*THE POPULAR SCIENCE MONTHLY.*

that geometry could shed on the most obscure and difficult questions; and M. Bertrand has said of them that they gave demonstrations and results admirable as models of elegance and generality.

M. Chasles gained notoriety a few years ago by his connection with a number of manuscripts and autographs purporting to be by distinguished men of the past, among them Galileo, Pascal, Sir Isaac Newton, and even Julius Cæsar and other Roman emperors and the apostles, which he bought of one Irène Lucas and which proved to be nearly all forgeries by that adventurer. Among them were some which claimed for Pascal the merit of Newton's most celebrated discoveries. M. Chasles earnestly defended the authenticity of the documents, of which he was fully and honestly convinced, and was sustained by some eminent members of the Academy, until Lucas was unmistakably shown to have fabricated them. Out of twenty-seven thousand papers which he bought, only about a hundred were genuine.

M. Bertrand, summing up the mathematical work of M. Chasles, says that more than once, without abandoning the geometric method, he “has shown with a rare felicity how all mathematical truths are connected by a close and mysterious bond. We owe to him, in one of the highest and most difficult theories of the integral calculus, elegant theorems admired by analysts; he has added to mechanics a chapter which has become classic on the displacement of solid bodies; he has found in the theory of attraction beautiful and general theorems which have revived the theory of static electricity. . . . All geometricians, without distinction of nationality or school, have bowed before this venerable old man; all have admired his inventive power, his fertility, which age seemed to rejuvenate; his ardor and his zeal continued into his latest days.”