aintains its ancient glory.

NOTES FOR LECTURE XVIII

Tides are due to incomplete rigidity of bodies revolving round each
other under the action of gravitation, and at the same time spinning on
their axes.

Two spheres revolving round each other can only remain spherical if
rigid; if at all plastic they become prolate. If either rotate on its
axis, in the same or nearly the same plane as it revolves, that one is
necessarily subject to tides.

The axial rotation tends to carry the humps with it, but the pull of the
other body keeps them from moving much. Hence the rotation takes place
against a pull, and is therefore more or less checked and retarded. This
is the theory of Von Helmholtz.

The attracting force between two such bodies is no longer _exactly_
towards the centre of revolution, and therefore Kepler's second law is
no longer precisely obeyed: the rate of description of areas is subject
to slight acceleration. The effect of this tangential force acting on
the tide-compelling body is gradually to increase its distance from the
other body.

Applying these statements to the earth and moon, we see that tidal
energy is produced at the expense of the earth's rotation, and that the
length of the day is thereby slowly increasing. Also that the moon's
rotation relative to the earth has been destroyed by past tidal action
in it (the only residue of ancient lunar rotation now being a scarcely
perceptible libration), so that it turns always the same face towards
us. Moreover, that its distance from the earth is steadily increasing.
This last is the theory of Professor G.H. Darwin.

Long ago the moon must therefore have been much nearer the earth, and
the day was much shorter. The tides were then far more violent.

Halving the distance would make them eight times as high; quartering it
would increase them sixty-four-fold. A most powerful geological denuding
agent. Trade winds and storms were also more violent.

If ever the moon were close to the earth, it would have to revolve round
it in about three hours. If the earth rotated on its axis in three
hours, when fluid or pasty, it would be unstable, and begin to separate
a portion of itself as a kind of bud, which might then get detached and
gradually pushed away by the violent tidal action. Hence it is possible
that this is the history of the moon. If so, it is probably an
exceptional history. The planets were not formed from the sun in this
way.

Mars' m