EPOCH OF YOUNG AND FRESNEL. 457 



have described, are, it appears from the principles 

 of mechanics, propagated in a manner quite dif- 

 ferent from anything which had been anticipated. 

 The "surface of the waves" (that is, the surface 

 which would bound undulations diverging from a 

 point,) is a very complex, yet symmetrical curve 

 surface ; which, in the case of uniaxal crystals, re- 

 solves 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 de- 

 termined 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 polariza- 

 tion of the two rays follow from the same investi- 

 gation; the plane of polarization in every case being 

 supposed to be that which is perpendicular to the 

 transverse vibrations. Now it appeared that the 

 polarization of the two rays, as determined by Fres- 

 nel's theory, would be in directions, not indeed ex- 

 actly accordant with the law deduced by M. Biot 

 from experiment, but deviating so little from those 

 directions, that there could be small doubt that the 

 empirical formula was wrong, and the theoretical 

 one right. 



The theory was further confirmed by an expe- 

 riment showing that, in a biaxal crystal (topaz), 



