Clairaut , Alexis Claude

(1713–1765) French mathematical physicist

The Parisian-born son of a mathematics teacher, Clairaut was introduced to the subject at an early age. By the age of ten he was studying L'Hôpital's work on conic sections and two years later he read a paper to the French Académie des sciences. He was elected to the Académie at the age of 18 following the publication in 1731 of his Recherches sur les courbes à double courbes.

Soon after, in 1736, he accompanied Maupertuis on an expedition to Lapland to determine the length of 1° of a meridian within the Arctic circle. The aim of the expedition was to determine the shape of the Earth by measuring its curvature at the places where it differed most – the equator and poles. A similar expedition under the direction of La Condamine measured the equatorial curvature in the Andes. Behind the expeditions lay a crucial test of Newtonian mechanics that the Earth's rotation should cause it to bulge at the equator and flatten at the poles. Cartesian science predicted that the reverse position should hold. As Clairaut revealed in his Théorie de la figure de la terre (1743; Theory of the Shape of the Earth) the Earth had, as Newton had claimed, a larger diameter through the equator than through the poles, a shape known to geometers as an oblate spheroid.

In 1747 Clairaut turned his attention to the Moon and once again the issue was the accuracy of Newtonian mechanics. The motion of the lunar apogee – the point in the lunar orbit furthest away from the Earth – differed from Newton's predicted value by a factor of two. At first Clairaut was tempted to question the validity of Newton's inverse square law, but in 1749 he discovered that no such drastic step need be taken; several factors of the lunar orbit had been ignored. When these were included in Newton's lunar equations the correct value for the motion of the lunar apogee was obtained.

Clairaut was also involved in the dramatic events surrounding the return of Halley's comet. Halley had claimed that the comet of 1682 would return in 1758. Clairaut realized that if Newtonian mechanics was to be an exact science it must make a more precise prediction. He informed the Académie in November 1758 that the comet would be at perihelion on April 13, 1759; the actual date was March 13, just within the allowed-for margins of error.

Clairaut also collaborated with the Marquise du Châtelet in her French translation of Newton's Principia.