mass, that even if the exact conditions were fulfilled, it
could scarcely last long, and, if it did, the immense
preponderance of one side of the ring would be easily
observed, contrary to experience. These considerations,
with others derived from the mechanical structure of
so vast a body, compel us to abandon any theory of
solid rings.

"We next examined the motion of a ring of equal
satellites, and found that if the mass of the planet is
sufficient, any disturbances produced in the arrangement
of the ring will be propagated around it in the
form of waves, and will not introduce dangerous confusion.
If the satellites are unequal, the propagations
of the waves will no longer be regular, but disturbances
of the ring will in this, as in the former case,
produce only waves, and not growing confusion. Supposing
the ring to consist, not of a single row of large
satellites, but a cloud of evenly distributed unconnected
particles, we found that such a cloud must
have a very small density in order to be permanent,
and that this is inconsistent with its outer and inner
parts moving with the same angular velocity. Supposing
the ring to be fluid and continuous, we found that
it will be necessarily broken up into small portions.

"We conclude, therefore, that the rings must consist
of disconnected particles; these must be either
solid or liquid, but they must be independent. The
entire system of rings must, therefore, consist either