PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
467 
tional momentum, which may be called the momentum of the fly-wheel reduced to 
the driving-point. The unbalanced force acting on the driving-point increases this 
momentum, and is measured by the rate of its increase. 
In the case of electric currents, the resistance to sudden increase or diminution of 
strength produces effects exactly like those of momentum, but the amount of this mo- 
mentum depends on the shape of the conductor and the relative position of its different 
parts. 
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 con- 
trary to the other. 
Dynamical Illustration of Deduced 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 lx, 
ly, Iz be their simultaneous displacements, then by the general equation of dynamics*, 
C^lz=lLlx+Yly, 
where X and Y are the forces acting at A and B. 
But 
dw du dv 
dt=P~di+2Jt' 
and 
lz—plx-\-qly. 
Substituting, and remembering that lx and ly are independent, 
X~=j t (Cfu+Cpqv), | 
^=J t (Cpqu+Cq 2 v). 
We may call Cp 2 u-\-Cpqv the momentum of C referred to A, and Cpqu-\-Cq 2 v its 
momentum referred to B ; then we may say that the effect of the force X is to increase the 
momentum of C referred to A, and that of Y to increase its momentum referred to B. 
If there are many bodies connected with A and B in a similar way but with different 
values of p and q, we may treat the question in the same way by assuming 
L=2(Cp 2 ), M=2(Cp2), andN=2(C f), 
* Lagrange, Mec. Anal. ii. 2. § 5. 
3 s 
MDCCCLXV. 
