rd and forward by means of tides;
and the earth, to free itself from this irritating interference, tries
to push off the aggressor and to make him move further away.

[Illustration: FIG. 2.]

Another way in which we can illustrate the retreat of the moon as the
inevitable consequence of tidal friction is shown in the adjoining
figure, in which the large body E represents the earth, and the small
body M the moon. We may for simplicity regard the moon as a point, and
as this attracts each particle of the earth, the total effect of the
moon on the earth may be represented by a single force. By the law of
equality of action and reaction, the force of the earth on the moon is
to be represented by an equal and opposite force. If there were no
tides then the moon's force would of course pass through the earth's
centre; but as the effect of the moon is to slacken the earth's
rotation, it follows that the total force does not exactly pass
through the line of the earth's centre, but a little to one side, in
order to pull the opposite way to that in which the earth is turning,
and thus bring down its speed. We may therefore decompose the earth's
total force on the moon into two parts, one of which tends directly
towards the earth's centre, while the other acts tangentially to the
moon's orbit. The central force is of course the main guiding power
which keeps the moon in its path; but the incessant tangential force
constantly tends to send the moon out further and further, and thus
the growth of its orbit can be accounted for.

We therefore conclude finally, that the tides are making the day
longer and sending the moon away further. It is the development of the
consequences of these laws that specially demands our attention in
these lectures. We must have the courage to look at the facts
unflinchingly, and deduce from them all the wondrous consequences they
involve. Their potency arises from a characteristic feature--they are
unintermitting. Most of the great astronomical changes with which we
are ordinarily familiar are really periodic: they gradually increase
in one direction for years, for centuries, or for untold ages; but
then a change comes, and the increase is changed into a decrease, so
that after the lapse of becoming periods the original state of things
is restored. Such periodic phenomena abound in astronomy. There is the
annual fluctuation of the seasons; there is the eighteen or nineteen
year period of the moon; the