"The most serious demands upon his powers and upon his time were made by his investigations on the Stability of Saturn's Rings. This was the subject chosen by the Examiners for the Adams Prize Essay to be ajudged in 1857, and was advertised in the following terms:— "The problem may be treated on the supposition that the system of Rings is exactly or very approximately concentric with Saturn and symmetrically disposed about the plane of his equator and different hypotheses may be made concerning the physical constitution of the Rings. It may be supposed (1) that they are rigid; (2) that they are fluid and in part aeriform; (3) that they consist of masses of matter not materially coherent. The question will be considered to be answered by ascertaining on these hypotheses severally whether the conditions of mechanical stability are satisfied by the mutual attractions and motions of the Planets and the Rings." It is desirable that an attempt should also be made to determine on which of the above hypotheses the appearances both of the bright rings and the recently discover dark ring may be most satisfactorily explained; and to indicate any causes to which a change in form such as is supposed from a comparison of modern with the earlier observations to have taken place, may be attributed.""