﻿482 On the Theory of Dispersion. 



39. The various equations appropriate to an elastic medium 

 are then found to have their analogies in the electric 

 theory. 



Thus the equation 



yields the electrostatic equation for a material medium, 

 in the form 



on properly choosing the signs. 



40. The equation of motion of such a medium, viz. : 



yields f" = VVf 



or /;-=vv/i, 



i. e. /+A=vv(/+A) = vy/, 



if v 2 A=0, 



while for the free aethereal medium we have 



;=v„v/, 



41. Again Boussinesq's equation, viz., 



°"o ^o + PiXJ = ^v 2 f , yields^ 



if we put o- Q u=f and p 1 U = A, — — Vq--, 



/+A=V V/ 



The other equation of condition of Boussinesq, viz., 



0.'' 

 gives similarly A=\'/-r D V"/ 



> 



and similarly for the equations of Helmholtz and Ketteler. 



