86

HISTORY OF PHYSICAL ASTRONOMY.

found that, during thirteen months which elapsed between two eclipses,observed in 1750 and 1751, the inclination presented a diminution of ■18' 20". These great changes occurred in such brief intervals, that itwas impossible they could have proceeded from the periodic variation of :the inclination. Maraldi finally discovered that the observations might Ibe reconciled with the generally received theory of the inclination, by 1supposing the nodes to librate continually on each side of their mean place ;to the extent of 10° 13' 48", the period of libration being equal to that jwhich restored the same values of the inclination. Having compared this !hypothesis with observation, he was gratified to find that a remarkable jaccordance generally prevailed between the results derived from both isources. Among 127 eclipses which he calculated, the difference between 1the observed and computed durations did not exceed 2 m , except in one iinstance ; and only 8 were found in which the difference exceeded l m *. 1Bailly shewed that the libration of the nodes proceeded from their !retrograde motion on the orbit of the first satellite, which was in this case :the principal disturbing body. He also remarked that the inclination wasconstant with respect to the orbit of this satellite, and that it was variablewith respect to Jupiter ’s orbit, in consequence of the retrograde motion of ■the nodes upon the former orbit. This explained the coincidence of the pe-riod of libration with that which restored the inclination to the same value.

When we consider the complicated character of the phenomenon in-vestigated by Maraldi, his explanation of it must be regarded as one of themost ingenious conceptions which mere observation has ever suggested tothe astronomer. Laplace has employed this libration of the nodes as oneof the data from which he derived the masses of the satellites. Wargentinpublished tables of the second satellite for the Nautical Almanack for1770 ; the most remarkable peculiarity of which was the libratory motionof the nodes, which he admits to have been first suggested by Maraldi.

The period in which the inclination of the third satellite passed throughall its values was much longer than the corresponding period of the secondsatellite. Maraldi had found that during the current century it had beencontinually increasing. In 1763 he fixed it at 3° 25' 41". This indi-cated an increase of 22 ' since the publication of Cassini’s tables. In 1769he discovered that the inclination was only 3° 23' 33". Pursuing his 'researches, he found that the inclination reached its maximum in the years j1683 and 1765, and its minimum in 1699. Hence it followed that the incli- jnation increased during 66 years, and then diminished during an equal 1space of time ; the whole variation being consequently comprised within a. jperiod of 132 years. Maraldi also fixed the mean place of the nodes in j10 s 13° 52', and estimated the extent of libration at 1° 32' 24" f. i

The inclination of the fourth satellite had long been considered in- ivariable. We have seen that Bradley estimated it at 2° 42'. Wargentin,in 1750, made it 2° 39', and Maraldi, in 1758, made it 2° 36'. In 1781 :

Wargentin concluded from his researches that during a few precedingyears the inclination had been slowly increasing. This opinion has beenconfirmed by the observations of subsequent astronomers, who have found ;that the increase of inclination has been going on down to the present day. iBailly, before becoming acquainted with the researches of Wargentin, :

made the following sagacious remark upon this subject in his History of j

Astronomy—“ The inclination of the fourth satellite has not hitherto j

* Mem. Acad, des Sciences, 1768. + Ibid. 1769.