424 Prof. J. H. Poynting on the Discharge 



We have 



x=i^ (i) 



Now we know that the rate of decrease of charge on the 

 ends is proportional to the charge cr, and therefore to X. 



The decrease of charge or of induction in the medium is 

 therefore 



da X 



dt 



(2) 



where r is a constant, which we may term the specific 

 resistance. 



Hence from (1), 



S+.fe-o < 3 > 



or 



_4jrf 



a=a e Kr (4) 



If we use p to denote the decrease of induction per second, 

 da K <£X /cx 



P=-Tt == -^-df (5) 



KX 2 



The energy per unit volume is -~ — ; its rate of decrease 



is therefore 



"5FdF (6) 



Substituting from (2) and (5), we get the expression which 

 here corresponds to Joule's law for the heating effect, viz. 

 rate of decrease of electric energy per unit volume =p 2 r. 



If at any moment the two end plates be connected by a 

 wire, transfer of induction will at once take place into the 

 wire, and the whole system will be completely discharged. 

 During this discharge there will be magnetic energy accom- 

 panying the motion of electric induction. 



We will now investigate the more complicated case of a 

 stratified dielectric in which the different layers have different 

 specific resistances. Before proceeding to the mathematical 

 account, we shall consider the process generally, taking the 

 simple case in which K is the same throughout. Let the 

 condenser be charged very rapidly and then insulated. At 

 the first moment there will be equal and opposite charges on 

 the two end plates, and the number of induction-tubes running 

 through unit area parallel to the plates will be the same in 

 each layer. But decay of induction and dissipation of energy 



