[Illustration: FIG. 28.]
103. An iron rod A B, capable of revolving round an axis passing
through its centre P, is shown in Fig. 28.
The centre of gravity lies at the centre B, and consequently, as is
easily seen, the rod will remain at rest in whatever position it be
placed. But let a weight R be attached to the rod by means of a binding
screw. The centre of gravity of the whole is no longer at the centre
of the rod; it has moved to a point S nearer the weight; we may easily
ascertain its position by removing the rod from its axle and then
ascertaining the point about which it will balance. This may be done
by placing the bar on a knife-edge, and moving it to and fro until the
right position be secured; mark this position on the rod, and return it
to its axle, the weight being still attached. We do not now find that
the rod will balance in every position. You see it will balance if the
point S be directly underneath the axis, but not if it lie to one side
or the other. But if S be directly over the axis, as in the figure, the
rod is in a curious condition. It will, when carefully placed, remain
at rest; but if it receive the slightest displacement, it will tumble
over. The rod is in equilibrium in this position, but it is what is
called _unstable_ equilibrium. If the centre of gravity be vertically
below the point of suspension, the rod will return again if moved away:
this position is therefore called one of _stable_ equilibrium. It is
very important to notice the distinction between these two kinds of
equilibrium.
104. Another way of stating the case is as follows. A body is in
stable equilibrium when its centre of gravity is at the lowest point:
unstable when it is at the highest. This may be very simply illustrated
by an ellipse, which I hold in my hand. The centre of gravity of
this figure is at its centre. The ellipse, when resting on its side,
is in a position of stable equilibrium and its centre of gravity is
then clearly at its lowest point. But I can also balance the ellipse
on its narrow end, though if I do so the smallest touch suffices to
overturn it. The ellipse is then in unstable equilibrium; in this case,
obviously, the centre of gravity is at the highest point.
[Illustration: FIG. 29.]
105. I have here a sphere, the centre of gravity of which is at its
centre; in whatever way the sphere is placed on a plane, its centre is
at the same height, and therefore cannot be said to have any highest
or lowest point; in such a case as this the equilibrium is _neutral_.
If the body be displaced, it will not return to its old position, as
it would have done had that been a position of stable equilibrium,
nor will it deviate further therefrom as if the equilibrium had been
unstable: it will simply remain in the new position to which it is
brought.
106. I try to balance an iron ring upon the end of a stick H, Fig. 29,
but I cannot easily succeed in doing so. This is because its centre of
gravity S is above the point of support; but if I place the stick at
F, the ring is in stable equilibrium, for now the centre of gravity is
below the point of support.