A special interest attached at that time to the question whether the ring is divided or not, for Laplace had then recently published the results of his mathematical inquiry into the movements of such a ring as Saturn's, and, having _proved_ that a single solid ring of such enormous width could not continue to move around the planet, had expressed the _opinion_ that Saturn's ring consists in reality of many concentric rings, each turning, with its own proper rotation rate, around the central planet. It is singular that Herschel, who, though not versed in the methods of the higher mathematics, had considerable native power as a mathematician, was unable to perceive the force of Laplace's reasoning. Indeed, this is one of those cases where clearness of perception rather than profundity of mathematical insight was required. Laplace's equations of motion did not express all the relations involved, nor was it possible to judge, from the results he deduced, how far the stability of the Saturnian rings depended on the real structure of these appendages. One who was well acquainted with mechanical matters, and sufficiently versed in mathematics to understand how to estimate generally the forces acting upon the ring-system, could have perceived as readily the general conditions of the problem as the most profound mathematician. One may compare the case to the problem of determining whether the action of the moon in causing the tidal wave modifies in any manner the earth's motion of rotation. We know that as a mathematical question this is a very difficult one. The Astronomer Royal, for example, not long ago dealt with it analytically, and deduced the conclusion that there is no effect on the earth's rotation, presently however, discovering by a lucky chance a term in the result which indicates an effect of that kind. But if we look at the matter in its mechanical aspect, we perceive at once, without any profound mathematical research, that the retardation so hard to detect mathematically must necessarily take place. As Sir E. Beckett says in his masterly work, _Astronomy without Mathematics_, 'the conclusion is as evident without mathematics as with them, when once it has been suggested.' So when we consider the case of a wide flat ring surrounding a mighty planet like Saturn, we perceive that nothing could possibly save such a ring from destruction if it were really one solid structure. To recognise this the more clearly, let us first notice the dimensions of the planet and rings.