and
* the refractivity of air. The theory is based on Radau's 1889 paper.
* An interesting sidelight is that the "3/8" that often appears in the
* water-vapor term is 1 minus the ratio of mol.wts. of H 2O and dry air
* (here taken to be 0.622), or 0.378 .
* This is the exact English translation of the previous entry.
* de Ball's refraction-constant discussion
* Here the "constant" is the factor before the whole series of tangent
* terms, rather than just the coefficient of the first term in the
* r = A tan z - B tan3 z two-term version.
* de Ball's aim is to reconcile various "constants" used at different
* observatories -- some of which included water vapor effects, and some did
* not. The comparisons are reduced to the form given in his 1905 MN paper
* (above) which is obliquely mentioned but not explicitly cite, complete to
* the "3/8" fraction.
* This seems to be the work that Nefed'eva (1975) criticized. It
* cites Courvoisier's paper in Heidelberg Pubs., vol. 3. (1904); Nefed'eva
* phonetically Russianizes his name, which became "Kurvuav'e" in
* transliterating back to Latin letters.
* H.H.Turner's paper. GOOD Cassini derivation.
* Models the refraction with 2 or 3 homogeneous layers. Largely an
* exercise in numerology. He derives the Cassini model simply.
* "It does not seem likely that these figures can have any physical
* interpretation. They merely emphasize the fact that a serious part
* of the refraction takes place near the Earth, and not high in the
* atmosphere." (p. 509; quoted approvingly by Plummer, 1931)
* He continues: ". . . it will be seen how rapid is the increase in
* importance of the inner shells as we approach the horizon. . . . This
* suggests that any influence of meteorological phenomena on astronomical
* refractions must be sought at large Z.D.'s, which is in accordance
* with experience."
* Cites Bakhuyzen.
* The paper was read at the May 8 meeting of the RAS; see
* Obs. 31, 225-228 (1908)
* for the interesting discussion at the meeting.
* Lieutenant Henry RAPER's classic
* Nothing here on green flashes, so it's put in General Refraction.
* Paragraph 205 (p.60) explains DIP.
* Paragraph 207 (p.61) explains TERRESTRIAL REFRACTION, and that it
* ". . . is, on the average, about 1/14 of the intercepted arc, or
* distance in miles . . . . This proportion, however, is subject to great
* irregularity, and varies between 1/3 and 1/23 of the intercepted arc.
* The apparent elevations of the summits of high land are thus subject to
* great variations, depending on particular states of the air.
* Paragraph 208 (p.61) explains the temperature effects: "When the sea
* is warmer than the air, the horizon appears below its mean place
* . . . ; when the sea is colder than the air, the horizon appears above
* its mean place . . . ." [Parry is cited in a footnote.]
* Paragraph 209 (p.62) gives credence to claims of "a sensible change in
* the horizontal direction of objects", citing Nautical Mag. (1847).
* The effects of WAVES are discussed in Para. 545 (p.196), where
* Du Petit-Thouars is mentioned.
* The ellipticity due to differential refraction is mentioned in
* Paragraph 852 (p.313).
* BEMPORAD's refraction-calculation paper
* This paper gives his transformation of the refraction integral.
* He argues that the previous analytic models of the atmosphere are
* unrealistic, and that refraction should be integrated numerically on
* the basis of measured atmospheric profiles. These were known only up to
* about 20 km in his day; but he finds that quite diverse assumptions about
* structure above 20 km leads to inappreciable differences in refraction.
* So he is forced to conclude that ". . . seeing that the most rigorous
* calculations and the most minute observations of the refractions at the
* horizon would not even allow to decide if the atmosphere be 250 or 600
* km high, it seems very problematic that these theories can, as was once
* hoped, cast light on the constitution of the atmosphere at great heights."
* So he gives only the structure tables for 4 seasons (and the yearly
* mean), "to communicate the definitive results afterwards."
* (Cf. his 1907 paper in Mem.Soc.Spett.)
* Charlier's attempt to formulate the inverse theory via integral eqns.
* Note that his new variable x is the reciprocal of nR. Its monotonic
* decrease with R (here called rho) requires the usual condition,
* and a mention (but not citation) of Schmidt's theory.
* Banakhevich's "Three Sketches"; the last devotes a page to GREEN FLASH
* Of these, the first and third are most interesting.
* The first is "The influence of temperature inversions on refraction".
* It starts out:
* "All tables of refraction are based on the assumption that the
* temperature decreases with height. But really, as is well known at
* the present time, so-called inversions of temperature are frequently
* observed in the atmosphere at night . . . . We are not speaking here of
* the inversion at a height of about 10 km (stratosphere), discovered by
* Tesseren de Borom [Teisserenc de Bort], which can have no significance
* for the question of refraction (cf. Fabritius - Astronom. Nachr. V. 93,
* p. 17-18); we mean the normal nocturnal inversion of temperature in the
* first kilometer of height." He cites Bauschinger's 2° inversion at
* 200 m, but thinks it isn't as important as Bauschinger did. (In
* particular, it isn't important for the refraction constant.) He shows
* that Bauschinger's inversion has negligible effect out to 84° ZD,
* and is only 3.5 seconds at 87° 56' -- values about an order of
* magnitude smaller than Bauschinger's.
* The second essay deals with the ZD dependence of image motion.
* It's basically a statistical analysis of meridian-circle errors; he fits
* an empirical formula, but unfortunately chooses sec Z instead of airmass
* as the independent variable, even near the horizon. So it's largely an
* exercise in numerology.
* The third essay is "Dependence of the refraction on its constant",
* by which he means the refractivity, and the question of its dependence
* on density. There is a good comment on p. 22: "The majority of authors
* assume, without direct explanation, that R is proportional to 2c [i.e.,
* the constant in the refractivity formula]." Gyldén and E. Oppolzer are
* criticised for doing this. He has a nice table on p. 26 showing how
* much larger the fractional change in refraction is than the fractional
* change in surface pressure (keeping the temperature distribution fixed).
* It amounts to nearly 10% for a refraction of 35'.
* This is followed by remarks on the wavelength dependence of
* refraction: the refraction varies more near the horizon than does the
* refractivity. "This question has interest for the explanation of the
* so-called green light [i.e., the GREEN FLASH] or blue light at sunset
* and sunrise." So he calculates the duration of green after red at sunset
* as 1.75 seconds of time (at 45° latitude), and 3.18 sec. for blue.
* [This is the ONLY calculation I have found that takes the nonlinearity
* of the refraction into account!] He concludes that the length of the
* atmospheric spectra must be 1/120 of the whole refraction, between red
* and green, or 1/67 between red and blue.
* Cites Fabritius, Bauschinger, etc., and refers to Radau's tables.
* Of course this uses the old, pre-Revolutionary alphabet.
* Comstock's Presidential address at the 41st meeting, Dec. 1928
* (He was president of the AAS from 1925-28.)
* A good review of refraction, from the standard point of view.
* He starts by quoting Newcomb's infamous remark. Many well-known works
* are mentioned, but there are no references. He gives special attention
* to the works of Radau, de Ball, Emden, and Harzer. He recognizes that
* refraction "is almost wholly due to the lower atmospheric strata."
* "Harzer’s refractions may be described as theoretical results whose
* relation to practical astronomy remains to be determined. A provisional
* comparison between them and the tables of Gyldèn and Radau shows a very
* satisfactory agreement for normal circumstances and moderate zenith
* distances. It should not escape notice that Harzer’s appeal to physics
* and meteorology, as constituting in themselves and without reference
* to astronomical observation an adequate basis for refraction tables,
* has in some respects greatly complicated the problem in hand. In lieu
* of the two, three, or four parameters used by his predecessors, Harzer
* finds need for twice as many. For the computation of his numerical
* refraction in a given case there is required a process much longer and
* more burdensome than that hitherto employed, e.g. these new refractions
* commonly involve and depend upon not only the current temperature and
* barometric pressure at the time and place of observation but require also
* such further elements as the time of day at which the observation was
* made (diurnal variation), the time of year (annual variation), color of
* the star (dispersion effect), wind velocity (effect of, upon barometric
* pressure), and discrimination may be required between observations made
* upon opposite sides of the zenith. The astronomer with long routine
* experience with meridian observations may be unpleasantly impressed by
* such an array of new factors to be considered . . . ." (p. 226)
* On the next page, he supposes that the Oriani-Laplace theorem still
* applies in the presence of turbulent fluctuations and waves. He also
* mentions possible effects of tilts and atmospheric tides.
* Then comes a discussion of navigation, and variable dip; he mentions
* the Carnegie observations at sea. As this was done when the conflicting
* evidence had not yet been rationalized by Freiesleben and by Hasse,
* he thinks more observations are needed: "An extended series of
* observations of the time of sunrise or sunset at the sea horizon could
* be made to furnish much pertinent information . . . ". (p. 230)
* Reprinted in Proc.AAS,vol.6, pp.214-223 (1931)
* Alan Fletcher's first paper
* This seems to be his very first publication, while he was still Smart's
* graduate student. The Cambridge U. library shows the full text (evidently
* never published) was 1/3 of his Ph. D. thesis (1935).
* Some good things here: he presents an explicit formula for the
* refraction at all zenith distances for a generalized Laplace-type model
* atmosphere in terms of the error function. Unfortunately, most of the
* details are suppressed, so that the answer appears pulled out of a hat.
* His notation is: µ is the index of refraction; ν is the refractivity
* (µ -1); ν' = ln µ = ν - ½ν2 . . . "and differs little from ν" while
* making the notation more confusing. A zero subscript "indicates values
* at the place of observation." Then:
* "It is well known that the refraction at a given moderate zenith
* distance depends for all practical purposes on the two independent
* variables ν0 and H0, the latter being the ratio l0/r0 of the height
* l0 of the homogeneous atmosphere to r0" [i.e., the radius of curvature
* of the Earth.] He then attributes the 2-term tangent expansion to
* Lord Rayleigh -- who does indeed derive it simply at the end of his 1893
* paper in scintillation, but who also attributes it to Laplace. He says
* "no reasonable theory differs from [this] by more than a few
* thousandths, hundredths, tenths of a second at ζ = 60°, 70°, 75°
* respectively. . . . At large zenith distances the refraction depends to
* an appreciable extent, and beyond ζ = about 85° to an undue extent for
* practical purposes, on the particular function . . . used [to represent the
* model atmosphere], and no introduction of a third independent variable
* suffices to the same extent; nevertheless, the refraction depends mainly
* on ν0, H0 and the value of dµ/dr in the first few kilometres above
* the ground . . . ."
* He even deals with the choice between the Laplace and Gladstone-Dale
* formulae for the refractivity in terms of the density, and introduces a
* parameter k that "would be 1/2 or 0 if ρ were proportional to µ2 - 1
* or µ - 1 respectively." (A nice touch.)
* Unfortunately, he accepts Radau's (1889) treatment of water vapor,
* which requires its mixing-ratio to be constant throughout the
* atmosphere. So his simplification of Radau's results is not all that
* useful. However, he has a good comment on atmospheric structure:
* "For ζ > 85° it becomes of decreasing importance that our fictitious
* atmosphere shall have the right H0, and of increasing importance that
* it shall have the right µ in the first few kilometres; . . . beyond ζ =
* 85° or even less the ability of any theory to predict the amount of
* refraction rapidly dwindles."
* The scans at ADS lack a few glyphs. Those in the text on p. 562
* seem to be due to pieces of type that fell out of the forms; they
* are also missing on that page of the copy in your library.
* The l.c. "l" that is missing on the left side of Eq.(15) is a typo,
* corrected in the Erratum on p. 1009.
* Plummer's paper (cited by Horak)
* "The difficulties and complexities of the treatment of astronomical
* refraction on the classical lines laid down by Bessel are well known.
* They are not made more attractive by the fact that the structure of the
* atmosphere . . . is certainly different from what it was formerly supposed
* to be. Hence any attempt to simplify the theory may be justified."
* The smallness of the variation of nR through the atmosphere gives
* ". . . evidence that r/a differs little from 1, and that the upper
* atmosphere plays a very small part in astronomical refraction."
* He then investigates the assumption that r dn/d(nr) is constant,
* which leads to the Bradley/Simpson model, which gives a horizontal
* refraction about 20% low -- not surprising, he says, as d(ln n)/d(ln nr)
* must go to zero. But simple attempts to model this fail; so he then
* tries the sum of two atmosphere models with different scale heights --
* which he identifies (!) with oxygen and nitrogen. -- cf. Turner (1908)
* (whom he cites). The paper degenerates into numerology.
* Horak's first paper
* Here he revives Laplace's notion of orbital motion as an analogue of
* refraction, and finds hyperbolic orbits that reproduce the tables out
* to 83° ZD (!) [Hardly surprising, as his model is similar to the
* Simpson/Bradley/Mayer model.] He notes that the radius of curvature
* of a horizontal ray is about 8 times that of the Earth.
* Cites Radau, but (strangely) not Laplace.
* Issue Nr. 5923 closed Jan 25. 1933.
* Horak's second paper
* He introduces the nice form R = (ln n0)(sin Z)/M, and discusses the
* denominator function M, which is roughly cos Z. Noting that M = cos Z
* corresponds to the flat model, which gives too much refraction, and that
* Cassini's model gives M = sqrt(cos2 Z + \delta), which gives too little,
* he proposes to interpolate between them. The straight mean corresponds
* to Mayer's formula, which still gives too little near the horizon.
* Then he suggests using a weighted mean, which helps; but he gets
* carried away with the idea of adding some constants to the numerator
* and denominator to get an even better fit to the *mean* refraction --
* instead of keeping the analytical values of the parameters, which would
* have given a more useful result. Still, there are useful references
* (including Radau).
* Issue Nr. 5951 closed Mai 16. 1933.
* Ingénieur Hydrographe Général Pierre de Vanssay de Blavous
* GOOD REVIEW of TABLES for MARINERS
* This is a thorough review of refraction and dip tables, and also tables
* for correcting geodetic refraction. Both the histories of the tables and
* the bases of their computation are fully described, from early days.
* Many references to little-known tables for mariners & geodesists.
* This is now called the International Hydrographic Review.
* Available at:
* https://journals.lib.unb.ca/index.php/ihr/article/view/27073/1882519828
* PDF: dVdB1944.pdf
* (in Meyer's 1935 GF file) GOOD REVIEW ARTICLE
* (published in sections dated 1955 and 1956)
* geometric interpretation of the refractive invariant (p.774)
* nice proof of "Fraser's theorem" (pp.776/7 and 800)
* The GF section (pp. 804-806) reproduces Lagaaij's drawings in color.
* Chuck Whitney & George Veis introduce the term "parallactic refraction"
* In a 3-sentence paragraph on p. 12 we see:
* ". . . there is a small effect, which might be called parallactic
* refraction, arising from the fact that the satellite is much closer than
* the stars."
* This was later reprinted in:
* Smithsonian Contributions to Astrophysics, Vol. 6, pp.17-24 (1963)
* (both available from ADS)
* Liisi Oterma's treatment of parallactic refraction
* Here parallactic refraction is called "rocket refraction" as opposed
* to astronomical refraction. The approach is the usual series expansion,
* following Radau; I think it's not very different from the Saastamoinen
* papers. There are numerical tables that extend to 85 deg. ZD.
* "Informo" was published in Turku, Finland.
* (Cited by Bruin)
* only a 1-line abstract, though listed by AJB -- useless
* The full paper was never published, nor does the author ever appear in
* the Citation Index. But his 1938 paper in Gerl. Beitr. Geophys. was
* cited by Sugawa (1956).
* SAASTAMOINEN's papers in BULLETIN GÉODÉSIQUE (1972)
* A gross overdevelopment of the series-expansion approach, with some
* conceptual errors: ". . . it follows from the law of Gladstone and
* Dale that the height integral . . . of the atmospheric refractivity . . .
* is directly proportional to the ground pressure. The refractivity
* integral, therefore, can be determined without detailed knowledge of
* the height distribution of the refractive index . . . ." (p. 279)
* He carries out the series to the tan11 power term, but then substitutes
* approximations for the lower-order ones, beginning with tan3 z.
* (The approximations either assume n = 1, or r/r o = 1; see p. 281)
* Vertical structure in the lower atmosphere is brushed aside: "But since
* only a small contribution to these integrals comes from the lower levels,
* it will be quite sufficient merely to extend the constant temperature
* gradient of the free troposphere down to the ground level, neglecting
* the small error thus involved." (p. 291)
* The peculiar-looking refraction constant in the abstract (cf. pp. 386
* and 388 of the second part) is due to having divided out T o/p o.
* NOTE: Bull.Géod. was issued in about 4 numbers a year from its founding
* in 1922 to WW II. The issues were numbered and paginated separately.
* After No. 76 (1941/42), a New Series began, ending with No. 118 (1975).
* After that, there are annual volumes -- beginning with Vol. 50 in 1976!
* In 1996, Bull.Géod. merged with manuscripta geodaetica to form
* the Journal of Geodesy (which continued the volumes of BG).
* Saastamoinen, part 2
* Here he adopts the obsolete 1966 Edlén dispersion formula (already
* shown to be in error by Owens (1967). (p. 384)
* Eq.(35) on p. 385 is used in the RGO refraction program.
* ". . . any significant variation of the tropospheric contribution,
* whether of regional or seasonal origin, is largely compensated by the
* stratosphere . . . ." (p. 386)
* Worst of all: "The most direct method of determining the apparent
* colours of the stars is by visual colorimetry, notably employed by
* H. Osthoff [1900] . . . . In the Osthoff catalog, which still [sic!]
* provides a chief source of information . . . ." (p. 388)
* More interesting is his attempt to estimate TILT of the isopycnic
* surfaces from meteorological data (pp. 390 ff.) He finds 1' 52".
* He also claims (p. 395) that tilts of "a few degrees" occur in the
* boundary layer near coasts, due to the land-breeze/sea-breeze effect.
* ". . . refraction errors will not be present in ordinary inversion layers
* which lie horizontal, such as the nocturnal ground inversions which are so
* typical of conditions best suited for astronomical observations." (p. 396)
* [This is sometimes listed as Journal of Geodesy 46, No.4 (Dec. 1972).]
* Saastamoinen, part 3
* This is all about parallactic refraction, range delays, and the like.
* [This is sometimes listed as Journal of Geodesy 47, No.1 (Mar. 1973).]
* A. I. NEFED'EVA discusses the humidity corrections
* This is the English translation of the paper in Astron.Zh.51, 1346-1347
* (1974). See the translator's note about earlier related papers. The
* translator did not recognize Courvoisier's name, printing "Kurvuaz'e".
* The translation also gives Gyldén's paper the date 1968; it's 1868.
* Everyone seems to have done it incorrectly. The 4th edition of the
* Pulkovo Tables (1956) was farther from the truth than the 3rd (1930).
* "At zenith distances of 88° and 89° the ray curvature is affected very
* strongly by the lowest air layers, where the decline in air density is
* retarded because of the rapid decrease in humidity with height. . . .
* During the cold season an inversion occurs in the layer near the ground,
* while above there is a sharp drop in humidity, . . . .
* "Thus humidity corrections can be computed to high accuracy for a given
* time only if the distribution of water vapor with height is known."
* This mentions de Ball's attempt (1906) without citing it. The
* historical review is informative.
* Strange note: attributes Oriani's theorem to Newcomb; raises issues
* already raised by Biot about the distance to the upper atmosphere
* when looking near the horizon: "Beyond 60°, however, the state of
* the atmosphere at heights of 10 km and greater begins to exert an
* increasing influence . . . ."
* How did this get published in a Letters journal?
* Original version was Pis'ma Astron.Zh. 1, 46-48 (Oct. 1975)
* Another attempt to relate terrestrial and astronomical refraction
* (cf. Faye!)
* Thanks to William M. Robertson for a copy!
* Kolchinskii on Oriani's theorem
* A clear explanation and derivation, with some discussion of claims
* that the theorem is not adequate to calculate refraction out to 70°.
* He shows that it is -- cf. Green's book (1985).
* Cites Laplace, Bruhns, and Newcomb.
* Nefed'eva infers wavelengths from adopted refraction constants
* [translation of A.Zh.57,878-880(1980).]
* MEAN REFRACTION FORMULAE
* See the comment on this below.
* Fukaya & Yoshizawa confirm Nefed'eva's result
* "We conclude that the true effective wavelength of the Pulkovo table is
* close to 595 nm. This conclusion is in good agreement with Nefed'eva's
* (1974)." [p. 756]
* An inverse for Bennett's formula
* In Roger Sinnott's "Astronomical Computing" column.
* Recognizes the importance of tropospheric lapse rate; says that height
* of tropopause is also important.
* Probably this should be Hao-Jian Yan, but the name is printed as "Haojian".
* STONE uses Green's approximation, with the Owens refractivity formula
* Wittmann's comparison of approximate formulae (cf. Fletcher, 1952)
* He uses the old (1953) Edlén dispersion formula, and H = 7.632 km
* as the height of the homogeneous atmosphere. On p. 308, he uses the
* numerically unstable solution of a quadratic equation in deriving his
* "new formula" (eq. 10).
* Refraction below the astronomical horizon is treated superficially;
* giving constants for this to 4 significant figures is absurd.
* Parallactic refraction is discussed in section 5 (p. 310). He cites
* the 1838 paper by Hansen here.
* Peter Noerdlinger's interesting paper on satellite geodesy & sensing
* His main result uses the geometric invariant to locate the *apparent*
* target point on Earth as seen from the satellite. Note the warning
* that topography effects are much larger!
* ISPRS = International Society for Photogrammetry and Remote Sensing
* Thanks to Peter Noerdlinger for a reprint!
* SIEBREN VAN DER WERF's refraction program and study
* "There have been many attempts . . . to relate refractions, obtained
* by accurately timing the moment of sunset, with the predictions of
* atmospheric models. This example shows that such studies are sensitive
* to the temperature gradient just above ground or sea level, rather than
* to the global features of the atmospheric model." [Cf. Fletcher's (1931)
* "It is well known. . . " comment.]
* "This temperature profile is characterized by piecewise constant
* temperature gradients." (p. 356)
* This paper gives the details of his method of integrating the refraction;
* see his 2008 "Comment" paper for further details.
* He has an interesting discussion of the water-vapor corrections, too.
* Note the erratum on Siebren's website: "In eq. 21 the constant
* 1167917 should be replaced by 167917".
* Cites Fletcher (1952), but not Fletcher's 1931 paper.
* Paper IV
* Where (in the atmosphere) does the refraction come from?
* Shows why structure is really not important out to 75 or 80° Z.D..
* Refutes the errors of Newcomb, O'Connell, etc.
* Cites Biot's invention of the transformed integral.
* George Kaplan's treatment of parallactic refraction, using the
* old homogeneous model (cf. Bouguer, 1753).
* Available at https://apps.dtic.mil/sti/pdfs/AD1094247.pdf
* Dated 2014 June 10.
* Richard F. Olson, Jr. describes a method based on LOWTRAN 6
* He gives the method, but not the source code used. Refractivity is
* the "new" (1966) Edlén formula. The 6 model atmospheres from the
* LOWTRAN-6 report are used. He uses N for (n - 1), and C for
* the refractive invariant, and Thomas & Joseph's Chebyshev quadrature.
* The RGO method is used to show agreement to 1 arcsec with LOWTRAN,
* using 1600 quadrature modes. An example of PARALLACTIC REFRACTION is
* shown.
* Citations include Ciddor, Dan Bruton's thesis, Smart, TN 63, etc.
* This is also
* "Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXVI."
* edited by Gerald C. Holst, Keith A. Krapels.
* DOI: 10.1117/12.2179771
* RAY SEPARATIONS
* some discussion of parallactic refraction and meteors; mostly
* numerical results. Their "lateral" means "vertical".
* DOI: https://doi.org/10.1051/0004-6361/202142338
* (see also Ivory, 1821, 1824, 1825; Bauernfeind, 1864; Radau, 1882.)
* (also Brocks, 1949)
*
* First use of linear temperature gradient after Bauernfeind (1864)?
* Shows the negligible influence of the upper atmosphere:
* "Auf diese Betrachtungen gestützt, darf man also den Schluss ziehen,
* dass die Constitution der Atmosphaere in den höchsten Schichten ohne
* jeden merkbaren Einfluss selbst auf die Horizontalrefraction sein wird."
* ARNAUD's papers on astronomical refraction
* Good, clear exposition. He is mainly interested in terrestrial
* refraction, but also deals with astronomical. Good discussion of
* ray curvature and lapse rate.
* Full title is Mémoires de l'Académie des sciences, belles-lettres et
* arts de Lyon. Sciences et letters.
* Begins with a formula for ray curvature that involves lapse rate
* Astronomers should avoid the region near the horizon
* Finds that beyond 87°, "Il faudrait faire entrer dans les formules
* une variable nouvelle θ, valeur moyenne de (-dt/dz). Les Tables
* devendraient ainsi très compliquées et sans utilisation pratique, étant
* donné que les observations sont rendues incertaines par les phénomènes
* de diffraction.
* Cette région doit être considerée comme interdite aux observations
* de précision."
* EARLY USE OF POLYTROPIC MODEL
* Robert Emden's first installment in Met. Zs. This is a clear and
* detailed exposition of the structure of a polytropic atmosphere,
* assuming a constant gravitational acceleration. All the classic
* power-law relations are derived. The polytropic index here is n ,
* which he calls its "Klasse".
* On p. 353, he refers to the earlier mention of his model in Encyc.
* der Math. Wiss., Bd.VI, 1B, Heft 3.
* On p. 354, he finds the lapse rate requied to produce constant density
* to be 34.2°/km (cf. Fabritius), and cites "Gaskugeln". On the next
* page, he points out that the index for an isothermal atmosphere is
* infinity. Eq. (18) shows that the height of a polytrope is (n+1) times
* the height of the homogeneous atmosphere. There is a nice table of the
* heights and lapse rates for 14 different indices from 0 to ∞ .
* Eqs.(19) give the formulae for the temperature, density, and pressure
* as functions of height, and he immediately shows that the limit for
* n --> ∞ is the exponential law of the isothermal model.
* On p. 356, he proposes to replace a curve with a piecewise polytropic
* model -- "eine Sehnenzug" or string of chords -- as a better alternative
* to the "usual division into isothermal layers."
* Then come examples of applications: the polytropic height formula
* instead of the isothermal one; he proposes a polytrope of index 4 [lapse
* rate 6.83 K/km] as a good barometric model. (The Standard Atmosphere
* proposal was still a few years off, remember.)
* P. 358: he considers the thermal energy in a vertical column, and
* tries to apply this to storms, and to the radiation balance of the
* atmosphere -- again referring to "Gaskugeln".
* The volume's Index bears the subtitle:
* LI. Band der ,,Zeitschrift der k. k. Österr. Ges. für Meteorologie''
* Emden's second installment has to do with sound propagation, both with
* and without winds. He makes some toy models with single polytropic
* layers, but admits that these are only rough approximations.
* I list it here only for completeness; but there are nice ray diagrams
* that resemble optical ray traces for superior mirages (cf. p.81).
* (Note the hidden "shadow" zones, as in optical mirages.) In fact, on
* p.118, he comments on the multiple auditory detections of a single
* detonation, and compares these multiple images with those in mirages,
* citing Pernter's Meteorologische Optik.
* Notice that the equations are continuously numbered through all 3
* installments; so the first one here is Eq.(27).
* The first part is in the Jan/Feb issue (Nr.1/2); the second, in
* March/April (3/4); the third in Mai/Juni (5/6).
* Origin of the STANDARD ATMOSPHERE explained, part 1
* Albert Toussaint's article on supercharged aircraft engines
* The crudeness of his methods is indicated by his remark that his study
* had been done "en utilisant un abaque de comparaison des avions, qui
* évite des calculs nécessaires au passage des perfomances d'un avion
* ordinaire à celles d'un avion à moteur suralimenté." (and the graphs
* and nomograms in this paper.)
* "De plus, notre attention avait été attirée sur les caractéristiques
* de l'atmosphère aux très hautes altitudes. et nous avons dû abandonner
* ls lois de Radau, admise jusqu'à ce jour, pour lui substituer une loi
* nouvelle plus conforme, espérons-nous, à la réalité des phénomènes."
* [This refers to Radau's 1901 "Tables Barometriques et Hypsometriques pour
* La Calcul des Hauteurs, Gauthier-Villars, 1901. See Minzer, 1966.]
* Origin of the STANDARD ATMOSPHERE explained, part 2
* "With the advance of aeronautics and the science of artillery, engineers
* and specialists in these fields have come to require a specific knowledge
* of the varying states of the atmosphere from the ground to very great
* elevations. This has led to the introduction of a conventional term
* commonly known as the standard atmosphere, which pretends to specify the
* normal or average condition. As is well known, the ‘standard atmosphere’
* is never found; that is to say, at no time or place do ‘standard’ or
* average conditions of all the meteorological elements at all altitudes
* simultaneously occur. Nevertheless, it is proper, and in certain fields
* (especially those of aviation and ordnance) it is necessary, to adopt
* so-called ‘standard’ values, and it is desirable to have these represent
* as closely as possible true mean values . . . ."
* ". . . Prof. Pericle Gamba . . . has employed a large number of
* observations in several countries, resulting in a reasonably close
* representation of the average conditions of free air. Prof. Toussaint has
* utilized Gamba's analysis of the meteorological data in the formulation of
* a proposed interallied agreement as to the law of decrease of temperature
* with increase of altitude. Toussaint proposes the adoption of a ‘law’ of
* linear decrease of temperature with altitude, starting at a temperature
* of 15° C. at sea level and attaining -50° C. at an altitude of
* 10,000 meters. This ‘law’ is expressed by the formula t = 15 - 0.0065
* Z , in which t = temperature in ° C. and Z = altitude in meters.
* "Although the adopted rate of temperature decrease is arbitrary,
* the resulting values nevertheless agree quite well with annual means as
* published by various investigators for Europe and the United States. . . .
* Prof. Toussaint remarks:
* "It has been found preferable to take a linear law rather than to seek
* an equation approximate to Prof. Gamba's curve, for the following reason:
* "In order to define the standard atmosphere, what is needed is not
* an exact representation of that curve, but merely a law that can be
* conveniently applied and which is sufficiently in concordance with the
* means adhered to. . . .
* "The deviation is of some slight importance only at altitudes below
* 1,000 meters, which altitudes are of little interest in aerial navigation.
* The simplicity of the formula largely compensates this inconvenience."
* Toussaint's paper is:
*
* A.Toussaint
* Étude des performances d'un avion muni d'un moteur suralimenté
* l'Aeronautique 1,No.5,pp.188-196(Oct. 1919)
*
* Dr. Willis Ray Gregg was the Chief of the Weather Bureau, 1934-1938.
* When he wrote this report, he was Chief of its Aerological Section.
* He was the author of the NACA "Standard Atmosphere", 1922.
* Gregg's "Standard Atmosphere" paper (NACA TR-147)
* The pages are numbered 397-409, so this is probably from the Annual Report
* for 1922 that would be dated 1923.
* Available at https://ntrs.nasa.gov/search.jsp?R=19930091212
* Origin of the STANDARD ATMOSPHERE explained, part 3
* Gives all the gory details of the various atmosphere models.
* [https://ntrs.nasa.gov/api/citations/19670002897/downloads/19670002897.pdf]
* EARLY USE OF POLYTROPIC MODEL
* The 3rd installment of Emden's series in Met. Zs.
* Once again, the equations are numbered sequentially from the earlier
* installments; though only the first is mentioned here.
* See also Brocks (1949) in terrestrial refraction file!
* ROBERT EMDEN's important paper on polytropes and refraction
* "Liegt eine beliebig temperierte Atmosphäre vor, so kann dieselbe stets
* in konzentrische Schichten geteilt werden, in der Art, dass innerhalb
* jeder Schicht der Temperaturgradient hinreichend genau konstant angenommen
* werden kann." (p.52)
* Note that section 10 deals briefly with TILT of layers; he misreads
* Oppolzer's treatment in Valentiner, saying it gives numbers 3000 times
* too big! (He confuses the argument with the value in the ref. table.)
* In fact, his numbers are quite consistent with Oppolzer's.
* BORIS GARFINKEL's model (original)
* "The trajectory of light will be symmetric about the axis drawn to the
* ‘perigee’. . . . Consequently the refraction . . . along the entire trajectory
* can be obtained . . . ." -- so he shows that refraction below the horizon
* can be computed by doubling half the part below eye level. (p. 171)
* This paper is an abstract of Garfinkel's Ph.D. thesis, done under
* Dirk Brouwer.
* GARFINKEL's model (revised)
* His isothermal stratosphere begins at 11 km; this is where RGO got that.
* (Actually, it goes back to Toussaint, 1919.)
* Note that he uses the term "the ray perigee" for the lowest point.
* AUER & STANDISH PREPRINT
* This uses the method invented by Biot in 1836.
* NOTE: this paper was not published for 21 years -- but it became a classic!
* You should be able to get a copy from E. Myles Standish at JPL.
* PIECEWISE POLYTROPIC model
* This gives the details promised in his paper in IAU Symp.89.
* He gives a procedure for calculating the total refraction for a single
* polytropic atmosphere; but then he proposes to treat a polytropic
* layer as the difference of two polytropes. This might be acceptable
* for coarse layers (like Garfinkel's model), but the catastrophic
* cancellation it would cause in a realistic model with thin layers makes
* it hopelessly inaccurate in the real world. Also, the fudge factors that
* were determined by least-squares fits mean this is not very accurate to
* begin with. (Note the remark about errors of "only tenths of a second of
* arc and thus negligible.")
* The concluding statement that "the present method is probably the most
* convenient known today" means he was unaware of the Auer & Standish work.
* Is this the last gasp of the analytical approaches?
* AUER & STANDISH's published paper -- at last!
* This uses the method invented by Biot in 1836.
* Unfortunately, they chose to evaluate the integrand by using Newton-
* Raphson iterations that diverge where the invariant changes slowly with
* height.
* Michael Nauenberg's refraction paper tries to use radiosonde profiles
* This physicist thinks that the nocturnal inversion in the lowest
* kilometer "has been ignored previously." [Cf. Oppolzer (1901);
* Bauschinger (1896); Banakhevich (1915); Saastamoinen, Part 2 (1972); etc.]
* He fits the density profile in the lowest km with a parabola, and
* calculates the refraction for a wavelength of 0.633 micron . . . .
*
*
* (See also the 2022/3 Special Issue of C.R.-Physique)
*
* DELAMBRE's "Hist. MODERNE"
* Bruhns leaned very heavily on this, especially for the work of Cassini
* -- see pp. 722-725 of Vol. 2.
* [note that Biot & Arago's saga was also published by Courcier that
* same year!]
* DELAMBRE's 18th-Century-history book, published posthumously by Mathieu
* N.B. This is *not* the Mathieu of the Mathieu functions; that is
* Émile Léonard Mathieu.
* Here (see footnote, p. 696) is where Mathieu says the drawings in Biot's
* book are his own. On the next page, he mentions seeing inferior mirages
* "over ice or snow". He also has many interesting comments on Delambre's
* text, including a *long* "Note on refraction" (pp. 774-796). There is
* much interesting discussion of the Simpson/Bradley/Mayer model, as well.
* On p. 339 Delambre shows that Bouguer's scheme is equivalent to this;
* and Mathieu discusses the matter more clearly on pp. 777-779.
* A few other items of note:
* P. 151 (speaking of Horrebow's Atrium Astronomiæ ): "Un amateur qui
* habitait en Islande, l'assurait que le réfraction au solstice d'hiver
* était d'un degré. Mais il n'avait qu'un quart de cercle de bois, et
* Horrebow doute s'il peut y avoir quelque confiance." [See §17, p. 8
* of Horrebow's 1732 book.]
* Mathieu does place some emphasis on Oriani's discovery (pp. 790-791).
* So why did Bruhns not pick up on this?
* Mathieu mentions "great heights" (pp. 793-4); he seems to have been
* influenced by Ivory's concerns about "the height of the atmosphere".
* Throughout, the emphasis is on the Simpson-Bradley formula, and on
* the development in powers of tan z. There are useful pointers to
* obscure earlier works, such as Legendre's 1772 paper (p. 786) and the
* work of Du Séjour (p. 724, p. 783), who coined the term "Equations
* of condition".
* Available from Gallica.
* Carl Christian BRUHNS's prize essay on HISTORY of ASTRONOMICAL REFRACTION
* This is a classic, written in a clear and enthusiastic style.
* It was originally a prize essay, and I can see why it won the prize!
* Based on Delambre's "Hist. Moderne"; and succeeded by Bemporad's 1907
* article in Enz. Math. Wiss.
* Bruhns divides the history into two periods: before and after Kramp.
* He is much more thorough on the first part; I suspect he ran out
* of time. He treats the second period largely as though only the
* numerical tables resulting from it are worthy of note. In particular,
* the theoretical niceties of Ivory's 1823 paper, and Biot's 1836 monograph,
* are completely missed; Biot's wonderful method of calculating refraction
* for a *real* atmosphere is dismissed as a mere "mechanische Quadratur".
* In particular, he overlooked Biot's important theorem.
* Consequently, those [like Newcomb (1906) and Mahan (1961)] who rely
* heavily on Bruhns are badly misled. Note that Bruhns was only 31 when
* this was published.
* However, despite using only secondary sources (Delambre's "Histoire
* de l'astronomie moderne"), he has some useful things to say about
* Cassini -- pointing out the way of solving the equations quadratically,
* which might have been Cassini's own approach. In particular, he says:
* "Man sieht also, dass, wenn die Constanten genau genug bestimmt sind,
* die Cassini'schen Tafeln bis zu z = 74° mit den Laplace'schen
* übereinstimmen müssen." (p. 38)
* On the other hand, I cannot agree with his remark that "nur Wenige
* waren der irrigen Meinung gewesen, dass die ganze Atmosphäre nicht
* die brechende Kraft besässe" (p. 79). Kepler, the first 3 Cassinis,
* de Mairan, Flamsteed, Bouguer, . . . ?
* Caution: although he first says Cassini's second altitude was 19°
* (p. 33), he then says ZD = 80° in the sequel. As the refraction at
* this altitude is given as 5' 28'', 80° is certainly correct. [This
* typo is corrected to 10° in the "Verbesserungen" following p. 181]
* The final correction, which refers to p. 183, probably refers to line
* 8 from the bottom of p. 180.
* Our library has this only on the nearly unreadable Readex Microprint
* cards, but I have managed to get my own copy at last. This was No. 148
* in Carl Bamberg's Geschäfts-Bibliothek; later taken over as 148 in the
* Askania-Werke library. The copy appears hardly to have been read; there
* were no marginal notations, nor were the corrections entered in the text.
* Cited by Chauvenet, Newcomb, and every writer on refraction history.
* HISTORY OF REFRACTION
* A curious literature survey by an applied physicist with little
* understanding of astronomical refraction. Like most beginners, he
* supposes the upper atmosphere is important.
* Contains some useful early references; misses several important works.
* An historical correction
* "This article aims to prove that the Liber de crepusculis , which
* has always been attributed to Ibn al-Haytham (Alhazen, d. c. 1039)
* since it was published in 1542, is in fact the work of the Andalusian
* mathematician Abu 'Abd Allah Muhammad ibn Mu 'adh, who lived in the
* second half of the eleventh century."
* A really bad stab at the history of refraction
* Sample quotes: "Around 1850 it could be said that the subject was
* practically exhausted and that little further improvement could be
* expected." (second sentence, p. 1)
* The usual square-root form is attributed to Lagrange (1772) with no
* citation; Mayer, Simpson, Bradley and Lambert are not mentioned. (p.2)
* The simple tangent formula "is Domenico Cassini's formula for
* atmospheric refraction (1662)." And no citation. (p. 3) "For most
* astronomical observations, therefore, the integral in (1-6) is of no
* great importance." [So what was everyone arguing about the last 200 yrs?]
* Newcomb is credited with Oriani's theorem (p.4), where we find that as
* tan z goes to infinity at the horizon, "the series no longer converges."
* [As if it ever did! Where's Ivory's warning?]
* "The first useful table of atmospheric refractions was constructed
* by Johann Kepler (1604) on the basis of a homogeneous atmosphere of
* given height. Because of this we will call this model atmosphere
* Kepler's model." (No mention of Tycho Brahe, or Ptolemy!)
* On p. 7 we have "James Bradley's formula (1798)." (no citation.)
* [Bradley died in 1762; Maskelyne published it in 1763 and 1764.]
* And: ". . . the atmospheric refraction is proportional to (n o - 1)".
* P.8: we jump from Bradley to Ivory, with no mention of Oriani,
* Kramp, or Laplace; "With Ivory's work the basic problems of atmospheric
* refraction had come to a completion." [. . . as if he did it all himself;
* and what about Biot, who came later?]
* P.11: He supposes a superior mirage, where "In particular, we may
* see a reflected image of the setting sun." (after mis-using "Fata
* Morgana" to refer to looming.) On p. 12 the "forbidden" strip is
* mentioned, without Wegener's name.
* P.12: "Systematic work" on stellar photometry "began only after Norman
* Pogson had defined stellar magnitudes (1850) and J. C. F. Zoellner had
* built his visual photometer (1861)." [Pogson's paper was 1857; and
* what about Steinheil, and all the people whose works Pogson was trying
* to reconcile??? But there are no citations for any of these works.]
* P.15: Now for a real howler: "The fundamental concepts of ray optics
* follow from the observation . . . that light is a periodic phenomenon . . . ."
* P.16 ". . . Fermat's principle . . . is the basis of ray optics."
* P.16 "It was only in 1621, when Willebrord Snell . . . found the law
* named after him." [This was written over 20 years after the proof that
* Harriot found it first.]
* Then there are the typos, like "Williams Chauvenet" (p.1) and "km"
* for meters (p.11) . . . . A sorry sight, indeed. The only possible utility
* is in the fudged variants on Bradley's rule.
* Frans Bruin was Owen Gingerich's successor at the American University
* in Beirut. He seems to have been trained as an electrical engineer;
* see the 2002 obituary in JHA.
* Thanks to Jed Buchwald for a copy!
* A. Mark Smith has another shot at Ptolemy
* Despite the title, this really has nothing to do with refraction.
* It's mostly about the Moon Illusion, with a little on the height
* of the atmosphere inferred from twilight. The only connection with
* refraction is the notion of "vapors near the horizon", so it might
* help explain Tycho's idea that refraction occurs only at low altitudes.
* The copy on Blackwell's web site is nearly illegible.
* HISTORY of atmospheric refraction
* Not an historian's history, but an account for opticists that leans on
* secondary sources. Only the period from antiquity to Kepler is included,
* so the Moon Illusion gets a lot of attention.
* There are some slips: the coin-in-the-basin demo is attributed to
* Archimedes (in Note 10) rather than Euclid (or, properly, some unknown
* earlier person); Ptolemy's measured angles of refraction in water and
* glass are "quite accurate by modern standards"; "Ibn Mu'adh expressed
* his result in Italian miles"; "Tycho Brahe was the first to measure
* atmospheric refraction properly" and "Tycho's measurements, the
* first ever made of atmospheric refraction" (no mention of Walther);
* the anaclastic lens is "a paraboloid" (note 36).
* On the other hand, citing Kepler's rejection of "vapors" is a nice touch.
*
* source of some bad data used by Sinclair
* This is the set of Resolutions approved by the IAG at their 13th
* (1963) General Assembly in Berkeley. Only the first and fourth are
* of interest here:
* Resolution No. 1 recommends "either the Eflen [sic!] formula . . .
* or the Barrell and Sears formula" for refractivity of air.
* (Unfortunately, Sinclair chose the Barrell and Sears formula.)
* [The French version is even worse, confounding Edlén with Essen of the
* Essen & Froome formula for radio refractivity!]
* (Note that they mean the old (incorrect and obsolete) Edlén formula.)
* The English version is just p. 390.
* NOTE: This was finally revoked in Resolution 3 of the 1999 General
* Assembly; see J. Geodesy 74, pp. 66-67 (2000).
* Resolution No. 4 says that "the determination of refractive index
* now constitutes a most difficult problem and serious source of error in
* electromagnetic distance measurement; and that further scientific
* research into this problem, in all its aspects and in all conditions,
* is urgently required;" but then veers off into checking via invar tapes,
* rather than direct measurements of refractivity.
* This is now (retroactively) called Journal of Geodesy 37, No.4.
* RGO MODEL - origin
* RGO MODEL - development
* Available on the Web at http://astro.ukho.gov.uk/data/tn/naotn63.pdf
* That seems to be an accurate transcription into PDF format of the
* original TN 63; however, the typeface is different from the original,
* and the figure has been re-drawn and re-labelled. Apart from that,
* the PDF is bug-for-bug compatible with the original: the confusion of
* DELTA and GAMMA in the program listing; the erroneous "respectively"
* in the Conclusion (where the order of the last two items was reversed);
* and the use of an absolute value in the Subroutine AREF, which prevents
* its use with an inverted lapse rate in the troposphere, are all preserved.
* Much of the text is taken over verbatim in ES II Section 3.281.
* (see also Gergonne, 1829, in Mirage Theory file)
* (see also Everett, 1873 in Mirage file, and 1874 in Mirage Theory file)
* (see also Julius, 1900, and Einstein's 1925 obit. of him)
* (see also Hillers, 1914, in Mirage File)
* (see also Nölke, 1917, in Mirage Theory File)
*
* JAMES CHALLIS makes the brightness error
* Challis is notorious as the fellow Airy entrusted with Adams's
* prediction of where to look for Neptune.
* After some unremarkable observations on the apparent enlargement of
* a planet by refraction in its atmosphere, he considers "an eclipse
* of the Sun by the Earth, as seen from the Moon, . . . " [p. 233] and
* continues: "There will, consequently, be a condensation of light . . .
* bordering the Earth's limb . . . ." He also notes the extinction,
* "as is evident from the fact that the Sun's face, when near setting,
* loses so much brightness that it can be looked at with impunity with
* the naked eye."
* He then asserts [p. 234] that during an eclipse of the Sun by the
* Moon, as seen from Earth, "if there be a lunar atmosphere" there would be
* "a slight condensation of solar light bordering the part of the Moon's
* periphery which crosses the Sun's disk." And he suspects this has been
* observed.
* Also, [p. 235] he considers the case -- later taken up with much
* fervor by Schmidt and by Julius -- of refractive curvature exceeding
* that of the body: "It is reasonable to suppose that this is the case in
* the Sun's atmosphere . . . ," claiming [p. 236] that "The foregoing
* theory fully explains why the contour of the Sun is generally observed
* to be entirely free from inequalities. This fact is the more remarkable
* because the unevenness of the Sun's surface, as indicated by the mottled
* appearance spread over its whole extent, with the occasional occurrence
* of deep depressions (the spots), surrounded generally by lofty ridges
* (the faculæ), gives reason to expect that inequalities would be
* perceptible on the periphery."
* Note: This volume of M.N. falls in the group (from vol. 19 to vol. 27)
* that was re-published in 2-column, quarto format, to match that of the
* Memoirs of the R.A.S. and be bound with them. See pp. 239-240 of
* "History of the Royal Astronomical Society", Vol. 1, for details of
* "this curious arrangement". Infotrieve produced a copy from the
* quarto edition for our ILL people.
* GEORGE BIDDELL AIRY, Astronomer Royal, refutes Challis's error
* Airy quotes Challis's "condensation" remark, and announces that
* "It is my principal object in this paper to show, by optical
* investigation, that no refraction can cause a change in the apparent
* brightness of the surface viewed." He then goes on to establish the
* Lagrange invariant, "not aware that any optical writer has examined into
* this question . . . ." The treatment is perhaps excessively mathematical,
* which obscures the physics somewhat; but he correctly concludes:
* "And therefore refraction by a lunar atmosphere cannot explain the more
* luminous band which appears to surround the Moon's limb where it crosses
* the Sun." [p. 18]
* He has "no difficulty in explaining to myself the origin of the
* luminous band in question. It is strictly an ocular nervous phenomenon,
* not properly subjective, but sensational -- a mere effect of contrast.
* I have seen it so frequently under circumstances very different from
* these, that I cannot have the smallest doubt on the matter.
* "A person who stands before a moderately illuminated whitish wall,
* and swings a piece of black cloth upwards between his eye and the wall,
* will almost always see the edge of the black cloth preceded by a broad
* luminous band. I should once have said that such a band is always seen,
* but I find that I do not see it so conspicuously now as formerly."
* (Note that this volume begins with the Nov. 13 meeting.)
* CHALLIS persists in his error
* Here Challis is disputing Airy's (correct) conclusion "that the
* brightness of an object seen through the refracting medium is the same
* as if no medium were interposed, loss of light in the transmission being
* left out of account." (p. 50)
* "But there remains a fatal objection to the application of this
* result to the question under consideration. No account has been taken
* of the variation of the refractive index (n ) in passing from one point
* to another of the medium. In every investigation respecting the courses
* of rays in atmospheres, . . . " and off he goes! After more talk of
* "rays", we get:
* "The disk of the Sun, as seen by a spectator on the Earth's surface,
* is diminished by the effect of atmospheric refraction, the lower limb
* being more raised than the upper, and the vertical diameter and parallel
* ordinates being consequently diminished, while the horizontal dimensions
* remain unchanged. Hence [sic!] if no light were lost by passage through
* the atmosphere, the brightness of the Sun, so far as it depends on the
* number of pencils in a given space, would be increased by the refraction."
* (p. 51)
* Issue dated January 8, 1864.
* Airy tries again . . .
* Here he argues that a continuously varying medium can be decomposed
* into a series of homogeneous ones, so that the conclusion can be applied
* to each internal boundary in succession -- each time preserving the
* brightness. With the physics thus brought out more clearly, Challis is
* finally convinced (see below).
* In addition, Airy offers a demonstration using photographs and strips
* of black paper. . . .
* (June 10, 1864 issue)
* Challis recants at last!
* "The question is purely mathematical, and one on which two
* mathematicians ought certainly to be able to come to an agreement. . . . It
* is still true that to an eye situated within the medium the apparent
* brightness of an external object may be increased by the refraction;
* but from Mr. Airy's argument it follows that if the eye, and the object
* from which the rays originally proceeded, be in the same medium, the
* brightness of the object cannot be increased by transmission of the light
* through an intervening transparent substance, whatever be its form . . . ."
* Evidently Airy's second paper convinced him.
* RUDOLF CLAUSIUS comes up with the same conclusion independently
* Notable for the section that describes the inverse relation between the
* area and solid angle of a beam -- or what we would consider "conservation
* of throughput" today. Of course, this is famous for his connecting the
* optical question with the Second Law of thermodynamics. Clausius cites
* Helmholtz's "Physiol. Optik", p. 50; but goes well beyond Helmholtz.
* Available via ADS.
* This is vol. 197 in the whole series; v.121 of Pogg.Ann.
* Clausius's paper reprinted in the first edition of his Abhandlungen
* Thomas Archer Hirst's edition of Clausius's reprint in English
* The English translations first appeared in Phil. Mag.
* The paper of interest to us here is the "Eighth Memoir".
* Available at Google Books.
* Clausius's revised, second edition
* (A 3rd edition appeared in 1887, where this is pp. 315-354.)
* Walter R. Browne's translation of Clausius's second edition
* Now it is Chapter XII.
* Available at Google Books.
* Friedrich Dobe's thesis
* Dobe finds the focal point is some 500 km behind the observer, for
* *normal* atmospheric structure, in the vertical plane; but over a
* thousand times larger in the horizontal plane. He mistakenly contrives
* to make this out to be a significant effect.
* Schmidt's mistaken attempt to explain solar limb-darkening as due to
* the astigmatism of refraction in its atmosphere ". . . bei die durch die
* Brechung bewirkte ungleiche Strahlenverteilung . . . ." Unlike most of
* his ilk, he is aware of the solid-angle considerations; but -- alas!
* forgets that area is also involved:
* "Helligkeit ist S t r a h l e n m e n g e p r o E i n h e i t
* d e s R a u m w i n k e l s . . ." So there is talk about rays
* leaving a point, etc. (Typical radiance/irradiance error.)
* (As we have this on a micro-opaque only, I have no hard copy.)
* Fraser & Mach introduce the "Bromosa" error
* This is just a 4-line meeting abstract.
* NICE PHOTOGRAPHS by Fraser; confusing (and confused) explanations
* This otherwise standard account of mirages is badly marred by the
* authors' insistence that ASTIGMATISM can change image brightness. As
* their discussion on p. 110 shows ("Consider a point source of light . . . "),
* they have made the standard mistake of confusing radiance with
* irradiance. Unfortunately, this theme was taken up again by Fraser's
* disciple Alfred Löw (the "Luftspiegelungen" book).
* The same error was made by the Editor of Met. Mag. -- cf. Bates, 1921.
* LABORATORY mirage simulations and simple theory
* [filed here because their Fig. 5 nicely shows the effects of ASTIGMATISM.]
* They use a vertical hot plate, and show 3 images in their mural mirage.
* Their lab setup corresponds to Schmidt's theory of 3-image mirages.
* Yngve Öhman suggests that mural mirages in chimneys might magnify stars
* The discussion is in terms of magnification in 1 dimension. Cylindrical
* lenses are mentioned, but not astigmatism per se.
* There is a plate showing a mural mirage.
* Note the resemblance of this idea to Huddart's 1797 suggestion about
* the apparent brightness of lighthouses.
* Available from ADS.
* WALTER TAPE's "topology" review
* NOTE: The published version was garbled by the editors; this is based
* on the (supposedly) corrected reprint. (see p.6 of the Sept. issue)
* "If no mirage conditions exist, the rays are straight . . . ."
* "I believe the multiple horizontal spikes sometimes seen on the rising
* or setting sun may be multiple images of parts of the sun that have been
* highly demagnified." [So he spotted the mock mirage as a mirage.]
* Note also the caption to the last figure: "When the transfer mapping
* is smooth, some mirage images must be compressed if there is to be room
* for multiple images. . . ."
* This paper introduces the concept of "folding" in mirage mapping.
* WALTER TAPE's "topology" review (German version)
* This is a "Scientific American"-level article, centered on the
* odd-number theorem and its basis in topology. The main virtue is the
* collection of excellent mirage photos from the Great Lakes (badly
* reproduced in my photocopy, however). Fraser & Mach are cited, but
* nothing else.
* "Liegt keine Luftspiegelung vor, so sind alle Lichtstrahlen
* geradlinig . . . ." (p. 50)
* "Ich glaube, daß die vielfachen horizontalen dünnen Streifen auf
* der Sonne, die manchmal bei Sonnenaufgang oder Sonnenuntergang sichtbar
* sind, Mehrfachbilder von Teilen der Sonne sind, die stark verkleinert
* erscheinen." (p. 55)
* MIRAGE MISCELLANEA
*
*
* ALFRED LÖW's book on mirages
* There is much to be liked about this book; it fills in the gap about
* "Morgana" being derived from the same root as "Margaret" (p. 18), and
* insists on the variety of mirage phenomena; has good examples reproduced
* in color plates; provides a good (but incomplete) list of references; an
* Appendix gives Wegener's theory clearly; the author insists that "Fata
* Morgana" should be restricted to complex displays; and there is a
* chapter on the psychological aspect of mirages.
* On the other hand, it misses some important papers: Hillers, Schmidt,
* Woltmann, and Forel are all missing, and Biot appears only in the text,
* not in the references. Tait is called "französische" (p. 92); Fraser's
* mistake about astigmatism is repeatedly invoked as factual; many
* phenomena are arm-waved away as due to inclined layers; a double-image
* mirage is thought possible without an intervening inverted image
* (p. 82); Raman's nonsense is treated with respect (p. 94), as are some
* of Gordon's more fantastic claims, and "lateral" mirages; and looming
* and sinking are included as varieties of mirage.
* Not for beginners, but a good source for further research.
* Thanks to Rolf-Dieter Auer for bringing this to my attention!
* Christopher Pinney's book
* A curious history of mirages, indeed! There is only one photograph
* of a superior mirage display, and none of the common inferior mirages.
* A variety of 19th-Century artistic efforts to depict mirages are shown,
* some factual but most quite phony (as well as a couple of fakes). No
* effort is made to explain the physics of mirages; though the word
* "refraction" appears a few times in the text, there's no hint of the
* law of refraction, nor any ray diagrams. Fortunately, the sources of
* the various quotations and pictures are documented -- though these are
* often taken from encyclopedias and other secondary sources, not the
* originals. Many obscure old references to mirages are provided.
* This appears to be a more factual effort to deal with the cultural
* significance of mirages than Marina Warner's fantastic botch. Curiously,
* it cites this bibliography for a reference to her book. It's more of
* a history of mistaken notions about mirages than a history of mirages
* themselves; no effort is made to distinguish fact from fiction.
* Thanks to Christopher Pinney for a copy of his book!
* An historian admires Pinney's effort
* Fiona Amery calls Pinney's book "the only historical work devoted to the
* history of the mirage". Evidently she's unaware of the works of Biot,
* Erdmann, Tait, Pernter & Exner, Löw, . . . -- not to mention Delambre,
* C. C. Bruhns and his disciple A. I. Mahan, and F. Bruin's sloppy effort.
* On p. 457, she reproduces Brewster's representation of Vince's 3-image
* mirage, calling the lowest image "the real ship", and the upper images
* "projections".
* Shows no understanding of optics, but contains some marginally useful
* citations: James Abbott (1844)
* and
* Henry Hasted,‘Reminiscences of Dr. Wollaston’,in Proceedings of the Bury
* and West Suffolk Archaeological Institute Established March 1848 for the
* Collection and Publication of Information on the Ancient Arts and Monuments
* of the Western Division of Suffolk and Archdeaconry of Sudbury, Bury
* StEdmunds: Barker and Son, 1853, pp. 121–34, 125.
* (All the references are in English.)
*
* Available at
*
* https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B6987E17A024924D6939138D6AA0A01A/S0007087420000369a.pdf
*
*
* Cf. Bouguer (1753) !
*
* GEODETIC REFRACTION (std.work on GEODESY)
* ray can be treated as arc of a circle, pp.553-561
* See longer comments on Helmert (1884) in GENERAL BOOK file.
* RADII of CURVATURE
* Konstantinos Nikolitsas, Evangelia Lambrou
* Mansoor Sabzali, Lloyd Pilgrim
* A useless Master's project, written in badly broken English.
* Some of the text and figures were taken from the 2019 paper by Nikolitsas
* and Lambrou.
*
* Here is where she shows the rapid transition near ZD 85°
* Cf. Freiesleben (1951)
* Both these deal with the water-vapor problem. In the second paper, she
* shows that the water-vapor correction given in the Pulkovo tables is wrong.
* However, they seem OK for *DRY* air.
* PULKOVO TABLES - methods of calculation
* methods used for PULKOVO TABLES, 5th ed.
* NOTE:
* ISO adopts g = 980.616 (1 - 0.0026373 cos 2phi + 0.0000059 cos2 2phi)
* which it calls Lambert's eqn. and cites Smithsonian Met.Tables, 1963.
*
* g = g0 (1 - .0026373 cos 2phi + 0.0000059 cos-sq 2phi)
* and
* g0*M/(R*T0) = 1.1855, where
* M = 28.9644 (mol.wt.); R = 8314.32 j/k kmole (gas const.);
* T0 = 288.16 K
* PULKOVO REFRACTION TABLES FILE (all editions)
*
* There have been 5 editions, published in 1870, 1905, 1930, 1956 and 1985.
* It may be useful to list them all together here.
*
* FIRST EDITION (1870)
* This is the one that used the calculations of Hugo Gyldén.
* The logarithms of the various factors are tabulated for every minute of
* arc of Z.D.
* Available at Google Books. 39 numbered pages + IV
*
* SECOND EDITION (1905)
* Basically a reprint of the first edition, but with an added preface
* by Oskar Backlund; and the table referring exclusively to the Pulkovo
* meridian circle has been omitted. Struve's Latin preface is retained.
* Formerly available at Google Books. Only 26 pages, including covers.
* Currently available at HathiTrust:
*
* https://babel.hathitrust.org/cgi/pt?id=mdp.39015073268875;view=1up;seq=7
*
* https://babel.hathitrust.org/cgi/pt?id=uc1.b5012362;view=1up;seq=1
*
* THIRD EDITION (1930)
* 22 pages + X
* Substantial revisions and corrections, including the addition of
* several tables from Harzer, including the one for star colors on
* Osthoff's visual scale.
* The back of the title page says it was printed at the request of the
* Main State Astronomical Observatory at Pulkovo (signed by Director A.
* Ivanov); the printing was done at the Dunaev cartographic printing plant
* in Moscow. (They also printed the multi-color maps that are tipped into
* the volumes of the Great Soviet Encyclopedia, or Большая советская
* энциклопедия.) The title page says "Moscow 1930" without naming a publisher.
* If we follow the rule that the "publisher" is whoever ordered the book
* to be printed, that must be Pulkovo Observatory.
* FOURTH EDITION (1956)
* 32 pages
* Таблицы рефракции Пулковской обсерватории
* (Изд-во Академии наук СССР, 1956)
* FIFTH EDITION (1985)
* 48 pages
* Таблицы рефракции Пулковской обсерватории, Издание пятое
* (Изд-во «Наука»,Ленинград, 1985)
* P. 39 lacks a page number. The corrections for chromatic refraction
* are on the (unnumbered) inside back cover, following p. 48.
*
* MELCHIOR's jeremiad about terminology
* "The useless introduction of the new words "wobble" and "sway"
* has produced a flourishing rise in confusing terminology in most of the
* recent papers. These two words even if picturesque are fundamentally
* unprecise."
* "Because of this new fashion introduced by some geophysicists, many
* astronomers have become really confused and, instead of keeping the
* very clear Poinsot-Tisserand terminology, started to stammer into the
* following extensive terminologies, never clearly defined, which I. . . ."
* There is a lucid description of nutation theories; refraction is
* not mentioned.
* MENDES et al.
* "The main accuracy-limiting factor in modern space geodetic
* techniques, such as the Global Positioning System (GPS), very long
* baseline interferometry (VLBI), and satellite laser ranging (SLR),
* is atmospheric refraction." (First sentence of Introduction.)
* NOTE: What the radio people call a "mapping function" is just what
* astronomers and solar-energy people call the "airmass finction";
* see Rapp-Arrarás and Juan M. Domingo-Santos (2008).
* REFRACTION FROM SUNSETS and SUNRISES
* Temperature inversions explain the greater refraction and flattening than
* predicted by the Pulkovo tables. Wegener (1918) cited.
* Biggest deviation on a morning in Feb.1920.
* Shows that INVERSIONS of ordinary size can produce the observed effects,
* including Wegener's blank strip.
* Jules de Kort, S.J.
* REFRACTION FROM SUNSETS
* REFRACTION FROM SUNSETS; MAGNIFICATION rule
* ". . . the squashing of the sun's disk when the sun is on the horizon
* depends only on the temperature and lapse rate at the height of the
* observer's eye."
* ". . . if the sun reaches its minimum aspect ratio above the astronomical
* horizon, γ must decrease with height (to give a lifted inversion)."
* REFRACTION FROM LOW SUN
* This is Pub. Obs. astron. Belgrade No. 35
* REFRACTION FROM SUNSETS
* DAN BRUTON's thesis, published version
* The method is an exact integral equation for the inversion.
* N.B.: the method fails in cases of ducting; cf. Ao (2007).
* This uses my sunset sequence as an example.
* Historical addendum to the previous paper, discussing priority issues
* Konstantin P. Gaikovich's monograph
* Cf. Gaikovich et al (1983) in "Mirage Theory" file for inversion theory.
* Chapter 3, "Gas media. Atmosphere Remote Sensing", is the relevant part
* (pp. 85-189). There is a section (§3.2. Reflection in Atmosphere
* Diagnostics) on ducting (pp. 134-138). The rest of the chapter deals
* with radiometric observations.
* The list of 264 references at the back includes O'Connell's book and a
* couple of Lehn's papers, but no mention of Link's works.
* Chi O. Ao compares radiosonde profile with GPS retrievals
* Cites papers by Gorbunov (2002,2004) for wave-optical retrieval theory,
* and "failure of Abel inversion when ducting layers (also referred to as
* superrefraction or critical refraction layers) are present". [Intro.]
* "The radiosonde profiles . . . retain the very high vertical resolution
* of ≈30m". He denotes the nR function as a .
* Note that parallactic effects are neglected, "Since the transmitter and
* receiver are located far from the atmosphere in a GPS RÖ.
* Appendix A shows that "An infinite number of refractive index
* profiles -- of which the Abel inversion offers but one possibility --
* that differ only within and below the duct can be shown to give an
* identical" bending angle profile. [UNIQUENESS problem]
* He describes the algorithm for finding the top, "middle", and bottom of
* a duct (bottom of p.4). [By "middle" he means the place where nR is a
* local maximum.]
* The retrieved refractivity profiles are underestimated in and just
* beneath the duct, but are less strongly affected closer to the surface.
* This is paper number RS2008, paginated from 1-15.
* DOI: https://doi.org/10.1029/2006RS003485
* NICE SUNSET PHOTOS in SERIES
* Wonderful 7-image mirage of setting Sun by Jay Meisel
*
* These papers try to simulate mirages numerically. Most use very
* unrealistic models -- often just "internal reflection". The emphasis
* is on making fake images, not realistic simulations of *real* mirages
* as in Lehn's papers.
*
* Layers of constant n used; unrealistic
* The correct terms for mirages are used, but they say the inf. & sup.
* mirages are below/above the "actual position". Based on 2 papers in
* Am. J. Phys. from 1977 & 1982.
* Fig. 1 shows a typical mis-placed image for an inferior mirage.
* All the images came out a strange dark blue here -- looks as if they
* had trouble preparing the CMYK separations for the journal. The PDF
* on the IEEE website has saturated image simulations (mostly black).
* Response to the previous item, with a GREEN FLASH mention in passing
* Musgrave correctly sees that "if the formation of a mirage were by
* some continuous deformation in the ray path, then we would expect to see
* a different image than if it were formed by some discontinuous process
* such as total reflection." But he is unaware that the continuity of
* the erect and inverted images *is* observed. Then he correctly says
* that "if refraction were the primary engine in mirage formation, then
* we would expect to see the effects of dispersion in a mirage, smearing
* the image into its component colors by a prismatic effect (an important
* factor in the generation of the famous and elusive `green flash' of the
* setting sun)." But then: "My subject experience indicates little to no
* dispersion in mirages observed in nature. Furthermore, as the index of
* refraction of the air at room temperature and pressure is only 1.00025
* versus 1.0 for a vacuum, there is precious little refractive power to
* work with . . . .
* "This would indicate that the primary `bending agent' in mirage
* formation is total reflection, not refraction . . . ." So, by being
* ignorant of mirage observations, as well as missing the infinite slope
* at grazing incidence in the sine law, he picks the wrong model.
* Berger's reply to Musgrave compounds his errors
* "Ken Musgrave is correct in pointing out that the major contribution
* to the mirage effect is total internal reflection, which results in a
* discontinuity of the first derivative at that point." (See what happens
* when you use layers of constant index?) "In addition, Musgrave's
* observation that a `purely reflective model, without refraction, might
* well be sufficient' is well taken." Yuck.
* [This appears on the last page of Musgrave's paper, above.]
* Layers of constant n used; unrealistic
* ". . . optical illusions brought about by atmospheric refraction."
* "A single image may appear side by side . . . ."
* "Stooping Mirages" and "Towering Mirages" sub-heads . . .
* Meeting was in September, so I assume this followed the previous ref.
* Jaroslav Sloup has a good idea (circular arcs)
* But his "omega" simulation has unrealistic artifacts, because he
* chooses layers that are too thick.
* Cites Berger (above) and Dan Bruton's thesis.
* qualitative theory: rays are straight lines
* Beiträge zur Physik der freien Atmosphäre
* quantitative mirage theory: rays are circular arcs
* Here is where the BLANK STRIP or "obscured strip" or "reflecting strip"
* was introduced, together with the Nachspiegelung.
* [Note that the horizontal blocking was predicted by Biot (1836).]
* He simulates inversion sunsets with both supercritical and subcritical
* lapse rates. At the end, he describes a sunset in which the lower edge
* of the strip is below the horizon: "Here the Sun sets behind an invisible
* wall, . . . at considerable height above the [astronomical] horizon."
* O'C #149
* Wegener's big review article (mostly a re-hash of the earlier papers)
* The GF is item C (section 5), pp.203-204. The standard story is given:
* "Es kann kein Zweifel daran herrschen, daß auch hier die spektrale
* Zerlegung des Lichtes durch die Refraktion die Ursache ist, und daß das
* Spektrum nur aus dem Grunde bei Grün aufhört, weil Blau und Violett, wie
* die rote Farbe der untergehenden Sonne zeigt, am Horizont ausgelöscht
* werden." But: "Indessen bleibt hierbei zunächst unerklärt der
* plötzliche Übergang von Rot zum Grün ohne erkennbaren Durchgang durch
* die dazwischen liegende spektrale Farbenfolge."
* It's nice to see that he has seen GFs himself: "Die Erklärung einiger
* Autoren, nach der es sich nur um ein subjektives Nachbild handelt, ist
* für jeden, der die Erscheinung selbst beobachtet hat, schon wegen ihres
* Glanzes ausgeschlossen . . . ."
* O'C #150
* Wegener's chapter on atmospheric optics
* Section 373 is "Der Grüne Strahl". He quotes Bemporad's dispersion
* table. He gives the textbook explanation, but admits that "Die
* Erscheinung . . . scheint aber außerdem noch an besondere Bedingungen,
* vielleicht hohe Feuchtigkeit, gebunden zu sein." He rejects Julius's
* anomalous-dispersion theory (interestingly, because "die Erscheinung
* zu glänzend ist.") He recognizes that "Auffallend bleibt nur der
* plötzliche Übergang von Rot zum Grün ohne erkennbaren Durchgang
* durch die dazwischen liegenden Farbenfolge," but attributes this to the
* "rain bands": "Hierdurch erklärt sich auch die Unregelmäßigkeit des
* Auftretens." Not a bad try for 1929.
* SPLENDID DRAWING of SUN above BLANK STRIP, with reflected ship in it !!
* This observation directly contradicts FEENSTRA KUIPER's error.
* STRIP described as "a bank of medium cloud."
* (Cf. Pinkhof, 1933, for a similar ship mirage without the Sun.)
* "Air temp. 71 F, wet bulb 64, sea 68."
*
* See also Biot's monograph, and the works by Bravais, and
* Ao (2007) in "Sunsets --> refraction" file.
*
* Gergonne's obscure 1808 paper: an extended abstract, with a few quoted
* passages from Gergonne's full memoir. He thinks that the mirage is of
* local interest, "le département du Gard étant peut être la seule
* contrée de l'Europe ou le mirage puisse annuellement être observé."
* [Here a footnote explains that the mirage is seen every summer at the
* hottest time of day in the south of Gard.]
* He begins by citing, and quoting from, Biot's Traité élémentaire
* d'astronomie physique -- but without realizing that Biot took his
* description of the mirage in Egypt almost verbatim from Monge's 1799 account.
* Thus the description on pp. 222-223 is mostly wording taken directly from
* Monge's work (which he says he has not seen, on p. 251).
* Gergonne realizes that the inverted image means that at least one
* of the two rays from a point has not followed a straight path from the
* object to the eye, which implies that either reflection or refraction
* must be involved. He can't see where the reflecting surface would be,
* or how reflection would not act on objects at all distances, or how the
* concentration of heat could produce a reflection; so, for all the wrong
* reasons, he decides that refraction must be responsible. And, as the
* refracting medium has to be air, which we know is strongly affected by
* heat and cold, he proceeds in that direction. (pp. 223-224)
* So he develops the theory of refraction in a medium whose refractive
* power varies continuously. (pp. 225 ff.) He derives the differential
* equation of the ray trajectory (p. 227), and treats the atmosphere as
* plane-parallel. Although there is no general solution (because the
* distribution of refractivity with height is not known), Gergonne obtains
* several results from the structure of the differential equation itself.
* He shows how to make a geometrical construction that relates the
* trajectory to a curve related to the refractivity profile, so that each
* of these curves can be deduced from the other.
* As a simple example, he assumes the trajectory is a parabola with its
* axis vertical; then the related "regulator" curve is a straight line.
* In a real case, the regulator can be considered as made up of successive
* line segments; and the trajectory, a series of parabolic arcs whose
* slopes match where they join. [We would say it is a spline of parabolic
* segments.] This single observation gives rise to a multitude of results
* that Gergonne develops. (p. 229)
* For example, if the regulator has a maximum, the trajectory must wind
* back and forth about a horizontal line corresponding to this maximum;
* and its differential equation does not have an algebraic solution.
* [In modern terms, this is a ray trapped in a duct.] (p. 230)
* This raises the question of how two rays leaving the same point can
* intersect again, so that an eye placed at that intersection sees two
* separate images of the source. Gergonne asserts that a necessary and
* sufficient condition is that the second differences of the refractive
* powers of the different atmospheric layers do not continually have the
* same signs as their first differences. (p.231)
* Applying this result to a particular example, he finds the condition
* that all the rays of light leaving a certain point are reunited at the
* eye, as "a common focus". (p. 233) [This is the Fata Morgana case.]
* He notes that the observer "serait frappé d'une impression semblable à
* celle d'un brouillard qui , empruntant sa couleur de celle du point qui
* en produirait l'apparence, pourrait en changer , lorsque l'œil se
* déplacerait." (p.234)
* He then asks how many images of a given point are seen, in general.
* He first remarks that for points near the observer, the rays can be
* considered straight, and the spectator sees objects as if they were in a
* vacuum or a homogeneous medium of constant density, and sees only a
* single image of each object. Then his basic equation has only one real
* root; it must be of odd degree; so that whatever the intervening medium
* may be, it can "only give rise to an odd number of images". (p. 235)
* Besides the number and positions of the images, Gergonne considers
* whether they are erect or inverted. And, because of the unlimited
* variety of possible functions, he considers the "physical constitution"
* of the atmosphere." (p.240) He remarks that our ignorance of how heat
* is transferred from one layer to another does not allow us to know how
* the density varies. Nevertheless, when the ground is heated by the sun,
* the small thermal conductivity of air restricts the heating to only
* a small height. So he concludes that, near the ground, the second
* differences of the refractive powers, naturally negative, become null
* or even positive; but that, as the variations are never very rapid, one
* deviates very little from the truth by supposing that the density of the
* air in the lower regions, and consequently it refractive power, is
* constant, or that it varies little, so that the medium is divided by a
* horizontal plane into two parts, in one of which the density varies
* gradually, while in the other it is constant or varies in a different
* way. This corresponds to assuming that the regulator is a straight line,
* or that it is made of two lines with different slopes, which means that
* the trajectory is linear or parabolic, or that it is formed of part of
* a parabola, following the tangents at its ends, or following the arcs
* of another parabola. (p.243)
* Gergonne analyses all these different cases in detail. Most of
* them produce no remarkable phenomena. The case where the density is
* constant near the earth and then decreases upward, and that in which
* the density initially increases upward and then becomes constant,
* give rise to three images, provided that the eye and the object are not
* both in the variable medium. (p. 244) Of the three images, one of
* the extremes which is direct, and the intermediate one which is inverted,
* are both visible, while the third, which is formed beyond the spectator,
* cannot be seen. . . . The same things occur in the case of a medium composed
* of two parts varying in density according to two different progressions,
* provided that the eye is in one of these media, and the object in the
* other; but if they are both in the same medium, the number of images can
* rise to five . The multiplicity of images can only occur for objects
* suitably placed. Finally, Gergonne remarks that in the case where the
* density decreases toward the ground, the ray paths have their convexity
* turned from upward to downward; some of them can be intercepted by the
* ground: a circumstance that necessarily reduces the effective number of
* images, and can make it much less than the theory indicates.
* Gergonne finishes by considering the case where the regulator is a
* parabola with its axis horizontal, so that the refractive power decreases
* with the squares of the distances of the atmospheric layers from a
* certain plane. Then, in general, each object has only a unique image;
* however, whatever the situation of the spectator, there is always a set
* of isolated points whose rays reach the eye in all sorts of directions,
* so that the observer must see these points everywhere. (p. 245)
* Gergonne compares the various cases with the description of the mirage
* quoted from Biot (i.e., Monge's description), and says: (p. 246)
* "il n'est pas difficile de reconnaître à laquelle de ces
* hypothèses ce phénomène doit être rapporté. Voici donc de
* quelle manière il me semble devoir être expliqué. Le matin ,
* lorsque le sol n'est pas encore échauffé , la densité de l'air
* va croissant vers la terre, mais d'une manière si peu sensible que ,
* dans les limites qui embrassent l'œil et les objets qu'il peut
* apercevoir , il est permis de la considérer comme constante ; alors
* donc l'aspect du pays est tel que le comporte la disposition
* réelle des objets et leur éloignement ; mais , lorsque le sol s'est
* échauffé par la présence du soleil , il communique une partie
* de la chaleur qu'il a acquise , à l'air qui est en contact avec lui ;
* et cette chaleur , se transmettant de proche en proche , dilate le milieu
* jusqu'à une certaine hauteur , probablement peu considérable , au-delà
* de laquelle sa densité est sensiblement uniforme, tandis qu'au contraire
* elle décroît continuellement vers la terre. Il arrive donc que ,
* parmi les rayons de lumière qui partent des objets suffisamment
* éloignés du spectateur , et placés à une hauteur con venable ,
* ceux qui , à raison de leur inclinaison , ont une vitesse verticale
* peu con sidérable , venant à pénétrer les couches inférieures de
* l'air , sont attirés par les couches supérieures , plus denses , dont
* l'action parvient bientôt à éteindre cette vitesse , et à leur en
* faire ensuite acquérir une autre de bas en haut ; il arrive donc que
* ces rayons , dont la direction était d'a bord sensiblement rectiligne ,
* après avoir décrit dans le milieu variable une courbe convexe vers la
* terre , se relèvent et repassent dans le milieu constant où ils prennent
* de nouveau la direction rectiligne , selon laquelle ils parviennent enfin
* à l'oeil du spectateur. Dans le cas le plus ordinaire , le spectateur
* recevra par cette voie une image renversée de l'objet : indépendamment
* de l'image directe qui lui parviendra; par l'entremise des rayons de
* lumière entièrement situés dans le milieu constant ; il verra donc
* simplement au-dessous de chaque objet , son image renversée , comme elle
* paraitrait effectivement dans l'eau ; et comme cette double impression ne
* pourra avoir lieu que pour des objets suffisamment distans du spectateur ,
* il arrivera qu'à mesure qu'il avancera , les limites de l'inondation
* apparente s'éloigneront ; mais alors le phénomène se reproduira pour
* d'autres objets plus éloignés ; et , ce qui achèvera sur-tout de
* compléter l'illusion , c'est que l'air , près du sol , étant dans une
* agitation continuelle , l'image renversée qu'on observera au-dessous
* de chaque objet , au lieu d'être immobile comme l'objet même ,
* éprouvera une sorte de mouvement d'ondulation , pareil à celui que
* produit l'agitation de la surface de l'eau , sur les images des corps
* qui s'y réfléchissent." (p. 248)
* He then discusses the third image that is formed behind the observer,
* and is therefore invisible.
* Gergonne then points out that this model implies that the heated part
* of the air should not extend to the height of the observer's eye, and
* that the limits of the apparent inundation should contract as the heating
* increases, "so that one could, in a way, measure the extent of the
* phenomenon by means of a thermometer suspended freely a few inches
* from the ground." (p.249)
* Furthermore, the mirage should be seen daily in places with smooth flat
* land, during the summer, in the hot part of the day. (p. 250)
* "Je sais que M. Monge a traité le même sujet, dans le premier volume
* de la décade égyptienne ; mais n'ayant pu encore me procurer cet ouvrage,
* j'ignore absolument quel rapport il peut y avoir, sur ce point, entre mes
* idées et celles de cet illustre géomètre." (p.251)
* As Gergonne's memoir was accompanied by many plates, the editors have
* thought they should put at least one at the end of this extract, showing
* the simplest case where the mirage can occur. Pp. 253 ff. give the
* explanation of this plate.
* This seems to be the earliest work after "EMERITUS" (1807) in which the
* POSITION of the image is considered. (Nölke took it up again in 1917.)
* These are the proceedings of the Academy at Gard. Notice the spelling
* "Nismes" throughout.
*
* Title page reads:
*
* N O T I C E
*
* DES TRAVAUX DE L'ACADÉMIE
*
* DU GARD,
*
* PENDANT L'ANNÉE 1808.
*
* Available (with the figure mutilated) at
* https://books.googleusercontent.com/books/content?req=AKW5QacmcKk4_gN4ijpaPfon4Zd6_rSVDZh5NmLFmAy7RfjZ0-8FW18Qtip-W_bhVltSdHdvlrCnPlH_IxCbR93QG3vAsN7iB3B7pF2BXd--Uo3fDbBhwhioYGseQyNm4HLeRpQu3cQZkTpnXEWgCIKws5OxpwsyDFwpdjikAo1mEAGMRdZwOCXs4vPylmpSFYr-IqBuTQMmhlwYFASuwywr03Ru173miapJesrook4DuyNDhAcJ4alx-SKsLe0nRoKAdcZvrrTXYqTohNT-ONUSy2pGj_oDyUTDCS5CaTnIQYAf7yJLPOk
*
* The figure is available in the copy at Gallica:
* https://gallica.bnf.fr/ark:/12148/bpt6k486370q/f220.item
*
* The text is clearer at Google, but the figure is only readable at Gallica.
* Thanks to Eric Frappa for locating these PDFs!
* Gergonne's paper in Vol.19 (1829)
* This contains his comments on Monge's "wretched" abstract!
* "Plusieurs années avant que M. Biot eût fait paraître son ouvrage
* sur les Réfractions extraordinaires qui ont lieu près de l'horizon ,
* et à l'occasion d'une pitoyable explication du phénomène du Mirage ,
* que j'avais rencontrée dans la Décade philosophique , je m'étais
* déjà occupé de la recherche des lois du mouvement de la lumière
* et de la vision , dans un milieu transparent de densité variable.
* Bien qu'alors le phénomène du mirage fût connu et observé depuis
* long-temps , dans diverses contrées de l'Europe , personne néanmoins,
* n'avait songé à en déduire l'explication mathématique des lois
* connues de l'optique. La route dans laquelle je n'engageais n'était
* donc point encore frayée. Je n'avais jamais eu l'occasion d'observer le
* phénomène que j'entreprenais de soumettre à l'analyse ; il ne m'était
* même connu que par la courte description qu'en avait donné M. Biot ,
* dans ses Elémens d'astronomie ; cependant je fus assez heureux pour
* parvenir à des résultats que l'observation directe , elle-même ,
* n'avait fait apercevoir qu'assez tardivemeni à M. Monge , durant
* son séjour en Egypte , comme on en peut juger par le post-scriptum
* de son Mémoire sur le mirage , inséré d'abord dans la Décade
* égyptienne , et reproduit postérieurement par M. Hachette , dans son
* Programme d'un cours de physique . Le mémoire de Monge parait , au
* surplus , beaucoup moins écrit pour les géomètres que pour les hommes ,
* en très-grand nombre , qui aspirent uniquement à prendre une teinture
* superficielle des causes des phénomènes variés que le spectacle de la
* nature peut offrir à notre observation ; ce mémoire ne m'aurait donc
* pu être d'aucun secours pour mon travail , qui était terminé depuis
* plus d'un an , lorsqu'il me tomba pour la première fois sous la main ."
* Here he actually cites his 1808 paper; then he proposes to treat
* the subject from a completely general point of view. He adopts the
* Newtonian emission theory in much the same form used by Laplace, and
* "derives" the sine law for refraction. Then the equations look just
* like Biot's.
* On p. 278, he applies his general theory to the spherically
* symmetrical case. Other symmetries are also considered. The paper
* ends with a promise to consider mirages in a following paper.
* The reference to "Décade philosophique" is apparently to its abstract
* of Monge's paper in An VII, No.10 (cited by Bravais, 1853). That is
* a 1-page summary on pp. 4 and 5 of that issue, where the meeting of 11
* Fructidor is described. That text is nearly identical to the Ann. Chim.
* abstract.
* This paper is referenced several times in the sequel on mirages
* in vol. 20.
* The signature footers say "1.er mars 1829."
* Gergonne computes the image locations for Biot's simple analytic examples
* (He was the editor and publisher of this series.)
* This paper fills in some of the analytical development that was
* omitted from the 1808 summary.
* Possibility of MULTIPLE DENSITY MAXIMA and PREDICTIONS:
* "Il ne serait même pas impossible que, dans des circonstances
* probablement fort rares, la densité des couches fût alternativement
* croissante et décroissante, de manière à présenter, le long d'une
* même verticale, plusieurs maxima et minima ; or , ce sont toutes
* ces variétés de circonstances, comme nous le verrons bientôt,
* qui donnent naissance à cette multiplicité d'images d'un même
* objet qui constitue proprernent le phénomène du mirage, ainsi qu'à
* beaucoup d'autres phénomènes non moins piquans, dont quelques-uns,
* à la vérité, n'ont point encore été observés, mais que le calcul,
* dévançant ici l'observation, comme en tant d'autres rencontres, ne
* nous montre pas moins comme très-possibles." (p. 2)
* The first few pages reprise in detail some of his mostly unpublished
* 1808 memoir; e.g., on p. 7 here he discusses the ducted ray. On p. 8
* he shows that maxima and minima of the density correspond to points of
* inflection of the ray. He also suggests that the inverse problem can be
* solved: given the path of a ray, find the structure of the medium.
* For example, he shows that his theory can infer a constant density if
* the rays are straight, and a density changing linearly with height if
* the rays are parabolas with vertical axes. (pp. 10-11)
* He then proceeds to consider the location of the image of an object
* point: it is the center of curvature of the ray normals [i.e., the
* wavefronts] at the eye. (p. 16) If the image is behind the observer, the
* rays are converging at the eye. He also considers whether the image is
* erect or inverted (pp. 21-22), and the number of images (p. 23). Finally,
* there is the question of double roots of his equation, corresponding to
* the place where two images meet (p. 24). If the two images are distinct,
* we have the phenomenon of mirage (p. 25).
* Prediction of BIFURCATIONS in the ray diagrams:
* "Les rayons émanés du point lumineux pourront donc ne pas occuper
* en totalité, le plan qui les contient ; ou du moins ils pourront
* ne pas concourir, en même nombre, en tous les points de ce plan ;
* ces rayons pourront donc avoir une ou plusieurs courbes limites ou
* enveloppes communes, lesquelles diviseront le plan qui les contient en
* plusieurs régions, telle qu'en passant d'une région à celle qui lui
* sera consécutive, le nombre des rayons concourant en un même point,
* et par suite, le nombre des images du point rayonnant qui pourront
* être aperçus par un oeil situé en ce point, augmentera ou diminuera
* d'une unité." (p.23)
* He then says these were called "déterminatrices" in his 1808 memoir.
* In elaborating the parabolic ray paths in the atmosphere with a
* linear density gradient, he finds an illustration of Biot's theorem
* about the locations of the ray vertices. (pp. 26-27) In a footnote,
* he points out the analogy between the two ray paths connecting the eye
* with their common source point, and the two elevations of a gun that
* send its projectile to the same target.
* The signature footers say "1.er juillet 1829."
* Google's scan shows that the plate follows p. 36 (but does not show the
* plate itself).
* Everett is preparing for his mirage reviews
* He cites Scoresby's works, and mentions Latham, Vince, Wollaston, and
* Monge's "Annales de Chimie" paper, and Gorsse in the same volume; adding
* papers in Nature in July 28 and Aug. 25, 1870, and Aug. 25, 1872. Then:
* "If any of your readers can inform me os any important contributions to
* the literature of Mirage besides those above mentioned I shall be greatly
* obliged."
* A reader responds to Everett's appeal for references
* More than a dozen good references, including the elusive 1808 memoir
* by Gergonne (though its page digits are transposed) and other obscure
* publications.
* Prof. Joseph David Everett's descriptive lecture (1872)
* This is the run-up to his more technical papers of 1873. The text
* here appears to be exactly the same as its reprint in Nature (1874).
* Here he gives an account of the well-known observations, identifying
* Scoresby's observations of "a mural precipice of great elevation" as
* essentially the same as the "magnificent columns . . . of the Fata Morgana,
* at the Straits of Messina". (p. 28)
* The treatment is all qualitative. He gives Monge credit for "the
* earliest explanation for mirage," but raises the objection that "it
* seems to imply not a curvature, but an angle in the course of the rays,"
* which would require a perfectly sharp transition" in density; "no such
* harsh supposition is necessary." (pp. 30-31)
* He then discusses at some length the distinction between reflection
* and refraction, and introduces "quasi reflection". (p.33) This leads
* into a 3-liquid tabletop demonstration, using alum on the bottom, pure
* water on top, and "Scotch whiskey mixed with enough sugar to make its
* specific gravity intermediate between those of the other two liquids."
* The title page says:
* "Proceedings of the Belfast Natural History and Philosophical Society
* for the Session 1872-73"; the paper is dated November 27th, 1872.
* Everett's technical papers; cf. the Nature (1874) ones.
* He starts by deriving the radius of curvature of the ray in terms of
* the refractive-index gradient along the wave-front. "This proof is due
* to Professor James Thomson, who gave it in a paper to Section A at the
* recent meeting of the British Association at Brighton." (Cf. Thomson's
* 1872 paper in the "HORIZONTAL-RAY PARADOX" file.) From this he obtains
* the harmonic motion of a ray about a plane of maximum refractivity, and
* the resulting focusing property: "It thus appears that . . . every object
* will yield a series of real images, alternately inverted and erect . . . .
* It is of course to be understood that the images are formed in one
* dimension only, like those formed by a cylindrical lens." (p. 165)
* On p. 167, he discusses ray trapping, and the critical angle, between
* regions of constant index joined by a continuous transition region.
* In section VI on that page, he allows the surfaces of constant index
* to be curved, so as to follow the curve of the Earth. Then the rays
* oscillate about the level where the ray curvature matches the Earth's.
* Section VII (p. 169) relates the refractivity to the state variables
* (using the work of Biot & Arago): "Hence, when the diminution of
* temperature per foot of ascent is 1/96 of a degree Centigrade, the
* density of the air is uniform and the rays are straight." He finds
* the ratio of curvatures to be 5.2 at 0° C and 5.6 at 10°. (p. 170)
* Then the curvatures are equal if the temperature increases 1 C in 29.4
* ft., or 1 F in 16.3 ft. "Any portion of the earth with such a state of
* things prevailing over it will appear plane, distant objects being no
* longer hidden by the intervening convexity. A still more rapid increase
* will make the surface of the earth appear concave."
* [Note observation of CONCAVE surface.]
* [The concave appearance is also described by Forel (1895), p. 541.]
* Section VIII takes up looming and mirages. "The inverted images are
* formed by rays incident from below . . . at such an obliquity that . . .
* they cannot get through, but are compelled to descend again, and thus
* undergo a kind of reflection." (p. 171) He attributes multiple images
* to either multiple inversions, or irregularities on a single one,
* rather than multiple "reflections". He attributes the Fata Morgana
* and Scoresby's Greenland mirages to "the vertical magnification of
* real objects." The inferior mirage is attributed to rays concave
* upward "and a quasi reflection," as for the superior mirage.
* Section IX (p. 172): "In the transmission of rays through a medium of
* continuously varying index, no proper distinction can be taken between
* refraction and reflection. They shade insensibly into one another;
* or rather, I should perhaps say, both names are equally inappropriate
* in this application."
* In section X, he comments on the HORIZONTAL-RAY paradox: "The
* mistake of supposing that a ray can pursue a straight course parallel to
* planes of equal index in a continuously varying medium. The contrary
* was pointed out so long ago as 1799 and 1800 by Vince and Wollaston in
* the Philosophical Transactions, but appears to have since dropped out
* of mind."
* No references are cited.
* Available at the HathiTrust site:
*
* https://babel.hathitrust.org/cgi/pt?id=uc1.b3728171;view=1up;seq=188
*
* In the March 1873 issue; the next paper is from the April issue.
* Everett's second paper (April issue)
* Here he extends the work beyond mirages, to gradient-index lenses.
* He begins with cylindrical symmetry (in section XI), and proceeds to
* spherical symmetry, which applies to the atmosphere again:
* "Required the law of index-variation which will cause all circles
* described about the common centre to be paths of rays." Of course,
* this produces the nR = Const. condition. (p. 251)
* After again doing a cylindrical case, he considers plane surfaces
* of constant index, and shows that the rays are circular arcs if the
* index is inversely proportional to distance from a fixed plane. This
* "might have been deduced at once from the undulatory theory without
* any application of analysis. For if μ is inversely as the distance
* from a fixed plane, velocity is directly as this distance . . . . Hence
* the wave-front will swing round the line of intersection like a door
* upon its hinges, and each point in the wave-front will describe a
* circular arc, which will be the path of a ray." (p. 256)
* Various other analytically elegant but physically improbable cases
* are explored in the remainder of the paper, which casts little light
* on mirages.
* Schmidt's clear mirage explanation, with the MINT quote:
* There is a lot of nonsense here in which Schmidt tries to explain
* aberration by the "piling-up" of the luminiferous aether in front of the
* moving Earth. The useful parts are section II ("Die cyklische
* Refraction") and III ("Die Luftspiegelung"). The best part is the
* elegant construction in Fig. 5, p. 10, in which he shows how the
* change in density gradient is responsible for the triple-image mirage.
* He has some penetrating remarks about textbook accounts: Biot's theory
* "ist wegen der Allgemeinheit der Behandlung des Problems mit einem zu
* grossen geometrischen Apparat verbunden, es scheint unmöglich, ohne
* genaue Kenntniss der caustischen Linie in die Geheimnisse der
* Erscheinungen einzudringen. Daher ist diese Theorie nicht gut
* popularisirbar, sie ist eine Barre edlen Metalls, das seit 70 Jahren im
* Gewölbe der Münzstätte ruht, das Niemand in courante Münze umsetzt.
* Die Lehrbücher der Physik, welche sie kennen, wie z. B. Biot's
* Experimentalphysik selbst, berichten wohl die Erscheinungen, verweisen
* aber in Betreff der Erklärung einfach auf obige Abhandlung, und
* diejenigen, welche sie nicht kennen, behelfen sich mit der Erklärung
* durch totale Reflexion. Für die Theorie der mehrfachen Bilder, ihrer
* relativen Annäherung, ihrer Verzerrung ist damit nichts gewonnen, das
* aufrecht Bild über dem umgekehrten soll durch mehrfache Reflexion
* entstehen, das aufrechte Bild eines Schiffes (Fig. 4) z. B. soll das
* Bild des Bildes im Meere sein.
* "Eine populäre Erklärung der Erscheinungen der Luftspiegelung wird
* es sein, wenn man unter Annahme einfacher Verhältnisse einen
* Specialfall schafft, welcher die Erscheinungen, so wie sie gewöhnlich
* sich darstellen, in der Natur und im Experiment, mit möglichst
* elementaren geometrischen Vorstellungen zum Verständniss bringt.
* Diess glaube ich im Folgenden zu leisten." (And he does!) (p. 9)
* On p. 11, he derives the magic number of 1° 23' for the limiting
* extent of mirages.
* He also points out the ease with which the inferior and superior
* mirages can be confused, if only 2 images appear. But (p. 16) he
* thinks that 5-image mirages involve both superior and inferior ones
* simultaneously, and tries to explain the observations of Biot and
* Arago of the signal fire on "Iviza" as seen from Desierto de las
* Palmas.
* Quoting the German translation of Flammarion's book, he comments on
* the frequent reports of images well above the horizon: "Wir müssen
* daran festhalten, dass die Höhe des Bildes über der geraden Luftlinie
* nach dem Gegenstande den Betrag von 1° 23' wohl nie erreichen wird.
* Was darüber hinausgeht, gehört entweder in das Reich der Fabel oder
* ist es nicht mehr die Wirkung der Refraction, sondern die einer
* wirklichen Reflexion." (p. 17)
* In discussing the terrestrial refraction constant, he notes that
* Glaisher's balloon data show a very different lapse rate than that
* required to produce the usual values of refraction, and suggests using
* the optical measurements to determine the lapse rate (p. 20).
* Section V on parabolic refraction compares the two upper images of
* the triple-image mirage to the two ballistic trajectories reaching the
* same target for a given muzzle velocity.
* According to Kleinschmidt's obituary, this was Schmidt's very first
* publication!
* N.B.: cited by Hillers. The mirage model is very similar to that
* proposed by Thomas Young (1807).
* ANTONIO GARBASSO's papers on mirages: 1
* This is the paper discussed by Bemporad in his 1907 paper, where it
* is cited as "Memorie della accademia reale delle Scienze di Torino,
* Anno 1906-1907".
* The title page of the volume says "1908".
* P. 1 says "Approvata nell'adunanza del 2 Dicembre 1906."
* The date at the end of p. 57 is "Ottobre 1906".
* The text ends on p. 57; but the "due Tavole" occupy pp. 58 and 59.
* This is a broad review of mirages; there is an extended abstract,
* outlining the paper, followed by a good review of the observations
* (pp. 4-11), and another review of the theory (pp. 12-18); He calls
* Biot's mirage monograph "the first truly important theoretical work,"
* explicitly passing over Monge. But he seems not to have read through
* Biot's work, and gives the most credit to Tait's.
* Then he turns to "the experiments of Wollaston," and later laboratory
* experiments on diffusion in liquids (pp. 18-21) by Macé de Lépinay and
* Perot, by Wiener, and by Wood.
* Now comes Garbasso's own contribution, beginning with a statement of
* the problem in curvilinear coordinates (Chapter 4). This he applies to
* Wollaston's experiments (Ch. 5, p. 29). He finds (p. 31) that "the
* index of refraction is propagated with the laws found by Fourier in
* the analytical theory of heat." Then the index is described by a Fourier
* series, and the ray path is expressed in elliptic integrals. The
* subsequent numerical results become more complicated and less
* interesting, as Bemporad showed (see below).
* On p. 47, he returns to mirages, beginning with "the mirage of Monge".
* Unfortunately, he is still thinking in terms of diffusion; so he comes
* up with an error function for the refractivity profile. So he tries to
* force the laboratory simulation to fit the geophysical situation.
* ANTONIO GARBASSO's papers on mirages: 2
* This is the paper "presentato al Congresso di Parma della Società
* Italiana di Fisisa." [sic]
* Here, he is more hesitant about real mirages than he was in the
* previous paper, which concluded with the flat assertion that there are two
* kinds of mirages. Now, instead of Pernter's two kinds, we have three:
* "the mirage of Monge" (2 images); "the mirage of Vince", with 3 images;
* and "the mirage of Parnell", with 5 images. [But Kelly (1846) saw
* five images 23 years before Parnell (1869) did.]
* He is even harder on Monge than before: "Monge truly had a very
* rudimentary concept of the matter; he thought of two superimposed and
* sharply separated layers of air, and made a total reflection occur
* at the limiting surface." (p. 412)
* After referring to the principles of Huygens and Fermat, and Lagrange,
* and Hamilton, he criticizes the models of Biot and Tait for "not having
* any experimental basis." (p. 416) So he comes back again to the lab
* model -- i.e., diffusion. "The mirage of Monge can be reproduced with
* this artifice," he says, citing his earlier paper. So it's back to the
* error-function refractivity profile, and Fourier series again. "In
* reality, in suitable conditions, it is experimentally verified that the
* rays are rigorously parabolic." (And he cites his earlier paper.)
* P. 418: He claims the experiment of Wollaston provides a satisfactory
* explanation of the mirage of Vince. On the next page, he cites Rolla's
* simulation as explaining the mirage of Parnell. Then we get arm-waving:
* "In nature, the process comes according to all probability from the
* presence of two layers of air, differing in thermal conditions and
* hygrometric state." (p. 420) But "The analytic theory encounters
* material difficulties . . . ."
* This paper is dated "Settembre 1907"; he cites his first paper as
* "Mem. R. Acc. di Torino, (2), 58, 1906, 1."
* There is a third paper on the wave surface in N.C. 18, 25-32 (1909).
* BEMPORAD's note, criticizing Garbasso's 1906 paper on mirage theory
* Sub-titled: "A proposito della Memoria del Prof. A. Garbasso sul
* MIRAGGIO"
* He starts from the recent papers of Boccara on the Fata Morgana,
* regarded from the point of view of Garbasso's curvilinear theory.
* The equations are numbered as in Garbasso's first paper.
* Here again, Bemp. notes that numerical integration is less work than
* series expansions; cf. his 1907/1913 Encyc. article.
* PDF available at ADS.
* This is the paper Lehn et al. (1978) called "the first adequate analysis";
* I am not so impressed. Nölke was not familiar with the literature of
* atmospheric refraction, or he would not say: "Ist es jemals bemerkt
* worden, daß sich bei der Wüstenspiegelung der Horizont senkte und
* bei der Seespiegelung hob? Hat man beobachtet, daß bei der
* Wüstenspiegelung gelegentlich nur die Kronen der Palmen und unmittelbar
* unter ihnen ihr Spiegelbild erschien? Hat man festgestellt, daß bei der
* Annäherung an das Gegenstand Bild und Spiegelbild immer weiter
* auseinanderwuchsen, bei der Entfernung aber sich von der Basis her
* verkurtzen und schließlich ganz verschwanden? Von derartigen
* Beobachtungen wird nicht berichtet . . . ." [How about Huddart (1796),
* Woltman (1798), Gruber (1798, 1800), Atkinson (1830/31), Kelly (1846), . . . !]
* Likewise, of multiple-image mirages, he says: ". . . so umfassen
* die Bilder nur beschränkte Teile des Gegenstandes. Auf diese
* unvollständigen, vielfachen Bilder scheint man noch nicht aufmerksam
* geworden zu sein . . . ."
* His introductory complaints about the earlier mirage literature are
* well taken -- "Auch die vielfach zur Illustration der Naturerscheinungen
* ausgeführten Versuche, bei denen man durch Übereinanderschichten
* verschiedener Flüssigkeiten die atmosphärischen Verhältnisse
* nachzuahmen sucht, haben keinen grossen Wert, da es sehr Zweifelhaft
* ist, ob die durch Diffusion der Flüssigkeiten sich herausbildenden
* Verhältnisse mit den in der Atmosphäre vorliegenden Ähnlichkeit
* besitzen. . . . Die anschauliche, geometrische Art der Erklärung ist nun
* zwar schon lange, besonders in populären Lehrbüchern der Physik, üblich
* gewesen, aber die Darstellung ist meistens eine sehr oberflächliche,
* nicht selten sogar fehlerhafte." -- but he himself fails to meet these
* objections. His whole treatment is based on Tait's "vertex" approach
* --- which was actually discovered by Biot!
*
* His insistence on the flat-Earth approximation leads him astray from the
* correct explanation of multiple-image mirages, so that he thinks a 5-image
* mirage requires two "refracting layers" (cf. Garbasso, 1907).
*
* Finally, though the paper is entirely based on Tait's method, there is
* no mention of Tait (or Biot!); the only papers cited are those of Hillers.
*
* Despite all these weaknesses, the paper has some unique virtues: "Je
* dünner die lichtbrechende Schicht ist, desto kürzer ist der Weg, den die
* in der Nähe ihrer oberen Grenzfläche umkehrenden Strahlen in derselben
* zurücklegen, desto mehr nähert sich also auch das umgekehrte Bild einem
* einfachen Spiegelbilde" is a good point often overlooked. And "Im
* allgemeinen haben die Bilder nicht dieselbe Entfernung vom Beobachter wie
* der Gegenstand." This IMAGE LOCATION problem tripped up Hofmann (1902).
* Cf. Gergonne (1809, 1829), who also treated the image POSITION.
* (Of course it is more easily treated by lens theory.)
* Odd Haug: Multiple images solved analytically in an elevated duct
* The theory resembles Schmidt's 2-layer model. A modified refractivity
* m = (n-1) + h/R is used to trace rays, so a piecewise-linear profile
* of (n-1) is assumed; obviously, this is a sort of dip-diagram scheme.
* The altitude of the ray is used, instead of Z.D. Both the observer and
* the miraged object are assumed to be in the lower part of the duct,
* below the inversion base. To simplify the problem, both object and
* observer are assumed to be at the same height (cf. Dettwiller, 2019).
* The periodic motion is emphasized, and the period used to locate
* image distances.
* Multiple-image mirages are attributed to multiple reflections in
* the inversion. Despite the analytical results, only qualitative
* comparisons are made with Vince, Scoresby, and Parnell.
* FLAT EARTH ASSUMED (no refs. to P&E nor Wegener)
* SUNSET (sunrise!) SIMULATIONS showing Mock Mirages
* This and the next paper really belong in the "Sunsets --> refraction" file
* THEORY for rapid decrease of influence of structure above eye level
* OMEGA shapes shown over warm water
* Sunsets from satellites (cf. Link's book)
* Quadratic approximation to T(h) required for ray curvature = Earth's.
* This condition gives unit magnification. The treatment is restricted
* to heights of 100 m and altitudes of 15' because "based on long-term
* experience in observing mirages . . . heights above 15 arcmin are
* extremely rare."
* At STP he gets the critical gradient of 0.1127 K/m.
* Explicit theory for linear and quadratic refractivity profiles
* Basically a repeat of Biot's work, 2 centuries later. Useless.
* (not copied)
* My inferior-mirage model
* Luc Dettwiller's analytical treatment
* Makes good use of Biot's transformation of the refraction integral!
* Many instructive results are produced for unrealistically simple models.
* This is restricted to objects at eye height, and so does not apply
* directly to Fata Morgana mirages.
*
* See Everett's comment on this, in his March, 1873, Phil. Mag. paper.
*
* The notice of Bravais's paper on horizontal turning points (see below)
* This is in the account of the Société Philomathique de Paris,
* Séance du 21 mai 1853.
* The remark on Grunert in the last paragraph refers to G.'s 1850 paper
* in the Beiträge reviews (see the Clausius entry here.)
* Symmetry at vertex; "paradox" of ray optics resolved (cf. Raman)
* This is the full paper announced in 1853.
* JAMES THOMSON (elder brother of Sir William Thomson, later Lord Kelvin)
* Shows that the horizontal ray has maximum curvature; nice paper for
* treating the problem both by ray and wave optics.
* RAMAN & PANCHARATNAM
* Much concern about inadequacy of geom.optics -- cf. Bravais (1856)
* and Thomson (1872) who already resolved this paradox a century earlier!
* Rediscovers Gruber's use of a cold breeze to enhance the experimental
* effect.
* Mentions "caustics" but not Biot; has "Hiller" for Hillers.
* A curiously deficient paper in many respects, re-inventing many a wheel.
* RAMAN
* A shorter version of the previous paper
* Bush & Robinson paper on teaching mirages
* This only briefly touches on the horizontal-ray problem; but the next
* two papers dwell on that issue, in commenting on this one. So, it's here.
* Dyson's comment on Bush & Robinson
* ". . . it is important . . . that the students' difficulty with the ray
* picture is due to a lack of understanding of ray theory and not, in this
* instance, to any inadequacy of ray theory itself."
* Sastry's further comment on Bush & Robinson
* Michael Berry's correction of Raman
*
* See similar references in the DIP FILE.
*
*
* Colonel WILLIAM ROY's study in Scotland
* Little mention of refraction here; but Atkinson (1826) made much use of
* these data. Atkinson cites him as "General Roy", but he had only just
* been promoted to Colonel at this time.
* Note that one of the places he measured was Dunsinane-hill. . . .
* Cites and uses many of Bouguer's observations in Peru. See Clarke's
* "Geodesy" (1880) for Cassini de Thury's 1783 role in connecting the French
* meridian to the Survey of England and Wales.
* Available as a 169MB PDF at:
* https://royalsocietypublishing.org/doi/10.1098/rstl.1777.0035
* LE GENTIL's terrestrial refraction observations
* Not much of interest here, as all the objects were fairly nearby. He
* finds more variation over land than over the sand dunes of the coast,
* and mentions earlier observations made by Picard. There is a remark
* about a considerable change in the dip (p. 705).
* The footnote says:
* "Ces Observations ont été lûes à l'Académie Royale des Sciences,
* le 29 Novembre 1775."
* GILBERT's review
* Lots of observations; not much useful
* Brandes bemoans his lack of decent help
* "Meine Absicht war, zugleich durch ein Nivellement die wahre Höhe
* einiger jener Gegenstrände zu bestimmen, um die Grösse der Erhebung
* kennen zu lernen. Aber dieses an sich schon nicht leichte Unternehmen
* wurde dadurch ganz unausführbar, dass es mir an einem nur mässig
* brauchbaren Gehülfen fehlte: Personen, die ein Paar Zolle für etwas
* ganz unbedeutendes halten, und von Viertelzollen als von etwas unendlich
* kleinem sprechen, sind bei solchen Untersuchungen schlechte Helfer."
* The original French version of the Delcros paper
* Here the subtitle is:
* par des observations successives ; comme aussi par leurs correspondantes
* faites à Genève, à Strasbourg, et à Paris, employées simultanément ;
* exécuté en 1813, avec un baromètre de Fortin, pendant le cours d'une
* reconnoissance géodésique; et examen critique des nivellemens
* baromètriques et de ceux qu'on obtient par les distances au zénith.
* Communiqué aux Rédacteurs par Mr. Delcros, capitaine au Corps Royal
* des Ingénieurs-géographes français, Membre de plusiers Sociétés savants,
* (avec fig.)
* The first few pages have the continuation of a very long footnote from
* the previous paper.
* The part written by Delcros ends on p. 177, whereupon the Editors'
* commentary begins. A footnote on p. 178 explains that Broussaud was
* "Chef d'escadron au corps des Ingénieurs-géographes, occupé des travaux
* exécutés sous la direction dû dépôt de la guerre pour rattacher le
* Mont-Blanc à la méridienne de Dunkerque." The editorial addition ends
* on p. 179, where the legend for the Plate appears. The Plate itself is
* at the end of the issue, following p.228. (image 260 of the BHL pdf.)
* Available from the BHL.
* PDF saved to ~/images/PDF/bibliothqueuni07univ.pdf
* Delcros: refraction variations at Mount Jura (English translation)
* "Translated from the Bibliotheque Universelle, vii. 164, for March, 1818."
* The "Bibliothèque universelle des sciences, belles-lettres, et arts"
* was published in Geneva, from 1816. It became Arch. Sci. Genève in 1947.
* Delcros was Captain of the Royal Corps of French Geographical Engineers.
* Little is known about him; but there are numerous letters from both
* "F.J.Delcros" and "J.F.Delcros" to Rudolf Wolf in the "Notizen" of the
* Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich,
* Zweiunddreissigster Jahrgang, 1887. (This was the Wolf of sunspot
* numbers, and also Maurer's thesis adviser.) These letters make very
* interesting reading, and give a picture of the lives of astronomers in
* the middle of the 19th Century.
* That VJS is available from: https://libsysdigi.library.uiuc.edu
* [My copy is filed in ~/images/PDF/vierteljahrsschr32natu.pdf ]
*
* The interesting part for us here is on p. 364:
* "The coefficient of the refraction is a quantity so variable and so
* vague, that I cannot express a sufficient degree of astonishment that a
* constant value is employed for it, applicable in all circumstances and
* seasons. Each mathematician gives his own according to his ideas and
* his experiments. I have also attempted to form one ; and after having
* combined a great number of good zenith distances, I have satisfied myself
* that there is nothing constant in the coefficient but its inconstancy.
* I have seen it vary between 0.06 and 0.21 of the terrestrial arc.
* The different times of the day and the changes of the seasons occasion
* this enormous difference. I believe that sufficient attention has not
* been paid to the influence of the time of day."
* There is a fine Plate illustrating the DIURNAL VARIATIONS in dip of the
* apparent land horizon from early morning to just before sunset, between
* p.364 and 365. The key to its features is on pp.367-368.
* The signature at the end is dated Feb.15, 1818; the observations were
* made in 1813. It is followed by an "Appendix by the Editors of the
* Bibliotheque Universelle" on pp. 366-367, confirming that hypsometry
* is generally more reliable than trigonometric surveys, unless the latter
* use "reciprocal and very numerous observations, made with excellent
* instruments and by very skilful persons, with all the conveniences and
* all the time requisite for such operations."
* The Annals of Philosophy was a short-lived technical journal that was
* merged into Phil. Mag. in 1827 -- see its Wikipedia entry.
* This is Article V., with an excessively long subtitle, concluding:
* "With a Critical Comparison of the Barometrical Measurements with those
* obtained by Zenith Distances." [These long subtitles seem to be the
* seeds of Abstracts, which became common later.]
* Available from BHL and archive.org
* FILED at ~/images/PDF/annalsofphilosop12phil.pdf
* BIOT's monograph on terrestrial refraction
* Contains some astute remarks on DIP at the end (pp. 70-??):
* "Toutefois, on ne peut se dissimuler qu'il est très difficile de
* déterminer la température propre et réelle de l'air en contact avec
* la surface de la mer . . . ." (p. 75)
* My copy is missing pp. 78-79.
* Paul Michel HOSSARD's DIURNAL VARIATIONS in summer, 1844
* The figure on p. 455 shows a very abrupt change in the refraction at
* dawn. The line of sight was just a few meters above the ground.
* Published by Maulde & Renou, Paris (Dec. 1853)
* Col. Walker's detailed measurements of terrestrial refraction at 2 heights
* A brief treatment is in Chapter IV, "The Measurement of the Angles",
* sections 3 and (especially) 5. The details are in Appendix No. 3,
* "On Observations of Terrestrial Refraction at certain stations situated
* on the plains of the Punjab," by Colonel Walker.
* NOTE: the Appendices begin anew at p. 1, following the 426 pages of
* main text. So App. 3 (dated 5th October 1874) starts on p. 77 of the
* Appendices.
* "Probably all observers, who are familiar with the phenomena of
* refraction over heated plains, will readily recall instances in which
* a distant signal, seen standing well above the ground while the sun was
* behind a belt of clouds, has suddenly sunk down to the ground when the
* clouds passed away and the sun shone out fiercely." (App. p. 91)
* HARTL -- temperature gradient "most important"
* Heinrich Hartl, k.k. Hauptmann im Militär-geographischen Institute
* ``Auf Grund der . . . rein empirischen, von keiner Hypothese beeinflussten
* Untersuchungen glaube ich zu dem Ausspruche berechtigt zu sein: Die
* Temperaturabnahme mit der Höhe ist der w e s e n t l i c h s t e
* Factor in der täglichen und jährlichen Periode der terrestrischen
* Refraktion, die anderen meteorologischen Elemente sind nur von
* sekundärem Einflusse.'' (p.134)
* (actually, all in italics from colon to comma, not just "wesentlichste".)
* OBSERVATIONS of refraction at the seashore
* Audouard was concerned with the applicability of military rangefinders
* in seacoast positions. He begins with a summary of Biot's work, and
* includes as one of Biot's conclusions that "Lorsque la mer est plus
* chaude que l'air, la densité des couches atmosphériques va en
* augmentant de bas en haut jusqu'à une certaine hauteur à partir de
* laquelle elle va en décroissant normalement. . . . Le point d'inflexion
* est vers 8 or 10 mètres au-dessus de la mer." [An early determination
* of the Obukhov length!] (p. 213)
* He makes extensive observations, hoping to show that rangefinders are
* useful despite the peculiar refraction at the shore. One result is that
* "Il semble . . . que la réfraction est un peu plus forte lorsque la surface
* de la mer est nette, c'est-à-dire débarrassée de cette légère brume
* qui la recouvre souvent, même par un beau temps." (p. 225)
* The refraction is found to be larger than over land, which he
* attributes to the colder water.
* This paper is an ANNEXE to the main publication.
* Summary of HEINRICH DENZLER's remarkable unpublished 1843 treatise
* Much emphasis on the importance of the vertical temperature gradient
* J. de GRAAFF HUNTER's varied effort
* Definitely a mixed bag; but it contains several interesting items:
*
* Chapter IV (pp. 65ff.) deals with diurnal changes in refraction.
*
* Chapter V (p. 80) is an attempt to use astronomical refraction to
* determine terrestrial refraction -- the reverse of Faye's folly, but
* subject to similar criticisms. He proposes using 4 stars at different
* altitudes to find the necessary adjustable constants, apparently not
* realizing that there is no information at altitudes above 10 degrees.
* Of course it all depends on the atmosphere being representable by a
* low-degree polynomial and series expansions.
*
* The magic Z.D. of 88° 38' appears on p. 86.
*
* Allowing for his use of μ instead of n for refractive index, we
* see our old friends nR and [R(dn/dR) + n] on p.88; he sets x = nR,
* and then does the path-length integral with x as independent variable.
*
* Notice his comment that "In India the pole star is often hard to
* discern at latitudes not lower than . . . 13° and it is probable that
* these equations will not have a chance of application for [Z.D.] greater
* than 85°." (p.92)
*
* The best part is his derivation of the correct DIP formula (p. 99),
* with the realization that the WAVES cut off the line of sight; but he
* just misses seeing that there is a Kimmfläche (p. 100). He does
* consider the super-refracting case, and says that "For more rapid
* increase of temperature the sea surface will appear concave and there
* will be no true horizon." [This wording appears to have been lifted
* from Professor Everett's 1873 paper in Phil. Mag.]
* Again (p. 110): "I think the term horizon in this case has no
* strict meaning. With the ray of light of greater curvature than that
* of the earth it would be possible to see all round the earth where there
* were no obstacles above sea-level, were it not for absorption of light.
* This limitation would not give a sharp horizon."
* [Note observation of CONCAVE surface.]
* He does catch a flaw in Chauvenet's argument (p. 99).
*
* He repeatedly notes the effects of the waves at sea: ". . . we must
* remember that we see only the crests of the waves at the horizon.
* Accordingly we are concerned with the difference of level of the points
* of observations and the crests of the waves, not of the mean
* water-level.
* ". . . r is the radius of the sea-level surface or, more strictly, of
* the sphere which envelops the crests of the waves, and h is the height
* of the point of observation above this sphere." (p.97)
* "Now the ray of light to the horizon is obviously tangential to the
* water at the horizon. (p. 97)
* "In my opinion the temperatures which affect the problem are the
* temperature at the height of the eye and that at the level of the crests
* of the waves: and the difference of height of the eye and wave crests is
* the other quantity concerned." (p. 111)
*
* On p. 102, he refers to "the fact that refraction in a horizontal
* plane is in general so small as to be scarcely measurable." He also
* associates the afternoon minimum refraction with the adiabatic lapse
* rate: "The rate . . . can hardly be exceeded, except momentarily, for
* convection must be set up if it is; and this adjusts the gradient. The
* adiabatic gradient is found then to give a natural minumum refraction."
*
* There is a tantalizing reference to General Walker's observations of
* "other curious effects" (p. 105) -- presumably, mirages.
* Regarding temperature corrections for dip, he quotes Raper's 10th ed.
* (1870); and cites "Navigation" in 10th ed. E.B. as saying "The effect
* of refraction in displacing the apparent sea horizon was partially
* investigated by the French about a century ago," leading to the temp.
* effects, as mentioned by Raper.
*
* The author is listed as ``Mathematical adviser to the Survey of India.''
* According to Bomford's obituary of him, this was his second position
* after serving as Lord Kelvin's assistant; and this was his first
* major publication. He was John Eccles's successor there. Bomford
* (1967) says the results here "cannot yet be bettered."
* DIURNAL & ANNUAL VARIATIONS in TERRESTRIAL REFRACTION
* followup to Wegener
* Systematic errors due to drift of refraction with time;
* contains useful data on the run of temperature gradient with time of day
* Summary of COLE's paper, with comments:
* ". . . it might be profitable to set up telescopes with the object of
* measuring the variation of the lapse-rate near the ground as part of the
* routine of a meteorological observatory." [cf. McAdie's remarks on Fisher!]
* "The difficulty in direct measurement of air temperatures is so great that
* an indirect method would be of great service."
* A peculiar exchange; apparently Mallock independently "discovers"
* terrestrial refraction, but insists it has a particular value.
* J. de Graaff Hunter then tries to educate him, but Mallock won't listen.
* A surveyor points out that Mallock's value is rather larger than is
* employed in surveying -- but I suppose this is because the surveyors
* choose to work when the atmosphere is convective and so less refracting
* than for the Std. models.
* Mallock nit-picks at minor points while ignoring the main thrust of his
* critic.
* Ball and Baker enter the fray:
* Ball introduces the factor of 2 . . .
* Baker's first letter, mentioning DIP and DISTANCE to HORIZON
* . . . while Baker complains the ray is not a circular arc, because
* "The temperature-gradients in the first 30 ft. (the average height of
* the bridge of a ship above the sea) are very frequently greater than any
* of the gradients mentioned above, and show wide variations in that space."
* "Measurements made by Blish off the coast of California showed that a
* zero dip is quite possible. In the Red Sea the sea horizon is often
* refracted above the true horizontal." But he thinks the ray is actually
* tangent to the surface in such cases, as Lutz Hasse has not yet invented
* the concept of the Kimmfläche.
* [Note observation of CONCAVE surface.]
* Baker's second letter
* Reduces Ball's claim of difference in refraction for plane and spherical
* waves to an absurdity.
* Cites Herman's "Geometrical Optics", p.305; and Heath, "Geom.Optics",
* p.329, for the relation involving the perpendicular to the ray.
* ". . . we can only admit uniform curvature [of the ray] if we are prepared
* to admit that the density of the air in its lowest levels is a linear
* function of the height. To such an admission I take the strongest
* exception. It is quite insufficient to account for a refraction of the
* visible sea horizon above the true horizontal -- a phenomenon which, as
* every seaman knows, is by no means uncommon."
* [Note observation of CONCAVE surface.]
* John BALL finally sees where the problem lies:
* "It is only under isothermal conditions, such as seldom or never occur
* in practice, that Mr. Mallock's result can be even approximately true;
* it was evidently incorrect to consider, as Mr. Mallock did in his reply to
* Dr. Hunter, that temperature effects could produce merely a difference in
* the result of 1 or 2 per cent. per 1000 ft. The mistake of assigning an
* insignificant part to temperature considerations is one which is very
* easily fallen into by anyone who first considers the isothermal condition
* with its accompanying relation between density and pressure, because of
* the small effect which the existence of a temperature gradient has on the
* rate of decrement of pressure as distinguished from density."
* Hunter has another go at Mallock, pointing out that his model "is
* incorrect as regards the density and refractivity gradients, except in the
* special case when the temperature gradient is zero."
* Baker responds to Hunter
* Now Baker attacks Hunter's formula for dip (much discussion of rays with
* zero dip -- i.e., rays that remain in a level surface):
* "The fact is that in an atmosphere where the layers of uniform
* refractive index are spheres concentric with the earth, the dip can
* only be zero, if at all, at one height. Below that height the dip
* will be positive with a maximum value at some lower level; above that
* height no ray tangential to the earth's surface can be seen at all,
* and the depression or elevation of the sea horizon requires an entirely
* different explanation."
*
* ". . . in such a case a ray once horizontal would remain horizontal for a
* complete circuit of the Earth."
* Of course by now Kummer's 1860 paper is long forgotten!
* LAPSE RATE and REFRACTION
* LAPSE RATE and REFRACTION
* Brocks's early review, citing Brandes (1804)
* Shows that temp. gradient is far more important than T itself.
* (cf. Kurzyńska)
* followup to EMDEN
* "Es ist eine bekannte aerologische Erfahrung, dass die Lufttemperatur
* ausserhalb der bodennahen Störungsschicht sich im allgemeinen in der
* Weise mit der Höhe ändert, dass der vertikale Temperaturgradient in
* mehr oder weniger ausgedehnten Höhenbereichen annähernd konstant ist
* und sich nur an den Schichtgrenzen unstetig ändert."
* [Actually, more like an assumption than an experimental fact.]
* "Hierbei bewirkt der Beobachtungsfehler des vertikalen
* Temperaturgradienten mehr als 90% der Fehlerquadratsumme. . . " (p.202)
* CONDITION FOR CIRCULAR ARCS:
* "Für γ = 1.71° /100 m ist der lokale Refraktionskoeffizient
* mit der Höhe konstant, d.h. die Lichtstrahlen sind kreisbogenförmig."
* (p.203) -- so in general, the curvature is greatest in the lowest parts.
* Robert G. Fleagle cites Brocks, and Johnson & Roberts
* See also Freiesleben, 1950 & 1951
* J. de Graaff-Hunter again
* Notable for section 5 (pp.12-15), which discusses refraction, and
* concludes that "There is scope for fuller inquiry into the refraction
* question."
* J. de Graaff-Hunter once again
* Notable for the historical discussion of refraction corrections in geodesy.
* E.g.: ". . . diurnal variation of refraction . . . had been well known
* to Colonel Everest . . . , for in his reconnaissance for the Great Arc of
* triangulation at the crossing of the featureless plains north of Agra
* he was making use of maximum refraction . . . : 'The extent of view at
* time of maximum refraction; this varies from midnight to sunrise and
* is generally about 3 o'clock . . . .' (p. 21). And:
* ". . . General J. T. Walker was investigating refraction in the Punjab
* plains where extreme and even negative refraction was encountered --
* diurnal variation of refraction of the kind that makes the observer feel
* as though in a saucer at dawn, later on seeing objects sinking below
* the horizon as receding ships at sea!" (p. 22)
* [Note observation of CONCAVE surface.]
* The SURVEY OF INDIA records cited in proof by de Graaff-Hunter (1955)
* The passage excerpted by de Graaff-Hunter is on p. 23. Other good quotes:
* P. 41: "The marvels . . . of refraction which were experienced by Captain
* Waugh . . . were of a similar kind to those of which I have before spoken
* . . . , but of a still more astounding extent. . . . Instances [included] . . .
* two stations 20 miles and upwards asunder, the observed vertical angle
* and its reciprocal were both elevations at the same instant." [Everest]
* On p. 93, Phillimore says that Everest tried to obtain simultaneous
* observations of vertical angles from both ends of each arc. "He did
* not insist on observation at the hours of minimum refraction when --
* with his long rays -- signals were often below the line of sight."
* [He means, below the horizon.] Everest continues:
* ". . . vertical angles . . . have been observed at all hours of the day,
* generally, however, in the morning. . . . I have not been able to infer
* that the elevations and depressions of distant stations were affected
* in any certain way by the change of temperature at different hours."
* Everest was evidently aware, however, that there is a regular diurnal
* variation in refraction; he recommended measuring from opposite ends
* of the same arc at the same time of day, when only one observer was
* available. He says: "About 3 or 4 in the afternoon is generally . . . the
* instant of minimum, and the same hour after midnight . . . that of maximum.
* In certain conditions the difference is immense."
* The main discussion of refraction is on pp. 105 - 107. It begins with
* Phillimore's remark about "the vagaries of terrestrial refraction,
* whereby a distant point which is entirely out of sight during the day
* may become clearly visible after dark, provided there is a lamp or fire
* to mark its position." Here are some of Everest's comments:
* ". . . the disk of the Godhna heliotrope made its appearance very late
* on the evening of the 25th November. It was then obviously rising very
* rapidly. . . . When seen it was at a depression of between 7 and 8 minutes,
* and had probably risen 2 minutes, thus standing at the time of minimum
* refraction at a depression of 10 minutes.
* "At 3 hours 55 minutes after midnight on the 25th November the Godhna
* lamp stood at an elevation of 2' 55'', and on the 27th November at the
* same hour, at a depression of 18'', thus shewing a discrepancy . . . of 13
* minutes or more between the after noon and after midnight refraction,
* and an uncertainty . . . of 3' 13'' . . . at the same hour. . . . The vast
* difference . . . between observations made at the same hour without any
* visible cause baffles all computation."
* P. 106: "At Nojhili on the 27th November 1835, at 8 a.m., the
* phenomenon was first noted of the heliotrope assuming the columnar form,
* in which that of Dahera shewed itself tall, slim, and erect. The same . . .
* has since occurred so frequently as to have become a matter of common
* notoriety. . . ." [cf. Biot & Arago (1810); Hodges (1953)! ]
* "Between 3 and 4 p.m. is the hour of minimum, and the same hour after
* midnight is the period of maximum refraction."
* "In some instances in the month of January the image of the distant
* heliotrope had its periodic hour of rising before sunset, but was never
* seen at any other hour of the day. In the months of March and April,
* however, the heliotropes at sunrise, and for sometimes an hour after,
* were seen projected high up on the sky, and frequently in the form of
* a tall column.
* "The afternoon rise of the distant heliotrope is curious and
* beautiful. The first rays spread themselves like a running fire along
* the surface of the obstructing land, . . . the light then descends and
* re-ascends, till after a few oscillations it ultimately rises into a
* clear round disk, and remains visible till the rays of the sun become
* too feeble for reflection.
* [p. 107] "The descent in the morning is equally remarkable.
* In favorable weather the round disk appears immediately subsequent to
* sunrise, projected high up in the sky, and after . . . a short time it
* gradually descends . . . or . . . suddenly vanishes as if by an explosion."
* [This would be the disappearance in the inferior mirage at the surface.]
* Later, Everest says: "Every observation is made . . . through a medium
* of very uncertain consistency and variable temperature. . . . The smoke
* and vapours which are perpetually rising from the earth have palpably
* not an uniform density at a given height above the surface. . . ."
* [What a Ptolemaic remark!]
* "The state of the atmosphere immediately after sunrise . . . is rarely
* to be depended on; . . . the disk of the heliotrope then often shows small
* and round . . . near the horizon, like a candle shining dimly through a
* hole in a curtain, but, even whilst the observer is . . . intersecting this
* object, another image exactly similar to it rises to the right or left,
* above or below, after which the first disappears, . . . ."
* cites a few references; comments on the range-finder method of
* Fleagle (1956) and IMAGE POSITION.
* Unfortunately, they assume an incorrect (exponential!) analytic form for
* the refractivity profile; so the results are only qualitative.
* Cites the 1966 note by Aggarwal and Kaw for the image position idea.
* [Cf. Gergonne (1809, 1829) and Nölke (1917).]
* correction to their earlier note
* cites a few references; comments on the range-finder method of
* Fleagle (1956)
* Many REFS to literature; 12 to methods for extracting Tgrad data.
* Full title: Archives of Meteorology, Geophysics and Bioclimatology
* This journal became "Meteorology and Atmospheric Physics" in 1986.
* IR mirages; examples shown; multiple horizon inside surface duct
* from elevated inversion.
* Steve Church, Arete Associates, P.O.Box 6024,Sherman Oaks, CA 91413
* church@arete.com (another reprint in the mirage file)
* TEMPERATURE PROFILES (and refraction) FILE
*
* See also ABBE (1886) in TILT file.
*
*
* HUGO GYLDÉN's 1866 paper on refraction and atmospheric structure.
*
* Two different copies have been scanned and are available on the Web:
*
* The Google scan at
* https://babel.hathitrust.org/cgi/pt?id=umn.31951d00011877d;view=1up;seq=9
* lacks OCR text. A better scan at
* https://www.biodiversitylibrary.org/item/112869#page/7/mode/1up
* has generally good OCR text, but some of the text on the first page
* is missing. (It's the Harvard scan from the MCZ copy.)
*
* The text begins on image 15 of the Harvard scan (p.1 of the paper).
* some of its content is not OCR'd properly. (Later pages are largely OK.)
*
* He begins by considering the atmospheric structure. His word for the
* lapse rate is "Temperaturabnahme". Already on p. 2 he says that
* "Untersuchungen, in wiefern merkliche Veränderungen in der
* Temperaturabnahme mit veränderter geographischer Lage des Punktes, von
* welchem an dieselbe gerechnet wird, hervorgehen, nicht unwichtig sein."
* Then he considers time variations: the daily and annual periodic ones,
* which can be inferred from "aeronautic expeditions". But the short
* duration of these flights makes it difficult to distinguish the regular
* variations from "accidental" ones, such as "discontinuities"; of which,
* Gyldén says:
* "Einige bei den Luftfahrten gemachte Wahrneh-
* mungen deuten darauf hin, dass in einiger Entfernung
* von der Erdoberfläche die Wärmeabnahme plötzlich klei-
* ner wird, und sodann wieder rascher vor sich geht.
* Diese Erscheinung ist indessen noch nicht sicher genug
* festgestellt, um berücksichtigt werden zu können."
* (footnote on p. 4)
* or:
* Some observations made in flight indicate that the lapse rate suddenly
* decreases at some distance from the surface, and then increases faster
* again. However, this phenomenon is not yet certain enough to be considered.
* (This seems to be an early hint of the ubiquitous "sheets and layers".)
* He continues: 'If these circumstances exert an appreciable influence
* on the refraction . . . , the mean refraction would not depend on the
* zenith distance alone.'
*
* On pp.5 and 6, he comes to the heart of the matter:
* "Die jetzt allgemein gebrauchten Refractionstafeln von Bessel beruhen
* auf einer Voraussetzung über die Temperaturabnahme, welche bekanntlich
* den Thatsachen sehr ungenügend entspricht. Die von ihm angenommene
* Wärmeabnahrae ist nehmlich eine viel geringere, als die wirklich
* stattfindende mittlere Temperaturabnahme, und dem entsprechend sind die
* Refractionen, wie sie aus seinen Tafeln berechnet werden, für grosse
* Zenithdistanzen zu gross. Die Gründe, welche Bessel bewogen hatten,
* dieses falsche Temperaturgesetz anzuwenden, können wir aus seinem
* lehrreichen Aufsatze «Einige Resultate aus Bradleys Beobachtungen»1)
* ersehen. Bradley hatte nehmlich einige sehr tief stehende Sterne
* beobachtet, und die aus diesen Beobachtungen gefolgerten Refractionen
* wollte Bessel durch seine Theorie darstellen. Die fraglichen
* Beobachtungen waren aber meistens bei Nacht und im Winter angestellt,
* wesshalb die aus ihnen folgenden Refractionen grösser ausfallen mussten,
* als diejenigen, welche man unter Berücksichtigung der Veränderlichkeit
* der Temperaturabnahme mit der Zeit erhalten haben würde. Um nun diese
* grossen Refractionen darstellen zu können, wählte Bessel diejenige
* Hypothese, welche auch jetzt nach ihm benannt wird, und welche, wie er
* selbst zugab, nicht die Temperaturabnahme an der Erdoberfläche darstellt."
* (The footnote cites "Königsberger Archiv für Naturwissenschaften und
* Mathematik. I. Bd." as Bessel's instructive treatise.)
* So his aim was to find a realistic temperature profile that would
* reproduce observed refractions. Of course, this is easy to do; as Ivory
* had found; there are lots of profiles that work well in the region of
* small and moderate Z.D. Today we know that where the ray is so nearly
* straight that the local ZD hardly depends on atmospheric structure, the
* refraction depends almost entirely on the refractivity at the observer.
* The matter is quite different near the horizon. Gyldén struggled to
* produce analytical results for the horizon region, but did manage to get
* approximations for the horizon itself, using all the standard calculus
* tricks (series expansions, integration by parts, partial fractions, etc.)
* Having read Ivory's papers, he was aware of convergence problems; the term
* "halb-convergirende Reihe" is on p. 46. Kramp is mentioned on pp. 57 ff.
* Hypergeometric series, p.61,63.
*
* The concluding paragraph on p. 80 is:
* "Eine Vergleichung der Tafeln mit den beobachteten Refractionen wird
* hier nicht gegeben, da eine solche mit den aus Argelander's Beobachtungen
* gefolgerten Mittelwerthen in den Tab. Reg. ohne Weiteres auszuführen ist,
* hauptsächlich aber, weil eine von Herrn Abbe in Pulkowa, eigens zu
* diesem Zwecke angestellte Beobachtungsreihe, welche sicherlich einen
* sehr werthvollen Beitrag zu unseren Kenntnissen der Refractionen in
* grossen Zenithdistanzen liefern wird, noch nicht geschlossen ist."
*
* In English, this says:
*
* "A comparison of the tables with the observed refractions is not given
* here, since such a comparison can easily be carried out using the mean
* values deduced from Argelander's observations in the Tab. Reg., but
* mainly because a series of observations made by Mr. Abbe in Pulkovo
* specifically for this purpose, which will certainly make a very valuable
* contribution to our knowledge of refractions at large zenith distances,
* has not yet been completed."
* But Abbe's observations were never published.
*
* NOTE: Gyldén's paper was presented to the Academie on 20. April 1865,
* and has a cover page dated 1866; it is written in German. and was printed
* by Buchdruckerei der Kaiserlichen Akademie der Wissenschaften, although
* Gyldén's German pages have a signature footer that says "Mémoires de
* la Acad. Imp. des Sciences, VIIme Série".
* The volume as a whole is dated 1867, as the other numbers in it were
* set in type later. Some of them are in German, some in French, and
* some in Latin. Most are medical, botanical, or biological.
* lowest 300 m, including details of lowest 50 cm for INFERIOR MIRAGES
* review article
* KARL BROCKS
* Mostly a theoretical discussion of inverting measured terrestrial
* refractions; but he has tried it at the mouths of the Elbe (!) and
* recommends symmetrical targets rather than the corners of towers and
* other objects. He allows for targets at a different height from the
* observer, and finds that the method is so sensitive to height errors
* that precision levelling is necessary. A tripod is not stable enough
* as a theodolite support; he used stone pillars in the mountains, and
* concrete or stone parapets at the North Sea. The theodolite must be
* protected from solar heating.
* The results of the actual measurements will be published elsewhere.
* BOMFORD: GEODESY (3rd edition, 1971)
* TEMPERATURE PROFILE OVER WATER: pp.63-66.
* His treatment of refraction is vastly better than in the first (1952)
* edition. Here it is on pp. 300 and 301, where he quotes from (but does
* not cite) Bessel's error table from the 1823 A.N. discussion (col. 385),
* and mentions the tilt effect.
* GOSSARD et al. (1985) on fine structure at the Boulder 300m tower
* Note: they use "sheets" for the stable inversions, and "layers"
* sometimes for the convectively unstable (nearly or super-adiabatic)
* regions of high turbulence between the "sheets". Also, their examples all
* have very slow winds (< 2 or 3 m/s; see Figs. 4-6 and 9), and weak shear.
* ". . . such observations have not been reported . . . because the
* temperature and humidity sensors used in radiosondes have had inadequate
* response for the usual rates of ascent of balloons . . . ." [p. 2156]
* There is also discussion of "over-the-horizon" (i.e., concave apparent
* surface) radio propagation.
* Figs. 8-10 show very steep elevated inversions (typically 5°C in 5 m) at
* heights on the order of 100m. These would cause very strong superior
* mirages. Cf. Fig. 5 (p.2162).
* There is some insteresting discussion on p.2168:
* "The observations show that active wave development occurs when the
* macroscopic Richardson Number is large and that mechanical turbulence
* is weak and dying under these conditions. Wave development and breaking
* then creates a turbulent zone of convective mixing. As the cooler air
* above mixes with the warm air below, the superadiabatic lapse rate is
* erased and is eventually replaced by a slightly stable turbulent zone of
* downward heat flux entraining warmer air from the zone above into its
* upper boundary (and entraining cooler air at its lower boundary). . . .
* Both the entrainment process and the pattern of heat convergence and
* divergence, shown by the solid arrows, tend to sharpen the gradients
* within the bounding sheets."
* The most interesting Conclusions are:
* 1) Thermally stable elevated atmospheric layers are
* commonly made up of thin transition zones of very
* high gradients of wind, humidity and temperature.
* 4) The profiles sometimes adjust to nearly evenly
* spaced layers that persist over long periods.
* [NOTE: these multiple layers were discussed by Tait (1883).]
* In Conclusion 5, they argue that "Simple and quite general reasoning
* leads to a ratio of sheet-to-layer thickness" that is the ratio of
* critical Richardson numbers for starting and stopping turbulence --
* i.e., about 4. [Cf. van de Wiel et al. (2012); Grachev et al. (2013);
* Lan et al. (2018); Srivastava & Sharan (2019).] For a more recent look
* at "sheet & layer" structure, see Doddi et al (2022) in the BLMrefs.
* Most of the figures are replays of their 1984 paper in Radio Sci.
* RADIATIVE effects
* The first sentence of the Introduction is:
* "The structure of the stable nocturnal boundary layer (NBL) is not well
* known." He finds that radiative exchange tends to smooth the profiles
* in the lowest few meters, as well as pulling the lowest layers closer
* to the surface temperature. "When the surface winds fall below about
* 1 - 1.5 m/sec . . . the Monin-Obukhov theory should be revised to include
* radiative effects." [Abstract] For moderate winds (6 m/s at the
* geostrophic level) the "simulated potential-temperature profiles are
* fairly logarithmic in z in the lowest 5 - 10 m down to the ground." (p.155)
* "An alternative analytic representation for the near-surface NBL
* temperature profile is that the temperature deficit between the surface
* and 2 m decays exponentially upwards with a scale height of about 1 m."
* (p. 159)
* Christian Hirt et al. introduce the method of multiple total stations
* Measurements are expressed in terms of the ratio k of ray curvature
* to Earth curvature "around 1.8 m above the grass surface".
* "For mostly sunny days, we found wave-like and sawtooth-like
* fluctuations of the refraction coefficient with amplitudes of 1--1.5 at
* time scales of 10--30 min. On cloudy days, the amplitudes of fluctuations
* were on the order of 0.5. Our refraction experiments show a variation
* range of k between -4 and +16 near the ground on sunny summer days. This
* equates to vertical temperature gradients between -0.5 and -0.1 K/m
* during the day and 1--2 K/m shortly after sunset. Cloud cover reduces
* the variability of k to a range of -2 to +5. Our results show that the
* frequently used Gaussian refraction coefficient of +0.13 is not suited
* for describing refraction effects in the lower atmosphere." (Abstract)
* NOTE: Their terminoogy is far from the usual meteorological usage:
* "We follow a frequently used model concept that subdivides the
* atmosphere into three different regions, i.e., the higher, intermediate,
* and lower atmosphere [Brocks, 1948; Wunderlich, 1985]. (p. 2)
* "For the higher atmosphere, some 100 m above the ground and higher,
* the vertical temperature gradient is fairly independent of the temperature
* of Earth's surface. The vertical temperature gradient ∂T/∂z is about
* -0.006 K/m, . . . " (p. 3)
* "The intermediate atmosphere, about 20--30 m to some 100 m [cf. Webb,
* 1984; Wunderlich, 1985], is weakly influenced by the temperature of the
* surface and characterized by temperature gradients frequently of about
* -0.01 K/m, [cf. Bomford, 1980]. This gradient equates to a refraction
* coefficient of +0.15. Also, the Gaussian refraction coefficient of
* +0.13 refers to the intermediate atmosphere and is appropriate for dry
* adiabatic conditions."
* "In contrast to the higher and intermediate atmosphere, the thermal
* characteristics of the air strata of the lower atmosphere (lowest
* 20--30 m) are strongly subjected to the varying thermal properties of
* the surface [e.g., Angus-Leppan, 1969]."
* There are extensive references to older measurements in the geodetic
* literature, and subsections devoted to refraction below 3 m, below 1 m,
* and refraction over ice and water. (But no mention of the 19th-Century
* and earlier works.)
* Figs. 5 and 7 show time-plots of k that include an abrupt peak at
* sunset on sunny days. But there are no wind data, so it's not possible
* to do a MOST analysis.
* [Cites my 2006 tutorial, but also the unreliable Thomas & Joseph paper
* (1996).]
* DOI: doi:10.1029/2010JD014067
* Stephen C. McCluskey's 2018 paper, citing Bomford (among many others)
* Nice distinction of astronomical, terrestrial, and "archaeoastronomical"
* refractions. As in Marcel Tschudin's 2019 paper, he emphasizes the
* rapid changes in the effects of atmospheric structure close to the
* horizon; these changes explain the discrepancies between the repeatable
* observations at elevated foresights and the wildly varying observations
* at a sea horizon. (Cf. Kayser, 1877)
* Layer/Sheet structures studied with new technology
* (See the 2018 paper by Balsley et al. in "capping" for an earlier report.)
* Intensive campaign at Dugway Proving Ground in 2017, using drones and
* fast-response 5-micron Pt wires. The Intro. says:
* "Under stable conditions, the vertical structure of the atmosphere is
* characterized by thin, strongly stable non-turbulent “sheets” separated
* by thicker, less stable, and often weakly turbulent “layers”. . . ."
* Preliminary results (p. 4032): "Following the criterion described
* by Muschinski and Wode (1998) and Dalaudier et al. (1994), temperature
* gradients on the order of 17Γ (Γ --- adiabatic lapse rate) were used
* to identify the edges of stable sheets. A total of 58 individual stable
* sheet structures roughly 25 to 50 m thick were identified from the DH2
* measurements in this campaign. Stability ducts, consisting of large
* N2 sheets constraining weakly stable and weakly turbulent layers as
* deep as 400 m, were also prevalent (see ε in Figs. 11 and 13). Such
* structures, often persisting up to 5 h under very stable conditions,
* were commonly observed near the peak altitude of Granite Mountain (850
* to 900 m a.g.l.). . . . Temperature gradients as steep as 0.18 K m(-1)
* or ~ 18Γ (with tropospheric dry adiabatic lapse rate Γ ~ 9.8 × 10(-3)
* K m(-1) ) were typically observed across most sheets." [These would
* produce super-refraction and superior mirages.]
* PAIRED INVERSIONS: They continue: "A shallow nocturnal boundary layer
* (200 m deep), with recurring sheet activity at the mountaintop (850 m)
* and higher aloft (1450-1600 m) separated by deep, intermittent
* turbulent layers (600-800 m deep), was the general theme underlying the
* observations at FS1. Escalation of shear at altitudes coincidental with
* the undulating sheet pairs may be responsible for their recurring decay,
* providing intermittent forcing for the turbulence inside the layers."
* And the Conclusion begins:
* "Sheet and layer (S&L) structures appear to be ubiquitous in the
* nocturnal boundary layer under relatively quiescent conditions, often
* extend to higher altitudes in the lower troposphere, and have parallels
* extending to much higher altitudes at larger spatial scales."
* Abhiram Doddi, Dale Lawrence, David Fritts, Ling Wang, Thomas Lund,
* William Brown, Dragan Zajic, Lakshmi Kantha
* PDF: amt-15-4023-2022.pdf downloaded; mv to Doddiet al amt-15-4023-2022.pdf
* DOI: https://doi.org/10.5194/amt-15-4023-2022
* Nice pedagogical use of ray curvature, lapse rate, etc. by Sergio Giudici
* DOI: https://doi.org/10.1088/1361-6404/ac6d29
* "At Greenwich the polar axes of the photographic equatorials have been
* adjusted so that when the instrument is pointed to, or near, the Pole, and
* the clock is rated to sidereal time, no elongation of the image occurs.
* This implies that the polar axis of the telescope does not point to the
* true, but to the apparent Pole (as affected by refraction)."
* Nov. 1897 issue
* Discussion of field rotation and distortion due to differential
* refraction
* June 1898 issue, but still vol.58
* Edward S. KING's classic paper
* ". . . the adjustment on the refracted pole is commended . . . ."
*
* papers from Juergen Richter at NCCOSC
*
* "multiple images were commonly observed. Of the 7 days, 2 had
* an optical duct. . . . The remaining days had subrefractive
* conditions. . . ." (i.e., inferior mirages).
* This uses a *model* to calculate the refractivity profile from surface
* conditions!
* Badly flawed by (a) assumption of Monin-Obukhov theory where it isn't
* valid; and (b) confusion between radiance & irradiance (much garbage about
* attenuation by ray divergence in discussing radiance).
* However, they do describe the separation of ducted from escaping rays
* as a "bifurcation".
* (contains several badly-reproduced mirage photos)
* "For air temperature gradients less than -1degC/m, it was demonstrated
* that a severe shortening of the optical and infrared horizons consistently
* occur."
* the same stuff, condensed.
* as in all the other references, a constant temperature gradient with
* height is assumed. This is certainly contrary to our observations!)
© 1999 – 2024 Andrew T. Young