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

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                                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) 
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

James Clerk Maxwell
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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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