# J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’

```                                On the determination of Coefficients of Induction
by the Electric Balance
[diagram]
(43) The Electric Balance consists of <s>five<\s> six conductors
joining four points A C D E two and two. One pair, AC of these
points is connected through the battery, B. The opposite pair DE
is connected through the galvanometer G. Then if the resistances
of the four 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 being z.
Let the potantials at the four points be A C D E. Then the conditions
of steady currents may be found from the equations
Px = A - D Q(x - z) = D - C
Ry = A - E S(y + z) = E - C
Gz = D - E B(x + y) = -A + C + F (21)
Solving these equations for z we find
<s>Z{1/P + 1/Q + 1/R + 1/S + G(1/P + 1/G)(1/R + 1/S)} = B(1/PS - 1/QR)
If PS = QR then z = 0 <\s>
Z{1/P + 1/Q + 1/R + 1/S + B(1/P + 1/R)(1/Q + 1/S) + G(1/P + 1/Q)(1/R + 1/S) + BG/PQRS(P + Q + R + S)} = F(1/PS - 1/QR) (22)
<s>If PS = QR then z = 0 <\s> In this expression F is the electromotive force of the battery z the <s>consta<\s>
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
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.

```
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## Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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## Cite as

J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7