NOTES TO BOOK VII. 303 



own observations 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 antici- 

 pated, and was not performed without several trials and 

 errours. One of the equations was at first published (in 

 Gregory's Astronomice 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 

 considerably later that this amount of exactness was at- 

 tained. 



The late Mr. Daily, to whom astronomy and astro- 

 nomical literature are so deeply indebted, in his Supple- 

 ment to the Account of Flamsteed, has examined with great 

 care and great candour 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 physical Theory in the modern ac- 

 ceptation of the term. He shows, too, that Flamsteed 

 had read the Principia with attention (Supp. p. 691). 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 fornWse, but also a magnificent 

 physical discovery, we are obliged, I think, to make 

 Flamsteed, in this respect, an exception to the first class 

 of astronomers of his own time. 



The suggestion that the annual equations for the 



