-.74 



A DYNAMICAL THEORY OP THE ELECTROMAGNETIC FIELD. 



Let the corresponding quantities at the boundary of the first and second 

 surface be V, and e u and so on. Then by equations (G) and (H), 



^1 = Jit ~jTf ~Pv 



(51), 



&c. 

 But by equations (E) and (F), 



,-, = ,,/,= -r.fr 



( 52 )' 

 &c. &c. &c. J 



After the electromotive force has been kept up for a sufficient time the 

 current becomes the same in each layer, and 



T 



where is the total difference of potentials between the extreme layers. We 

 have then 



yj = ^ , f t = ^- 1 &c. 



J * C*iVj i Utt/v* / f n\ 



and I (53). 



e i ~ r e t= ( ~~r r ) > & c - 



These are the quantities of electricity on the different surfaces. 



(87) Now let the condenser be discharged by connecting the extreme surfaces 

 through a perfect conductor so that their potentials are instantly rendered equal, 

 then the electricity on the extreme surfaces will be altered, but that on the 

 internal surfaces will not have time to escape. The total difference of potentials 

 is now 



whence if e', is what e t becomes at the instant of discharge, 



e', = - -^- - -j~ei--T (55). 



r a,k, ok ak 



