ALEMBERT, JEAN LE ROND D' (1717-1783)., French mathematician and philosopher, was born at Paris in Nov. 1717. He was a foundling but it afterwards became known that he was the illegitimate son of the Chevalier Destouches and Madame de Tencin. The infant was entrusted to the wife of a glazier named Rousseau who lived close by the Church of St. Jean le Rond, where the child was found. Destouches, without disclosing his identity, provided for the boy, who was educated at the Mazarin College under the Jansenists.
On leaving college he returned to the house of his foster-mother, where he continued to live for 3o years. Having studied law, he was admitted as an advocate in 1738, but did not enter upon practice. He next devoted himself to medicine; but his natural inclination proved too strong for him, and within a year he re solved to give his whole time to mathematics. In 1741 he received his first public distinction in being admitted a member of the Academy of Sciences, to which he had previously presented several papers, including a Memoire sur le calcul integral (1739). In his Memoire sur la refraction des corps solides (1741) he was the first to give a theoretical explanation of the phenomenon which is witnessed when a body passes from one fluid to another more dense in a direction not perpendicular to the surface which sepa rates the two fluids. In 1743 he published his Traite de dynamique, a work famous as developing the mechanical principle, known as "d'Alembert's principle," first enunciated in 1742 (see MECHAN ICS). In 1744 d'Alembert applied this principle to the theory of the equilibrium and the motion of fluids, Traite de l'equilibre et du mouvement des Aides, and all the problems before solved by geometricians became in some measure its corollaries. This dis covery was followed by that of the calculus of partial differences, the first trials of which were published in his Reflexions sur la cause generale des vents (1747)• This work was dedicated to Frederick the Great, who made several unsuccessful attempts to induce him to settle in Berlin. In 1763 he visited Berlin, and on that occasion finally refused the office of president of the Academy of Berlin, which had been already offered to him more than once. In 1747 he applied his new calculus to the problem of vibrating chords, the solution of which, as well as the theory of the oscillation of the air and the propagation of sound, had been given but incompletely by the geometricians who preceded him. In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and in 1754 he solved the problem of the precession of the equinoxes, determined its quantity and explained the phe nomenon of the nutation of the earth's axis. In '752 he published an Essai d'une nouvelle theorie sur la resistance des Aides, which contains a large number of original ideas and new observations. In 1746 and 1748 he published in the Memoirs of the Academy of Berlin "Recherches sur le calcul integral," a branch of mathemat ical science which is greatly indebted to him. In his Recherches sur differents points importants du systeme du monde (1754-56) he perfected the solution of the problem of the perturbations of the planets, which he had presented to the academy some years bef ore.
D'Alembert's association with Diderot in the preparation of the Dictionnaire Encyclopedique led him to a wider range of work. He contributed the Discours preliminaire on the rise, progress, and affinities of the various sciences, which he read to the French Academy on the day of his admission as a member, Dec. 18,1754. He also wrote several literary articles for the first two volumes of the encyclopaedia, and to the remaining volumes he contributed mathematical articles chiefly. Of d'Alembert's works on other than mathematical subjects the most important is the Elements de Philosophie (1759) in which he discussed the principles and methods of the different sciences. D'Alembert was much inter ested in music both as a science and as an art, and wrote Elements de musique theorique et pratique (1779), which was based upon the system of J. P. Rameau with important modifica tions and differences.
D'Alembert continued to the end to lead the quiet and frugal life dictated by his limited means as well as his simple tastes. His later years were saddened by the death of Mademoiselle de Les pinasse, whose acquaintance he made at the house of Madame du Deffand. She nursed him assiduously during an illness he had in 1765, and from that period till her death in '776 they lived in the same house. On her part there .ieems to have been from first to last nothing more than warm friendship, but his feelings towards her were of a stronger kind and her death deeply affected him. He never recovered his elasticity of spirits, though he continued to occupy himself with his favourite pursuits, and to frequent the society of his brother philosophers. After the death of Voltaire (1778), whose friend and correspondent he had been for more than 3o years, he was regarded as the leader of the philosophical party in the Academy. He died at Paris on Oct. 29, 1783.
BIBLIOGRAPHY.-The scientific works of d'Alembert have never been Bibliography.-The scientific works of d'Alembert have never been published in a collected form. The most important of them have been mentioned above, with the exception of the Opuscules mathematiques (1761-8o). His literary and philosophical works were collected and edited by Bastien (18os). A better edition by Bossange was published at Paris in 1821. The best account of the life and writings of d'Alem bert is contained in Condorcet's Eloge, presented to the Academy and published in 1784.