256 Dr. J. A. Fleming on the Distribution of 



which is 



!3(Q+G) + (R+B)(Q + S+G). 



Now the difference of potential e between a and b when the 

 condenser is just beginning to be charged is 



=E 



or 



_ESG ER(Q + S + G) 

 e ~ 8 + S 



SG+R(Q + S + G) 



-G, -R 



Q + S + G, -S 



S(Q+G) + (R + B)(Q + S+G)-S(Q + G) + (R + B)(Q + ! 



?=E 



Gfy R 



Q + S + G, -S 



Now if the electromotive force e be employed n times in a 

 second to charge a jar of capacity K, the average current 

 flowing into the jar is nKe = z. 



Now to find z we have to consider the distribution of cur- 

 rents when the fork or commutator is in operation, and the 

 condenser allowing a flow of electricity to take place through it. 



Let P be the resistance which could equivalently replace 

 the jar and fork — that is, would allow an equal quantity of 



electricity to pass per second ; then, since — ^ is the opposing 



electromotive force in this branch, we have the following 

 equation for the three cycles x, x + z, and y: — 

 -Stf+(R+S + B)#-(R + S>=E, 



-G*-Ry + (P + R>=-^, 



(Q+S+G)*-S#+(Q+S>=0. 



Now let A stand for the determinant 



-S, R + S + B, -(R + S) 



— G, — R, 



Q + S + G, -S, Q+S 



Then the solution of the above equations for z and x are 



P+^+R 



E 



G, 



-R 



Q + S + G, -B 

 A 



