‎"CLAIRAUT, ALEXIS-CLAUDE. - CORRECTING NEWTON'S INVERSE SQUARE LAW.‎
‎De L'orbite de la Lune dans le Systeme de M. Newton.‎

‎(Paris, L'Imprimerie Royale, 1746). 4to. Without wrappers. In ""Histoire de L'Academie Royale des Sciences. Année MDCCXLIII. Avec les Memoires de Mathematiques & de Physique, pour la même Année."" Pp. 17-32 and 3 folded engraved plates.‎

Reference : 53475

‎First printing of this controverial paper. ""In 1743 Clairaut read before the Academy a Paper entitled ""L’orbite de la lune dans le systeme de M. Newton,"" Newton was not fully aware of the movement of the moon’s apogee, and therefore the problem had to be reexamined in greater detail. However, Clairaut - and d’Alembert, and Euler, who were also working on this question - found only half of the observed movement in their calculations. It was then that Clairaut suggested completing Newton’s law of attraction by adding a term inversely proportional to the fourth power of the distance. This correction of the law elicited a spirited reaction from Buffon, who opposed this modification with metaphysical considerations on the simplicity of the laws of nature. Clairaut, more positive and more a pure mathematician, wanted to stick to calculations and observations. The controversy that arose between these two academicians appears in the Mémoires of the Academy for 1745 (published long afterward)."" (DSB).‎