traction on the earth is about 175 times as
great as the attraction of the moon. Hence it is, of course, that the
earth obeys the supremely important attraction of the sun, and pursues
an elliptic path around the sun, bearing the moon as an appendage.

But when we come to that particular effect of attraction which is
competent to produce precession, we find that the law by which the
efficiency of the attracting body is computed assumes a different form.
The measure of efficiency is, in this case, to be found by taking the
mass of the body and dividing it by the _cube_ of the distance. The
complete demonstration of this statement must be sought in the formulae
of mathematics, and cannot be introduced into these pages; we may,
however, adduce one consideration which will enable the reader in some
degree to understand the principle, though without pretending to be a
demonstration of its accuracy. It will be obvious that the nearer the
disturbing body approaches to the earth the greater is the _leverage_
(if we may use the expression) which is afforded by the protuberance at
the equator. The efficiency of a given force will, therefore, on this
account alone, increase in the inverse proportion of the distance. The
actual intensity of the force itself augments in the inverse square of
the distance, and hence the capacity of the attracting body for
producing precession will, for a double reason, increase when the
distance decreases. Suppose, for example, that the disturbing body is
brought to half its original distance from the disturbed body, the
leverage is by this means doubled, while the actual intensity of the
force is at the same time quadrupled according to the law of
gravitation. It will follow that the effect produced in the latter case
must be eight times as great as in the former case. And this is merely
equivalent to the statement that the precession-producing capacity of a
body varies inversely as the cube of the distance.

It is this consideration which gives to the moon an importance as a
precession-producing agent to which its mere attractive capacity would
not have entitled it. Even though the mass of the sun be 26,000,000
times as great as the mass of the moon, yet when this number is divided
by the cube of the relative value of the distances of the bodies (386),
it is seen that the efficiency of the moon is more than twice as great
as that of the sun. In other words, we may say that one-third of the
movemen