428 HISTORY OF PHYSICAL ASTRONOMY. 



[2d Ed.] [I do not see any reason to retract what was thus said ; 

 but it ought perhaps to be distinctly said that on these very accounts 

 Flamsteed's rejection of Newton's rules did not imply a denial of the 

 doctrine of gravitation. In the letter above quoted, Flamsteed says 

 that he has been employed upon the Moon, and that " the heavens 

 reject that equation of Sir I. Newton which Gregory and Newton 

 called his sixth : I had then [when he wrote before] compared but 72 

 of my observations with the tables, now I have examined above 100 

 more. I find them all firm in the same, and the seventh [equation] 

 too." And thereupon he comes to the determination above stated. 



At an earlier period Flamsteed, as I have said, had received New- 

 ton's suggestions with great deference, and had regulated his own ob- 

 servations and theories with reference to them. The calculation of the 

 lunar inequalities upon the theory of gravitation was found by Newton 

 and his successors to be a more difficult and laborious task than he 

 had anticipated, and was not performed without several trials and er- 

 rors. One of the equations was at first published (in Gregory's Astro- 

 nomies Elementa) with a wrong sign. And when Newton had done 

 all, Flamsteed found that the rules were far from coming up to the 

 degree of accuracy which had been claimed for them, that they could 

 give the moon's place true to 2 or 3 minutes. It was not till consider- 

 ably later that this amount of exactness was attained. 



The late Mr. Baily, to whom astronomy and astronomical literature 

 are so deeply indebted, in his Supplement to the Account of Flamsteed, 

 has examined with great care and great candor the assertion that 

 Flamsteed did not understand Newton's Theory. He remarks, very 

 justly, that what Newton himself at first presented as his Theory, might 

 more properly be called Rules for computing lunar tables, than a phys- 

 ical Theory in the modorn acceptation of the term. He shows, too, 

 that Flamsteed had read the Principia with attention. 9 Nor do I 

 doubt that many considerable mathematicians gave the same imperfect 

 assent to Newton's doctrine which Flamsteed did. But when we find 

 that others, as Halley, David Gregory, and Cotes, at once not only saw 

 in the doctrine a source of true formulas, but also a magnificent phys- 

 ical discovery, we are obliged, I think, to make Flamsteed, in this re- 

 spect, an exception to the first class of astronomers of his own time. 



Mr. Baily's suggestion that the annual equations for the corrections 

 of the lunar apogee and node were collected from Flamsteed's tables 



9 Supp. p. 691. 



