the Electrical Capacities of two Condensers. 373 



™- -n 2 ) tGOVR + p W + f/J 



RK- 



♦J(A-ft)} < 15 » 



and similar values for A/ A/. 

 Hence we find 



_. _, f R' R ) 



+ ^[(e^-rc)^"' ( -^) 



Let us take the case in which there is no leakage first, 

 p = p f = go , and 



^(W'-BO)^-^'- • < 17) 



Gr(wi— n 2 ) 



Thus, if RC = R'CK, we see that a? is zero for all values of t. 



The total effect on the galvanometer, since the time of 

 charging is short, is proportional to the quantity of electricity 

 which passes. To find this we integrate the value of x with 

 respect to t from to t, and suppose r so large that 



Then, if P be the quantity, 



p _ E(R'CK-RC) 



GRR'CC'%V 



also G + R + R' 



?h n = 



"1 ,t 2 



GRR'CO 



. E(RC'-RC) 



• • r ~ G + R+R ' • • • • ( 18 > 



and if H be the strength of the field in which the needle 

 hangs, T the time of a complete oscillation, k the galvano- 

 meter-constant, and « the angle through which the needle is 

 turned, HT . « 



. « wA E(R'C'-RC) nm 



•• sm 2 _ HT - (G + R+R)'" ' ' ( ' 



