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

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

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