134 DISTRIBUTION OF ELECTRICITY ON MOVING CONDUCTORS
III
position of the charges on the outer and inner curved surfaces.
The lines occupying the substance of the cylinder represent
the lines of flow.
It remains to inquire in what practically realisable cases
the effects discussed could become appreciable. Clearly they
FIG. 16.
attain a measurable value
when the angle of rota-
tion becomes measurable,
and this occurs when for
solid bodies the quantity
K/T, or when for very
thin shells the quantity
KR/T, has a finite value.
Here R denotes the mean
distance of the shell from
theaxis of rotation. Since
T cannot well become less
than To second, must reach at least several hundredths of
a second. Thus it is obvious that in metallic conductors, for
which is of the order of trillionths of a second, the rotation
phenomenon can never be appreciable. On the other hand, it
is obvious that even at moderate velocities no measurable
charge can be formed upon insulators such as shellac and
paraffin, for which is many thousand seconds. But for
certain other substances, which lie at the boundary between
semi-conductors and bad conductors, the phenomenon should
be capable of complete demonstration; e.g. for ordinary kinds
of glass, for mixtures of insulators with conductors in form of
powder, for liquids of about the conductivity of petroleum, oil
of turpentine, or mixtures of these with better conducting
ones, etc.
As the specific resistance x is connected in a simple
way with the angle of rotation, measurements of the latter
might serve to determine the former. However, in bodies of
the necessary resistance the phenomena of residual charge
occur, and our differential equations only hold roughly for
these. The effect of a residual charge will always be to make
the constant appear less than it is found to be from observa-
tions on steady currents, and less too by an amount increasing
with the velocity of rotation. The dielectric displacement
acts in the same sense, since it is equivalent to partial con-