Hence 



Comparing Capacities. 



±% A+B 



239 



y = 



D 



di]2 



alt' 



C + D 



or 



where 

 Integrating, 



A + B + G, A + B 

 -G, C + D 



A, = A(0 + D)|-(A + B)d| ) . 



A = G(A + B) + (A + B + G)(C + D). 



(1) 



A Vydt = A(0+D) f°rf ?1 -(A + B)D f°<fy 2 , 



Jo JXiAarj, Jk 2 Dx 



where x is the permanent current through A and D when 

 the battery is on. 



But 1 y dt is the quantity which passes through the gal- 

 vanometer, = q. 

 Therefore 



Ag=^ {K 2 D 2 (A + B)-K 1 A 2 (C + D)}. 



If x x is the permanent current in B and 0, 



C . 

 oc — Xi jz ; 



and since AC = BD, we have 



^^GtB + CJ + B^ + Dr ... (2) 

 which may be written 



K2C — KjB 

 g = ^G(B + C) C ' 

 BD + D + 



If now A and D be made infinite, which will obviate the 

 necessity of first adjusting for a permanent balance, 



Also 



E 

 ^-p + B + G' 



