In the following year (1749) the French mathematician D’Alembert (chapter XI., § 232) published a treatise[120] in which not only precession, but also a motion of nutation agreeing closely with that observed by Bradley, were shewn by a rigorous process of analysis to be due to the attraction of the moon on the protuberant parts of the earth round the equator (cf. chapter IX., § 187), while Newton’s explanation of precession was confirmed by the same piece of work. Euler (chapter XI., § 236) published soon afterwards another investigation of the same subject; and it has been studied afresh by many mathematical astronomers since that time, with the result that Bradley’s nutation is found to be only the most important of a long series of minute irregularities in the motion of the earth’s axis. 216. Although aberration and nutation have been discussed first, as being the most important of Bradley’s discoveries, other investigations were carried out by him before or during the same time. The earliest important piece of work which he accomplished was in connection with Jupiter’s satellites. His uncle had devoted a good deal of attention to this subject, and had drawn up some tables dealing with the motion of the first satellite, which were based on those of Domenico Cassini, but contained a good many improvements. Bradley seems for some years to have made a practice of frequently observing the eclipses of Jupiter’s satellites, and of noting discrepancies between the observations and the tables; and he was thus able to detect several hitherto unnoticed peculiarities in the motions, and thereby to form improved tables. The most interesting discovery was that of a period of 437 days, after which the motions of the three inner satellites recurred with the same irregularities. Bradley, like Pound, made use of Roemer’s suggestion (chapter VIII., § 162) that light occupied a finite time in travelling from Jupiter to the earth, a theory which Cassini and his school long rejected. Bradley’s tables of Jupiter’s satellites were embodied in Halley’s planetary and lunar tables, printed in 1719, but not published till more than 30 years afterwards (§ 204). Before that date the Swedish astronomer _Pehr Vilhelm Wargentin_ (1717-1783) had independently discovered the period of 437 days, which he utilised for the construction of an extremely accurate set of tables for the satellites published in 1746. In this case as in that of nutation Bradley knew that his mathematical powers were unequal to giving an explanation on gravitational principles of the inequalities which observation had revealed to him, though he was well aware of the importance of such an undertaking, and definitely expressed the hope “that some geometer,[121] in imitation of the great Newton, would apply himself to the investigation of these irregularities, from the certain and demonstrative principles of gravity.”