PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
475 
The total quantity of electricity is <7 ^ , and the value of §y 2 dt is c 2 • 
The effects on the galvanometer and dynamometer are equal to those of a uniform 
current 4 c ^ for a time 2 • 
2 N S 
The heating effect is therefore greater than that of the current on making contact. 
(42) If an electromotive force of the form £=E cos pt acts on the circuit R, then if 
the circuit S is removed, the value of x will be 
E 
x= ^ sin (pt—ot), 
where 
A 2 =R 2 +Ly, 
and 
tan 
The effect of the presence of the circuit S in the neighbourhood is to alter the value 
of A and a, to that which they would be if R become 
and L became 
R+y 
MS 
S 2 +p 2 N 2 ’ 
T » MN 
L'-JP S 2 +/ 2 N 2 ‘ 
Hence the effect of the presence of the circuit S is to increase the apparent resistance and 
diminish the apparent self-induction of the circuit R. 
On the Determination of Coefficients of Induction by the Electric Balance. 
(43) The electric balance consists of six con- 
ductors joining four points, A C D E, two and two. 
One pair, A C, of these points is connected through 
the battery B. The opposite pair, D E, is connected 
through the galvanometer G. Then if the resistances 
of the four remaining conductors are represented by 
P, Q, R, S, and the currents in them by x, x—z, y, 
and y-\-z , 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 
P*=A — D Q(x—z)=D—C, I 
R^=A — E S(y+z)=E-C, i (21) 
Gs=D— E B(x+y)= - A+C+F. ] 
Solving these equations for z, we find 
■e 
p+q+r+s+ b (p+ r) (q+s) + g (p+q) (r + i) +p^|s( p + q+r+s ^}— f (ps~qr)- 
MDCCCLXV. 
3 T 
