Shortly after the beginning of the nineteenth century, Ampère, as one of his French biographers rather characteristically declares, redeemed whatever of mathematical sinning there might have been, in indulging in fond dalliance with the squaring of the circle, by a series of mathematical papers, each of which was in itself a distinct advance on previous knowledge, and at the same time, definite evidence of his mathematical ability. The first paper, published in 1801, was a contribution to solid geometry, bearing the title, "On Oblique Polyhedrons." His next paper, written in 1803, though not published until 1808, was a treatise on the advantages to be derived in the theory of curves from due consideration of the osculating parabola. Another treatise, written about the same time, had for title, "Investigations on the Application of the General Formulæ of the Calculus of Variations to Problems in Mechanics." This concerned problems which had interested and, in most cases, proved too hard of solution even for such men as Galileo, Jacques Bernoulli, Leibnitz, Huyghens and Jean Bernoulli. Arago's expression with regard to this work is: "The treatise of Ampère contains, in fact, new and very remarkable properties of the _catenary_ (la chainette) and its development." He adds: "There is no small merit in discovering hiatuses in subjects explored by such men as Leibnitz, Huyghens and the two Bernoullis. I must not forget to add that the analysis of our associate unites elegance with simplicity." It is not surprising, after such marks of mathematical genius, that Ampère was appointed to the chair of mathematics at the École Polytechnique, where he came to be looked upon as one of the most distinguished of French mathematicians. In 1813, he became a candidate for the position left vacant by the death of the famous Lagrange; and at this time, presented to the Academy general considerations on the integration of partial differential equations of the first and the second order. After his election to the Academy, Ampère continued to present important papers at its various sessions. Among these, three are especially noteworthy: one was a demonstration of Père Mariotte's law (known to English students as Boyle's law); another bore the title, "Demonstration of a new Theory from which can be deduced all the Laws of Refraction, ordinary and extraordinary"; a third was a memoir on the "Determination of the curved surfaces of Luminous Waves in a medium whose Elasticity differs in each of the three dimensions."