SEQUEL TO THE EPOCH OF KEWTOX. 437 



apogee, which period is performed in somewhat less than nine yeM*s." 

 lie found the agreement very remarkable, and conceived hopes of at- 

 taining the great object, of finding the Longitude with the requisite 

 degree of exactness ; nor did he give up his labors on this subject till 

 he had completed his Plinian period in 1739. 



The accuracy with which Halley conceived himself able to predict 

 the moon's place 12 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. 13 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 it was superseded by the more direct prosecution of Newton's views.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, considered as one of the cases of the Problem 

 of Three Bodies, no advance was made beyond what Newton had done, 

 till mathematicians threw aside the Newtonian artifices, and applied 

 the newly developed generalizations of the analytical method. The 

 first great apparent deficiency in the agreement of the law of uni- 

 versal gravitation with astronomical observation, was removed by 

 Clairaut's improved approximation to the theoretical Motion of the 

 Moon's Apogee, in 1750 ; yet not till it had caused so much disquiet- 

 ude, that Clairaut himself had suggested a modification of the law of 

 attraction ; and it was only in tracing the consequences of this sugges- 

 tion, that he found the Newtonian law of the inverse square to be that 

 which, when rightly developed, agreed with the facts. Euler solved 

 the problem by the aid of his analysis in 1745, 14 and published Tables 

 of the Moon in 1746. His tables were not very accurate at first; 15 but 

 he, D'Alembert, and Clairaut, continued to labor at this object, and the 

 two latter published Tables of the Moon in 1754. 16 Finally, Tobias 

 Mayer, an astronomer of Gottingen, having compared Euler's tables 

 with observations, corrected them so successfully, that in 1753 he pub- 

 lished Tables of the Moon, which really did possess the accuracy which 

 Halley only flattered himself that he had attained. Mayer's success in 

 his first Tables encouraged him to make them still more perfect. He 

 applied himself to the mechanical theory of the moon's orbit; cor- 

 rected all the coefficients of the series by a great number of observa- 

 tions ; and in 1755, sent his new Tables to London as worthy to claim 

 Hhe prize offered for the discovery of longitude. He died soon aftei 



" Phil. Trans. 1731. p. 195. ' Bailly, A. J/. c. 181. 



Lai. 1460. 13 Bradley's Correspondence. 16 Lai. 1460. 



