2io Notes on some Points in the Theory of Light. 



nel. The coincidence, however, is only approximate ; but 

 M. Cauchy is so far from being embarrassed by this circum- 

 stance, that he does not hesitate to regard his own theory as 

 rigorously true, and that of Fresnel as bearing to it, in point of 

 accuracy, the same relation which the elliptical theory of the 

 planets, in the system of the world, bears to that of gravita- 

 tion.* Nor is he at all embarrassed by the supernumerary ray 

 belonging to the third sheet of his wave-surface ; he assumes 

 at once that such a ray exists, though it was never seen, and 

 promises, for the satisfaction of philosophers, to make known 

 the means of ascertaining its existence. f But he afterwards 

 contented himself with observing that as its vibrations are in 

 the direction of propagation they probably make no impression 

 on the eye, and he then gave it the name of the "invisible 

 ray."J 



In these investigations, the suppositions which M. Cauchy 

 had made respecting the constants led to the result that the 

 vibrations of a polarized ray are parallel to its plane of pola- 

 rization ; but in the year 1836 he changed his opinion on this 

 point, and then, by reinstating the constants that he had be- 

 fore supposed to vanish, and establishing proper relations 

 amongst them and the rest, he arrived at the conclusion that 

 the vibrations are perpendicular to the plane of polarization. 

 All his other results, of course, underwent some correspond- 

 ing change ; and it is this new theory which must now be 

 regarded as rigorous, while that of Fresnel is to be looked 

 on as approximate. But it is needless to say, that if the 

 accuracy of Fresnel's law of double refraction is to be disputed, 

 it must be on much better grounds than these ; and the results 

 of M. Cauchy are certainly too far removed from that law to 

 have any chance of being consonant with truth. Although, for 

 example, his new views respecting the direction of the vibra- 



* Memoires de VInstitut, torn. x. p. 313. 



t Ibid. p. 305. 



% Nouveaux Exercices, p. 40. 



Comptes Rendus, torn. ii. p. 342. 



