ould execute a complete swing from high
tide to high again.

Very well, now leave the earth, and think what has been happening to the
moon all this while.

We have seen that the moon pulls the tidal hump nearest to it back; but
action and reaction are always equal and opposite--it cannot do that
without itself getting pulled forward. The pull of the earth on the moon
will therefore not be quite central, but will be a little in advance of
its centre; hence, by Kepler's second law, the rate of description of
areas by its radius vector cannot be constant, but must increase (p.
208). And the way it increases will be for the radius vector to
lengthen, so as to sweep out a bigger area. Or, to put it another way,
the extra speed tending to be gained by the moon will fling it further
away by extra centrifugal force. This last is not so good a way of
regarding the matter; though it serves well enough for the case of a
ball whirled at the end of an elastic string. After having got up the
whirl, the hand holding the string may remain almost fixed at the centre
of the circle, and the motion will continue steadily; but if the hand be
moved so as always to pull the string a little in advance of the centre,
the speed of whirl will increase, the elastic will be more and more
stretched, until the whirling ball is describing a much larger circle.
But in this case it will likewise be going faster--distance and speed
increase together. This is because it obeys a different law from
gravitation--the force is not inversely as the square, or any other
single power, of the distance. It does not obey any of Kepler's laws,
and so it does not obey the one which now concerns us, viz. the third;
which practically states that the further a planet is from the centre
the slower it goes; its velocity varies inversely with the square root
of its distance (p. 74).

If, instead of a ball held by elastic, it were a satellite held by
gravity, an increase in distance must be accompanied by a diminution in
speed. The time of revolution varies as the square of the cube root of
the distance (Kepler's third law). Hence, the tidal reaction on the
moon, having as its primary effect, as we have seen, the pulling the
moon a little forward, has also the secondary or indirect effect of
making it move slower and go further off. It may seem strange that an
accelerating pull, directed in front of the centre, and therefore always
pulling the moon the way it is goin