TRANSACTIONS OF THE SECTIONS. 9 



may be found in the history of tliese phenomena of variable stars. Tyclio Bralie 

 thought the celebrated new star of 1572, which he detected on returning home 

 from his laboratory, and which was then shining as a star of the first magnitude, could 

 not have been visible an hour or so previouslj', and yet, keen observer as he was, 

 he is well known to have been preceded by several clays in the discovery of that 

 wonderful object. Astronomers generally, however, may not be disposed to attach 

 so little weight to negative evidence in a case of this kind, as from his own expe- 

 rience Mr. Hind was inclined to do, and it will be most desirable to possess every 

 particular relating to Mr. Barker's observations between the 4th and 14th of May, 

 which it may be in his power to furnish. ]Mr. Barker thinks he saw this star one 

 or two years earlier, when the constellation was in the S.E., about 9 p.m., and Sir 

 John Herschel announces his having recorded a star in this very position in one of 

 his revisions of the heavens. The apparition of this star will be memorable as 

 having afforded an opportunity of applying the spectrum-analysis to one of this 

 class of objects. The valuable and highly interesting observations by Mr. W. Hug- 

 gins and others are the results. 



Light. 



Optics of Photof/rciphy. — On a New Process for equalizing the Definition of all 

 the Planes of a Solid Figure represented in a Photographic Picture. Means 

 of producing Harmonious and Artistic Portraits, By A. Claijdet, F.R.S. 

 [This paper was published in the Philosophical Magazine for September 1866.] 



On a New Geometrical TJieorem relative to the Theory of Reflexion and Re- 

 fraction of Polarized Light {hotropic Media). By M. A. Coentt. 



The direction of the luminous vibration relatively to the plane of polarizatiou 

 of a ray has not been yet stated in a way which is quite incontestable. Fresnel, in 

 his admirable memoir ' On the Mechanical Theorv of the Reflexion and Befraction 

 of Bolarized Light,' concludes that the vibration is perpendicular to the plane of 

 polarization. JPCullagh and Neumann have arrived at the same formula}, but 

 by supposing, on the contrary, that the vibration is within the plane of polariza- 

 tion. It seems that no middle temi can exist between these two theories, and 

 that the three rays have necessarily their vibration in the identical position com- 

 pared Avith their respective plane of polarization. However, there is a third me- 

 thod, or, in other words, a third theory, extremely simple, — the author would not 

 say extremely plausible,^ — which will lead us to the opinion of Fresnel respecting 

 the refracted ray, and to the opinion of M'^Cullagh respecting both the others. 

 The onlj' principle to be admitted, besides the exact transversality of the vibrations, 

 is the following — the refracted vibration is perpendicular to the incident and re- 

 flected vibrations. We have, indeed, no theoretical gi-ound for admitting, a priori, 

 this principle ; but if the consequence of it agree with the results of the other 

 theories, it deserves to attract the attention of theorists in optics, and, in fact, 

 it -will constitute a new theorem. With the help of this principle, it is easy to 

 detei-mine the position of the reflected and refracted vibrations, if the position of 

 the incident vibration is given. The resulting formula is 



tan X tan /3 , 



; _ 1 — = cot y, 



cos (^— ?•) cos {i-\-r) 



in which os, ^, y are the angles of the incident, reflected, and refi-acted vibrations 

 Avith the plane of incidence, i and r the angles of incidence and refraction. Seeing 

 that the vibrations are besides transversal, the above formula determines them 

 completely. But if this theoiy is exact, that formida is nothing else than the ana- 

 lytical translation of the law of the rotation of tlie planes of polarization of the 

 three rays — a law first stated by Fresnel, and which, according to the same rota- 

 tions, may be written 



cot ct cot H . 



— = ~ — = cot y, 



cos (* — r) cos (1+ /■) 



St) (3, y being the angle of the vibration with the plane of incidence. M'^Cullagh 



