410 On the Ring of Saturw. 
Property can enly be rendered complete by a rapid motion of 
rotation of the ring in its own plane, and round its own centre, 
which is not very distant from that of Saturn. I have also 
shown, that the section of the ring by a plane perpendicular to 
itself passing through its centre is an ellipsis, elongated towards, 
this point. 
The second principle relates to the suspensicn of the ringy 
round the body of Saturn. A hollow sphere, and generally a 
hollow ellipsoid, whese interior and exterior surfaces are similar’ 
and concentrie, would be in equilibrio rewnd Saturn, whatever 
might be the point of concavity occupied by the centre of the 
planet; but this equilibrium would be indiffer ent, that is, bemg 
acted upon, it would neither tend to take its priereine state again, 
nor to remove away ;—the slightest cause, such as the action of 
a@ satellite, or of a comet, would therefore be suffieient to preci- 
pitate the ellipsoid on the planet. The indifferent equilibrium 
which: takes place for a hollow sphere enveloping Saturn, would 
not exist for a circular zone, surrounding this planet. I have 
shown in the above cited book of the Mécanique Céleste, that 
if the two centres of the circular ring,and the planet, do not eo- 
incide, they will then repel, and the ring will end by being pre- 
eipitated on Saturn. The same thing would take place what- 
ever might be the constitution of the ring, if it were without any 
moticn of rotation: but if we conceive that it is not similar in 
all its parts, and so constituted that its centre of gravity does 
not coincide with that of its figure ;— if moreover we suppose it 
to be endowed with a rapid motion of rotation in its plane, then 
its centre of gravity would turn round the centre of Saturn, and 
gravitate towards this point like a satellite, with this difference, 
that it might move in the interior of the planet: it would then 
have a permanent state of motion. Thus, the two properties I 
have mentioned, concur in showing that ‘the ring turns in its 
plane, on itself, and with rapidity. "The duration of this rotation 
ought to be nearly that of the revolution of a satellite moving 
round Saturtt at the distance of the ring itself; and this dura- 
tion is about ten hours and a half. Dr. Herschel has confirmed 
this result by his observations; but how are we toreconeile these 
facets, and the theory, with the observations of M. Schréter, in 
which, points of the ring, more luminous than others, have ap- 
peared stationary for a long time? I believe we may account for 
this in the following manuer. 
Saturn’s ring is composed of several concentrie rings; with 
good telescopes two may be perceived very distinctly; but irra- 
diation confounds these into one, in bad telescopes. It is very 
probable that each of these rings is itself formed of several rings, 
so that Saturn’s ring may be considered as an assemblage * 
severa 
