maximum value, and in the other the energy of the system is
at a minimum value. It is impossible to over-estimate the significance
of these two states of the system.

I may recall the fundamental notion which every one has learned in
mechanics, as to the difference between stable and unstable
equilibrium. The conceivable possibility of making an egg stand on its
end is a practical impossibility, because nature does not like
unstable equilibrium, and a body departs therefrom on the least
disturbance; on the other hand, stable equilibrium is the position in
which nature tends to place everything. A log of wood floating on a
river might conceivably float in a vertical position with its end up
out of the water, but you never could succeed in so balancing it,
because no matter how carefully you adjusted the log, it would almost
instantly turn over when you left it free; on the other hand, when the
log floats naturally on the water it assumes a horizontal position, to
which, when momentarily displaced therefrom, it will return if
permitted to do so. We have here an illustration of the contrast
between stable and unstable equilibrium. It will be found generally
that a body is in equilibrium when its centre of gravity is at its
highest point or at its lowest point; there is, however, this
important difference, that when the centre of gravity is highest the
equilibrium is unstable, and when the centre of gravity is lowest the
equilibrium is stable. The potential energy of an egg poised on its
end in unstable equilibrium is greater than when it lies on its side
in stable equilibrium. In fact, energy must be expended to raise the
egg from the horizontal position to the vertical; while, on the other
hand, work could conceivably be done by the egg when it passes from
the vertical position to the horizontal. Speaking generally, we may
say that the stable position indicates low energy, while a redundancy
of that valuable agent is suggestive of instability.

We may apply similar principles to the consideration of the earth-moon
system. It is true that we have here a series of dynamical phenomena,
while the illustrations I have given of stable and unstable
equilibrium relate only to statical problems; but we can have
dynamical stability and dynamical instability, just as we can have
stable and unstable equilibrium. Dynamical instability corresponds
with the maximum of energy, and dynamical stability to the minimum of
energy.

At tha