In his Adams Prize Essay for the year 1856 J. CLERK MAXWELL* took the first step towards a comprehensive theory of the unique system of rings associated with Saturn. The main theme of MAXWELLs work was to devise a model for the system of rings which could move in a steady state of motion round Saturn and which could be stable for small disturbances, provided the law of gravitation was applicable to the Saturnian system. MAXWELL considered the case a single ring, concentric with Saturn. He concluded that— (i) the steady motion of a uniform rigid circular ring would be unstable ; and that the steady motion of a non-uniform rigid circular ring could be stable only if the density were very irregular, (ii) the steady motion of a ring composed of discrete particles, of equal mass, moving in a circle round the planet would be stable if a certain condition were satisfied, and (iii) the steady motion of a liquid ring would be unstable.