He obtained in 185 9 the Adams prize in Cambridge for a very original and powerful essay, " On the Stability of Saturn's Rings."
In Bode's Jahrbuch (1776-1780) he discusses nutation, aberration of light, Saturn's rings and comets; in the Nova acta Helvetica (1787) he has a long paper "Sur le son des corps elastiques," in Bernoulli and Hindenburg's Magazin (1787-1788) he treats of the roots of equation and of parallel lines; and in Hindenburg's Archiv (1798-1799) he writes on optics and perspective.
It may be added that he first examined the conditions of stability of the system formed by Saturn's rings, pointed out the necessity for their rotation, and fixed for it a period (Io h 33 m) virtually identical with that established by the observations of Herschel; that he detected the existence in the solar system of an invariable plane such that the sum of the products of the planetary masses by the projections upon it of the areas described by their radii vectores in a given time is a maximum; and made notable advances in the theory of astronomical refraction (Mec. cel.
A discussion of the equilibrium of Saturn's rings led him to conclude in 1855 that they must be of a fluid nature.
Focal length, he discovered the brightest of Saturn's satellites (Titan) in 1655, and in 1659 he published his Systema Saturnium, in which was given for the first time a true explanation of Saturn's ring, founded on observations made with the same instrument.
Cassini discovered Saturn's fifth satellite (Rhea) in 1672 with a telescope of 35 ft., and the third and fourth satellites in 1684 with telescopes made by Campani of looand 136-ft.
Notwithstanding this difference in the brightness of the objects, we were able with this reflecting telescope to see whatever we have hitherto discovered with the Huygenian, particularly the transits of Jupiter's satellites and their shadows over his disk, the black list in Saturn's ring, and the edge of his shadow cast on his ring.
Laplace's mathematical theory of the form of Saturn's rings.