376 Prof. Kelland on the explanation of Dispersion, 



Caiicbv's Excrciccs, for by turning to the following j^age we 

 find that equations (26.) (which give the values of the con- 

 stants) render equations (23.) in Mr. O'Brien's notation the 

 following : — 



= (3R + G)^^ + (R-G)(^ + ^,) 





d X dy d xdt 



Thus the difference between the medium and a common 

 elastic medium is only this, that the particles of aether are at- 

 tracted by the particles of matter. Now the same /ij//;o/Z!fS2S pre- 

 cisely is made by myself in my memoir ' On the Motion of a 

 System of Particles,' p. 244. But as I have adopted the law of 

 force varying inversely as the square of the distance, the quan- 

 tity C vanishes. The effect of such a term, however, I felt clearly 

 to be needed, and accordingly, I restored it in my ' Theory of 

 Heat', p. 153, by the consideration stated above. The equa- 

 tion which is there obtained is nearly the same as one of Mr. 

 O'Brien's equations, and the conclusion from it appears to 

 me the very same, in form at least, as his. The expression 

 which I obtained for the square of the velocity of transmission 

 is this: — 



D' ''" "2^ 



o2 = -:^V2 + 2(Q-M)2.F 



3. But I proceed to examine Mr. O'Brien's results in or- 

 der. The first is, that the velocity of propagation is in ge- 

 neral different for transversal and for direct vibrations. Here 

 I cannot help observing that it is much to be desired that an 

 appearance of generality should be avoided whenever it can 

 be done with propriety. By making the axis of x (which is 

 arbitrary) that of transmission, the equations assume the form 



'di-- = ^-dx- -^"^ 

 -Ji^-^-d^-^^ 



and the result is an interpretation of the difference of value 

 of A and B. M. Cauchy arrives at the same conclusion in 

 the Comptes Rcndus for 1840, vol. x. p. 905: and, of course, 

 he gets it in the same way. (See also Exerciccs, vol. v. p. 69.) 

 It is not a little remarkable that M. Cauchy should have 



