﻿Tkeory of Dispersion. 481 



which yields the solenoidal condition for magnetic induction, 

 viz. : 



B« ~bb dc _ 

 since ^. d^ ^o^ _ 



(provided w/i is constant). 



38. When we proceed to identify the kinetic energy 



W$(u 2 + v 2 + w 2 )ch 



of the elastic medium with the electrostatic energy, we 

 observe that if the elastic medium is sethereal, the equation of 

 condition should be 



i<r | '(«■>' + V + W)dr = ^j'(/ 2 +f + V)dr, 

 while if the medium is a material medium Ave must have 

 \a jV + ^ + ™*)dT = ~ JW +.?o 2 + V)<*t. 

 These yield the following results : — 



where Yo is the velocity of light in the aether; 



where V is the velocity of light in any medium (o% n or /•, ^) . 

 Also 



a/-^\-^ _L ^ J_ d™0_ 1/3/ 3,? 9A\ /0 



where A is the dilatation of the medium. 

 Also |^ + + = M ++=0j 



z. e. the total displacement (ethereal and electronic) is sole- 

 noidal, while the volume density of electricity is proportional 

 to setherenl expansion. 



Phil Mag. S. 6. Vol. 29. No. 172. April 1915. 2 I 



