220 HISTORY OF PHYSICAL ASTRONOMY. 



his labours on this subject till he had completed 

 his Plinian period in 1739. 



The accuracy with which Halley conceived him- 

 self able to predict the moon's place 11 was within 

 two minutes of space, or one fifteenth of the breadth 

 of the moon herself. The accuracy required for 

 obtaining the national reward was considerably 

 greater. Le Monnier pursued the idea of Halley 12 . 

 But before Halley's method had been completed, it 

 was superseded by the more direct prosecution of 

 Newton's views. 



We have already remarked, in the history of 

 analytical mechanics, that in the lunar theory, con- 

 sidered as one of the cases of the problem of three 

 bodies, no advance was made beyond what New- 

 ton had done, till mathematicians threw aside the 

 Newtonian artifices, and applied the newly-deve- 

 loped generalizations of the analytical method. 

 The first great apparent deficiency in the agreement 

 of the law of universal gravitation with astrono- 

 mical observation, was removed by Clairaut's im- 

 proved approximation to the theoretical motion 

 of the moon's apogee in 1750 ; yet not till it had 

 caused so much disquietude, that Clairaut himself 

 had suggested a modification of the law of attrac- 

 tion ; and it was only in tracing the consequences 

 of this suggestion, that he found the Newtonian 

 law of the inverse square to be that which, when 

 rightly developed, agreed with the facts. Euler 

 11 Phil. Trans. 1731, p. 195. " Bailly, A. M. c. 131. 



