Though he had a venerable figure, he would never al low his portrait to be drawn. More than once, by a very excusable piece of address, persons have been introduced during the meeting of the Institute, to take a sketch of him without his knowledge. An artist sent by the Acade my of Turin drew in this manner the outline, from which wac constructed the bust that was exhibited for some months in the hall of the Institute, and is at present in the library. A cast was taken of him after his death ; and some time before, while he slept, a picture of him was ta ken, which is said to resemble him very much.
Gentle and even timid in conversation, he took a plea sure in asking questions, either to draw out others, or to add their reflections to his own vast knowledge. When he spoke, it was always in a tone of doubt, and his first words usually were, I do not know. He respected the opinions of others, and was very far from laying down his own as a rule. Yet it was not easy to make him change them. Sometimes he even defended them with a degree of heat, which continued to increase till he was sensible of some alteration in himself; then he immediately resumed his usual tranquillity. One day, after a discussion of this kind, M. Ia Grange having left the room, Borda remain ing alone with me, allowed these words to escape him : I am sorry to say it of a man like M. la Grange, but I do not know a more obstinate person." If Borda had gone away first, La Grange might have said to me as much of our associate, who was a man of excellent sense and con siderable wit ; but who, like La Grange, did not easily abandon those opinions which he had adopted after a ma ture examination.
A gentle and good-natured irony was often remarkable in the tone of his voice ; but I never saw any person hurt at it ; because it was necessary to have well understood every thing that went before, to perceive the true intention of it.
Among• all the master-pieces which we owe to his ge DIus,hisillecanique is certainly the most remarkable and the most iinpertant. The Fonctions Analytiques hold only the second place, notwithstanding the fruitfulness of the principal idea, and the beauty of the developments. A no
tation less commodious, and calculations more embarrass ing, though more luminous, will prevent mathematicians from employing, except in certain difficult and doubtful cases, his symbols and names. It is sufficient that he has proved the legitimacy of the more expeditious processes of the differential and integral calculus. He has himself fol lowed the ordinary notation in the second edition of his Mecanique.
This great work is entirely founded on the calculus of variations, of which he w as the inventor. The whole flows from a single formula, and from a principle known before his time ; but the whole utility of which was far from sus pected. This sublime composition includes all his other preceding labours which could be connected with it. It is distinguished likewise by the philosophical spirit which reigns from one end of it to the other. It is likewise the best history of that part of the science,—a history which could only have been written by a man perfectly master of his subject, and superior to all his predecessors, whose works he analyses. It forms a most interesting piece of reading, even to him who is not capable of appreciating all the details. Such a reader will at least find the intimate connection of all the principles on which the greatest mathematicians have founded their researches into mechan ics. He will there see the geometrical law of the celesti al motions deduced from simple mechanical and analytical considerations. From these problems, which serve to cal culate the true system of the world, the author passes to questions more difficult, more complicated, and which be long to another order of things. These researches are on ly objects of pure curiosity, as the author announces, but they show the extent of his resources. Finally, we see there his new theory of the variations of arbitrary constant quantities of the motion of the planets, which had appeared with so much eclat in the Memoirs of the Institute, where it had shown that the author, at the age of 75, had not sunk from the rank which he had filled for so long a time in the opinion of all mathematicians."