20 Prof. Maxwell an the Theory of Molecular Vortices
|
(116)
|
where P, Q, R are the forces, and f, g, h the displacements. Now when there is no motion of the bodies or alteration of forces, it appears from equations (77)[1] that
|
(118)
|
and we know by (105) that
|
(119)
|
whence
|
(120)
|
Integrating by parts throughout all space, and remembering that
vanishes at an infinite distance,
|
(121)
|
or by (115),
|
(122)
|
Now let there be two electrified bodies, and let
be the distribution of electricity in the first, and
the electric tension due to it, and let
|
(123)
|
Let
be the distribution of electricity in the second body, and
the tension due to it; then the whole tension at any point will be
, and the expansion for U will become
|
(124)
|
Let the body whose electricity is
be moved in any way, the electricity moving along with the body, then since the distribution of tension
moves with the body, the value of
remains the same.
also remains the same; and Green has shown (Essay on Electricity, p. 10) that
, so that the work done by moving the body against electric forces
|
(125)
|
And if
is confined to a small body,
|
|
- ↑ Phil. Mag. May 1861.