(4 avril 1737) 24 mars 1736 : À la Royal Society :

A letter from M[onsieu]r Celsius, dated at Tornea Feb 19 [cf. (2 mars 1737) 19 février 1736] concerning the progress they have made towards the accomplishing their work was read. […] He takes occasion in his letter to recommend Mons[ieu]r Clairaut, a gentleman in their company for a member of this Society, on account of his signal and early merit in mathematical knowledge and which is such as to have distinguished him to the notice of Mons[ieu]r de Fontenelle in his history of the Academy, for having published a treatise of algebra at the age of fourteen. M[onsieu]r Celsius refers for further knowledge of his abilities to a paper of his own concerning the figure of the Earth, which he sends inclosed with his letter to Dr. Mortimer (RS, JBC 16, pp. 69-71). M[onsieu]r Clairaut's letter to Dr. Mortimer dated at Torneo in Westrobothnia Feb 20 1736/7 [cf. (3 mars 1737) 20 février 1736] was read, and his paper entitled Investigationes aliquot exquibus probetur Terra figuram secundium leges attractionis in ratione inversâ quadrati distanciarum maxime ad ellipsin accedere debere [C. 17]. In this letter he says that the memoir which he sends was written with an intention to remove an objection, to which Sir Isaac Newton's rule concerning the different gravity of a body on different parts of the Earth's surface seems liable; and which cannot be removed but by the preparatory knowledge of some propositions as those are which he delivers in this memoir. For granting that the hypothesis of the Earth's being of the figure of a spheroid made by the rotation of an ellipsis about its shorter axis, should be an hypothesis not attended with any considerable error, so far as it applied to the discovery of the proportion of the two axes, and the proportion of the gravity of a body at the pole and a body at the equator: yet when it is applied to as certain the rule according to which the gravity increases in different places on the Earth from the equator to the pole, it's seems to be an hypothesis altogether arbitrary and precarious. For since the gravity in different places on the Earth's surface must always be, by Sir Isaac Newton's Hydrostatical Principle, reciprocally proportional to the distances from the center; and since the variation of the distances from the center depends upon the property of the figure the variation of the gravity must necessarily depend upon the same also. Therefore he concludes that to presuppose a knowledge of the figure, in order to discover the rules of the variation, seems to be a repetition of the thing that is enquired after. To remove this objection, he lays down some propositions in this memoir, to prove that the true figure of the Earth, on supposing the longest diameter does not much exceed the shortest, or that the two axes are rather nearly in the proportion of equality, that on such a supposition the true figure will approach infinitely nearer to the figure of an ellipsoid than to that any other spheroid whatsoever: and ingeniously shows how by means of a lemma the figure may be found and the law of gravity ascertained sufficiently near the truth without the helps of quadratures. He says that if he finds this performance is acceptable, he has other matters further to communicate. Thanks were ordered for these communications (RS, JBC 16, pp. 71-73).

Abréviations

- C. 17 : Clairaut (Alexis-Claude), « Investigationes aliquot, ex quibus probatur terrae figuram secundum Leges attractionis in ratione inversâ quadrati distantiarum maxime ad Ellipsin accedere debere »,
*Philosophical Transactions*, Vol. XL (1737-1738), London, 1741, n° 445 (Jan-June 1738), pp. 19-25 [Télécharger] [(3 mars 1737) 20 février 1736] [(2 mars 1737) 19 février 1736] [Plus]. - RS : Royal Society, London.

Courcelle (Olivier), « (4 avril 1737) 24 mars 1736 : À la Royal Society », *Chronologie de la vie de Clairaut (1713-1765)* [En ligne], http://www.clairaut.com/npo4avril1737pf24mars1736.html [Notice publiée le 1 décembre 2008].