10 Mr. G. G. Stokes o« the Aberration of Light. 



from the surface, till, at no great distance, it is at rest in space. 

 According to the undulatory theory, the direction in which a 

 heavenly body is seen is normal to the fronts of the waves 

 which have emanated from it, and which have reached the 

 neighbourhood of the observer, the aether near him being sup- 

 posed to be at rest relatively to him. If the aether in space 

 were at rest, the front of a wave of light at any instant being 

 given, its front at any future time could be found by the method 

 explained in Airy's Tracts. If the aether were in motion, and 

 the velocity of propagation of light were infinitely small, the 

 wave's front would be displaced as a surface of particles of the 

 aether. Neither of these suppositions is however true, for the 

 aether moves while light is propagated through it. In the fol- 

 lowing investigation I suppose that the displacements of a 

 wave's front in an elementary portion of time due to the two 

 causes just considered take place independently. 



Let u, V, w be the resolved parts along the rectangular axes 

 of j:", y, s, of the velocity of the particle of aether whose co- 

 ordinates are x, j/, z, and let V be the velocity of light sup- 

 posing the aether at rest. In consequence of the distance of 

 the heavenly bodies, it will be quite unnecessary to consider 

 any waves but those which are plane, except in so far as they 

 are distorted by the motion of the aether. Let the axis of z 

 be taken in, or nearly in the direction of propagation of the 

 wave considered, so that the equation to the wave's front at 

 any time will be 



z = c + vt + i;, (1.) 



C being a constant, t the time, and ^ a small quantity, a func- 

 tion of ^, y and t. Since n, u, w and ^ are of the order of 

 the aberration, their squai'es and products may be neglected. 

 Denoting by a, /3, <y the angles which the normal to the 

 wave's front at the point {x,i/, z) makes with the axes, we have, 

 to the first order of approximation, 



^°-^"=-^' "^^^=-z|' <^^'^=^-> ' • (2-) 



and if we take a length V dt along this normal, the co-ordi- 

 nates of its extremity will be 



If the aether were at rest, the locus of these extremities would 

 be the wave's front at the time t + d t, but since it is in mo- 

 tion, the co-ordinates of those extremities must be further in- 

 creased by ?^ rf ^, vdt, wdf. Denoting then by ^', y, 2' the 

 co-ordinates of the point of the wave's front at the time t + dty 



