es vary over a
range of 31,355 miles, the moon is always in a determinable place.
A simple revolution of one world about another in a circular orbit
would be a problem of easy solution. It would always be at the
same distance from its centre, and going with the same velocity.
But there are over sixty causes that interfere with such a simple
orbit in the case of the moon, all of which causes and their
disturbances must be considered in calculating such a simple matter
as an eclipse, or predicting the moon's place as the sailors guide.
One of the most puzzling of the irregularities [Page 11] of our
night-wandering orb has just been explained by Professor Hansen, of
Gotha, as a curious result of the attraction of Venus.

[Illustration: Fig. 3.--Changes of orbit by mutual attraction.]

Take a single instance of the perturbations of Jupiter and Saturn
which can be rendered evident. The times of orbital revolution of
Saturn and Jupiter are nearly as five to two. Suppose the orbits of
the planets to be, as in Fig. 3, both ellipses, but not necessarily
equally distant in all parts. The planets are as near as possible
at 1, 1. Drawn toward each other by mutual attraction, Jupiter's
orbit bends outward, and Saturn's becomes more nearly straight, as
shown by the dotted lines. A partial correction of this difficulty
immediately follows. As Jupiter moves on ahead of Saturn it is held
back--retarded in its orbit by that body; and Saturn is hastened
in its orbit by the attraction of Jupiter. Now greater speed means
a straighter orbit. A rifle-ball flies nearer in a straight line
than a thrown stone. A greater velocity given to a whirled ball
pulls the elastic cord far enough to give the ball a larger orbit.
Hence, being hastened, Saturn stretches out nearer its proper orbit,
and, retarded, Jupiter approaches the smaller curve that is its
true orbit.

But if they were always to meet at this point, as they would if
Jupiter made two revolutions to Saturn's one, it would be disastrous.
In reality, when Saturn has gone around two-thirds of its orbit to
2, Jupiter will have gone once and two-thirds around and overtaken
[Page 12] Saturn; and they will be near again, be drawn together,
hastened, and retarded, as before; their next conjunction would be
at 3, 3, etc.

Now, if they always made their conjunction at points equally distant,
or at thirds of their orbits, it would cause a series of increasing
deviations; for Jupiter would be co