Crystalline Reflexion and Refraction. 39 



every point T on the one having a point P reciprocally corresponding to it on 

 tlie other. 



It is remarkable that the transversal of the ray OT is perpendicular to the plane 

 OPT ; for in the theory of Fresnel, as I formerly proved,* the direction of the 

 vibrations is the right line TG ; and as I suppose the transversal to be perpen- 

 dicular 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 perpen- 

 dicular to both the right lines TG and OP, and therefore perpendicular to their 

 plane OPT. Therefore conceiving the transversal to be drawn through O at 

 right angles to the plane OPT, the plane of polarisation 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 in 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, however, the 

 polar plane, because the liame, plane of polarisation, is a long one ; and the 

 signification of the latter may, if any one chooses, be kept distinct, though in an 

 ordinary medium both terms must mean the same thing. The polar plane then 

 of the ray OT is a plane passing through its transversal and parallel to the right 

 line PT ; so that if OK be drawn parallel to PT, the polar plane will pass 

 through OK. In general, to find the transversal and the polar plane of any ray, 

 we take the point where the ray meets its own nappe of the wave surface, and 

 join it with the corresponding point on the index surface, drawing a plane 

 through the origin and the joining line. Then a right line perpendicular to 

 this plane at the origin will be the transversal, and a plane drawn through the 

 transversal parallel to the joining line will be the polar plane. 



Now let a polarised ray be Incident at O upon the crystal. It will in 

 general be divided into two rays. But each of these rays in turn may be made 

 to disappear by polarising the incident ray in a certain plane. Let us suppose 

 then that there is only one refracted ray OT. In what direction must the inci- 

 dent ray be polarised, or, In other words, what must be the position of its 

 transversal, In order that this may be the case ? and what will be the correspond- 



* Ibid. vol. xvi. p. 76. 



