336 Prof. A. Anderson on 



NAB, and let the currents round these circuits be denoted 

 respectively by x, z, y, and u. Then, if B be the resistance 

 of the battery, G of the galvanometer, L the coefficient of 

 self-induction of the coil in the branch DC, X that of the 

 galvanometer-coil, K the capacity of the condenser and u its 

 charge, we have, employing the same notation as that used in 

 Prof. Niven's paper 



F=i{Y{x + u) 2 + r(x + u-zy 2 + Qz 2 + U(y-zy 



+ G(x-z) 2 + S(y--zy + Bf}, 

 H=w 2 /2K. 



Hence, if x, y, z denote the total transient flow round the 

 respective circuits during the time of setting up or destroy- 

 ing the permanent state at make or break of the battery- 

 circuit, and x , y , z the steady values of the currents, we 

 easily find : — 



(E + S + B)y-R^-S^=~L( 2 /o-%)-X(^o- 2 ; ); 

 (r + a> + ^-(r + Q+0+S>==-L(^ o -«b)-^*-*)-KrP^ ; 

 (P +r+B, + Gt)x-'Ry-(r+G)z=-KP(P + r)x . 



Writing for x Q , fit, for y —z , a, and for oc — z } q, and 

 observing that x ~z and that PS = QR, we find without 

 difficulty 



_ K/3P{PQ + r(P +_Q} 2 PL * 

 q ~ P(Q + S)+(P + Q)(r+G) • 



Thus, when q = 0, 



L=^K(PQ + ,(P + Q)), 



= ~K(PQ + r(P + Q)), 



= K(BQ + >»(R + S)), 



which is the same equation as before. 



To estimate the sensitiveness of the final adjustment, we 

 will calculate the ratio of the small change produced in a to 

 the small change made in r when ^ = 0, 



