to the Wave Theory of Light. 49 



parallel to the normal at the point R of the ring-trace which is 

 described when the intercept (Pm) between the letters that mark 

 the rays is supposed to remain constant. 



54. In all that precedes we have made no supposition about 

 the surface of refraction except that it is a surface of two sheets ; 

 and if we supposed it to have three sheets, the conclusions would 

 be easily extended to this hypothesis. 



In the theory of FRESNEL, the wave surface is* a biaxal 

 whose generating ellipsoid has its centre at the point 0, and its 

 semiaxes parallel to the three principal directions of the crystal, 

 the length of each semiaxis being equal to 08 divided by one 

 of the principal indices of refraction. The surface of refraction 

 is reciprocal to the wave surface, and is (11) therefore another 

 biaxal generated by an ellipsoid reciprocal to the former, having 

 its centre at the same point 0, and the directions of its semiaxes 

 the same as before, the rectangle under each coincident pair of 

 semiaxes being equal to & 2 or OS 2 . Hence the semiaxes of the 

 ellipsoid which generates the biaxal surface of refraction are 

 equal in length to OS multiplied by each of the three principal 

 indices. This biaxal surface is of course to be substituted for 

 the surface of refraction in the preceding observations. 



55. When the line US, produced below S, passes through a 

 node N of the biaxal surface of refraction, the points P, M, 

 coincide in the point N, and the interval PM vanishes. At the 

 point N there are an infinite number of tangent planes, and the 

 perpendiculars from on these tangent planes give a cone of 

 refracted rays whose sections we have already shown how to 

 determine (20). All the rays in this cone, on arriving at the 

 second surface of the crystal, emerge parallel to the incident ray 

 OS ; and if the rays in the emergent cylinder be cut by a plane 

 perpendicular to their common direction, they will all arrive at 

 this plane at the same instant, because the interval PM vanishes. 

 See Art. 47. 



56. Suppose fig. 12 to be a section of the wave surface. The 



* Transactions of the Royal Irish Academy, VOL. xvi., p. 76 (supra, p. 11). 



E 



