of brake on the earth's
rotation. These masses of water, _held back by the moon_, exert a kind
of dragging effect on the rotating earth. Doubtless this effect,
measured by our ordinary standards, is very small; it is, however,
continuous, and in the course of the millions of years dealt with in
astronomy, this small but constant effect may produce very considerable
results.

But there is another effect which can be shown to be a necessary
mathematical consequence of tidal action. It is the moon's action on the
earth which produces the tides, but they also react on the moon. The
tides are slowing down the earth, and they are also driving the moon
farther and farther away. This result, strange as it may seem, does not
permit of doubt, for it is the result of an indubitable dynamical
principle, which cannot be made clear without a mathematical discussion.
Some interesting consequences follow.

Since the earth is slowing down, it follows that it was once rotating
faster. There was a period, a long time ago, when the day comprised only
twenty hours. Going farther back still we come to a day of ten hours,
until, inconceivable ages ago, the earth must have been rotating on its
axis in a period of from three to four hours.

At this point let us stop and inquire what was happening to the moon. We
have seen that at present the moon is getting farther and farther away.
It follows, therefore, that when the day was shorter the moon was
nearer. As we go farther back in time we find the moon nearer and nearer
to an earth rotating faster and faster. When we reach the period we have
already mentioned, the period when the earth completed a revolution in
three or four hours, we find that the moon was so near as to be almost
grazing the earth. This fact is very remarkable. Everybody knows that
there is a _critical velocity_ for a rotating flywheel, a velocity
beyond which the flywheel would fly into pieces because the centrifugal
force developed is so great as to overcome the cohesion of the molecules
of the flywheel. We have already likened our earth to a flywheel, and we
have traced its history back to the point where it was rotating with
immense velocity. We have also seen that, at that moment, the moon was
barely separated from the earth. The conclusion is irresistible. In an
age more remote the earth _did_ fly in pieces, and one of those pieces
is the moon. Such, in brief outline, is the tidal theory of the origin
of the earth-moon