Nov. 21, 1889] 



NA TURE 



71 



"original cow." Just below or on the line (i3), vertically 

 above \}t\z first cow, and, like it, erect, would be a second cow, a 

 repetition of the first. And often, above this again, below or 

 on the line (7), would be a third cow, also erect. 



Sometimes there were confused images hanging from the 

 second cow and joining other confused images piled on \\\q first 

 caiv ; sometimes the first cow was clear of images, while they 

 hung down from the second cow ; sometimes the second cow 

 was clear, and there were images piled on the first. Often the 

 third cow was missing (see Fig. i). As the original cow moved, 

 these images changed their disposition or vanished, and the third 

 cow appeared or vanished. But in all these changes it seemed 

 to me that the first cow, second cow, and (when visible) the 

 third cvw, were the permanent images. These, it appeared, 

 were always erect. 



(3) After the sun had risen, all continued in statu quo for a 

 short time. But soon, at various parts of the horizon, the land 

 just above the edges (a), (j8), and (7) paled away, and finally 

 melted into the appearance of "sky" or " water." There were 

 left, in the later stages of the mirage, first, the plain itself, with 

 an extension, the limits of which were not sharp, beyond the 

 normal horizon ; secondly, above this a strip of land, apparently 

 suspended in the air ; thirdly, in some parts of the horizon 

 another strip of land suspended in the air above this again. 

 The interval between (a) and {ff) was in all stages greater than 

 that between (i3) and (7). One of the appearances in the later 

 stages is indicated in Fig. 2. 



Other changes crept in, too. Very often the original objects 

 were wholly or partly sunk out of sight ; the images were less 

 defined ; and the confused images hanging from the second cow, 

 e.g. , or piled on the first cow, were now seen in the watery layers, 

 sometimes bridging it over. 



(4) As time went on, the watery layers widened. The images, 

 too, became still vaguer, and the original objects were usually 

 out of sight or only just indicated above the line (o). Moreover, 

 the aerial images, with their confused trails of images hanging 

 from them, began to assume more the appearance of " inverted 

 images suspended over objects hidden below the horizon." 



(5) In these later stages, no doubt, anyone would have guessed 

 that the aerial images were indeed very vaguely defined inverted 

 images. But to me, as I followed the phenomenon from the 

 beginning, it seemed that they were not so. It seemed to me 

 that each aerial image was really topped by an erect image, 

 which, with the trails hanging from it, seemed like an inverted 

 image. At least I can say that, so long as the images were well 

 defined at all, I never made out a clear case of the main, or 

 permanent, aerial images being inverted. Thus, as i\iQ first cozv 

 moved, it was the erect second (and sometimes third) cows that 

 remained clear. 



(6) In these later stages it was only trees and houses that 

 could be seen in the mirage, and these were ill-defined. 



(7) The mirage lasted until about an hour and a quarter after 

 sunrise. The last traces of aerial images of land appeared just 

 under the sun, and in that part of the horizon that lay just 

 opposite to it. Whether the abnormal extension of the horizon 

 entirely ceased at the same time, I cannot say ; but there did 

 not remain any noticeable extension. 



(8) As with the summer mirage, I found I could alter appear- 

 ances by altering my level above the earth. But the change in 

 level had to be more considerable. I have no good notes on 

 this matter ; but I believe that usually I could recover a past 

 stage of the mirage by a sufficient descent down a ladder from 

 my post of observation. 



General Conclusions as to Winter Mirage : — 



(i) It is due to the earth, and the air near it, being con- 

 siderably chilled below the temperature of the rest of the 

 atmosphere. 



(2) The phenomena of extended horizon and multiple images 

 are to be observed. 



(3) The "drawn up" appearance of objects is really due to 

 a number of images piled upon one another, only to be separated 

 by the use of a telescope. 



(4) No case of a terrestrial object having above it a single 

 inverted image, or images of which the uppermost was inverted, 

 came under my notice. W. Larden. 



SCIENTIFIC SERIALS. 



American journal of Mathematics, vol. xii. No, i, and index 

 to vols. i.-x. (Baltimore, 1889). — This volume opens with 



an instalment of sixty pages of a memoir by A. R. Forsyth, 

 F.R.S., on "Systems of Ternariants that are Algebraically 

 Complete." In this the writer has found it convenient to use 

 " ' ternariant ' as a generic term for concomitants of ternary 

 quantics, instead of giving it the signification which Prof. Sylves- 

 ter proposed {^Amer. J. of Math., vol. v. p. 81) to give to it, 

 viz. the leading coefficients of those concomitants." The memoir 

 is divided into three parts, and deals with the theory of the 

 algebraically independent concomitants of ternary quantics, 

 taking as the starting-point the six linear partial differential 

 equations of the first order satisfied by them. References are 

 supplied to numerous memoirs on the subject. — Captain (now 

 Major) P. A. Macmahon continues (pp. 61-102) his investiga- 

 tions (vol. xi. No. I) in a " Second Memoir on a New Theory 

 of Symmetric Functions." Herein he is engaged with functions 

 which are not necessarily integral, but require partitions, with 

 positive, zero, and negative parts for their symbolical expression. 

 The author thus summarizes his results : (i) a simple proof of 

 a generalized Vandermonde- Waring power law which presents- 

 itself in the guise of an invariantive property of a transcendental 

 transformation ; (2) the law of "groups of separations "; (3) the 

 fundamental law of algebraic reciprocity ; (4) the fundamental 

 law of algebraic expressibility which asserts that certain in- 

 dicated symmetric functions can be exhibited as linear functions 

 of the separations of any given partition ; (5) the existence is 

 established of a pair of symmetrical tables in association with 

 every partition into positive, zero, and negative parts, of every 

 number, positive, zero, or negative. — The closing portion of the 

 number (pp. 103-114) is taken up with an article entitled 

 " De I'Homographie en Mecanique,"by P. Appell. — A likeness 

 of M. Poincare faces p. I. — The index is of a twofold descrip- 

 tion — of authors and of subjects. From the forewords we 

 learn that papers have been published from eighty-nine con- 

 tributors ; these comprise "most of the leading mathematicians 

 of the world." 



SOCIETIES AND ACADEMIES. 

 Paris. 



Academy of Sciences, November 11. — M. Hermite in the 

 chair. — Presentation of Report of Proceedings of the permanent 

 International Committee for preparing a photographic chart of 

 the heavens, by M. E. Mouchez. Fifteen Observatories will be 

 ready by the middle of next year ; and five others before the end. 

 The zones are indicated. — Note of M. Daubree with descriptive 

 catalogue of the meteorites of Mexico prepared by M. Antonio 

 del Castillo. Meteorites are abundant in Mexico. A remarkably 

 wide area of dispersion is indicated by three portions of one 

 mass, found at the angles of a triangle, whose two longer sides 

 were 90 km. and 60 km. In one of these places two plates were 

 found 250 m, apart ; and they seem to have formed one huge 

 plate over 24,000 kgm. weight, which broke near the ground. — 

 On the incineration of vegetable matters, by M. G. Lechartier. 

 Trying various methods, he finds, that in the carbonization and 

 incineration of a plant, there is considerable loss of sulphur, 

 volatilized in various combinations ; and special precautions are 

 necessary in determining this constituent. Under the same 

 conditions, and care being taken to prevent loss of solid 

 matter carried away mechanically with the issuing gas, 

 there is no sensible loss of phosphorus. — M. Picard was 

 elected member in Geometry, in place of the late M. 

 Halphen. — On a rotating magnetic field formed with two 

 Ruhmkorff coils, by M. W. De Fonvielle. A current from 

 accumulators is sent through the primary of one coil, the 

 secondary of which is connected with that of the other coil, 

 which is in a line with the first, and the primary of which may 

 be open or closed. — On certain ellipsoidal areas, by M. G. 

 Humbert. — On a new calculating machine, by M. 1.. Bollee. 

 While in previous machines, multiplications, e.g., are done by 

 successive additions, this one has a multiplying apparatus which 

 determines immediately, in one function, the product of a number 

 by each figure of the multiplier. — On the solubility of the chlorides 

 of potassium and of sodium in the same solution, by M. Etard. The 

 results of experiment are shown in graphic form ; the curves of 

 solubility of each salt separately being compared with those of 

 the mixed salts, &c. The sum of the dissolved salts is re- 

 presented by a continuous straight line. The curves for the mixed 

 salts cross at temperature 97° ; that for NaCl falling while the 

 other rises. — On an application of thermo-chemistry, by M. A. 



