Prof. KelJand in the Phil. Mag. for May 1842. 485 



and similar expressions for -r^, -t4, adapting them to the 



case of a set of {Ethereal particles acted on by material. 



So far as this I lay no claim to originality, nor has Pro- 

 fessor Kelland any right to do so either. 



After this there is not a single step we have taken alike. 

 Professor Kelland's equations and results are essentially dif- 

 ferent from mine ; and not only do we differ, but we are dia- 

 metrically opposed to each other, so that if owe of us be right 

 the other must be wrong altogether. 



I lay claim to originality in the following particulars, viz. 



I have arrived at a result never obtained before, namely, 

 that dispersion must arise from the direct action of the parti- 

 cles of matter upon those of aether. This result is denied by 

 Professor Kelland. 



I have obtained by a simple process, the equations 



dra. . d- a. ^(d-a. d- a.\ . . -ns d /d^ dy\ 



and similar expressions for -^, ^^. These equations were 



originally obtained by M. Cauchy and the late Mr. Green 

 by vei-y complicated methods : they prove that Mr. Kelland's 

 equations in the Camb. Phil. Trans., vol. vi. page 159, are 

 essejitially erroneous. 



I have given a simple proof of what was only asserted by 

 Mr. Green, viz. that transverse and normal vibrations are in 

 general propagated with different velocities. I have learned 

 since that M. Cauchy had previously arrived at the same re- 

 sult. Professor Kelland distinctly denies the correctness of 

 this result in the Royal Edinb. Trans., vol. xiv. p. 396. 



And here I must enter a decided protest against all Pro- 

 fessor Kelland's reasoning on the subject of transverse and 

 normal vibrations. I assert that the equations at the foot of 

 page 162 of the Transactions of the Camb. Phil. Soc. are es- 

 sentially erroneous ; they ought to have been in the form 



'-j^ = — A« — B/3 — Cy, and similar expressions for j-^- j^; 

 for the term S < -^ Ixly sin^ -^— ^ > which Professor Kel- 

 land makes out to be zero (in the same page) is not zero, as 

 may easily be seen by putting for 8 g its value e 8 a,- +y' 8 y-\- g^z^ 



and expand mg sin — -^ m the series -«""" ~~^ TYs* 



