Encyclopædia Britannica, Ninth Edition/Jean le Rond D'Alembert

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D'ALEMBERT, Jean le Rond (17171783), French mathematician and philosopher, was born at Paris in November 1717. He was a foundling, having been exposed in the market near the church of St Jean le Rond, Paris, where he was discovered by a commissary of police on the 17th November. It afterwards became known that he was the illegitimate son of the Chevalier Destouches and Madame de Tencin, a lady of somewhat questionable reputation. Whether by secret arrangement with one or other of the parents, or from regard to his exceedingly feeble state, the infant was not taken to the foundling hospital, but intrusted to the wife of a glazier named Rousseau who lived close by. He was called Jean le Rond from the church near which he was found; the surname D'Alembert was added by himself at a later period. His foster-mother brought him up with a kindness that secured his life-long attachment. When, after he was beginning to be famous, Madame Tencin sent for him and acknowledged the relationship between them, he said that she was only a step-mother, and that the glazier's wife was his true mother. His father, without disclosing himself, recognized his natural claims by settling upon him while still an infant an annuity of 1200 francs. Furnished in this way with enough to defray the expense of his education he was sent at four years of age to a boarding school, where he had learned all the master could teach him ere he was ten. In 1730 he entered the Mazarin College under the care of the Jansenists, who soon perceived his exceptional talent, and, prompted perhaps by a commentary on the epistle to the Romans which he produced in the first year of his philosophical course, sought to direct it to theology. They checked his devotion to poetry and mathematics, and in the science in which he was to achieve his greatest distinction he received no instruction at college beyond a few elementary lessons from Caron. His knowledge of the higher mathematics was acquired by his own unaided efforts after he had left the college. This naturally led to his crediting himself with the discovery of many truths which he afterwards found had been already established, often by more direct and elegant processes than his own.

On leaving college he returned to the house of his foster-mother, where he continued to live for thirty years. On the advice of his friends he made two successive efforts to add to his scanty income by qualifying himself for a profession. He studied law, and was admitted as an advocate in 1738, but did not enter upon practice. He next devoted himself to medicine, and in order to detach himself effectually from his favourite subject, sent all his mathematical books to a friend, who was to retain them until he had taken his doctor's degree. His natural inclination, however, proved too strong for him; within a year the books had all been recovered, and he had resolved to content himself with his annuity and give his whole time to mathematics. He led a simple regular life in the house of the glazier, whose circumstances he contrived somewhat to better out of his limited means. His foster-mother continued to show a warm attachment to him, though she took no interest in his pursuits, and professed something like contempt for his fame. “You will never,” she said, “be anything but a philosopher. And what is a philosopher? A fool who plagues himself during his life that men may talk of him after his death.”

In 1741 D'Alembert 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 Mémoire sur le calcul integral (1739). In this he pointed out some errors in Reinau's L'Analyse démonstrée, which was regarded as a work of high authority. In his Mémoire sur la réfraction des corps solides (1741) he was the first to give a theoretical explanation of the familiar and curious phenomenon which is witnessed when a body passes from one fluid to another more dense, in a direction not perpendicular to the surface which separates the two fluids. Two years after his election to a place in the Academy he published his Traité de Dynamique. The new principle developed in this treatise, known as D'Alembert's Principle, may be thus stated—“If from the forces impressed on any system of bodies, connected in any manner, there be subtracted the forces which, acting alone, would be capable of producing the actual accelerations and retardations of the bodies, the remaining forces must exactly balance each other.” The effect of this is greatly to simplify the solution of complex dynamical problems by making them problems of statics.

So early as the year 1744 D'Alembert had applied this principle to the theory of the equilibrium and the motion of fluids; and all the problems before solved by geometricians became in some measure its corollaries. The discovery of this new principle was followed by that of a new calculus, the first trials of which were published in his Réflexions sur le cause générale des Vents, to which the prize medal was adjudged by the Academy of Berlin in the year 1746, and which was a new and brilliant addition to his fame. He availed himself of the favourable circumstance of the king of Prussia having just terminated a glorious campaign by an honourable peace, to dedicate his work to that prince in the following Latin lines:—


 
Hæc ego de ventis, dum ventorum ocyor alis
Palantes agit Austriacos Fredericus, et orbi,
Insignis lauro, ramum prœtendit olivæ.
 
Swifter than wind, while of the winds I write,
The foes of conquering Frederick speed their flight;
While laurel o'er the hero's temple bends,
To the tir'd world the olive branch he sends.


This flattering dedication procured the philosopher a polite letter from Frederick, and a place among his literary friends. The king made repeated attempts to induce him to settle in Berlin without success. In 1754 he induced D'Alembert to accept a pension of 1200 francs a year, and in 1763 the philosopher visited Berlin, where he was received with great respect. He finally refused on that occasion the office of president of the Academy of Berlin, which had been already offered to him more than once. In 1747 D'Alembert applied his new calculus of partial differences 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, and these his masters or his rivals. In 1749 he furnished a method of applying his principles to the motion of any body of a given figure; and he solved the problem of the precession of the equinoxes, determined its quantity, and explained the phenomenon of the nutation of the terrestrial axis, discovered by Dr Bradley. In 1752 he published a treatise on the Resistance of Fluids, to which he gave the modest title of an Essay, but which contains a large number of original ideas and new observations. About the same time he published, in the Memoirs of the Academy of Berlin, “Researches concerning the Integral Calculus,” a branch of mathematical science which is greatly indebted to him for the rapid progress it has made in the present century. In his Recherches sur différents points importants du système du monde (17546) he perfected the solution of the problem of the perturbations of the planets, which he had presented to the Academy some years before.

While the studies of D'Alembert were confined to geometry, he was little known or celebrated in his native country. His connections were limited to a small society of select friends; he had never seen any man in high office except the Marquis d'Argenson. Satisfied with an income which furnished him with the necessaries of life, he did not aspire after opulence or honours; nor had they been hitherto bestowed upon him, as it is easier to confer them on those who solicit them than to look out for men who deserve them. His cheerful conversation, his smart and lively sallies, a happy knack at telling a story, a singular mixture of malice of speech with goodness of heart, and of delicacy of wit with simplicity of manners, rendered him a pleasing and interesting companion; and his company, consequently, was much sought after in the fashionable circles. His reputation at length made its way to the throne, and rendered him the object of royal attention and beneficence. He received also in 1756 a pension from Government, which he owed to the friendship of M. d'Argenson.

D'Alembert's association with Diderot in the preparation of the celebrated Dictionnaire Encyclopédique led him to take a somewhat wider range than that to which he had hitherto confined himself. He wrote for that work the Discours préliminaire 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, the 19th December 1754. Condorcet, in his Éloge, characterizes it as one of those works which only two or three men in a century could produce. Comprehensive in its plan, and clear in its statement, it deserves this often quoted praise; but it is open to the criticism that the fundamental principle, adopted from Bacon, on which it classifies the sciences is untenable. D'Alembert distinguishes the human faculties into memory, reason, and imagination, and following out that distinction classifies all science under the three heads of history or the science of memory, philosophy or the science of reason, and poetry or the science of imagination. Now, it is obvious that even if these are in each case the faculties primarily concerned, which is not beyond question, no science is the product of any one faculty exclusively. D'Alembert wrote several literary articles for the first two volumes of the Encyclopædia, after which the work was suppressed for a time. To the remaining volumes he contributed mathematical articles chiefly. One of the few exceptions was the article on “Geneva,” which involved him in a somewhat keen controversy in regard to Calvinism and the suppression of theatrical performances within the town. During the time he was engaged on the Encyclopædia he wrote a number of literary and philosophical works, which extended his reputation and also exposed him to criticism and controversy, as in the case of his Mélanges de Philosophie, d'Histoire, et de Littérature. His Essai sur la société des gens de lettres avec les grands was a worthy vindication of the independence of literary men, and a thorough exposure of the evils of the system of patronage. He broke new ground and showed great skill as a translator in his Traduction de quelques morceaux choisis de Tacite. One of his most important works was the Éléments de Philosophie, published in 1759, in which he discussed the principles and methods of the different sciences. He maintained that the laws of motion were necessary, not contingent. The work furnished occasion for a renewal of his correspondence with Frederick the Great. A treatise Sur la destruction des Jésuites (1765) involved him in a fresh controversy, his own share in which was rendered very easy by the violence and extravagance of his adversaries. The list of his more noteworthy literary works is completed by the mention of the Histoire des membres de l'Académie française, containing biographical notices of all the members of the Academy who died between 1700 and 1772, the year in which he himself became secretary. D'Alembert was much interested in music both as a science and as an art, and wrote Éléments de Musique théorique et pratique, which was based upon the system of Rameau with important modifications and differences.

D'Alembert's fame spread rapidly throughout Europe and procured for him more than one opportunity of quitting the comparative retirement in which he lived in Paris for more lucrative and prominent positions. The offer of Frederick the Great has already been mentioned. In 1762 he was invited by Catherine of Russia to become tutor to her son at a yearly salary of 100,000 francs. On his refusal, the offer was repeated with the additional inducement of accommodation for as many of his friends as he chose to bring with him to the Russian capital. D'Alembert persisted in his declinature, and the letter of Catharine was ordered to be engrossed in the minutes of the French Academy. A foreign honour of a different kind had previously been bestowed upon him. In 1755, on the recommendation of Pope Benedict XIV., he was admitted a member of the Institute of Bologna. A legacy of £200 from David Hume showed the esteem in which he was held by that philosopher.

D'Alembert continued to the end to lead the quiet and frugal life which his limited means, as well as his simple tastes, dictated. He was abstemious in his habits, and never tasted any alcoholic beverages. His later years were saddened by circumstances connected with a romantic attachment he had formed for Mademoiselle de l'Espinasse. He made the lady's acquaintance at the house of Madame du Deffand, a noted resort of literary men and savans. She nursed him assiduously during an illness he had in 1765, and from that period till her death in 1776 they lived in the same house without any scandal attaching to their intimacy. On her part there seems 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 thirty years, he was regarded as the leader of the philosophical party in the Academy. He died on the 29th October 1783.

The chief features of D'Alembert's character were benevolence, simplicity, and independence. Though his income was never large, and during the greater part of his life was very meagre, he contrived to find means to support his foster-mother in her old age, to educate the children of his first teacher, and to help various deserving students during their college career. By his practice as well as by the work above referred to (Essai sur la société des gens de lettres &c.) he did much to destroy the unworthy subserviency of literary and scientific men to the socially great and the politically powerful. If his manner was sometimes plain almost to the extent of rudeness it probably set all the better an example of a much needed reform to the class to which he belonged. The controversy as to the nature of his religious opinions, arising as it did chiefly out of his connection with the Encyclopædia, has no longer any living interest now that the Encyclopædists generally have ceased to be regarded with unqualified suspicion by those who count themselves orthodox. It is to be observed, moreover, that as D'Alembert confined himself chiefly to mathematical articles, his work laid him less open to charges of heresy and infidelity than that of some of his associates. The fullest revelation of his religious convictions is given in his correspondence with Voltaire, which was published along with that with Frederick the Great in Bossange's edition of his works.


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 mathématiques (176180, 8 vols. 4to). His literary and philosophical works were collected and edited by Bastien (Paris, 1805, 18 vols. 8vo). A better edition by Bossange was published at Paris, in 1821 (5 vols. 8vo). The best account of the life and writings of D'Alembert is contained in Condorcet's Éloge, presented to the Academy and published in 1784.