fore it would have been possible
to understand the true relation between the tides and the moon.
Indeed, that relation is so far from being of an obvious character,
that I think I have read of a race who felt some doubt as to whether
the moon was the cause of the tides, or the tides the cause of the
moon. I should, however, say that the moon is not the sole agent
engaged in producing this periodic movement of our waters. The sun
also arouses a tide, but the solar tide is so small in comparison with
that produced by the moon, that for our present purpose we may leave
it out of consideration. We must, however, refer to the solar tide at
a later period of our discourses, for it will be found to have played
a very splendid part at the initial stage of the Earth-Moon History,
while in the remote future it will again rise into prominence.

It will be well to set forth a few preliminary figures which shall
explain how it comes to pass that the efficiency of the sun as a
tide-producing agent is so greatly inferior to that of the moon.
Indeed, considering that the sun has a mass so stupendous, that it
controls the entire planetary system, how is it that a body so
insignificant as the moon can raise a bigger tide on the ocean than
can the sun, of which the mass is 26,000,000 times as great as that of
our satellite?

This apparent paradox will disappear when we enunciate the law
according to which the efficiency of a tide-producing agent is to be
estimated. This law is somewhat different from the familiar form in
which the law of gravitation is expressed. The gravitation between two
distant masses is to be measured by multiplying these masses together,
and dividing the product by the _square_ of the distance. The law for
expressing the efficiency of a tide-producing agent varies not
according to the inverse square, but according to the inverse _cube_
of the distance. This difference in the expression of the law will
suffice to account for the superiority of the moon as a tide-producer
over the sun. The moon's distance on an average is about one 386th
part of that of the sun, and thus it is easy to show that so far as
the mere attraction of gravitation is concerned, the efficiency of the
sun's force on the earth is about one hundred and seventy-five times
as great as the force with which the moon attracts the earth. That is
of course calculated under the law of the inverse square. To determine
the tidal efficiency we have to divi