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plaining of his obscurity, or being discouraged by it, he pursued his studies for the love of them, and found glory without having done anything to secure it except to produce great works.”

M. Chasles was elected a corresponding member of the Academy in 1839, was appointed Professor of Mechanics and Geodesy in the École Polytechnique in 1841, and was elected the first occupant of the newly created chair of Modern Geometry in 1846. He resigned his position in the cole Polytechnique in 1851, in consequence of the introduction into the school of changes of which he did not approve. He was chosen a foreign member of the Royal Society in 1854, was awarded the Copley medal in 1865, and was elected, in 1867, the first foreign member of the London Mathematical Society.

M. Chasles's life was one of active, uninterrupted work in his favorite field, from the time he left the Lyceum till he was eighty-seven years old—a period of sixty-eight years. His contributions of papers to scientific societies and journals are estimated to number nearly two hundred and forty, on subjects which range “over curves and surfaces of the second and any degree, geometry, mechanics (and attractions), history, and astronomy.”

Of his greater works—“masterpieces that commanded attention”—the earliest was the “Aperçu Historique,” or “Historical View of the Origin and Development of Methods in Geometry,” which, says M. Bertrand, “under a title that is more than modest, remains the most learned, the most profound, the most original work that the history of science has ever inspired.” It was published in 1830, being an elaboration of a paper contributed several years before to the Royal Academy of Brussels, and was reprinted in 1875, with a preface, giving a short historical account of the book. It is, says Mr. Tucker, a perfect mine of geometrical facts, and is to the present day a high authority on the subject of which it treats.

The courses of lectures delivered by M. Chasles as Professor of Modern Geometry were embodied in 1852 in the “Traité de Géométrie supérieure,” or “Treatise on the Higher Geometry,” a work which, of late years scarce and high, has recently appeared in a second edition. This was followed by a sequel, a treatise on conic sections (“Traité des Sections Coniques, faisant suite au Traité de Géométrie supérieure,” the first volume of which appeared in 1865. The second volume has not been published, but the materials for it have been given from time to time in the “Comptes Rendus.”

In 1863 M. Chasles published his “Three Books on the Porisms of Euclid,” which was the origin of a short controversy with M. P. Breton. The question of attraction was presented to M. Chasles under several points of view, and gave occasion to a number of memoirs extending even to the consideration of the general problem of the attraction of a body of any form. Poinsot said of one of these papers that it offered a remarkable example of the elegance and light