Page:Encyclopædia Britannica, Ninth Edition, v. 6.djvu/811

Rh 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. 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, &ldquo;Researches concerning the Integral Calculus,&rdquo; 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 (1754–6) 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 &ldquo;Geneva,&rdquo; 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 BenedictXIV., 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 