488 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
it resides in the electrified bodies, conducting circuits, and magnets, in the form of an 
unknown quality called potential energy, or the power of producing certain effects at a 
distance. On our theory it resides in the electromagnetic field, in the space surrounding 
the electrified and magnetic bodies, as well as in those bodies themselves, and is in two 
different forms, which may be described without hypothesis as magnetic polarization 
and electric polarization, or, according to a very probable hypothesis, as the motion and 
the strain of one and the same medium. 
(75) The conclusions arrived at in the present paper are independent of this hypo- 
thesis, being deduced from experimental facts of three kinds : — 
1. The induction of electric currents by the increase or diminution of neighbouring 
currents according to the changes in the lines of force passing through the circuit. 
2. The distribution of magnetic intensity according to the variations of a magnetic 
potential. 
3. The induction (or influence) of statical electricity through dielectrics. 
We may now proceed to demonstrate from these principles the existence and laws of 
the mechanical forces which act upon electric currents, magnets, and electrified bodies 
placed in the electromagnetic field. 
PART IV.— MECHANICAL ACTIONS IN THE FIELD. 
Mechanical Force on a Moveable Conductor. 
(76) We have shown (§§ 34 & 35) that the work done by the electromagnetic forces 
in aiding the motion of a conductor is equal to the product of the current in the con- 
ductor multiplied by the increment of the electromagnetic momentum due to the 
motion. 
Let a short straight conductor of length a move parallel to itself in the direction of 
x:, with its extremities on two parallel conductors. Then the increment of the electro- 
magnetic momentum due to the motion of a will be 
(d¥ dx cJG dy dH dz\ . 
ds ' dx ds~^~ dx ds) ll ' 
That due to the lengthening of the circuit by increasing the length of the parallel con- 
ductors will be 
The total increment is 
/d F dx d F dy d1?dz\. 
ytfe ds ^ dy ds dz ds J ^ 
aha 
which is by the equations of Magnetic Force (B), p. 482, 
(dG 
d F\ 
1 d2 i 
fdY 
dli \\ 
[dx 
~~dy) 
\d* 
dx)\ 
aha: 
Let X be the force acting along the direction of x per unit of length of the conductor, 
then the work done is Xahx. 
