PREFACE.

After having explained, in the two preceding books, the theories of theplanets, and of the moon, it now remains to examine those of the othersatellites and comets, which are the chief objects of the present volume. Thesatellites of Jupiter are the most interesting of all the satellites, except that of [ 6000 ]the Earth . The observation of these bodies, the first which were discoveredin the heavens by the telescope, goes no farther back than two centuries; andin fact we ought not to estimate the interval of time in which their eclipseshave been observed, at more than a century and a half. But, in this shortinterval, these bodies have presented to our view, by the rapidity of theirrevolutions, all those great changes which time produces with extremeslowness in the planetary orbits, the system of the satellites being an imageof that of the planets. Their frequent eclipses have made known the principalinequalities of their motions, with a degree of accuracy which could never have [ 6000 ']been attained by observations of their elongations from Jupiter. To obtain thetheory of these motions, we shall develop, in the first place, the differentialequations of the orbits, and then, by integrating these equations, we shallascertain the various perturbations. These inequalities differ but little in theirforms from those of the planets and moon; but the relations which existbetween the mean motions and the mean longitudes of the three inner satellitesof Jupiter, augment some of these inequalities so much as to give them a greatinfluence on the whole of their theory. These mean motions are very nearlyin a subduple progression, and from this peculiarity arise several very sensible "

VOL. IV. A