Alembert, Jean le Rond D'

[dalãbair] (1717–83) French mathematician: discovered d’Alembert’s principle in mechanics.

D’Alembert’s forename comes from that of the church, St Jean le Rond, on whose steps he was found as a baby. He was probably the illegitimate son of a Parisian society hostess, Mme de Tenzin, and the chevalier Destouches; the latter paid for his education while he was brought up by a glazier and his wife. He studied law, and was called to the bar in 1738, but then flirted briefly with medicine before choosing to study mathematics and to live on his father’s annuity.

Early research by d’Alembert clarified the concept of a limit in the calculus and introduced the idea of different orders of infinities. In 1741 he was admitted to the Académie des Sciences and 2 years later published his Traité de dynamique (Treatise on Dynamics), which includes d’Alembert’s principle, that Third Law of Motion holds not only for fixed bodies but also for those free to move. A wide variety of new problems could now be treated, such as the derivation of the planar motion of a fluid. He developed the theory of partial differential equations and solved such systems as a vibrating string and the general wave equation (1747). He joined , A I Clairault (1713–65), and in applying calculus to celestial mechanics and determined the motion of three mutually gravitating bodies. This then allowed many of the celestial observations to be understood; for example, d’Alembert explained mathematically (1754) Newton’s discovery of precession of the equinoxes, and also the perturbations in the orbits of the planets.

D’Alembert was then persuaded by his friend, Denis Diderot (1713–84), to participate in writing his encyclopedia, contributing on scientific topics. This project was denounced by the Church after one volume, and d’Alembert turned instead to publishing eight volumes of abstruse mathematical studies. Shortly before his death J H Lambert (1728–77) wished to name his ‘newly discovered moon of Venus’ after d’Alembert, but the latter was sufficiently acute to doubt (correctly) from calculations that it existed, and gently declined the offer.