
Electric Origin of Rigidity and Consequences. 425 
by purely molecular agency in metals as negligible in com- 
parison with that due fo electrons. 
In the conduction of electricity the gyrostats most affected 
by an E.M.F. are those having their axes at right angles to 
the E.M.F., for the couple acting on the electrostatic doublets 
is greatest when their axes are perpendicular to the E.M.F.. 
Accordingly we shall take as our 
typical case that represented in the 
diagram, where the circle in perspective 
may be taken to be a material fly- 
4 puget heel havi ing the same moment of inertia 
round its axis as the electric gyrostat. 
It is supposed to be rigidly connected 
with the doublet axis round which it 
revolves, the distance between $ and b 
being s and their charges e. The 
couple due to the E.M.F. ‘acting on the charges is denoted 
by the arrows. The electrical gyrostat is similar, then, to 
the tamiliar experimental case of a fly wheel revolving round 
a horizontal axis supported by a universal joint at one end. 
The couple due to gravity and supporting force at the joint 
corresponds to the eouple on the electric doublet. The 
general motion of such a gyrostat is a rotation of the axis in 
a horizontal plane with small vertical oscillations of the axis. 
The period of this vibration is 27A/Co, where @ is the 
velocity of rotation, and the amplitude of the angular vertical 
oscillation of the axis is 2HA/C?m?, where A is the moment 
of inertia of the flywheel round a horizontal axis through 
the centre of mass and perpendicular to the axis of rotation, 
and C is the moment of inertia round the axis of rotation, 
while H is the moment of the couple. Since for our pair of 
electrons 2A=C, we prescribe the same condition for our 
flywheel, and find its period of vibration to be 7/@ and its 
amplitude H/Co’.. In the case of our electric gyrostat, if X 
is the electric force near it, the couple esX takes the place of 
the couple of gravitation for the flywheel. Thus the angular 
amplitude of ‘the oscillations of the axis of the gyrostat is 
esX/Cw*. Denote the period of vibration by +t which we 
have seen to be half the period of rotation of the gyrostat, 
then the average linéar velocity of the electrons ¥ and b at 
the end of the axis is’ es*?X/2Cw?z, assuming the centre of 
inertia to. be at rest. 
We have found, then, that the effect of an electric force X 
on our typical doublet is to give the electrons a to-and-fro 
motion in the direction of X. We have now to show ‘how 
these reciprocating velocities produce a continuous velocity 
