IV
KINETIC ENERGY OF ELECTRICITY IN MOTION [II]
143
scale divisions, obtained for the part of the deflection mentioned
under the head (3 a):-
+3.6, — 1·0,
- 0·0,
- 2.7,
- 1·1, +0.1, -0.6,
+0.8, - 1·1,
+0.2,
- 0·4,
+ 0.5,
+0.7, +0.5,
+0.8,
+1.2,
+1.1,
+0.7,
+0.6,
+0.7.
The mean of these values is +0.23. The difference from
zero is somewhat larger than the probable error of the result,
but perhaps the cause of the difference is to be looked for in
the somewhat arbitrary calculation of the momentary deflection
rather than in any physical phenomenon. The effect of inertia
should have been a negative deflection, according to the cir-
cumstances of the experiment and the sign used; thus such
an effect could not be detected at all. If we attribute the
constant deflection 0.23 to some other cause, and calculate the
error of the experiments from zero, we still find that the odds
are 14 to 1, that no deflection exceeding a scale division,
and 3480 1, that no deflection exceeding 1 scale division
existed, which could be attributed to an inert mass.
In calculating the experiment on the basis of Weber's
hypothesis, for simplicity I assume that the mass of a positive
unit is the same as that of a negative unit, and that both
electricities flow in the current with equal and opposite velo-
cities. Let m be the mass of the electrostatic unit, v the
velocity with which it is compelled to move in the axis of the
plate AB or in a parallel straight line; and let w be the
velocity of rotation of the plate. Then the apparent force due
to rotation, which acts on the unit perpendicular to its path,
is equal to 2mvw+C, where C is the centrifugal force at the
position of the unit. The unit of opposite sign in the same
position is subject to a force - 2mvw+C. The sum of the
two forces, 2C, represents a ponderomotive force, namely, the
increase in the amount of the centrifugal force acting on the
material of the conductor, due to increase of its mass by that
of the electricity; but the difference, X = 4mvw, is in fact the
electromotive force which we tried to detect by the galvan-
ometer. Now m is equal to M, the mass of all the positive
and negative electricity contained in one cubic millimetre,
divided by the number of electrostatic units contained in one
cubic millimetre; this number again is equal to i, the current-