207] CONDUCTION IN DIELECTRICS. 401 



If after the steady state is established, we remove the electro- 

 motive force and leave the system to itself, we have flowing through 

 the wire R per unit of time the quantity 



F 

 R' 



Accordingly we have for the decrease of the charges 



which when combined with the equation 

 (8) ei = 



gives the differential equation 



*(, + .') 47T\ F 



< I4 > -3T ~f *--R- 



Substituting for the charges e l} e^, their values in terms of the 

 difference of potential V, we have 



which being integrated gives 



Putting R= oo , K' we obtain the solution (i i) just found. 

 Considering the condenser B alone discharging through the wire, 

 we obtain, putting K=Q, 



(17) V=V e~^. 



A conducting condenser accordingly behaves, when left to itself, 

 exactly like a perfectly insulating condenser discharging through a 

 wire. The relaxation-time of such a condenser is KR, but for a 

 conducting condenser, although we may use the same formula, 

 the relaxation time is independent of the form or dimensions of 

 the condenser, since, as we have seen in 184, if K be the 

 capacity of the condenser with air as a dielectric, we have 



The relaxation-time is accordingly a characteristic constant of 

 the medium, and may be determined independently of other 

 w. E. 26 



