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Author. The problem of three bodies was solved independently about the same time by Euler, D'Alembert, and Clairaut. The two last-mentioned geometers communicated their solutions to the Academy of Sciences on the same day, November 15, 1747. Euler had already in 1746 published tables of the moon, founded on his solution of the same problem, the details of which he subsequently published in 1753.
The year 1759 had been marked by one of those great events, the memory of which is religiously preserved in scientific history. A comet, that of 1682, had returned at the epoch foretold by Clairaut, and very nearly in the region that mathematical analysis had indicated to him.
By this employment I should have entered a society of men of letters of the first merit; M. de Mairan, Clairaut, De Guignes and the Abbe Barthelemi, with the first two of whom I had already made an acquaintance, and that of the two others was very desirable.
In fine, the labours of Clairaut had produced a deeper impression on the public mind than the learned, ingenious, and acute reasoning of Bayle. The heavens offer to reflecting minds nothing more curious or more strange than the equality which subsists between the movements of rotation and revolution of our satellite.
Numerous observations have been made in all parts of the world by various explorers, and have led to a fairly complete knowledge of the distribution of gravity over the surface of the globe. Thus we have succeeded in making evident anomalies which would not easily find their place in the formula of Clairaut.
It is not the fashion in France; and, as there are here a few more men of wit and noblemen than in Prussia, it would require that I should have a very large table to assemble them all at it." And then he reckoned upon his fingers, Maupertuis, Fontenelle, La Mothe, Voltaire, Piron, Destouches, Montesquieu, the Cardinal Polignac. "Your Majesty forgets," said some one, "D'Alembert and Clairaut."
Clairaut confined himself to the same part; but he was not afraid of expressing to me the emotion which the reading of it had caused in him, and in the most direct terms wrote to me that it had warmed his old imagination: of all those to whom I had sent my book, he was the only person who spoke freely what he thought of it.
Clairaut found by a long process of calculation, conducted with great skill, that the action of Jupiter and Saturn ought to have retarded the movement of the comet; that the time of revolution compared with that immediately preceding, would be increased 518 days by the disturbing action of Jupiter, and 100 days by the action of Saturn, forming a total of 618 days, or more than a year and eight months.
This generality increased tenfold the difficulties of the problem; neither Clairaut nor D'Alembert was, however, arrested by them. Thanks to the efforts of these two eminent geometers, thanks to some essential developments due to their immediate successors, and especially to the illustrious Legendre, the theoretical determination of the figure of the earth has attained all desirable perfection.
This had been a known fact from the earliest ages. He also concluded that the line of apses would revolve in the plane of the lunar orbit also in about nineteen years; but the observed period is only ten years. For a long time this was the one weak point in the Newtonian theory. It was not till 1747 that Clairaut reconciled this with the theory, and showed why Newton's calculation was not exact.
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