604 PEOF. J. J. THOMSON" AND MR. G. F. C. SEARLE ON THE RATIO OF THE 
Thus, when the commutators are working, there will, owing to the flow’ of electricity 
to the condenser, be a succession of momentary currents through the galvanometer. 
The resistances are so adjusted that the effect of these momentary currents on the 
galvanometer just balances the effect due to the steady current, and there is no 
deflection of the galvanometer. 
To investigate the relation between the resistances when this is the case, let us 
suppose that when the guard ring and condenser are charging 
X — current through BC. 
y = current through AR. 
z z=: current through AD. 
%v — currrent through CL. 
Thus, if a, h, ol, 13 , y are the resistances in the arms BC, AC, AD, BD, CD 
respectively, L the; coefflcient of self induction of the galvanometer, and E the 
electromotive force of the battery, we have 
L2; + (^ + 7 + “) 2: -]- {& + y) 2/ “k 7 ^^‘ yx = 0 . . . . (l) 
{a-\-y^)x —(y-\- ^)y — yz — {y+/ 3 ) 7 V— E = 0 .... (2) 
Now it is evident that the currents are expressed by equations of the following 
kind 
x — x^-\- X.2, 
Z= + 22 , 
wdiere x^ and 2 ^ express the steady currents wdien no electricity is flowing into the 
condenser, and Xo, z^ are of the form Be~^‘, and express the variable parts of the 
currents due to the charging of the condenser, ij and tv will be of the form Ce”'^', 
De~^‘ ; t in all tliese equations is the time which has elapsed since the condenser 
commenced to charge. 
Ecjuations (1) and (2) will thus contain constant terms, and terms multiplied by 
the latter must separately vanish, hence we have 
D 22 + + 7 + “) ^2 + (^ + 7) 2 / + yio — yaq =0.( 0 ) 
{a + y + ^) a;3 — (7 + ^) y — 723 — (y + y8) ?<; = 0 .( 4 ) 
Let Z, X be the quantities of electricity w'hich have passed through the galvano¬ 
meter and battery respectively, in consequence of the charging of the condenser, and 
