On examining recorded observations of the planet evidence was found that this dark ring is not, as was at first supposed, a recent formation. Where it crosses Saturn it had been mistaken in former times for a dark belt. It had always been supposed that the rings are solid, or at any rate continuous bodies. The younger Cassini, indeed, ventured to express doubts on the subject, but with this solitary exception, no suspicion had ever existed among astronomers that the rings are otherwise than continuous, until the discovery of the dark ring. When the singular fact was discovered that the body of the planet can be seen through the slate-coloured ring, the solidity of _this_ ring, at any rate, began naturally to be questioned. The idea was suggested that this formation may be fluid. Mathematicians applied rigorous processes of investigation to the question whether a fluid ring can possibly exist in such a position. The inquiry led to a re-examination of the whole subject of the ring-system and its stability. Mathematicians took up the question where Laplace had left it more than half a century before. He had decided that solid rings might, under certain conditions, revolve around a planet without being broken. But his inquiry had not been carried to a conclusion. Now, when the work was completed, it was found that the requisite conditions are certainly not fulfilled by the Saturnian ring-system. The rings should be situated eccentrically, and heavier at one side than the opposite. In fact they should have a perceptible "bias." They exhibit, on the contrary, the most perfect symmetry of figure--this symmetry, indeed, constitutes the great charm of Saturn's telescopic appearance; and although, occasionally, the ball has not seemed to be quite in the middle of the ring-system, the displacement has never approached that which theory requires. The conclusion to which mathematicians arrived was accordingly the following:-- The rings may be held to be formed of a multitude of tiny satellites, travelling nearly in one plane, each pursuing its own course around Saturn, according to the laws of satellite motion, though of course disturbed by the attraction of its fellow-satellites. We owe this theory principally to the labours of Professor J. Clerk Maxwell, who gained the Adams Prize offered by the University of Cambridge for the best mathematical essay upon the conditions under which a ring-system such as Saturn's can exist. But Professor Pierce, of America, had (somewhat earlier) supplied a complete refutation of the idea that the rings are solid and continuous bodies.