294 ON THE STABILITY OF THE MOTION OF SATURN'S RINGS. 



inevitably precipitate the ring upon the planet, not necessarily by breaking the 

 ring, but by the inside of the ring falling on the equator of the planet. 



He therefore infers that the rings are irregular solids, whose centres of 

 gravity do not coincide with their centres of figure. We may draw the con- 

 clusion more formally as follows, " If the rings were solid and uniform, their 

 motion would be unstable, and they would be destroyed. But they are not 

 destroyed, and their motion is stable ; therefore they are either not uniform or 

 not solid." 



I have not discovered* either in the works of Laplace or in those of more 

 recent mathematicians, any investigation of the motion of a ring either not uni- 

 form or not solid. So that in the present state of mechanical science, we do 

 not know whether an irregular solid ring, or a fluid or disconnected ring, can 

 revolve permanently about a central body; and the Saturnian system still re- 

 mains an unregarded witness in heaven to some necessary, but as yet unknown, 

 development of the laws of the universe. 



We know, since it has been demonstrated by Laplace, that a uniform solid 

 ring cannot revolve permanently about a planet. We propose in this Essay to 

 determine the amount and nature of the irregularity which would be required 

 to make a permanent rotation possible. We shall find that the stability of the 

 motion of the ring would be ensured by loading the ring at one point with a 



* Since this was written, Prof. Challis has pointed out to me three important papers in Gould's 

 Astronomical Journal: Mr G. P. Bond on the Kings of Saturn (May 1851) and Prof. B. Pierce of 

 Harvard University on the Constitution of Satum't Rings (June 1851), and on the Adams' Prise 

 Problem for 1856 (Sept. 1855). These American mathematicians have both considered the conditions 

 of statical equilibrium of a transverse section of a ring, and have come to the conclusion that the 

 rings, if they move each as a whole, must be very narrow compared with the observed rings, so 

 that in reality there must be a great number of them, each revolving with its own velocity. They 

 have also entered on the question of the fluidity of the rings, and Prof. Pierce has made an 

 investigation as to the permanence of the motion of an irregular solid ring and of a fluid ring. 

 The paper in which these questions are treated at large has not (so far as I am aware) been 

 published, and the references to it in Gould's Journal are intended to give rather a popular account 

 of the results, than an accurate outline of the methods employed. In treating of the attractions of 

 an irregular ring, he makes admirable use of the theory of potentials, but his published investi- 

 gation of the motion of such a body contains some oversights which are due perhaps rather to the 

 imperfections of popular language than to any thing in the mathematical theory. The only part of 

 the theory of a fluid ring which he has yet given an account of, is that in which he considers 

 the form of the ring at any instant as an ellipse ; corresponding to the case where = o>, and 

 rn=l. As I had only a limited time for reading these papers, and as I could not ascertain the 

 methods uied in the original investigations, I am unable at present to state how far the results of 

 this essay agree with or differ from those obtained by Prof. Pierce. 



