Now 



and 



Hence 



Also 



Comparing Capacities. 241 



(„-v 2 )=g= ( v 1 -v 2 ) E ^ E2 ^ 

 ( v 1 - B ) = g=(v 1 -v 2 )(i- 1 ^- / -^). 



t 



v-V 2 = K t e ^ R 



^ 2 -V 2 C 



If, therefore, v = v 2 , or there appears to be a balance, 



t 

 C _ K,e ^ R 



B~ 



Ki(l-e K ^ R )+K 



or 



K i = ^x • 



(B + C)e K ^-G 



So that, unless t be made very small compared to K 2 R, we 

 cannot compare K, and K 2 unless we know R and t. In the 

 case of no leakage the conditions will be the same as if there 

 were no key in the galvanometer circuit. 



To find the best conditions for the test : — Taking equa- 

 tion (2), and substituting for x x its value 



E D 



(A-f-DKB + C) " C + D' 

 P+ A+D+B+C 



TTT) 



which equals —7^ — ^r — ^-tt; — ~-, since AC = BD, we obtain 



EBD^C-K.B) 



^~{ /^ (C + D) + D(B^-C)}{G(B + C)+B(C^-D)} , 



If y=0, KsC^KiB. 



Suppose a fractional error p to be made in the value of C 

 Phil. Mag. $. 5. Vol. 24. No. 148. Sept. 1887. R 



