S24 Rev. J. Challis on the Aberration of Light. 



impression that w and s are in the same direction. Suppose 

 the aether which is situated between e' and w to be moving 

 with a uniform velocity, and let n S represent in magnitude 

 and direction the space through which it is curried while light 

 travels from nso to ^. The line n d may be of any magnitude 

 less than ^ e, and in any direction not necessarily in the plane 

 eiio'ud ^. Join wn. Now the motion of the luminous waves 

 from ISO to e' is compounded of two motions represented by 

 w n and n /, the former of which is due to the motion of pro- 

 pagation of the wave through the aether, and the other to the 

 motion of the aether itself. It is well known that the motion 

 of propagation is in the direction of a normal to the front of 

 the wave, and that the front of a given wave continues par- 

 allel to a given plane so long as it is propagated through fluid 

 at rest, or through fluid moving with a uniform velocity in a 

 given direction. Also the normal to the front of a wave is in 

 the direction of vision. Hence if f' 5' be drawn parallel to 

 nw, this will be the common direction in which the objects w 

 and s will be seen. Consequently, if the front of the wave re- 

 tained its parallelism the whole distance from the object to the 

 eye, the true direction of the celestial object s from e' would 

 be e'5', when the true direction of the terrestrial object iso 

 from ^ is e' ixif. The aberration would consequently be an 

 angle s' e'w', different from the angle we'te/, which is known 

 from observation to be the actual angle of aberration. 



It is not, however, true, as we have supposed above, that 

 the front of a wave continues parallel to itself in passing 

 through the aether put in motion by the earth's motion. For 

 evidently the wave is propagated through portions of the 

 aether moving with different velocities in different dii'ectionSi 

 and the effect this circumstance has in altering the direction 

 of the normal to the front of the wave must now be consi- 

 dered. For the following method of calculating this effect, I 

 am indebted to the very ingenious and original mathematical 

 reasoning contained in Mr. Stokes's communication above al- 

 luded to. I have only given the reasoning a more geometri- 

 cal form. 



Let sa (fig. 3) be a portion of the path in space of a given 

 point of a wave of constant form, and let a and b be two 

 points of the wave indefinitely near each other in the same 

 phase at the same time. Join a b. Since the velocity impressed 

 on the aether by the earth's motion is very small compared to 

 the velocity of light, ab must be nearly perpendicular to sa. 

 Let V/ and V/ represent the velocity of the aether at a and b, 

 so far as it is due to the earth's motion, and let that at a take 

 place in the direction ?iam. Also let V represent the uni- 



