504 PHILOSOPHICAL TI! AN SACTI ONS. |ANN0 1731. 



Not long after, her late Majesty Queen Anne was pleased to bestow on the 

 public an edition of theinuch greater and most valuable part of Mr. Flamsteed's 

 observations; by help of which the great Sir Isaac Newton had formed his cu- 

 rious theory of the moon, a first sketch of which was inserted by Dr. David 

 Gregory, in his Astronomioe Physicae et Geometricas elementa, published at 

 Oxford in 1702; and again in the second edition of Sir Isaac Newton's Principia, 

 which came out in 1713, we have the same revised and amended by himself, 

 to that degree of exactness, that the fimlts of the computus, formed from it, 

 rarely exceed a quarter part of what is found in the best lunar tables extant 

 before that time. 



Being thus provided with proper materials, viz. a large set of observations, 

 and a theory of the motions so very near the truth. Dr. Halley resumed his 

 former design of filling up his abacus or synopsis of the defects of this lunar 

 theory, and made tables to expedite the calculus according to it, and compared 

 its numbers with several of the most certain of Mr. Flamsteed's places observed. 

 By this it was evident that Sir Isaac had spared no part of that sagacity and in- 

 dustry so peculiar to himself, in settling the epochas and other elements of the 

 lunar astronomy, the result many times, for whole months together, rarely 

 differing 2 minutes of motion from the observations themselves; nor is it un- 

 likely but good part of that difference may have been the fault of the observer: 

 and where the errors were found greater, it was in those parts of the lunar 

 orbit, where Mr. Flamsteed had very rarely given himself the trouble of ob- 

 serving; viz. in the 3d and 4th quarters of the moon's age, where sometimes 

 these differences would amount to at least 5 minutes. 



Mr. Flamsteed was long enough possessed of the Royal Observatory to have 

 had a continued series of observations for more than 2 periods of 18 years; by 

 which he had it in his power to have done all that could have been expected 

 from observation, towards discovering the law of the lunar motion. But he 

 contented himself with spare observations, leaving wide gaps between ; so as 

 to omit frequently whole months together; and in one case, the whole year 

 1716. So that notwithstanding what he has left us must be acknowledged 

 more than equal to all that was done before him, both as to the number and 

 accuracy of his accounts; yet foi- want of an uninterrupted succession of them, 

 they are not capable of discovering, in the several situations of the lunar orbit, 

 what corrections are necessary to be allowed, to supply the deficiency of our 

 computus. 



On Mr. Flamsteed's decease, about the beginning of the year 1/20, his 

 late Majesty King George 1, was graciously pleased to bestow on Dr. Halley 

 the post of his astronomical observer, expressly commanding him to apply liim- 



