Éloge de Lagrange, Mémoires de l’Institut. 1812.
The admissibility of discontinuous functions into the integrals of partial differential equations.
In 1764 he gained the prize proposed by the Academy of Sciences for an Essay on the Libration of the Moon; and in 1766, that for an Essay on the Theory of the Satellites of Jupiter. In the former of these we find him, for the first time, using the _principle of virtual velocities_, which had hitherto remained almost a barren truth, but which he afterwards made, in conjunction with the principle known after the name of D’Alembert, the foundation of the whole of mechanical science.
In 1766, Euler, intending to return to St. Petersburg, resigned the situation which he held at the Court of Berlin, that of director of the physico-mathematical class of the Academy of Sciences. Frederic offered this place to D’Alembert, who refused it for himself, but joined with Euler in recommending Lagrange. The King of Prussia acceded to their suggestion, and Lagrange was invited to establish himself at Berlin, with a salary equivalent to 6,000 francs.
Lagrange remained at Berlin till after the death of Frederic. He here married a lady who was related to him, and who came from Turin at his request. She died after a lingering illness of several years, marked by the most unceasing attention on the part of her husband, who abandoned his pursuits to devote himself entirely to her during her illness. Nevertheless the period of his sojourn at Berlin is perhaps the brightest of a life, most years of which, from the age of eighteen to that of seventy, were sufficient to ensure a lasting reputation. He here laid the foundation of his Theory of Functions, of his general method for determining the secular variations of the planetary orbits; and here he wrote his _Mécanique Analytique_.
At the death of Frederic, he found that science was no longer treated with the same respect at the Court of Berlin. He had found from the commencement of his stay there, that foreigners were looked upon with dislike, and his spirits had not recovered the loss of his wife. Many advantageous offers were made to him by different courts, and among the rest by that of France. Mirabeau, who was then at Berlin, first pointed out to the ministers of Louis XVI. the acquisition which was in their power. Lagrange removed to Paris in 1787, and remained there till his death.