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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