COMPARISON OF CAPACITIES WITH RESISTANCES. 469 



The intensity is modified in all the branches of the network; 

 but as the condition is the same after each break, the sum of the 

 induced currents by mutual or self-induction is zero. Hence in each 

 branch the mean intensity is independent of the manner in which 

 the discharges succeed between N and P ; consequently it is the 

 same as if these two points were joined by a conductor of re- 

 sistance Rj, which allowed the same quantity of electricity I to 

 pass as a continuous current, and conversely. But in this case, 

 if R 2 is the resistance which originally separated the two points, 

 we have, from the theorem of M. Thevenin (946), 



1 = 



If the resistance R x is adjusted so that in any given branch the 

 intensity is the same as with the discharges of the condenser, it 

 follows that 



2C = -^^: 



the capacity is thus found to be determined as a function of two 

 known resistances, and of the number of breaks. 



We may account more completely for the manner in which the 

 currents of discharge are distributed in the network, by referring to 

 the general equations. Let / be the intensity at a given moment in 

 any branch r which contains an electromotive force , L the co- 

 efficient of self-induction of this branch, and Q the flow of external 

 forces, magnets or currents. The difference of potential at the two 

 ends of the branch is 



For a closed circuit of which it forms a part, we have 



re 

 or calling m' = idt the quantity of electricity which traverses the 



Jo 

 branch during the discharge, 



+ [2 (Q + L/)]' - ^ed = . 



