298 NOTES TO BOOK VII. 



of Newton's (Isaaci Newtoni Propositiones de Motu) which 

 contained some of the principal Propositions of the first 

 two Books of the Principia. This paper, however, does 

 not contain the Proposition " Lunam gravitare in ter- 

 rain, 5 ' nor any of the other Propositions of the Third 

 Book. The Principia was printed in 1686 and 7, appa- 

 rently at the expense of Halley. On the 6th of April, 

 1 687, the Third Book was presented to the Royal Society. 

 (G.) p. 186. In the first edition of the Principia, 

 published in 1687, Newton showed that the nature of all 

 the then known inequalities of the moon, and in some 

 cases their quantities, might be deduced from the prin- 

 ciples which he laid down : but the determination of the 

 amount and law of most of the inequalities was deferred to 

 a more favourable opportunity, when he might be fur- 

 nished with better astronomical observations. Such ob- 

 servations as he needed for this purpose had been made 

 by Flamsteed, and for these he applied, representing how 

 much value their use would add to the observations. "If," 

 he says, in 1694, " you publish them without such a theory 

 to recommend them they will only be thrown into the 

 heap of the observations of former astronomers, till some- 

 body shall arise that by perfecting the theory of the moon 

 shall discover your observations to be exacter than the 

 rest, but when that shall be, God knows : I fear, not in 

 your lifetime, if I should die before it is done. For I 

 find this theory so very intricate, and the theory of gravity 

 so necessary to it, that I am satisfied it will never be 

 perfected but by somebody who understands the theory 

 of gravity as well, or better than I do." He obtained 

 from Flamsteed the lunar observations for which he ap- 

 plied, and by using these he framed the Theory of the 



