AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 163 



if n=2^ {cpir) + ^^ 5a;l sin^^, 

 it being evident that 



Now it must be observed that we have not deduced the above equa- 

 tions directly from the equations of motion; but have obtained them 

 by first solving for one particular case, and assuming that the same 

 Jbrm holds in the general one: our solution is 



a = a cos (nt—kp) 



(i — h cos {nt—kp), 



y = c cos {nt — kp), 



n being now that given by the equation 



These results appear to be very simple in their form, and recommend 

 themselves from the readiness with which they can be applied. It is 

 true, we have not obtained them on a general hypothesis, but I think 

 we may venture to say they rest on one which carries with it an air 

 of probability ; and I confess there seems more difficulty to conceive 

 an hypothesis different from this for uncrystallized media, than to con- 

 cede this. It is, moreover, the same which M. Cauchy adopts, but the 

 results obtained differ in one especial point, viz. that his assume, and 

 are of so general a form, that little construction beyond the explana- 

 tion of dispersion can be put upon them. Professor Powell has, it is 



true, deduced from them the expression H —^— for the velocity. 



I shall make no remark on this deduction, as it arose from the simple 

 consideration of one attracting particle, which is too limited to be re- 

 garded as even an approximation to a general result. I shall merely 



X2 



