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



distance much less than that of the moon from the earth, Uq 

 must be quite insensible. Hence for any celestial body the 



u 



deviation = —. So the deviation of the normal in the plane 

 of V and ia is ■^. The resulting deviation is therefore 



k^ — - in a plane containing the direction of the motion of 



the aether at the earth's surface and the direction of the course 

 of the wave j that is, in fig. 3, the plane nac^ and in fig. 2 the 

 plane iso^ n. Now since 11 ^ in fig. 2 represents the velocity 

 of the aether at the earth's surface, ^f drawn perpendicular 

 to tuw represents Vu,^ + v/^, so that the angle e'wf) which is 



the same as s^ ^, is equal to ^ — '-. This then is the 



aberration arising from the different states of motion of the 

 parts of the aether through which the wave is propagated, in 

 consequence of which, when the normal to the front of the 

 wave is in the direction e' s', the object is really in the direc- 

 tion ^ s. Thus the actual angle of separation between the di- 

 rections of the two objects s and w is se' isJ when they are 

 seen in the same direction e' s'. This angle is the same that 

 we found without considering the motion of the aether, and it 

 therefore follows that the amount and law of aberration are 

 the same whatever motion the earth impresses on the aether. 

 The foregoing mathematical reasoning does not appear in 

 any respect wanting in generality, and is equally true whe- 

 ther udx + vdy + niodz be or be not an exact differential. It 

 may, however, be remarked, that as the angle cao was found 



d u 

 to be equal to -7- S /, so we might find the angle e do equal to 



dix) 



-^ 8 1, the axis of x being supposed parallel to a b. But if 



the form of the wave alters in no respect, the angle e do is 



equal to the angle cao, and consequently -r- = -^— . So 



J- = -}—. It would seem therefore that the motion of the 

 d s dy 



aether must be such as to satisfy these equations, at least ap- 

 proximately, the reasoning being only approximate. Now 

 it happens that whenever the motion of an elastic fluid is such 

 that the terms involving the squares of the velocity may be 

 neglected (and the case before us is one of this kind), we have 



