t primitive epoch, when the energy of the earth-moon system was
a maximum, the condition was one of dynamical instability; it was
impossible that it should last. But now mark how truly critical an
occurrence this must have been in the history of the earth-moon
system, for have I not already explained that it is a necessary
condition of the progress of tidal evolution that the energy of the
system should be always declining? But here our retrospect has
conducted us back to a most eventful crisis, in which the energy was a
maximum, and therefore cannot have been immediately preceded by a
state in which the energy was greater still; it is therefore
impossible for the tidal evolution to have produced this state of
things; some other influence must have been in operation at this
beginning of the earth-moon system.

Thus there can be hardly a doubt that immediately preceding the
critical epoch the moon originated from the earth in the way we have
described. Note also that this condition, being one of maximum energy,
was necessarily of dynamical instability, it could not last; the moon
must adopt either of two courses--it must tumble back on the earth, or
it must start outwards. Now which course was the moon to adopt? The
case is analogous to that of an egg standing on its end--it will
inevitably tumble one way or the other. Some infinitesimal cause will
produce a tendency towards one side, and to that side accordingly the
egg will fall. The earth-moon system was similarly in an unstable
state, an infinitesimal cause might conceivably decide the fate of the
system. We are necessarily in ignorance of what the determining cause
might have been, but the effect it produced is perfectly clear; the
moon did not again return to its mother earth, but set out on that
mighty career which is in progress to-day.

Let it be noted that these critical epochs in the earth-moon history
arise when and only when there is an absolute identity between the
length of the month and the length of the day. It may be proper
therefore that I should provide a demonstration of the fact, that the
identity between these two periods must necessarily have occurred at a
very early period in the evolution.

The law of Kepler, which asserts that the square of the periodic time
is proportioned to the cube of the mean distance, is in its ordinary
application confined to a comparison between the revolutions of the
several planets about the sun. The periodic time