Alexis Clairault
Alexis Claude Clairault (or
Clairaut) (
May 3,
1713 –
May 17,
1765) was a
French mathematician and thinker.
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Alexis Clairault |
Clairault was born in
Paris, France, where his father taught
mathematics. He was a
prodigy - at the age of twelve he wrote a memoir on four geometrical curves and 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 discovered. When only sixteen he finished a treatise on tortuous curves,
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 as he was only eighteen.
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.
The
Théorie de la lune is strictly Newtonian in character. This contains the explanation of the motion of the
apsis which had previously puzzled astronomers, and which Clairault 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. Clairault 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.
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 Clairault 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 Clairault treated of
heterogeneous spheroids and contains the proof of his formula for the accelerating effect of gravity in a place of latitude. 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.
Clairault died in Paris in 1765.
*
Clairault's equation*
Clairault's theorem*
