Electric Currents in Networks of Conductors. 25? 



and 



E 



&■=• 



-R, P+^+R 



-B, Q + S 



z is the average current flowing through the condenser, and x 

 is the current through the galvanometer. Now let the resist- 

 ances R, S, and Q be so varied that the current through the 

 galvanometer is zero , then^ = 0; and therefore 



1 



= 0, 



or 



or 



-R, P+-^+R 



-S, Q + S 



RQ 



Now insert this value for P + 



iK 



in the determinant A 



above and calculate its value, and we arrive at the expression 



A = 



{B(Q + S) + Q(R+S)}{G(R+S) + B(Q + S)} 



S 



We have now, by substitution of this value of A in the value 

 obtained above for z, an expression for the value of the average 

 current through the condenser when the bridge is balanced, 

 and it is 



— Gr, — R 



Q+S + G, -S 



ES 



S- {B(Q + S) + Q(R + S)}{G(R+S) + R(Q + S)}' 

 Equating this to the other value for z, namely, 



?=7iK<?=rcKE 



— *- Gr, — ■ R 



Q + S + G, -8 



S(Q+G) + (R+B){Q+S + G} 



we have 



S{S(Q + G) + (R + B)(Q + S + G)j- 

 nJV -{B(Q + S) + Q(R + S)}{G(R + S) + R(Q + Sn 5 

 which gives us a value for nK in terms of 

 B, Q, R, S, Gr. 



