548 



A DYNAMICAL THEOKY OF THE ELECTROMAGNETIC FIELD. 



the current through G will be z. Let the potentials at the four points be A, C, 

 D, E. Then the conditions of steady currents may be found from the equations 



= A-D, Q(x-z) = D-C 



Ry = A-E, S(y + z)=E-C 

 Gz=D-E, E( 



Solving these equations for z, we find 



(21). 



EG 



In this expression F is the electromotive force of the battery, z the current 

 through the galvanometer when it has become steady. P, Q, R, S the resistances 

 in the four arms. B that of the battery and electrodes, and G that of the 

 galvanometer. 



(44) If PS=QR, then 2 = 0, and there will be no steady current, but a 

 transient current through the galvanometer may be produced on making or 

 breaking circuit on account of induction, and the indications of the galvano- 

 meter may be used to determine the coefficients of induction, provided we 

 understand the actions which take place. 



We shall suppose PS=QR, so that the current z vanishes when sufficient 

 time is allowed, and 



Let the induction coefficients between P, Q, R, S 

 l given by the following Table, the coefficient of in- 

 duction of P on itself being p, between P and Q, h, 

 and so on. 



Let g be the coefficient of induction of the gal- 

 vanometer on itself, and let it be out of the reach of 

 the inductive influence of P, Q, R, S (as it must be 

 in order to avoid direct action of P, Q, R, S on the 

 needle) Let X t Y, Z be the integrals of x, y, z with respect to t. At 



