486 The Rev. M. O'Brien's Reply to some Observations of 



Now this error in his fundamental equations vitiates all his 

 results, so far as they relate to the nature of the vibrations 

 and the velocity of propagation ; indeed his expression for 

 the velocity of propagation is manifestly erroneous, inasmuch 

 as it is the same for transverse and for normal vibrations 

 and is different for different values oi cf g. This error runs 

 through all Professor Kelland's papers and his ' Theory of 

 Heat,' so far as I have read them ; and it fully accounts for the 

 manner in which he has spoken on this subject in the Royal 

 Edinb. Phil. Trans., vol. xiv. p. 396. 



I have also proved that the velocity of light in transparent 

 bodies cannot be uniform unless the vibrations obey the cy- 

 cloidal law. From this result I have shown, in a paper read 

 before the Camb. Phil. Soc. last April, that homogeneous light 

 must in general suffer dispersion in passing through a prism, 

 and dispersion of a discontinuous nature ; and from this I have 

 shown that dark lines will be formed in the spectrum. 



I have in the same paper shown that the results I have ob- 

 tained on the hypothesis of perfect symmetry, are also true 

 when the symmetry is disturbed by the action of the particles 

 of matter. 



Having thus stated how far I lay claim to originality, I must 

 notice a formula for o^, which Professor Kelland has brought 

 forward in page 376 of the Philosophical Magazine for May 

 ]84'2. Just before he mentions this formula, he speaks of the 

 terms C «, C /3, C 7, which I have made use of in explaining 

 dispersion, in such a manner as to imply, that he has done 

 something of the kind himself. Now I cannot at all admit 

 that he has anywhere made use of such terms, or anything 

 equivalent to them, for he proceeds upon a hypothesis which, 

 according to his own statement, makes C zero. He certainly 

 endeavours, in his ' Theory of Heat,' to account for dispersion 

 independently of the hypothesis of finite intervals (see pages 

 152-154'), and accordingly by a process, which I confess I 

 cannot understand, and which, be it observed. Professor Kel- 

 land himself considers too uncertain to be trusted (see middle 

 of page 154-), by this process he obtains the following formula 

 for 0^: — 



sin^ IcAx- 



«2 = 0-'v2+2(Q^M) S 



Now I would ask Professor Kelland in the first place, why 

 he has brought forward this formula in the manner he has 

 done in the Philosophical Magazine, without at the same time 

 quoting the words which immediately follow it in his book, 



