tem would no more be able to resist such strains and
pressures than an arch of iron spanning the Atlantic would be able to
sustain its own weight against the earth's attraction.

It would be necessary then that the ring-system should rotate around the
planet. But it is clear that the proper rate of rotation for the outer
portion would be very different from the rate suited for the inner
portion. In order that the inner portion should travel around Saturn
entirely relieved of its weight, it should complete a revolution in
about seven hours twenty-three minutes. The outer portion, however,
should revolve in about thirteen hours fifty-eight minutes, or nearly
fourteen hours. Thus the inner part should rotate in little more than
half the time required by the outer part. The result would necessarily
be that the ring-system would be affected by tremendous strains, which
it would be quite unable to resist. The existence of the great division
would manifestly go far to diminish the strains. It is easily shown that
the rate of turning where the division is, would be once in about eleven
hours and twenty-five minutes, not differing greatly from the mean
between the rotation-periods for the outside and for the inside edges of
the system. Even then, however, the strains would be hundreds of times
greater than the material of the ring could resist. A mass comparable in
weight to our earth, compelled to rotate in (say) nine hours when it
ought to rotate in eleven or in seven, would be subjected to strains
exceeding many times the resistances which the cohesive power of its
substance could afford. That would be the condition of the inner ring.
And in like manner the outer ring, if it rotated in about twelve hours
and three-quarters, would have its outer portions rotating too fast and
its inner portions too slowly, because their proper periods would be
fourteen hours and eleven hours and a half respectively. Nothing but the
division of the ring into a number of narrow hoops could possibly save
it from destruction through the internal strains and pressures to which
its material would be subjected.

Even this complicated arrangement, however, would not save the
ring-system. If we suppose a fine hoop to turn around a central
attracting body as the rings of Saturn rotate around the planet, it may
be shown that unless the hoop is so weighted that its centre of gravity
is far from the planet, there will be no stability in the resulting
moti