So early as the year 17.14. D'Alembert haci applied this principle to the theory of the equilibrium, and the motion of' thicds ; and all the problems before resolved in physicsbeeathe in some meastnet its corol laries. The discovery of this new prin ciple was followed by that of a new calcu lus, the first essays of which were pub lished in a " Discourse on the General Theory of the Winds:" to this the prize medal was adjudged by the Academy of Berlin, in the year 174-6, which proved necv and'brilliant addition to the fame of D'Alembert. This new calculus of "Par tial Differences" he applied, the y ear fbl lowing, to "the problem of vibrating chords, the resoliition of which, aa well as the theory of' the oscillations of the air, and the propagation of sound, had been but imperfectly given by the mathemati clans who preceded him; and these were his masters or his rivals. In the year 1749 he fiirnislied a method of apply ing his, principle to the motion of any body of a given fig-iire. Ile also re solver! the problem of the precession of the equinoxes: determining its quantity, and explaining the phenomenon of the nutation of the terrestrial axis discoverect by Dr. Bradley.
In 1752, D'Iklembert published a trea tise 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, "Re searches concerning the Integral Calcu lus," which is greatly indebted to him for the rapid progress it has ma.de in the pre sent century.
While the studies of D'Alembert were confinedto me remathemati es, he waslittle known or celebrated in his native country. His_ connections were limited to a watt society of select friends. But his cheer ful conversation, his smart and lively sal lies, a happy method 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 ofroyal attention and beneficence. The consequence was, a pension from government, which he owed to the friendship of count D'Argen son.
But the tranquillity of D'Alembert was abated when his fame grew more exten sive, and when it was known, beyond the circle of his friends, that a fine and en lightened taste for literature andphiloso. pby accompanied his mathematical geni us. Our author's eulogist ascribes to envy, detraction, &c. all the opposition and cen sure that D'Alembertmet with on account of the famous Encyclopedie, 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'Alem bert has enriched that great work. Amotig others, the Preliminary Discourse he has prefixed to it, concerning the rise, pro gress, connections, and .affinities, of all
the branches of human knowledge, is perhaps one of the most capital produc tions the philosophy of the age can boast of.
Some time after this, D'Alembert pub lished his "Philosophical, Historical, and Philological Miscellanies." These were followed by the "Memoirs of Christiana, Queen of Sweden;" in which D'Alembert chewed that he was acquainted with the natural rights of mankind, and was hold enough to assert them. His "Essay on the Intercourse of Men of Letters with Persons high in Rank and Office" wound ed 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 des potism 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 Encyclopedic with a multitude of e xcellent art i cles in that line, and composed his "Researches on several Important Points of the System of the World," in which he carried to a high er 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 Philoso phy ;" a work much extolled, as remark able for its precision and perspicuity. The resentment that was kindled (and the disputes that followed it) by the article GENEVA, inserted in the Iincyclop6die, are well known. D'Alembert did not leave this field 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 ex posed him, even at home, to much con. tradiction and opposition. It was on this occasion that the late King of Prussia of fered 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 distinc tions, but cultivated an intimate friend ship with him during the rest of his life. He had refused, some time before this, a proposal made by the Empress of Rus sia, to entrust him with the education of the Grand Duke ;—a proposal accompa nied with all the flattering offers that could tempt a man, ambitious of titles, or desirous ofmaking an ample fortune ; but the oBjectsof his ambition were tranquilli ty and study. In the year 1765, he publish ed his " Dissertation on the Destruction of the Jesuits." This piete drew upon him a swarm of adversaries, who only confirmed the merit and crdit of his work by their manner of attacking it.