er the lunar theory, or problem of the moon's exact
motion, is one of the most complicated and difficult in astronomy; the
perturbations being so numerous and large, because of the enormous mass
of the perturbing body.

The disturbances experienced by the planets are much smaller, because
they are controlled by the sun and perturbed by each other. The moon is
controlled only by the earth, and perturbed by the sun. Planetary
perturbations can be treated as a series of disturbances with some
satisfaction: not so those of the moon. And yet it is the only way at
present known of dealing with the lunar theory.

To deal with it satisfactorily would demand the solution of such a
problem as this:--Given three rigid spherical masses thrown into empty
space with any initial motions whatever, and abandoned to gravity: to
determine their subsequent motions. With two masses the problem is
simple enough, being pretty well summed up in Kepler's laws; but with
three masses, strange to say, it is so complicated as to be beyond the
reach of even modern mathematics. It is a famous problem, known as that
of "the three bodies," but it has not yet been solved. Even when it is
solved it will be only a close approximation to the case of earth, moon,
and sun, for these bodies are not spherical, and are not rigid. One may
imagine how absurdly and hopelessly complicated a complete treatment of
the motions of the entire solar system would be.

No. 8. Each planet is attracted not only by the sun but by the other
planets, hence their orbits are slightly affected by each other.

The subject of planetary perturbation was only just begun by Newton.
Gradually (by Laplace and others) the theory became highly developed;
and, as everybody knows, in 1846 Neptune was discovered by means of it.

No. 9. He recognized the comets as members of the solar system, obedient
to the same law of gravity and moving in very elongated ellipses; so
their return could be predicted.

It was a long time before Newton recognized the comets as real members
of the solar system, and subject to gravity like the rest. He at first
thought they moved in straight lines. It was only in the second edition
of the _Principia_ that the theory of comets was introduced.

Halley observed a fine comet in 1682, and calculated its orbit on
Newtonian principles. He also calculated when it ought to have been seen
in past times; and he found the year 1607, when one was seen by Kepler;
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