16 novembre 1757 (2) : Clairaut (Paris) écrit à Gael Morris.

Dear Sir, More than six months without answering a letter for which I am in the real truth extremely obliged to you, load me with an appear[a]nce of ingratitude quite unpardonable. I, nevertheless, assure you that I am far from being guilty of forgetfulness for your goodness and Dr Bradley's to whom I desire you to present my respects and thanks. I have been informed of the death of his worthy lady and felt how much her loss ought to have afflicted him. The cause of my so long delaying the acknowledgement I owe to you, was that in order not to trouble you too often with explanations about observations, I thought differing my answer 'till I had made use of the excellent collection you sent me. But several other inquiries I had begun before and the success of which I desired to inform you with, have drawn out so insensibly in length, as to be quite any whole time, and hindered me, as now to make use of your observations. The first subject which I followed with eagerness was a new theory of the Sun with regard to the perturbations he (or rather the Earth) receives from the planets [C. 47]. The action of the Moon had been considered already and one lunary equation was known, its argument being the distance of the luminaries. I have found two other equations, depending upon the anomaly of the Sun, which tho' smaller are very comparable to the first. After having fixed those thrice equations for the supposition of the Moon's volume being 1/40 of the Earth's, according to Sir Isaac's sentiments, I have made use of Mr de La Caille observations of the Sun, to mend that supposition if necessary. I have found that they required a considerable diminution in the Moon's volume and reduced it to about 1/70 of the Earth. Thus the lunary equations of the Sun are [maths] in which t designs the Moon's place from which that of the Sun is subtracted, [maths] the mean anomaly of the Sun. After having considered those equations, I have examined the jovial equations. I have found them as follow [maths]. Venus tho' very small to Jupiter, deserves nevertheless a greater attention, because of her proximity to the Earth. The uncertainty about her volume gave the same trouble as the Moon's. But after having determined the venereal [!] equations of the Sun according to the supposition her volume was the same with the Earth's and calculated a single table for them, I gave it to abbé de La Caille who comparing it with his observations of the Sun has found that a diminution of ¼ was that agreed the best. Thus the venereal equations are [maths] Several months have been spent already since those determinations, but immediately after them, an enterprise much more fatiguing has engrossed my whole attention. It was the calculations of the perturbations which the comet now expected has received from the planets and especial[l]y Jupiter. The theory of such perturbation is more cumbersom[e] than the planet's, because of the comet's orb being so inclined, and its prodigious excentricity. The algebrical abbreviations growned upon the the vanishing of many terms in the first case, having no room here. I thought at first of going out the precepts which my theory gave to make the computations of those perturbations, in order to leave the incumbrance of it, to the astronomers that would be glad to calculate the time of the comet's next apparition : supposing that the inequality of her periods was only caused by the attraction of the planets. Considering afterword that my precepts were very troublesome to follow, and very easy to be misunderstood in some cases, and fearing that some errors arising from it, spoiled the whole work and disgraced the theory, I have with the help of a friend [Lalande] undertaken the whole and I'm very near the end. Hitherto I have been so hard at work, as to neglect all correspondence for fear the comet got the start of me and appeared before the end of my calculations. Now I have time to breathe, for tho' I have not finished the whole enterprise, I am advanced enough to know I have sufficient time. The comet which has newly appeared instead of the expected has plagued me at the beginning, but her elements, now determined, have tranquilised me. Mr. de La Caille has determined them as follow : [maths] When the calculations belonging to the other comet will be finished, I will let you know the result as well as the use I am to make of your observations, supposing, however, that an account of it will be agreable to you, this what I should be glad to know from you, if your engagements leave you the [...] of it. In the mean time, I am with a great regard, dear Sir, your most obedient humble servant Clairaut. Paris rue du Coq S[ain]t Jean. Nov[ember] the 16th. If you [...] sometimes the Royal Society, I shall be glad to let them know the content of this letter. If I had more time I had wrote a memoir and send it. [Adresse] To Mr Gabriel Morris / at Batson's Coffee House / London (RS, L & P III, 274).

La lettre est lue à la Royal Society le 22 décembre (cf. 22 décembre 1757 (1)). Un extrait de la lettre avait été publié dans (Taton 79b).

Abréviations

- C. 47 : Clairaut (Alexis-Claude), « Mémoire sur l'orbite apparente du Soleil autour de la Terre, en ayant garde aux perturbations produites par les actions de la Lune et des planètes principales »,
*HARS 1754*(1759), Mém., pp. 521-564 [Télécharger] [9 juillet 1757 (1)] [28 juin 1747 (1)] [Plus]. *HARS 17..*:*Histoire de l'Académie royale des sciences*[de Paris]*pour l'année 17.., avec les mémoires...*- Mém. : Partie
*Mémoires*de*HARS 17*.. - RS : Royal Society, London.

Référence

- Taton (René), « Clairaut et le retour de la comète de Halley »,
*Arithmos- Arrythmos : Skizzen aus des Wissenchaftgeschichte, Festschrift für Joachim Otto Fleckenstein zum 65. Geburstag*, Ed. K. Figala, E. H. Berninger, Munich, 1979, pp. 253-274 [15 octobre 1757 (1)] [Plus].

Courcelle (Olivier), « 16 novembre 1757 (2) : Clairaut (Paris) écrit à Gael Morris », *Chronologie de la vie de Clairaut (1713-1765)* [En ligne], http://www.clairaut.com/n16novembre1757po2pf.html [Notice publiée le 22 mars 2011].