Alexis Clairaut (1713-1765)

Chronologie de la vie de Clairaut (1713-1765)

(17) 6 avril 1750 : Patrick Murdoch (Stradishall) écrit à Robert Smith :
Read Jan. 31 1750 [1751 ns]

Reverend Sir,

Last summer, when I was to pay my respects to you at Trinity College, I gave you some account of the warm dispute, then lately arisen between Mr de Buffon and Mr Clairaut, two eminent academicians at Paris, the latter pretending [C. 33] that the newtonian law of attraction is inconsistent with the motion of the moon's apogee, and that its quantity ought not to be expressed by 1/x2 of the distance, but two, or perhaps more, terms of a series, as1/x2 + a/x4. Which new doctrine Mr Clairaut had got inserted in the memoirs of the academy, and Mr de Buffon had following him close with another memoire [(Buffon 45a)], confuting it.

When I first heard of this controversy, it was impossible to judge of the validity of Mr Clairaut's reasons, because he kept his calculous a profound secret. But an absurd consequence of his new law of attraction occur'd to me, as soon as Mr de Buffon mention'd the thing, that “if we should put the attraction, express'd by his two terms, of an assumed quantity G, and resolve the equation, there would necessarily arise two different values of the distance x, for the same attractive force".

Suspecting therefore, that some error must have flipt into Mr Clairaut's reasonings (as he himself afterwards found there had) I resolved to try, whether, by an arithmetical calculation, from Sir Isaac Newton's propositions only, the motion in question might not be accounted for.

The result of this inquiry I should have taken the liberty to send you before now, but that, other things intervening, I did not think of revising ans transcribing it, till lately ; that Mr Walmesley having made me a present of his ingenious treatise on the same subject [(Walmesley 49)], it appears, that, however Mr Clairaut's hypothesis is given up, yet a notion still prevails, as if Sir Isaac Newton's propositions, concerning the motion of apsids, were mere mathematical fictions, not applicable to nature.

How far I have succeeded in shewing the contrary is now submitted to your judgment. And I, at the same time, embrace, with pleasure, an opportunity of professing myself, with the highest respect, Reverend Sir, your most obliged, ans most obedient humble servant, Pat. Murdocke.

[Stradis]hall, 6 April 1750 (Murdoch 53).


À cette lettre est joint un mémoire de Murdoch confirmant la théorie newtonienne.
  • Buffon (Georges-Louis Leclerc, comte de), « Réflexions sur la loi d'attraction », HARS 1745, Mém., pp. 493-500 [Télécharger] [Buffon] [Calandrini] [Plus].
  • Murdoch (Patrick), « A letter from the Rev. Patrick Murdocke, F. R. S, concerning the mean motion of Moon's apogee, to the Rev. Dr. Robert Smith, Master of Trinity College, Cambridge », Philosophical Transactions 1751-1752, 47 (1753) 62-74 [Télécharger].
  • Walmesley (Charles), Théorie du mouvement des apsides en général, et en particulier des apsides de la Lune, Paris, 1749 [Télécharger] [15 novembre 1747 (1)] [21 juillet 1749 (1)] [Plus].
Courcelle (Olivier), « (17) 6 avril 1750 : Patrick Murdoch (Stradishall) écrit à Robert Smith », Chronologie de la vie de Clairaut (1713-1765) [En ligne], [Notice publiée le 6 septembre 2010].