ay be assumed by celestial bodies in the course of
their evolution. I believe further that homologous conceptions are
applicable in the consideration of the transmutations of the various
forms of animal and of vegetable life and in other regions of thought.
Even if some of my readers should think that what I shall say on this
head is fanciful, yet at least the exposition will serve to illustrate
the meaning to be attached to the laws of stability in the physical
universe.

I propose, therefore, to begin this essay by a sketch of the principles
of stability as they are now formulated by physicists.

I.

If a slight impulse be imparted to a system in equilibrium one of two
consequences must ensue; either small oscillations of the system will
be started, or the disturbance will increase without limit and the
arrangement of the system will be completely changed. Thus a stick may
be in equilibrium either when it hangs from a peg or when it is balanced
on its point. If in the first case the stick is touched it will swing to
and fro, but in the second case it will topple over. The first position
is a stable one, the second is unstable. But this case is too simple to
illustrate all that is implied by stability, and we must consider cases
of stable and of unstable motion. Imagine a satellite and its planet,
and consider each of them to be of indefinitely small size, in fact
particles; then the satellite revolves round its planet in an ellipse. A
small disturbance imparted to the satellite will only change the ellipse
to a small amount, and so the motion is said to be stable. If, on the
other hand, the disturbance were to make the satellite depart from its
initial elliptic orbit in ever widening circuits, the motion would be
unstable. This case affords an example of stable motion, but I have
adduced it principally with the object of illustrating another point
not immediately connected with stability, but important to a proper
comprehension of the theory of stability.

The motion of a satellite about its planet is one of revolution or
rotation. When the satellite moves in an ellipse of any given degree
of eccentricity, there is a certain amount of rotation in the system,
technically called rotational momentum, and it is always the same at
every part of the orbit. (Moment of momentum or rotational momentum
is measured by the momentum of the satellite multiplied by the
perpendicular from the planet on to the direction of the pat