and, although
if we were near them we should perceive that a considerable space
separates each individual from his neighbors.

The fact that this is the constitution of Saturn's rings can be
confidently stated because it has been mathematically proved that they
could not exist if they were either solid or liquid bodies in a
continuous form, and because the late Prof. James E. Keeler demonstrated
with the spectroscope, by means of the Doppler principle, already
explained in the chapter on Venus, that the rings circulate about the
planet with varying velocities according to their distance from Saturn's
center, exactly as independent satellites would do.

It might be said, then, that Saturn, instead of having nine satellites
only, has untold millions of them, traveling in orbits so closely
contiguous that they form the appearance of a vast ring.

As to their origin, it may be supposed that they are a relic of a ring
of matter left in suspension during the contraction of the globe of
Saturn from a nebulous mass, just as the rings from which the various
planets are supposed to have been formed were left off during the
contraction of the main body of the original solar nebula. Other similar
rings originally surrounding Saturn may have become satellites, but the
matter composing the existing rings is so close to the planet that it
falls within the critical distance known as "Roche's limit," within
which, owing to the tidal effect of the planet's attraction, no body so
large as a true satellite could exist, and accordingly in the process of
formation of the Saturnian system this matter, instead of being
aggregated into a single satellite, has remained spread out in the form
of a ring, although its substance long ago passed from the vaporous and
liquid to the solid form. We have spoken of the rings as being composed
of meteorites, but perhaps their component particles may be so small as
to answer more closely to the definition of dust. In these rings of
dust, or meteorites, disturbances are produced by the attraction of the
planet and that of the outer satellites, and it is yet a question
whether they are a stable and permanent feature of Saturn, or will, in
the course of time, be destroyed.[12]

[Footnote 12: For further details about Saturn's rings, see The Tides,
by G.H. Darwin, chap. xx.]

It has been thought that the gauze ring is variable in brightness. This
would tend to show that it is composed of bodies which have