Mr. G. G. Stokes on the Aberration of Light, 13 



aether may be neglected, then to a point near the earth where 

 we may still neglect the motion of the aether, and lastly to the 

 point of the earth's surface at which the planet is viewed. 

 For the first part we shall have ?<2 = 0, v^ = 0, and w„ u, will 

 be the resolved parts of the planet's velocity. The increments 



of a and /3 for the first interval will be, therefore, — ~, — ^. 



For the second interval « and |3 will remain constant, while 



for the third their increments will be -~, ^1, just as in the case 



of a star, 1L2 and Vg being now the resolved parts of the earth's 

 velocity. 



Fig. 1. 



JP//i 



\ 



Fig. 2. 



Fig. 1 represents what is conceived to take place. P is the 

 planet in the position it had when the light quitted it; E the 

 earth in the position it has when the light reaches it. The 

 lines a Z>, c</, &c. represent a small portion of a wave of light 

 in its successive positions. The arrows represent the direc- 

 tions in which P and E may be conceived to move. The 

 breadth a 6 is supposed to be comparable to the breadth of a 

 telescope. In fig. 2, pmne represents an orthogonal trajec- 

 tory to the surfaces ab, cd, &c. ; p is the point of the planet 

 from which the light starts, e the point of the earth which it 

 reaches. The trajectory pmne may be considered a straight 

 line, except near the ends p and e, where it will be a little 

 curved, as from p to m and from e to n. The curvature at e 

 will have the same effect on the apparent position of the planet 

 as it would have on that of a star in the same direction : as to 

 the curvature at p, if we draw jy^f perpendicular to mn pro- 

 duced, the curvature will have the effect of causing ^; to be 

 seen as if it were at q. Now the angle between the tangents 

 at;j and m being that through which a star in the direction of 

 e is displaced by aberration to an observer at p, and the di- 



* The lines towards P in fig. 1. should lean in the opposite direction. 



