404 ELECTROKINETICS. [PT. II. CH. X. 



and since J\ is finite, as we decrease r indefinitely, we have in the 

 limit, since -F'i(O), F. 2 (0) are zero, 



do) . 



That is, the forces jump suddenly from zero to F^ and F 2 , while 

 the total quantity of electricity e= lldt passes from one plate to 

 the other. This is called the instantaneous charge. 



From the equations (10), (7), we find 



(II) 



(12) 



the same as if there were no conductivity, as in 188. The 

 ratio 



e S 



(13) 



or the instantaneous capacity, is the same as the true capacity. 

 If we now keep the electromotive force E in the wire, electricity 

 continues to flow into the condenser, its plates always maintaining 

 the same difference of potential F a F 2 =E. The capacity appears 

 to increase without limit. In order to examine what goes on, we 

 must integrate the differential equations. Eliminating / from (8) 

 and (9), 



By means of the equation (7) we may introduce F z in terms of 

 F l and E, and differentiating the equation (7), 



from which we may obtain dF 2 /dt in terms of dFJdt, giving finally 



dF l 



dt ~ 



as 



the differential equation for F^ This is to be integrated with 



