and the Theory of Saturn’s Rings. 273 
But the size of the smallest orbits might fall considerably below 
this limit, in consequence of the rupture of many of the frag- 
ments at their least distances from the primary, either by the 
attraction of that body, or by the heat evolved when they are 
transformed into blazing meteoric masses. 
The condition which matter must ultimately assume in the 
central zone, where it can no longer exist as one great satellite 
or in a limited number of smaller ones, must depend in some 
degree on the form of the primary planet. If this body be an 
oblate spheroid, considerably flattened by rapid rotation, as is 
the case with Saturn, the orbits of the several fragments must 
be subject to apsidal motion, to an extent depending on their 
transverse axes and excentricities. Accordingly those fragments 
describing the same track will be equally affected by it, and will 
form a line which remains unbroken during many revolutions. 
As one ring of fragments is thus made to roll within another, it 
is evident that both must ultimately become circular; and the 
fragmentary host will at length exhibit the nearest approxima- 
tion to a state of repose, by moving in exact circles around the 
central planet. 
There are even more cogent provisions for equalizing the dis- 
tribution of the great ocean of disconnected matter over the vast 
zone in which it circulates. The attraction of the central body 
which led to the great dismemberment, must be adequate not 
only to forbid the reconstruction of a satellite, but even to pre- 
vent the parts of the mighty wreck from congregating to any 
point in an undue proportion. Whenever a preponderance of 
matter occurred at any locality, the impediments of friction 
would tend to equalize the angular velocity of the nearest and 
most distant fragments in the group ; and the new relations be- 
tween gravity and centrifugal force would immediately lead to 
their dispersion by the disturbing action of the primary. If the 
latter body were a very flattened spheroid, it would serve to con- 
fine the great annular ocean of fragments to the same plane, in 
opposition to small effects arising from the disturbances of di- 
stant spheres; and Laplace has shown that, supposing Saturn’s 
ring to consist of numerous independent satellites, they will be 
prevented from departing from a common plane, in consequence 
of the action of his equatorial matter. 
In addition to the foregoing agencies for securing the peculiar 
characters of the annular appendage, I must notice another which 
is inseparable from the movements of such collections of fluid or 
solid matter circulating in independent orbits. A vast amount 
of heat must be developed by their friction and their mutual 
collisions; while the calorific influence of such a mechanical 
action will be augmented by the slight excentricity impressed on. 
Phil. Mag. 8. 4, Vol, 21, No. 140. April 1861. T 
