Nothing but the division of the ring into a number of narrow hoops could possibly save it from destruction through the internal strains and pressures to which its material would be subjected. Even this complicated arrangement, however, would not save the ring-system. If we suppose a fine hoop to turn around a central attracting body as the rings of Saturn rotate around the planet, it may be shown that unless the hoop is so weighted that its centre of gravity is far from the planet, there will be no stability in the resulting motions; the hoop will before long be made to rotate eccentrically, and eventually be brought into destructive collision with the central planet. It was here that Laplace left the problem. Nothing could have been more unsatisfactory than his result, though it was accepted for nearly half a century unquestioned. He had shown that a weighted fine hoop may possibly turn around a central attracting mass without destructive changes of position, but he had not proved more than the bare possibility of this, while nothing in the appearance of Saturn's rings suggests that any such arrangement exists. Again, manifestly a multitude of narrow hoops, so combined as to form a broad flat system of rings, would be constantly in collision _inter se_. Besides, each one of them would be subjected to destructive strains. For though a fine uniform hoop set rotating at a proper rate around an attracting mass at its centre would be freed from all strains, the case is very different with a hoop so weighted as to have its centre of gravity greatly displaced. Laplace had saved the theoretical stability of the motions of a fine ring at the expense of the ring's power of resisting the strains to which it would be exposed. It seems incredible that such a result (expressed, too, very doubtingly by the distinguished mathematician who had obtained it) should have been accepted so long almost without question. There is nothing in nature in the remotest degree resembling the arrangement imagined by Laplace, which indeed appears on _à priori_ grounds impossible. It was not claimed for it that it removed the original difficulties of the problem; and it introduced others fully as serious. So strong, however, is authority in the scientific world that none ventured to express any doubts except Sir W. Herschel, who simply denied that the two rings were divided into many, as Laplace's theory required. As time went on and the signs of many divisions were at times recognised, it was supposed that Laplace's reasoning had been justified; and despite the utter impossibility of the arrangement he had suggested, that arrangement was ordinarily described as probably existing. At length, however, a discovery was made which caused the whole question to be reopened.