508 Mr. D. Vaughan on Phenomena which may be traced 
in all respects to those of Saturn. Butit might be premature to 
suppose that the annular appendage of Saturn has originated in 
this manner, or that it is to be regarded as an index of mutability 
in the heavens, if the conclusion were not supported by investi- 
gations of a different character. Were the rings two integral 
solid masses, the imner one, even with the most favourable 
velocity of rotation, would require to be composed of materials 
having over two hundred times the tenacity of wrought iron to 
escape being ruptured, in consequence of the enormous strain 
arising from a preponderance of centrifugal force on one part, and 
of gravity on the other. Even if this danger were removed, solid 
rings could not be prevented from striking the planet, unless 
each were loadedwith some inequality; and, according to the inves- 
tigations of Professor Maxwell, the load must contain about four 
anda half times as much matter as the remainder of the ring. 
A slight excess or deficiency in the amount of this load would be 
fatal to stability ; and the tendency of any fluid or loose solid 
matter to the locality where it occurs must add much to the 
serious perils and the infirmities of the annular structure. 
Regarding the hypothesis of two solid rings as untenable, 
Professor Maxwell considers the case of their fluidity, and he 
arrives at the conclusion that the fluid composing them would 
break up into satellites, unless its density were less than {', 
of that of the primary. But, from the result deduced in my 
articles in the Philosophical Magazine for December 1860 
and April 1861, it is evident that, in so great a proximity to the 
central body, any liquid matter would require a far greater 
density to exist in the form of independent satellites. In inyes- 
tigating the case of a rig of numerous solid satellites, or frag- 
ments, he finds a combination of very extraordinary conditions 
necessary to prevent the derangements and permanent changes 
which collisions and friction are expected to occasion. The bodies 
are to be all equal in mass, and placed in regular array around 
Saturn; but the intervals between them must be very great 
compared with the linear dimensions; and the ratio between 
the planet and the ring must, according to his formule, be 
greater than 4352 multiplied by the square of the number of 
satellites composing the latter. When we consider the vast 
number of such bodies required to maintain the continuity of 
the ring, and the great improbability that all the immense group 
should have the peculiar conditions for preventing one from 
striking another, we may regard the essay of the eminent mathe- 
matician as a proof that the disconnected matter composing the 
annular appendage, whether it be fluid or solid, cannot be main- 
tained in its present condition without the occurrence of friction — 
and collisions between its parts. 
