. The
day and the month were equal at the beginning, the day and the month
will be equal at the end. Yet how wide is the difference between the
beginning and the end. The day or the month at the end is some
hundreds of times as long as the month or the day at the beginning.

I have already fully explained how, in any stage of the evolutionary
progress in which the day and the month became equal, the energy of
the system attained a maximum or a minimum value. At the beginning the
energy was a maximum; at the end the energy will be a minimum. The
most important consequences follow from this consideration. I have
already shown that a condition of maximum energy corresponded to
dynamic instability. Thus we saw that the earth-moon history could not
have commenced without the intervention of some influence other than
tides at the beginning. Now let us learn what the similar doctrine
has to tell us with regard to the end. The condition then arrived at
is one of dynamical stability; for suppose that the system were to
receive a slight alteration, by which the moon went out a little
further, and thus described a larger orbit, and so performed more than
its share of the moment of spin. Then the earth would have to do a
little less spinning, because, under all circumstances, the total
quantity of spin must be preserved unaltered. But the energy being at
a minimum, such a small displacement must of course produce a state of
things in which the energy would be increased. Or if we conceived the
moon to come in towards the earth, the moon would then contribute less
to the total moment of momentum. It would therefore be incumbent on
the earth to do more; and accordingly the velocity of the earth's
rotation would be augmented. But this arrangement also could only be
produced by the addition of some fresh energy to the system, because
the position from which the system is supposed to have been disturbed
is one of minimum energy.

No disturbance of the system from this final position is therefore
conceivable, unless some energy can be communicated to it. But this
will demonstrate the utter incompetency of the tides to shift the
system by a hair's breadth from this position; for it is of the
essence of the tides to waste energy by friction. And the
transformations of the system which the tides have caused are
invariably characterized by a decline of energy, the movements being
otherwise arranged so that the total moment of momentum shall