g6 On the Laws of Crystalline 



very properly be called the index surface* because its radius 

 OP is the refractive index of the ray whose velocity is OT, or 

 rather of the wave TG, which belongs to that ray; for if we 

 conceive an incident wave, touching the sphere, to be refracted 

 into the wave TG, touching the wave surface in T, the sine 

 of the angle of incidence will be to the sine of the angle of 

 refraction as OS to OG, or as OP to OS ; so that, taking the 

 constant OS for unity, the index of refraction will be repre- 

 sented by OP. The wave surface and the index surface will 

 thus be reciprocal to each other, every point T on the one 

 having a point P reciprocally corresponding to it on the other. 

 It is remarkable that the transversal of the ray OT is per- 

 pendicular to the plane OPT; for in the theory of Fresnel, as 

 I formerly proved, f the direction of the vibrations is the right 

 line TG', and as I suppose the transversal to be perpendicular 

 to the vibrations of that theory, and to be, at the same time, in 

 the wave plane, which is perpendicular to OP, it follows that 

 the transversal must be perpendicular to both the right lines 

 TG and OP, and therefore perpendicular to their plane OPT. 

 Therefore conceiving the transversal to be drawn through 

 at right angles to the plane OPT, the plane of polarization 

 of the ray OT must needs pass through it. But there is 

 nothing else to fix the position of this last plane. We may 

 make it pass through the ray itself OT, as an ordinary media, 

 or we may draw it through the wave normal OP with Fresnel. 

 Or, instead of drawing it through either of these two sides of 

 the triangle OPT, we may make it parallel to the third side 

 PT. The last is what I should prefer, because the plane so 

 determined possesses important properties. I shall call it, how- 

 ever, the polar plane, because the name, plane of polarization, is 

 a long one ; and the signification of the latter may, if any one 



* This is the surface which I formerly called (Trans., p. 252) the surface of 

 refraction; a name not sufficiently descriptive. Sir W. Hamilton has called it 

 the surface of wave slowness, and sometimes the surface of components. But the 

 name index surface seems to recommend itself, as both short and expressive. 



t Ibid. Vol. xvi. p. 76. (Supra, p. 12.) 



