SEQUEL TO THE EPOCH OF NEWTON. 441 



Thus the satellites of Jupiter are not only disturbed by the sun, as the 

 moon is, but also by each other, as the planets are. This mutual ac- 

 tion gives rise to some very curious relations among their motions ; 

 which, like most of the other leading inequalities, were forced upon the 

 notice of astronomers by observation before they were obtained by 

 mathematical calculation. In Bradley's remarks upon his own Tables 

 of Jupiter's Satellites, published among Halley's Tables, he observes 

 that the places of the three interior satellites are affected by errors 

 which recur in a cycle of 43*7 days, answering to the time in which 

 they return to the same relative position with regard to each other, 

 and to the axis of Jupiter's shadow. Wargentin, who had noticed the 

 same circumstance without knowledge of what Bradley had done, ap- 

 plied it, with all diligence, to the purpose of improving the tables of 

 the satellites in 1746. But, at a later period, Laplace established, by 

 mathematical reasoning, the very curious theorem on which this cycle 

 depends, which he calls the libration of Jupiter'' s satellites ; and De- 

 lambre was then able to publish Tables of Jupiter's Satellites more 

 accurate than those of Wargentin, which he did in 1789. 24 



The progress of physical astronomy from the time of Euler and 

 Clairaut, has consisted of a series of calculations and comparisons of 

 the most abstruse and recondite ki'id. The formation of Tables of the 

 Planets and Satellites from the theory, required the solution of prob- 

 lems much more complex than the original case of the Problem of 

 Three Bodies. The real motions of the planets and their orbits are ren- 

 dered still further intricate by this, that all the lines and points to 

 which we can refer them, are themselves in motion. The task of 

 carrying order and law into this mass of apparent confusion, has re- 

 quired a long series of men of transcendent intellectual powers ; and a 

 perseverance and delicacy of observation, such as we have not the 

 smallest example of in any other subject. It is impossible here to give 

 any detailed account of these labors ; but we may mention one instance 

 of the complex considerations which enter into them. The nodes of 

 Jupiter's fourth satellite do not go backwards, 24 as the Newtonian 

 theory seems to require ; they advance upon Jupiter's orbit. But 

 then, it is to be recollected that the theory requires the nodes to retro- 

 grade upon the orbit of the perturbing body, which is here the third 

 satellite ; and Lalande showed that, by the necessary relations of space, 

 the latter motion may be retrograde though the former is direct. 



« Voiron, Hist. Ad. p. 322. 25 Bailly, iii. 175. 



