ALEMBERT (John le Rond D')
, an eminent French mathematician and philosopher, and one of the brightest ornaments of the 18th century. He was perpetual secretary to the French Academy of Sciences, and a member of most of the philosophical academies and societies of Europe.
D'Alembert was born at Paris, the 16th of November 1717. He derived the name of John le Rond from that of the church near which, after his birth, he was exposed as a foundling. But his father, informed of this circumstance, listening to the voice of nature and duty, took measures for the proper education of his child, and for his future subsistence in a state of ease and independence. His mother, it is said, was a lady of of rank, the celebrated Mademoiselle Tencin, sister to cardinal Tencin, archbishop of Lyons.
He received his first education among the Jansenists, in the College of the Four Nations, where he gave early signs of genius and capacity. In the first year of his philosophical studies, he composed a Commentary on the Epistle of St. Paul to the Romans. The Jansenists considered this production as an omen, that portended to the party of Port-Royal a restoration to some part of their former splendor, and hoped to find one day in d'Alembert a second Pascal. To render this resemblance more complete, they engaged their pupil in the study of the mathematics; but they soon perceived that his growing attachment to this science was likely to disappoint the hopes they had formed with respect to his future destination: they therefore endeavoured to divert him from this line; but their endeavours were fruitless. |
On his quitting the college, finding himself alone, and unconnected in the world, he sought an asylum in the house of his nurse. He hoped that his fortune, though not ample, would enlarge the subsistence, and better the condition of her family, which was the only one that he could consider as his own. It was here therefore that he fixed his residence, resolving to apply himself entirely to the study of geometry.—And here he lived, during the space of 40 years, with the greatest fimplicity, discovering the augmentation of his means only by increasing displays of his beneficence, concealing his growing reputation and celebrity from these honest people, and making their plain and uncouth manners the subject of good-natured pleasantry and philosophical observation. His good nurse perceived his ardent activity; heard him mentioned as the writer of many books; but never took it into her head that he was a great man, and rather beheld him with a kind of compassion. “You will never, said she to him one day, be any thing but a philosopher—and what is a philosopher?—a fool, who toils and plagues himself all his life, that people may talk of him when he is dead.”
As d'Alembert's fortune did not far exceed the demands of necessity, his friends advised him to think of some profession that might enable him to increase it. He accordingly turned his views to the law, and took his degrees in that faculty: but soon after, abandoning this line, he applied himself to the study of medicine. Geometry however was always drawing him back to his former pursuits; so that after many ineffectual struggles to resist its attractions, he renounced all views of a lucrative profession, and gave himself up entirely to mathematics and poverty.
In the year 1741 he was admitted a member of the Academy of Sciences; for which distinguished literary promotion, at so early an age (24), he had prepared the way by correcting the errors of a celebrated work (The Analyse Demontrée of Reyneau), which was esteemed classical in France in the line of analytics. He afterwards set himself to examine, with close attention and assiduity, what must be the motion and path of a body, which passes from one fluid into another denser fluid, in a direction oblique to the surface between the two fluids. Every one knows the phenomenon which happens in this case, and amuses children, under the denomination of Ducks and Drakes; but it was d'Alembert who first explained it in a satisfactory and philosophical manner.
Two years after his election to a place in the academy, he published his Treatise on Dynamics. The new principle developed in this treatise, consisted in establishing an equality, at each instant, between the changes that the motion of a body has undergone, and the forces or powers which have been employed to produce them: or, to express the same thing otherwise, in separating into two parts the action of the moving powers, and considering the one as producing alone the motion of the body, in the second instant, and the other as employed to destroy that which it had in the first.
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 resolved in physics, became in some measure its corollaries. The discovery of this new principle was followed by that of a new calculus, the first essays of which were published in a Discourse on the General Theory of the Winds, to which the prize-medal was adjudged by the Academy of Berlin in the year 1746, which proved a new and brilliant addition to the fame of d'Alembert. This new calculus of Partial Differences he applied, the year following, to the problem of vibrating chords, the resolution of which, as well as the theory of the oscillations of the air and the propagation of sound, had been but imperfectly given by the mathematicians who preceded him; and these were his masters or his rivals.
In the year 1749 he furnished a method of applying his principle to the motion of any body of a given figure. He also resolved the problem of the precession of the equinoxes; determining its quantity, and explaining the phenomenon of the nutation of the terrestrial axis discovered by Dr. Bradley.
In 1752, d'Alembert published a treatise on the Resistance of Fluids. to which he gave the modest title of an Essay; though it contains a multitude 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, which is greatly indebted to him for the rapid progress it has made in the present century.
While the studies of d'Alembert were confined to mere mathematics, he was little known or celebrated in his native country. His connections were limited to a small society of select friends. But 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, rendering him a pleasing and interesting companion, his company began to be 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. The consequence was a pension from government, which he owed to the friendship of count d'Argenson.
But the tranquillity of d'Alembert was abated when his same grew more extensive, and when it was known beyond the circle of his friends, that a fine and enlightened taste for literature and philosophy accompanied his mathematical genius. Our author's eulogist ascribes to envy, detraction, &c, all the opposition and censure that d'Alembert met with on account of the famous Encyclopédie, or Dictionary of Arts and Sciences, in conjunction with Diderot. None surely will refuse the well-deserved tribute of applause to the eminent displays of genius, judgment, and true literary taste, with which d'Alembert has enriched that great work. Among others, the Preliminary Discourse he has prefixed to it, concerning the rise, progress, connections, and affinities of all the branches of human knowledge, is perhaps one of the most capital productions the philosophy of the age can boast of.
Some time after this, d'Alembert published his Philosophical, Historical, and Philological Miscellanies. These were followed by the Memoirs of Christina queen of Sweden; in which d'Alembert shewed that he was acquainted with the natural rights of mankind, | and was bold enough to assert them. His Essay on the Intercourse of Men of Letters with Persons high in Rank and Ofsice, wounded the former to the quick, as it exposed to the eyes of the public the ignominy of those servile chains, which they feared to shake off, or were proud to wear. A lady of the court hearing one day the author accused of having exaggerated the despotism of the great, and the submission they require, answered slyly, “If he had consulted me, I would have told him still more of the matter.”
D'Alembert gave elegant specimens of his literary abilities in his translations of some select pieces of Tacitus. But these occupations did not divert him from his mathematical studies: for about the same time he enriched the Encyclopédie with a multitude of excellent articles in that line, and composed his Researches on several Important Points of the System of the World, in which he carried to a higher degree of perfection the solution of the problem concerning the perturbations of the planets, that had several years before been presented to the Academy.
In 1759 he published his Elements of Philosophy: a work much extolled as remarkable for its precision and perspicuity.
The resentment that was kindled (and the disputes that followed it) by the article Geneva, inserted in the Encyclopédie, are well known. D'Alembert did not leave this sield of controversy with flying colours. Voltaire was an auxiliary in the contest: but as he had no reputation to lose, in point of candour and decency; and as he weakened the blows of his enemies, by throwing both them and the spectators into fits of laughter, the issue of the war gave him little uneasiness. It fell more heavily on d'Alembert; and exposed him, even at home, to much contradiction and opposition.
It was on this occasion that the late king of Prussia offered him an honourable asylum at his court, and the office of president of his academy: and the king was not offended at d'Alembert's refusal of these distinctions, but cultivated an intimate friendship with him during the rest of his life. He had refused, some time before this, a proposal made by the empress of Russia to entrust him with the education of the Grand Duke; —a proposal accompanied with all the flattering offers that could tempt a man, ambitious of titles, or desirous of making an ample fortune: but the objects of his ambition were tranquillity and study.
In the year 1765, he published his Dissertation on the Destruction of the Jesuits. This piece drew upon him a swarm of adversaries, who only confirmed the merit and credit of his work by their manner of attacking it.
Beside the works already mentioned, he published nine volumes of memoirs and treatises, under the title of Opuscules; in which he has resolved a multitude of problems relating to astronomy, mathematics, and natural philosophy; of which his panegyrist, Condorcet, gives a particular account, more especially of those which exhibit new subjects, or new methods of investigation.
He published also Elements of Music; and rendered, at length, the system of Rameau intelligible: but he did not think the mathematical theory of the sonorous body sufficient to account for the rules of that art.
In the year 1772 he was chosen secretary to the French Academy of Sciences. He formed, soon after this preferment, the design of writing the lives of all the deceased academicians, from 1700 to 1772; and in the space of three years he executed this design, by composing 70 eulogies.
D'Alembert died on the 29th of October 1783, being nearly 66 years of age. In his moral character there were many amiable lines of candour, modesty, disinterestedness, and beneficence; which are described, with a diffusive detail, in his eulogium, by Condorcet, in the Hist. de l'Acad. Royale des Sciences, 1783.
As it may be curious and useful to have in one view an entire list of d'Alembert's writings, I shall here insert a catalogue of them, from Rozier's Nouvelle Table des Articles contenus dans les volumes de l'Academie Royale des Sciences de Paris, &c, as follows:
Traité de Dynamique, in 4to, Paris, 1743. The 2d ed. in 1758.
Traité de l'Equilibre et du Mouvement des Fluides. Paris, 1744; and the 2d edition in 1770.
Reflexions sur la Cause Générale des Vents; which gained the prize at Berlin in 1746; and was printed at Paris in 1747, in 4to.
Recherches sur la Précession des Équinoxes, & sur la Nutation de l'Axe de la Terre dans le Système Newtonien. Paris, 1749, in 4to.
Essais d'une Nouvelle Théorie du Mouvement des Fluides. Paris, 1752, in 4to.
Recherches sur differens Points importans du Système du Monde. Paris, 1754 and 1756, 3 vol. in 4to.
Elemens de Philosophie, 1759.
Opuscules Mathématiques, ou Memoires sur différens Sujets de Géométrie, de Méchaniques, d'Optiques, d'Astronomie. Paris, 9 vol. in 4to; 1761 to 1773.
Elémens de Musique, théorique & pratique, suivant les Principes de M. Rameau, eclairés, développés, & simplifiés. 1 vol. in 8vo. à Lyon.
De la Destruction des Jesuites, 1765.
In the Memoirs of the Academy of Paris are the following pieces, by d'Alembert: viz,
Précis de Dynamique, 1743, Hist. 164.
Précis de l'Equilibre & de Mouvement des Fluides, 1744, Hist. 55.
Methode générale pour déterminer les Orbites & les Mouvements de toutes les Planètes, en ayant égard à leur action mutuelle, 1745, p. 365.
Précis des Réflexions sur la Cause Générale des Vents, 1750, Hist. 41.
Précis des Recherches sur la Précession des Équinoxes, et sur la Nutation de l'Axe de la Terre dans le Système Newtonien, 1750, Hist. 134.
Essai d'une Nouvelle Théorie sur la Résistance des Fluides, 1752, Hist. 116.
Précis des Essais d'une Nouvelle Théorie de la Résistance des Fluides, 1753, Hist. 289.
Précis des Recherches sur les differens Points importans du Système du Monde, 1754, Hist. 125.
Recherches sur la Précession des Equinoxes, & sur la Nutation de l'Axe de la Terre, dans l'Hypothese de la Dissimilitude des Méridiens, 1754, p. 413, Hist. 116.
Reponse à un Article du Mémoire de M. l'Abbé de | la Caille, su<*> la Théorie du Soleil, 1757, p. 145, Hist. 118.
Addition à ce Mémoire, 1757, p. 567, Hist. 118.
Précis des Opuscules Mathématiques, 1761, Hist. 86.
Précis du troisième volume des Opuscules Mathématiques, 1764, Hist. 92.
Nouvelles Recherches sur les Verres Optiques, pour servir de suite à la théorie qui en à été donnée dans le volume 3e des Opuscules Mathématiques. Premier Mémoire, 1764, p. 75, Hist. 175.
Nouvelles Recherches sur les Verres Optiques, pour fervir de suite à la théorie qui en a été donnée dans le troisième volume des Opuscules Mathématiques. Second Mémoire, 1765, p. 53.
Observations sur les Lunettes Achromatiques, 1765, p. 53, Hist. 119.
Suite des Recherches sur les Verres Optiques. Troisième Mémoire, 1767, p. 43, Hist. 153.
Recherches sur le Calcul Intégral, 1767, p. 573.
Accident arrivé par l'Explosion d'une Meule d'Emouleur, 1768, Hist. 31.
Précis des Opuscules de Mathématiques, 4e & 5e volumes. Leur Analyse, 1768, Hist. 83.
Recherches sur les Mouvemens de l'Axe d'une Planete quelconque dans l'hypothese de la Dissimilitude des Méridienes, 1768 p. 1, Hist. 95.
Suite des Recherches sur les Mouvemens, &c, 1768 p. 332, Hist. 95.
Recherches sur le Calcul Intégral, 1769, p. 73.
Mémoire sur les Principes de la Mech. 1769, p. 278.
And in the Memoirs of the Academy of Berlin, are the following pieces, by our author: viz,
Recherches sur le Calcul Intégral, premiere partie, 1746.
Solution de quelques problemes d'astronomie, 1747.
Recherches sur la cour be que forme une Corde Tendue, mise en Vibration, 1747.
Suite des recherches sur le Calcul Intégral, 1748.
Lettre à M. de Maupertuis, 1749.
Addition aux recherches sur la courbe que forme une Corde Tendue mise en Vibration, 1750.
Addition aux recherches sur le Calcul Intégral, 1750.
Lettre à M. le professeur Formey, 1755.
Extr. de differ. lettres à M. de la Grange, 1763.
Sur les Tautochrones, 1765.
Extr. de differ. lettres à M. de la Grange, 1769.
Also in the Memoirs of Turin are,
Differentes Lettres à M. de la Grange, en 1764 & 1765, tom. 3 of these Memoris.
Recherches sur differens sujets de Math. t. 4.
