78 Mr. G. G. Stokes on Fresnel's 



uninfluenced by the motion of the earth. The method which I 

 employ will, I hope, be found simpler than Fresnel's ; besides 

 it applies easily to the most general case. Fresnel has not 

 given the calculation for reflexion, but has merely stated the 

 result; and with respect to refraction, he has only considered 

 the case in which the course of the light within the refracting 

 medium is in the direction of the earth's motion. This might 

 still leave some doubt on the mind, as to whether the result 

 would be the same in the most general case. 



If the aether were at rest, the direction of light would be 

 that of a normal to the surfaces of the waves. When the 

 motion of the aether is considered, it is most convenient to de- 

 fine the direction of light to be that of the line along which 

 the same portion of a wave moves relatively to the earth. For 

 this is in all cases the direction which is ultimately observed 

 with a telescope furnished with cross wires. Hence, if A is 

 any point in a wave of light, and if we draw A B normal to 



the wave, and proportional to V or — , according as the light 



is passing through vacuum or through a refracting medium, 

 and if we draw B C in the direction of the motion of the aether, 



and proportional to v or -|, and join A C, this line will give 



the direction of the ray. Of course, we might equally have 

 drawn A D equal and parallel to B C and in the opposite di- 

 rection, when D B would have given the direction of the ray. 

 Let a plane P be drawn perpendicular to the reflecting or 

 refracting surface and to the waves of incident light, which in 

 this investigation may be supposed plane. Let the velocity v 

 of the aether in vacuum be resolved into p perpendicular to 

 the plane P, and q in that plane; then the resolved parts of 



v 

 the velocity —^ of the aether within a refracting medium will 



r 



be ^, -^. Let us first consider the effect of the velocity p. 



It is easy to see that, as far as regards this resolved part of 

 the velocity of the .ether, the directions of the refracted and 

 reflected waves will be the same as if the aether were at rest. 

 Let BAC (fig. I) be the intersection of the refracting surface 

 and the plane P; D A E a normal to the refracting surface; 

 AF, AG, AH normals to the incident, reflected and refracted 

 waves. Hence A F, A G, A H will be in the plane P, and 

 Z GAD = FAD, ^sinHAE=sinFAD. 



Take AG = AF, A H = — A F. 



