PREFACE.

of the Royal Academy of Sciences at Par is, was a motive sufficient toinduce me (among many Others) to endeavour to discover , whether themotion of the moon's apogee, on which that objeSiion had its whole weightand foundation, could not be truly accounted for, without supposing achange in the received law of gravitation, from the inverse ratio of thesquares of the distances. 'Thesuccess was answerable to my hopes, and suchas induced me to looks ar ther into other parts of the theory of the moodsmotion, than I firs intended : but, before I had completed my design, Ireceived the honour of a visit from M. Clairaut (just then arrived inEngland) of whom 1 learned, that he had a little before printed a pieceon that fubjett ; a copy of which I afterwards received, as a present athis hands-, wherein I found most of the fame things demonstrated, besidesseveral others, to which I had not then extended my enquiry. Upon this,I at that time desisted from a farther prosecution of the subjedl j beingchiefly diverted therefrom by a call thensubfisting for a new edition ofanother work , in which some additions seemed wanting. But I cannotomit to observe here, in justice to M. Clairaut, that, tho' he indeed fellinto a mistake, by too hastily inferring a defecl in the received law ofat-traSiion,from the insufficiency of the known methods for determining theeffeSi of that attraSlion, in the motion of the moon's apogee, yet he washimself, thefirst who discovered the true source, of that mistake,and whoplaced the matter in a proper light: Though there are some * whohave , both before andstnce, undertaken to give the true quantity of thatmotion, from such principles, only, as are laid down in the ninth section ofthefirst Book of the Principia: but that these Gentlemen, however theymay have made their numbers to agree, have been greatly deceived in theircalculations, is very certain ; stnce a considerable part of the said motiondepends on that part of the solar force acting in the dire St ion perpendicu-lar to the Radius-vector, which is by them, either intirely disregarded,or the effeSi thereof not made one twentieth part of what it really oughtto be.—There are Others indeed, who have explained the matter, upontrue principles, and with better success. Since M. Clairaut ’j piece firstmade its appearance, the most eminent mathematicians, in different partso/~Europe, have turned their thoughts that way. But tho' what I nowoffer on the fame fubjeSl, may,perhaps,appear of less value, after whathas been already done by these great men, yet I am not very Jolicitousupon that account, as it will be found, that I have neither copied from

* Vid. Walruses sTheorie dumcuvement des apsides (translated into English) andV il. 47. N° 11. of the Philosophical Transactions. their