been called upon to solve. It presents peculiar features of difficulty arising from the exceptional character of the Jovian system; but these very difficulties, so far from deterring mathematicians from the study, have in some cases acted as a stimulus. A considerable part of Laplace's famous book, the "Mécanique Céleste," is devoted to the study of the system of Jupiter's satellites. He has contrived certain analytical methods for encountering the many points that arise, and he has succeeded in explaining some of the most remarkable dynamical features of the system. Many other mathematicians have also essayed the task of a thorough elucidation of the problem. Indeed, on more than one occasion the question has been propounded by the Academy of Sciences at Paris, and a considerable prize has been offered for a satisfactory discussion.
The test of the completeness of such a theory would be sought in the precision with which it would enable the movements of the satellites to be predicted. No doubt a good deal has been done in this way. Our "Nautical Almanac," for instance, announces, with all needful details, the various eclipses and occultations of the satellites, as well as their transits and the movements of the shadows across the disc. It is quite possible, even with our present knowledge of the subject, to predict such phenomena for some years in advance. The accuracy with which these indications can be made is amply sufficient for the ordinary purposes for which they are required. But in such investigations the requirements of science demand a much closer degree of approximation between what is observed and what is calculated than is possible in the present state of our
