﻿Theory oj Dispersion. 471 



Hence we have, if 



X=^7, (§21) 



S — W(g-g), where * =^. . (20) 



(on the understanding that /x=l), so that Y is the velocity 

 of propagation in free aether. 



19. From (14), (16), and (21) we get 



:=-^ v » 2 (|-E) • • • • ^ 



in stationary media 



20. Let T x = kinetic energy of an electron (e), 



T 2 = that of the aether, 



Y 2 = potential energy of the aether, 



V x = potential energy due to extraneous forces. 



Then since — /(/3A — yg) dr = momentum of the field in the 

 direction of x (J. J. Thomson, 'Recent Researches'), 



4K*~ 4,(lf'> 



a, y, z defining the position of an electron. 



Applying the Lagrangian equations of motion for the 

 system consisting of the aether and the electron, viz.: 



i/BT. 3T S \ SC^+T,) , d( v i+ v ^o 

 since ^T t 



= 0, obviously. 



9V 



a* 



=-HKI-S>-(l-l>]--J^-- ) - ( '-^ ] '" 



+ f«-l*. (23) 



