42 
^lESSRS. G. F. C. SEARLE AND T. G. BEDFORD 
The terms in this formnla which involve M are the complete dilFerential of MCc, and 
thus vanish on integration, since c = 0 at both limits. We thus have 
(+ X,)Al = I CN/A + |c I (wAB) dt - T' -f T 
If we multiply (11) by N^C/w and integrate we obtain 
•|Ccd« = -|C 
N/S 
01 
dt 01 dt^ ’ ' 
01 dt 
dt. 
Thus, by addition of the last two equations, 
(W, + X.) U = - I Codt - 1 C I (MC) dt + \c I(« AB) dt 
LNN 
01 
Ct di - T' + T. 
dt 
The first integral in this expression is pro23ortional to the “throw” of the moving 
coil, for, by (7), 
N/S f ^ , N/C'P „ 
— Qcdt = —-- A, 
n J n(f) ^ 
if we measure 0^ in the right direction. 
As regards the second integral. 
d 
Gj^(MC)dt = 
MC- 
Jo 
r dc 
- MC^ f/^. 
J dt 
But since the time of vibration of the suspended coil is comparatively large, the 
change in C is practically complete before the coil has moved far from its equilibrium 
position. Hence M may be treated as constant for the whole range of integration, 
and thus, since O' = at both limits, the value of the integral is zero. 
As regards the fourth integral. 
since c vanishes at both limits. 
Collecting these results, we have 
(W. + X,) a; = 0, + ^ c) dt - T' + T. 
The integral in this expression is the correction which makes its appearance when we 
take account of the finite conductivity of the secondary circuit. It will sufEce to use 
in it the value of Sc which obtains when l^dc/dt is iiegligible in comparison with 
