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 constantly swelling his orbit at
three points, and Saturn increasingly contracting his orbit at
the same points. Disaster would be easily foretold. But as their
times of orbital revolutions are not exactly in the ratio of five
and two, their points of conjunction slowly travel around the orbit,
till, in a period of nine hundred years, the starting-point is
again reached, and the perturbations have mutually corrected one
another.

For example, the total attractive effect of one planet on the other
for 450 years is to quicken its speed. The effect for the next 450
years is to retard. The place of Saturn, when all the retardations
have accumulated for 450 years, is one degree behind what it is
computed if they are not considered; and 450 years later it will
be one degree before its computed place--a perturbation of two
degrees. When a bullet is a little heavier or ragged on one side,
it will constantly swerve in that direction. The spiral groove in