Alexis Clairault

Alexis Claude Clairault (or Clairaut) (May 3, 1713 – May 17, 1765) was a French mathematician.

He was born in Paris, France, where his father taught mathematics. Under his father's tuition he made such rapid progress in the subject that in his thirteenth year he read before the Académie française an account of the properties of four curves which he had then discovered. When only sixteen he finished a treatise, Recherches sur les courbes a double courbure, which, on its publication in 1731, procured his admission into the French Academy of Sciences, although he was below the legal age.

In 1736, together with Pierre Louis Maupertuis, he took part in the expedition to Lapland, which was undertaken for the purpose of estimating a degree of the meridian, and on his return he published his treatise Théorie de la figure de la terre (1743). In this work he promulgated the theorem, known as "Clairault's theorem," which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the equator.

He obtained an ingenious approximate solution of the problem of the three bodies; in 1750 he gained the prize of the St Petersburg Academy for his essay Théorie de la lune; and in 1759 he calculated the perihelion of Halley's comet. He also detected singular solutions in differential equations of the first order, and of the second and higher degrees. Clairault died at Paris.

He was a prodigy - at the age of twelve he wrote a memoir on four geometrical curves; his first important work was a treatise on tortuous curves, published when he was eighteen - a work which procured for him admission to the French Academy. He was born and died in Paris.

In 1731 he gave a demonstration of the fact noted by Newton that all curves of the third order were projections of one of five parabolas.

In 1741 Clairaut went on a scientific expedition to measure the length of a meridian degree on the Earth's surface, and on his return in 1743 he published his Théorie de la figure de la terre. This is founded on a paper by Maclaurin, which had shown that a mass of homogeneous fluid set in rotation about a line through its centre of mass would, under the mutual attraction of its particles, take the form of a spheroid. This work of Clairaut treated of heterogeneous spheroids and contains the proof of his formula for the accelerating effect of gravity in a place of latitude l. In 1849 Stokes showed that the same result was true whatever was the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.

Impressed by the power of geometry as shown in the writings of Newton and Maclaurin, Clairaut abandoned analysis, and his next work, the Théorie de la lune, published in 1752, is strictly Newtonian in character. This contains the explanation of the motion of the apsis which had previously puzzled astronomers, and which Clairaut had at first deemed so inexplicable that he was on the point of publishing a new hypothesis as to the law of attraction when it occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables. Clairaut subsequently wrote various papers on the orbit of the Moon, and on the motion of comets as affected by the perturbation of the planets, particularly on the path of Halley's comet.

His growing popularity in society hindered his scientific work: engagé, says Bossut, à des soupers, à des veilles, entraîné par un goût vif pour les femmes, voulant allier le plaisir à ses travaux ordinaires, il perdit le repos, la santé, enfin la vie à l'âge de cinquante-deux ans.

See also: Clairaut's equation, Clairault's theorem.

This page is based on public domain text taken from 'A Short Account of the History of Mathematics' (4th edition, 1908) by W. W. Rouse Ball.de:Alexis-Claude Clairaut sl:Alexis Claude Clairaut