Still if the frequency of the impulses be very small, the loss caused
by the impacts and collisions would not be serious unless the
potential were excessive. But when extremely high frequencies and more
or less high potentials are used, the loss may be very great. The
total energy lost per unit of time is proportionate to the product of
the number of impacts per second, or the frequency and the energy lost
in each impact. But the energy of an impact must be proportionate to
the square of the electric density of the sphere, since the charge
imparted to the molecule is proportionate to that density. I conclude
from this that the total energy lost must be proportionate to the
product of the frequency and the square of the electric density; but
this law needs experimental confirmation. Assuming the preceding
considerations to be true, then, by rapidly alternating the potential
of a body immersed in an insulating gaseous medium, any amount of
energy may be dissipated into space. Most of that energy then, I
believe, is not dissipated in the form of long ether waves, propagated
to considerable distance, as is thought most generally, but is
consumed--in the case of an insulated sphere, for example--in impact
and collisional losses--that is, heat vibrations--on the surface and
in the vicinity of the sphere. To reduce the dissipation it is
necessary to work with a small electric density--the smaller the
higher the frequency.

But since, on the assumption before made, the loss is diminished with
the square of the density, and since currents of very high frequencies
involve considerable waste when transmitted through conductors, it
follows that, on the whole, it is better to employ one wire than two.
Therefore, if motors, lamps, or devices of any kind are perfected,
capable of being advantageously operated by currents of extremely high
frequency, economical reasons will make it advisable to use only one