156 



among the other six, three very strange and improbable re- 

 lations, by means of which each of the principal sections of 

 his wave-surface (considering only two out of its three sheets) 

 is reduced to the circle and ellipse of Fresnel's law ; and 

 the three principal sections being thus forced to coincide, it 

 would not be very surprising if the two sheets were found 

 to coincide in every part with the wave-surface of Fresnel. 

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

 Cauchy is so far from being embarrassed by this circumstance, 

 that he does not hesitate to regard his own theory as rigo- 

 rously 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 (^Memoires de I'lnstitut, tom. x. p. 313). 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 {Ibid, p. 305), But he afterwards 

 contented himself with observing that as its vibrations are in 

 the direction of propagation they probably make no impres- 

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

 ray." {Nouveaux Exercices, p. 40). 



In these investigations, the suppositions which M. Cauchy 

 had made respecting the constants led to the result that the 

 vibrations of a polarized ray dive 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 

 {Comptes Rendus, Tom. ii. p. 342). All his other results, of 

 course, underwent some corresponding change ; audit 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 



