214- The Rev. M. O'Brien on the Propagation 



supposing the vibrations of the aether transversal ; and simi- 

 larly, 



("— B)|^^ +C^-C/3, = (2.) 



(1.) J) + {2.)q + (3.) s gives, since p u + q^ + sy = 0, 



C[pci, + q^, + srf) =0; 

 hence the vibrations of the particles of matter are transverse, 

 and hence we have exactly, as in the case of the vibrations of 

 the aether, 



wherfe Uj is the velocity with which the vibrations of the 

 material particles are propagated. We here make no differ- 

 ence between u and ?/,, for supposing « /3 y and «^|3, y, to be- 

 long to contiguous particles, it is evident that u^ does not 

 differ sensibly from ii. 



We have supposed (u ) the velocity of propagation of the 

 vibrations of the material particles not the same as (w) that 

 of the aelhei-eal particles; for these quantities are evidently 

 quite independent of each other, so far as the above equations 

 of motion are concerned ; and whatever connexion subsists 

 between them must evidently be determined from initial or 

 other circumstances independent of the equations of motion. 



Let us now find a. from the equations 



('>^-B)^ + C(a-«,) = (1.) 



("/^-B.) ^-f-C, («-«,) =0 (2.) 



(I.) C, + (2.)C gives 



K_B) C,-p^,- + (.,^-B,) C ^"/ = 0; 

 ^ ' ' an- ' ' air 



and.-. «, = --,-_-g^^., 



adding no constants, because the motion is oscillatory. 



