EPOCH OF YCUXG AND FRESXEL. 10 



further in two Memoirs presented in 1822. Its import is very curious 

 The undulations which, coming from a distant centre, fall upon such a 

 medium as we have described, are, it appears from the principles of 

 mechanics, propagated in a manner quite different from anything 

 which had been anticipated. The " surface of the waves" (that is, tin 

 surface which -would bound undulations diverging from a point), is a 

 very complex, yet symmetrical curve surface ; which, in the case of 

 uniaxal crystals, resolves itself into a sphere and a spheroid ; but 

 which, in general, forms a continuous double envelope of the central 

 point to which it belongs, intersecting itself, and returning into itself. 

 The directions of the rays are determined by this curve surface in 

 biaxal crystals, as in uniaxal crystals they are determined by the 

 sphere and the spheroid ; and the result is, that in biaxal crystals, both 

 rays suffer extraordinary refraction according to determinate laws. 

 And the positions of the planes of polarization o5 the two rays follow 

 from the same investigation ; the plane of polarization in every case 

 being supposed to be that w r hich is perpendicular to the transverse 

 vibrations. Now it appeared that the polarization of the two rays, as 

 determined by Fresners theory, would be in directions, not indeed 

 exactly accordant with the law deduced by M. Biot from experiment, 

 but deviating so little from those directions, that there could be small 



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doubt that the empirical formula was wrong, and the theoretical one 

 right. 



o 



The theory was further confirmed by an experiment showing that, 

 in a biaxal crystal (topaz), neither of the rays was refracted according 

 to the ordinary law, though it had hitherto been supposed that one of 

 them was so ; a natural inaccuracy, since the error was small. 11 Thus 

 this beautiful theory corrected, while it explained, the best of the obser- 

 vations which, had previously been made ; and offered itself to mathe- 

 maticians with an almost irresistible power of conviction. The explana- 

 tion of laws so strange and diverse as those of double refraction and 



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polarization, by the same general and symmetrical theory, could not 

 result from anything but the truth of the theory. 



" Long," says Fresnel, 12 " before I had conceived this theory, I had 

 convinced myself, by a pure contemplation of the facts, that it was not 

 possible to discover the true explanation of double refraction, without 

 explaining, at the same time, the phenomena of polarization, which 

 always goes along with it ; ar.d accordingly, it was after having found 



1 An. Ch. xxviii. p. 204. K Sur la Double Rlf , Him. Inst. -1826, p. 174. 



