An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

SCHLICK'S METHOD OF STEADYING VESSELS AT SEA 69

tells us, not be influenced thereby, but will remain exactly as
great as before. That this is the case will also be readily
apparent, since no consumption of energy takes place in the
apparatus, the period only being influenced by the increase
which takes place in the swinging mass.
"Were it possible to fit a fly-wheel of this kind, able to swing
in its frame without experiencing friction, into a vessel, this
would be advantageous in so far that, to begin with, the rolling
motions would become slower, and therefore less unpleasant, and
then, on account of the great difference thus produced between
their period and that of the waves, they would cease to be of
any consequence. The rolling motions of the vessel would then
become considerably less in extent. If the frame which bears
the fly-wheel be screwed tight on the model, so that it can no
longer turn, the effect hitherto produced by it will cease, and the
pendulum will swing with the same period as it would if the
fly-wheel were not rotating.
"It will readily be seen that the effect produced upon the
swings of the pendulum by the rotating fly-wheel can be of
greater extent only so long as the plane of the frame bearing the
fly-wheel remains approximately vertical.
" If the axis of the fly-wheel be inclined at an angle a to the
vertical, the moment thus produced, acting against the motion of
the pendulum, will be proportional to the value of cos a. Should
the axis of the fly-wheel momentarily become horizontal, a
position which with a pendulum in violent motion it may almost
reach, that is to say, should a = 90~ and cos a = 0, the influence
of the fly-wheel will disappear altogether.
"Since, as already stated, there is a phase difference of 90~
between the swings of the pendulum and those of the axis of
the fly-wheel, the gyroscopic influence on the pendulum must be
least in amount when it is passing the middle position, i.e., at
the very position at which it has its greatest angular velocity,
because at the same moment the inclination of the axis of the
fly-wheel is at its greatest, while the velocity with which it is
changing its inclination has become very small or vanished
altogether. When, on the other hand, the pendulum has reached
its outermost position, and is changing the direction of its motion,
thus for an instant reaching a state of rest, the axis of the flywheel then proceeds with its greatest angular velocity through
the middle position, the fly-wheel thereby exerting its greatest
influence. It will thus be evident that the conditions for the
exertion of the greatest possible influence of the gyroscopic
action on the pendulum are not present here. In order that the
motion of the pendulum may be effectively influenced, the
oscillation of the frame with the axis of the fly-wheel will have
to be reduced in a suitable degree. In the model illustrated in
Fig. 32 this may be most simply effected by tightening the
screws pp to a suitable extent, so that they act as a brake on the