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

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                                and x(P + Q) = y(R + S) = F(P + Q)(R + S)/(P + Q)(R + S) + B(P + Q + R + S) (23) 

Let the induction coefficients between P Q R S be given by the 
following table, the coefficient of induction 
of P on itself being p, between P and Q h 
and so on. 

  P Q R S 
P p h k l 
Q h q m n 
R k m r o 
S l n o s 

Let g be the coefficient of induction of the 
galvanometer on itself and let it be out of 
the reach of the inductive influence of P Q R S 
(as it must be in order to avoid direct action of P Q R S on the needle). 
Let X Y Z be the integrals of x y z with respect to t. 
At making contact x y z are zero. After a time z disappears and 
x and y reach constant values. The equations for each conductor will therefore be 

<s>PX + px + h(x - z) + ky +l(y + z) <\s> 
PX + (p + h)x + (k + l)y = [integral]Adt - [integral]Ddt 
Q(X - Z) + (h + q)x + (m + n)y = [integral]Ddt - [integral]Cdt  
RY + (k + m)x + (r + 0)y = [integral]Adt - [integral]Edt 
S(Y + Z) + (l + n)x + (o + s)y = [integral]Edt - [integral]Cdt 
GZ = [integral]Ddt - [integral]Edt  (24) 
Solving these equations for Z we find 
Z{1/P + 1/Q + 1/R + 1/S + B(1/P + 1/R)(1/Q + 1/S) + BG/PQRS(P + Q + R + S)} = (25) 
= - <s>1/P(1/R + 1/S)<\s>F 1/PS{p/P - q/Q - r/R + s/S + h(1/P - 1/Q) + k(1/R - 1/P) + l(1/R +  1/Q) - m(1/P + 1/S) + n(1/Q) - 1/S) + o(1/S - 1/R)} 
(45) Now let the deflexion of the galvanometer by the instantaneous 
current whose intensity is Z be [alpha] 
Let the permanent deflexion produced by making the ratio of PS to QR 
[rho] instead of unity be [theta]. 
Also let the time of vibration of the galvanometer needle from rest to rest 
be T. 
Then calling the quantity 
                            
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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

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