On the Course of a Rai/ of Light from a Celestial Bodi/. 169 



could be said on the subject, a curvilinear motion of light 

 would result, and thus the undulatory theory would be found 

 to be inconsistent with fact. I have,however,shown(Phil.Mag., 

 vol. xxvii.p. 323-326, and again in Phil. Mag., vol. xxviii.p.92), 

 that in consequence of the motion of translation of the wave 

 caused by the motion of the asther, the direction of propaga- 

 tion in space of a given point of the wave deviates from the 

 normal to the front by exactly the above-mentioned angle, 

 and in exactly the opposite direction. It follows that the pro- 

 pagation in space is rectilinear; and thus the transmission of 

 light through the perturbed aether, without suffering aberra- 

 tion from the motion of the aether, is accounted for on the 

 hypothesis of undulations. Mr. Stokes has acquiesced in this 

 view (Phil. Mag., vol. xxix. p. 8), and there is consequently no 

 longer any point in dispute between us. 



The above solution of the proposed question rests however 

 on an assumption. The resolved parts of the motion of the 

 {Ether at any point x y z caused by the earth's motion being 

 M, V, TO in the directions of the axes of co-ordinates, it is as- 

 sumed that udx-\-vdy + v^dz is an exact differential. Is this 

 assumption allowable ? Does it not restrict too much the kind 

 of motion ? This is the only point relating to this subject 

 which remains to be cleared up. Mr. Stokes has given it 

 consideration in the communication last quoted. The follow- 

 ing solution of the difficulty, derived very simply from known 

 hydrodynamical equations, occurred to me very recently ; and 

 it is mainly for the purpose of bringing it under the notice of 

 mathematicians that I have returned to this subject. Let the 

 pressure at any point xyz at the time t be a\\ -\-s), s being 

 a small quantity whose powers above the first are neglected. 

 Then, as is known, 



^ds du cds dv ^ds , dw „ 



a^-7- + -7T=0, «-— + — =0, fit-— + -— =0. 

 ax at dif dt dz dt 



Hence by integration, 



n 2 P^^^ u r^ 9 d.fsdt 

 ^ ax ^ly, 



v^C'-a-r%dt=.0-a\'^'M, 

 ^ '^y dy 



J dz —f^' 



where C, C, and C" are functions of .r, y, ;:; which do not con- 

 tain the lime. The above are general values of «, v, iso, for 



TO: 



