350 Mr. A. Cayley on the Stercographic Projection 



to bodies which reflect light from their interior ; and in the case 

 of piles of polished glass plates, the most distinguished philo- 

 sophers, Arago, Young, and Sir John Herschel, would have 

 considered the light which the plates reflected, as they did that 

 which they transmitted, as consisting of polarized light, accom- 

 panied with a portion of common light, a combination incapable 

 of producing neutral points. 



The most important application of the preceding experiments 

 is to the polarization of the atmosphere. Arago, Babinet, and 

 others, in their theory of the neutral points, and of the partial 

 polarization of the atmosphere, took no account of the rays which 

 are polarized by refraction whenever light is polarized by re- 

 flexion, and they referred these abnormal phenomena to a hori- 

 zontal secondary reflexion from the atmosphere itself, modifying, 

 and, in three neutral points, extinguishing the light polarized 

 by reflexion. Whether or not such a secondary reflexion exists, 

 or is adequate, if it does, to account for these phenomena, are 

 questions which will be considered in another paper on the 

 polarization of the atmosphere. But however ingenious may be 

 the hypothesis, it has no support either from experiment or 

 observation. The reduction of complete to partial polarization, 

 by the opposite action of light polarized by reflexion and light 

 polarized by refraction, and the production of neutral points 

 where these two lights are equal, whenever light is incident on 

 surfaces which, like the atmosphere, disperse and polarize it, 

 is next to an ocular proof of the true laws of atmospherical 

 polarization. 



It is not one of the least wonders of terrestrial physics, that 

 the blue atmosphere which overhangs us exhibits, in the light 

 which it polarizes, phenomena somewhat analogous to those of 

 crystals with two axes of double refraction. 



XLVIII. On the Stereo graphic Projection of the Spherical Conic. 

 By A. Cayley, Esq.* 



IN order to the tolerable delineation of some figures relating 

 to spherical geometry, T had occasion to consider the stereo- 

 graphic projection of the spherical conic. To fix the ideas, 

 imagine a sphere having its centre in the plane of the paper, 

 and through the centre three rectangular axes, that of x hori- 

 zontal and that of y vertical, in the plane of the paper, and 

 the axis of z perpendicular to and in front of the plane of the 

 paper. The radius of the sphere is taken equal to unity (so that 

 its intersection by the plane of the paper is the circle radius 

 unity), and the points X, Y, and Z are taken to denote the 

 * Communicated by the Author. 



