128 DISTRIBUTION OF ELECTRICITY ON MOVING CONDUCTORS
III
charged bodies near them, and the same is true of charged
liquid jets.
The nature and magnitude of the phenomena indicated
will in the following be submitted to calculation.
In forming the differential equations we assume that the
only possible state of motion of electricity in a conductor is the
electric current. Hence if a quantity of electricity disappears
at a place A and appears again at a different place B, we
postulate a system of currents between A and B, not a motion
of the free electricity from A to B. The explicit mention
of this assumption is not superfluous, because it contradicts
another, not unreasonable, assumption. When an electric pole
moves about at a constant distance above a plane plate the
induced charge follows it, and the most obvious and perhaps
usual assumption is that it is the electricity considered as a
substance which follows the pole; but this assumption we
reject in favour of the one above mentioned. Further, we
leave out of account all inductive actions of the currents
generated. This is always permissible, unless the velocity of
the moving conductors be comparable with that of light.
Let u, v, w be components of current parallel to the axes
of x, y, z; the total potential, h the surface-density, the
specific resistance of a conductor, all measured in absolute
electrostatic units. Thus is a time, in fact the time in
which a charge arbitrarily distributed through the conductor
diminishes to 1/4" of its original value. If now we refer
everything to coordinates fixed in the conductor and consider
the motion in this conductor, we have
KU =
Эф
მეა
"
KV =
-
Әф
>
მყ
ди
du
av
=
4π
dw
+
KW =
эф
Əz
(1),
(2),
(3),
(4),
dAp
dt
Əx + by + əz
· = u cos a + v cos b+w cos c
dh
dt
офі
афе
-
- 4Th =
+
Əni
ane
in which equation n,, n, denote respectively the internal and