PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
483 
Electromotive Force in a Circuit. 
(63) Let | be the electromotive force acting round the circuit A, then 
«=J( p s+«S+ B £)^ < 32 ) 
where ds is the element of length, and the integration is performed round the circuit. 
Let the forces in the field be those due to the circuits A and B, then the electro- 
magnetic momentum of A is 
J’( f s+ g I+ h S)*= l “+ m »> ( 33 ) 
where u and v are the currents in A and B, and 
(34) 
Hence, if there is no motion of the circuit A, 
d F 
dV ] 
dt 
dx 5 
dG 
d'Y I 
dt 
~dy ’ ’ 
dYL 
~ dt 
(35) 
where Y is a function of x, y, z , and t, which is indeterminate as far as regards the 
solution of the above equations, because the terms depending on it will disappear on 
integrating round the circuit. The quantity Y can always, however, be determined in 
any particular case when we know the actual conditions of the question. The physical 
interpretation of Y is, that it represents the electric potential at each point of space. 
Electromotive Force on a Moving Conductor. 
(64) Let a short straight conductor of length «, parallel to the axis of x , move with 
a velocity whose components are and let its extremities slide along two 
parallel conductors with a velocity j ( . Let us find the alteration of the electro- 
magnetic momentum of the circuit of which this arrangement forms a part. 
In unit of time the moving conductor has travelled distances ^ along the 
directions of the three axes, and at the same time the lengths of the parallel conductors 
ds 
included in the circuit have each been increased by 
Hence the quantity 
jH:+ G f+ H £> 
3 u 
MDCCCLXV. 
