for estimating the intensity and duration of a current uniform while it lasts which would produce the same effects (39) Let n<sub>1<\sub> n<sub>2<\s> be the roots of the equation (LN  M<sup>2<\sup>)n<sup>2<\sup> + (RV + LS)n + RS = 0 and let the primary coil be acted on by a constant electromotive force Rc so that c is the constant current it could maintain then the complete solution of the equations for making contact is [equations] From these we obtain for calculating the impulse on the dynamometer [equations] The effects of the current in the secondary coil on the galvanometer and dynamometer are the same as those of a uniform current  [half]c MR/ RN + LS for a time 2(L/R + N/S) (40) The equation between work and energy may be easily verified. The work done by the electromotive force is [xi][integral]xdt = c<sup>2<\sup>(Rt  L) Work done in overcoming resistance and producing heat = R [integral] x<sup>2<\sup>dt + S [integral] y<sup>2<\sup>dt = c<sup>2<\sup>(Rt =3/2 L) Energy remaining in the system = [half] c<sup>2<\sup> L (41) If the circuit R is suddenly and completely interrupted while carrying a current c then the equation of the current in the secondary coil would be y = C M/N e<sup> S/N t<sup> This current begins with a value c M/N and gradually disappears The total quantity of electricity is c M/S and the value of [integral]y'<sup>2<\sup> dt is c<sup>2<\sup>M<sup>2<\sup> 2SN The effects on the galvanometer and dynamometer are equal to those of a uniform current [half] C M/N for a time 2 N/S The heating effect is therefore greater than that of the current on making cont[act?]
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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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