ther, the mutual attraction of the masses would cause no
disturbance of the spheres. The same would be the case if the polar
axis of one sphere stood precisely at right angles to that of the
other. If, however, the spheres were somewhat flattened at the poles,
and the axes inclined to each other, then the pull of one mass on the
other would cause the polar axes to keep up a constant movement which
is called nutation, or nodding.

The reason why this nodding movement of the polar axes would occur
when these lines were inclined to each other is not difficult to see
if we remember that the attraction of masses upon each other is
inversely as the square of the distance; each sphere, pulling on the
equatorial bulging of the other, pulls most effectively on the part of
it which is nearest, and tends to draw it down toward its centre. The
result is that the axes of the attracted spheres are given a wobbling
movement, such as we may note in the spinning top, though in the toy
the cause of the motion is not that which we are considering.

If, now, in that excellent field for the experiment we are essaying,
the mind's eye, we add a second planet outside of the single sphere
which we have so far supposed to journey about the sun, or rather
about the common centre of gravity, we perceive at once that we have
introduced an element which leads to a complication of much
importance. The new sphere would, of course, pull upon the others in
the measure of its gravitative value--i.e., its weight. The centre of
gravity of the system would now be determined not by two distinct
bodies, but by three. If we conceive the second planet to journey
around the sun at such a rate that a straight line always connected
the centres of the three orbs, then the only effect on their
gravitative centre would be to draw the first-mentioned planet a
little farther away from the centre of the sun; but in our own solar
system, and probably in all others, this supposition is inadmissible,
because the planets have longer journeys to go and also move slower,
the farther they are from the sun. Thus Mercury completes the circle
of its year in eighty-eight of our days, while the outermost planet
requires sixty thousand days (more than one hundred and sixty-four
years) for the same task. The result is not only that the centre of
gravity of the system is somewhat displaced--itself a matter of no
great account--but also that the orbit of the original planet ceases
to