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

```                                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
```
images

## 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