■Electromagnetic Capacity of a Condenser. 173 



If x, y, 2, w denote the integral cyclic currents reckoned 

 from the instant of make, 



F{x+y-iv)-j- Gx +R{x+y)=0 

 -Go; +Q(y -to) + S(y-e) =0 

 Y(io-x-y)+ Bio + Q{w-y)=$E . dt 



Substituting for 2 in the second equation and rearranging, 



(i.) 



r- 



#: 



(P + G+R> + (P + R)#- Pte =0 



-G* + (Q + S)y- Qio =.CS 2 ^ L (ii.) 

 -P.* -(P + Q)y+(P + Q+B)«7=(\E.<fc (iii.) 

 Hence 



P + R -P 



CS 2 2/ w Q + S -Q -(P'+Q) P + Q + B 



fE.<to -(P + Q) P + Q + B CS 2 ^ P + R -P 



P + G + R P+R -P 



-G Q+S -Q 



-P -(P+Q) P+Q + 



CS 2 2/ c 



= A 



(PB + PR + QR + BR). 



To find the steady current y n ultimately flowing through 

 S we have the same equations, except that the right-hand 

 side of (ii.) is zero, and x n1 y x , w x instead of .a?, y, iv. 

 Hence 



#• = 



P + G + R 







-P 



-G 







-Q 



-P 



E 



P + Q + B 



= |(PQ + GQ + RQ + PG). 



Therefore the integral current through the galvanometer is 

 ,^=^^(PB + PR + QR + BR)(PQ + GQ + RQ + PG). 



When the balance is disturbed by S becoming S + dS, the 

 cyclic equations for steady currents are 



(P + G + E)4.+ (P + R)&. - Pw„ =0 



-0*. + (Q + Sf<2S) 2 / oo - Qri. =0 



-P4. - (P+Q)tf. +(P + Q + B)w.=Ej 



