of a series of many concentric rings each moving with
its own velocity and having its own system of waves,
or else of a confused multitude of revolving particles
not arranged in rings and continually coming into
collision with one another.

"Taking the first case, we found that in an indefinite
number of possible cases the mutual perturbations of
two rings, stable in themselves, might mount up in
time to a destructive magnitude, and that such cases
must continually occur in an extensive system like
that of Saturn, the only retarding cause being the irregularity
of the rings.

"The result of long-continued disturbance was found
to be the spreading-out of the rings in breadth, the
outer rings pressing outward, while the inner rings
press inward.

"The final result, therefore, of the mechanical
theory is that the only system of rings which can
exist is one composed of an indefinite number of
unconnected particles, revolving around the planet with
different velocities, according to their respective distances.
These particles may be arranged in series of
narrow rings, or they may move through one another
irregularly. In the first case the destruction of the
system will be very slow, in the second case it will be
more rapid, but there may be a tendency towards arrangement
in narrow rings which may retard the