Mutual Action of two Currents (23) If there are two electric currents in the field, the magnetic force at any point is that compounded of the forces due to each current separately and since the two currents are in connexion with every point of the field they will be in connexion with each other so that any increase or diminution of the one will produce a force acting with or contrary to the other. <s>As a dynamical illustration suppose two horses harnessed to a carriage by the intervention of a lever so that each horse pulls at its own arm of the lever while the lever is attached to the carriage by its fulcrum. Then if one horse increases its speed the immediate effect will be to produce a tension in the traces of the other horse tending to pull him back. <\s> Dynamical Illustration of Reduced Momentum (24) As a dynamical illustration, let us suppose a body C so connected with two independent driving points A and B that its velocity is p times that of A together with q times that of B. Let u be the velocity of A v that of B and w that of C and let [delta]x, [delta]y, [delta]z be their simultaneous displacements then by the general equation of dynamics ("Lagrange Mec. Anal. II. 2. ff5) [equation] where X and Y are the forces acting at A & B. But [equation] and [equation] Substituting and remembering that [delta]x and [delta]y are independent [equations] (l) We may call Cp<sup>2u + Cpqv the Momentum of C referred to A and Cpqu + Cqv its momentum referred to B then we may say that the effect of X is to increase the momentum of C referred to A and that of <s>B<\s>Y to increase its momentum referred to B
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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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