<s>all such considerations and confine myself to the solution of problems on the mutual action of currents, the experimental det[erm]ination of coefficients of induction, and the calculation of these coefficients from the known form of the circuit.<\s> In order to bring these results within the range of experimental verification I shall next investigate the case of a single current, of two currents and of the six currents in the Electric Balance, so as to enable the experimenter to determine the values of L, M, N. (35) Case of a single circuit The equation of the current in a circuit whose resistance is R and whose coefficient of self=induction is L acted on by an external electromotive force [xi] is [xi]  Rx = d/dt Lx (13) When [xi] is constant, the solution is of the form x = b + (a — b) e<sup> R/L t<\sup> where a is the value of the current at the commencement and b is its final value. The total quantity of electricity which passes in time t where t is great is [equation] (14) The value of the integral of x<sup>2<\sup> with respect to the time is [equation] (15) The actual current changes gradually from the initial value a to the final value b, but the values of the integrals of <s>the<\s> x and x<sup>2<\sup> are the same as if a steady current of intensity [half](a + b) were to flow for a time 2 L/R and were then succeeded by the steady current b. The <s>quantity<\s> time 2 L/R is generally so minute a fraction of a second that the effects on the galvanometer and dynamometer may be calculated as if the impulse were instantaneous. If the circuit consists of a battery and a coil then when the circuit is first completed the effects are the same as if the current had only half its final strength during the time 2 L/R. This diminution
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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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