﻿Theory of Dispersion. 477' 



On this theory, the electrostatic 





5 energy 



%J 



will correspond to the energy of strain of an elastic medium, 

 since this is 



= 2n I (»/ + &)/ + a) z 2 )ch -h surface integrals if ( /c 4- t) n )A = 0, 



so that on this theory we have 



^^ =2ne» x s , Ac. (13), and ^ = -, . . (41) 

 It kfJL o~ 



provided we further postulate the identity of the kinetic 

 energy of a strained elastic medium, viz.: 



and electromagnetic energy 



AJV(a 2 + /3 2 -f 7 2 >/r, 



&, 

 where <? = density of the medium, 



f =x—iv , &c. = elastic displacements of the medium, 

 « ? /3, y = magnetic force, 

 6) x , ft) y , &); = molecular rotation. 



29. From (13) we derive, provided - = constant, 



27r/ 2 = ft) 2 , 



and this leads to the conclusion that the resultant twist is 

 made up of an sethereal motion in addition to an electronic 

 displacement, neither of which is however or the nature of a 

 pure rotation by itself. 



30. We are now in a position to consider the equations 

 of motion that have been proposed* to explain dispersion, 

 Boussinesq's formula is 



d 2 u d 2 U ( 4 \QA A2 



where m is the mass, u the displacement of the aether, and 

 /I, U, those of "matter," and & = volume elasticity, &c, 



* Glazebrook, B. A. Deport. 1885. 



m 



