Reflexion and Refraction, 95 



the wave plane is called the wave normal. It is scarcely 

 necessary to remark, that all the four wave planes intersect 

 the surface of the crystal in the same right line which is per- 

 pendicular to the plane of incidence; antLjhat the angles of 

 refraction are the angles which the refracted wave jiormals 

 make^ witb_a^ perpendicular to that surface. The index of 

 refraction is the ratio of the sine of the angle of incidence to 

 the sine of the angle of refraction, just as in ordinary media ; 

 but here it is a variable ratio, and has different values for the 

 same angle of incidence. I have elsewhere* shown how to find 

 the refracted rays and waves when the incident ray is given. 



As we suppose the ethereal molecules to vibrate parallel to 

 the transversals, we may take the lengths of the transversals 

 proportional to the magnitudes or amplitudes of the vibrations ; 

 these lengths being always measured from the common origin 

 0. Then, in virtue of our fourth hypothesis, the transversals 

 will be compounded and resolved exactly by the same rules as 

 if they were forces acting at the point 0. 



We must now conceive a wave surface of the crystal, with 

 its centre at 0, the point of incidence. As the veloci- 

 ties of rays which traverse the crystal in directions 

 parallel to the radii of its wave surface are repre- 

 sented by those radii, so let a concentric sphere be 

 described with a radius OS, which shall represent, 

 on the same scale, the constant velocity of light in 

 the medium external to the crystal. At any point 

 T on the wave surface apply a tangent plane, on 

 which let fall, from 0, a perpendicular OG, meeting 

 the plane in G. On this perpendicular take the length 

 OP from towards G, so that OP shall be a third proportional 

 to OG and the constant line OS. Then, while the point T 

 describes the wave surface, the point P will describe another 

 surface reciprocal! to the wave surface. This other surface may 



* Irish Academy Transactions, Vol. xvn. p. 252. 



f For the general theory of reciprocal surfaces, see Irish Academy Transactions, 

 Vol. xvii. p. 241. 



