476 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
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 z= 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 galvanometer 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 
tffiP+QWR+Sl— F(P+Q)(R + S) 
(P + Q)(R + S) + B(P+Q)(R+ S ) 
Let the induction coefficients between P, Q, R S, be 
given by the following Table, the coefficient of induction 
of P on itself being p, between P and Q, h, and so on. 
Let g be the coefficient of induction of the galvanometer 
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, Y, Z be the integrals of x, y , z 
with respect to t. At making contact x, y , z are zero. After a time z disappears, and 
x and y reach constant values. The equations for each conductor will therefore be 
P Q R S 
P p h k l 
Q li g m n 
R k m r o 
S l n o s 
PX +{p J rh )x+(k +Z )y=jAtf£— §Ddt, 
Q(X — )x-\-(in-\-n)y=^Ddt—^Cdt, 
RY -\-(k-\-m)x-{-(r -\-o)y=§Adt—]l!idt, 
S(Y+Z) +(£ +n )x+(o +s)y=ftdt-$Cdt, 
GZ =§Dtd —§Edt. 
(24) 
Solving these equations for Z, we find 
Z {p+4+l+i+ B (p+R) (^ + s) +G (p+^) (R+s)+PaRs( P + Q+Il + S )} 
= ~ F I^{p~Q“R+i+ /i (p~Q) +^(l-p) + / (i+s) “ m (p+|) 
(25) 
(45) Now let the deflection of the galvanometer by the instantaneous current whose 
intensity is Z be a. 
Let the permanent deflection produced by making the ratio of PS to QR, § instead of 
unity, be 0, 
Also let the time of vibration of the galvanometer needle from rest to rest be T. 
