SEQUEL TO THE EPOCH OF NEWTON. 227 



mutual action gives rise to some very curious rela- 

 tions 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 ob- 

 serves that the places of the three interior satellites 

 are affected by errours which recur in a cycle of 

 437 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 im- 

 proving 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 Ju- 

 piter s satellites; and Delambre was then able to 

 publish Tables of Jupiter's Satellites more accurate 

 than those of Wargentin, which he did in 1789 23 . 



The progress of physical astronomy from the 

 time of Euler and Clairaut, has consisted in a series 

 of calculations and comparisons of the most abstruse 

 and recondite kind. The formation of tables of the 

 planets and satellites from the theory required the 

 solution of problems much more complex than the 

 original case of the problem of three bodies. The 



23 Voiron, Hist. Ast. p. 322. 



Q2 



