PLANETARY RINGS AND NEW STARS. 469 



to its pi-imary. From these and other considerations it may be legiti- 

 mately concluded that the rings of Saturn are the remains of two former 

 satellites ; and their origin and their present condition must be regarded 

 as the ultimate consequence of a rare medium disseminated through 

 space. 



Though the dismemberment which I have shown to be inevitable in 

 small orbits differs, in some features, from that supposed to take place 

 in the nebular hj'pothesis, yet in tracing the effects of both it is neces- 

 sary to be guided by certain mathematically demonstrated principles in 

 regard to stability. Two homogeneous fluid planets varying widely in 

 size, but having the same density and occupying the same time in their 

 diurnal movement, would be similar spheroids, or have the same rela- 

 tive deviation from a true sphere. Stability would cease to be possible 

 in both if they were as dense as the earth and turned once in two hours 

 and twenty-five minutes. If they were as rare as hydrogen gas at the 

 level oT our seas, they could not endure a rotation which took place in 

 a less time than twenty-five days. In the investigations which I have 

 given in the "Philosophical Magazine " in regard to secondary planets 

 close to their primaries, the results have a like generality. Twelve 

 hours would be very nearly the shortest time of revolution for an homo- 

 geneous fluid satellite as dense as water, whether its diameter were a 

 hundred or a thousand miles, or whether it revolved around the earth 

 or around Jupiter. Such a body, however, would require to be about 

 thirteen times as dense as its primary in order to circulate in safety a 

 little beyond the surface of the latter orb. A small satellite composed 

 of fluid quicksilver would be capable of maintaining a planetary form 

 if revolving just outside the atmosphere of Saturn or of Neptune ; but 

 it would be doomed to dismemberment if moving in a similar proximity 

 to the surface of the earth or even of Jupiter. 



The results are not very different even in cases of the greatest pos- 

 sible deviation from the homogeneous character I have ascribed to the 

 bodies. If both planet and satellite were composed of rare gas envelop- 

 ing a central nucleus, the smaller body would require to have an aver- 

 age density nearly eight times that of the greater, in order to preserve 

 its integrity in such a dangerous proximity. A modern advocate of the 

 nebular hypothesis supposes that each planet, when formed from the 

 rarefied matter of a previous solar ring, was fifteen times less dense than 

 the sun would be if it were an homogeneous sphere inclosed by the 

 planetary orbit. In his own words, " After all their contraction during 

 their condition as rings, and during their aggregation into globes, we 

 may assume at a moderate estimate that when their rotation began 

 they were fifteen times less dense than the average density of the sun 

 expanded to their orbits." To change from a ring to a planet, how- 

 ever, the nebulous matter should have about one hundred times the 

 density which the writer ascribes to it. Before it could become dense 

 enough for the transformation, the nebulous expanse would, like 



