32
I
KINETIC ENERGY OF ELECTRICITY IN MOTION [I]
The kinetic energy of the electric flow in one cubic milli-
metre of a copper wire, which is traversed by a current of
density equal to 1 electromagnetic unit, amounts to less than
0.008 milligramme-millimetre.
As the kinetic energy is half the product of the mass by
the square of the velocity, the mass of the positive electricity
in 1 cubic millimetre
e.g. if v = 1
mm
sec
m
10
sec
0.008 mg
v2
the mass of positive electricity
<0·008 mg., <00008 mg., etc.
But we must bear in mind the possibility of the kinetic
energy of the current exceeding the limit here marked out,
without the observations necessarily being erroneous on that
account. For if the conductivity of the metals is in the ratio
of the densities of the electricity in them, then the electro-
motive forces arising from inertia will be equal in two wires
of equal resistance, whatever be the material, length, and cross-
section of the wires. In this case the extra-currents from
the four branches of the bridge, in so far as they were due to
mass, would also be equal, and would thus neutralise each
other. It is only on the assumption that the above propor-
tionality does not exist, but that the density of electricity is
approximately the same in different conductors, that it is
allowable to neglect, as we have done, the effect of the mass
moved in the short branches of German-silver and of gas-
carbon.
Vice versa, if by some other method we succeeded in prov-
ing that the kinetic energy of the electric current exceeds the
limit stated, the above experiments would show that the
densities of electricity in the materials used are in the ratio
of their conductivities.
A decision as to the possibility mentioned could theo-
retically be obtained by dynamometric experiments, or by
observing the values at different times of induction and extra-
currents; but in practice all the arrangements of experiment