THESES IIST MATHEMATICS AT THE UNTVEBSITY OF PAEIS. 1. Sur quelques points de la théorie des fonctions, par M. L

1. Sur quelques points de la théorie des fonctions, par M. L. DESAINT. Paris, Gauthier-Villars, 1897. 4to, 74 pp. 2. Sur une classe particulière de groupes hyper abéliens, par M. HENRY BOURGET. Ibid., 1898. 4to, 90 pp. 3. Sur Vintégration des équations de la chaleur, par M. EDOUARD LEBOY. Ibid., 1898. 4to, 258 pp. 4. Les équations différentielles linéaires et la théorie des groupes, par M. F. MAROTTE. Ibid., 1898. 4to, 92 pp. 5. Essai sur une théorie générale de V intégration et sur la classification des transcendantes, par M. JULES DRACH. Ibid., 1898. 4to, 144 pp.* THESE five theses were presented to the faculty of sciences of the University of Paris for the degree of doctor in mathematical science ; they were sustained in order of time as placed above during the academic year from November, 1897, to June; 1898, inclusive. Before proceeding to a brief review of each it may be interesting to observe that the creation of the faculties of mathematical and physical science in France dates from March 17, 1808.f The first degree of this kind conferred by the faculty of sciences at Paris was given to PierreLouise-Marie Bourdon in 1811 ; his two theses maintained respectively on the 19th and 23d of March of that year were 1° the motion of a solid body solicited by any accelerative forces and turning about a fixed point, and 2° the theory of the elliptic movement of the planets according to the principle of universal gravitation and its application to the determination of the masses of some planets. From 1811 to 1890 inclusive there were conferred one hundred and eighty-four such degrees at Paris, and fortyfour by the other universities of France. J The average age of the candidates is thirty years and a fraction ; the majority lie in the range from twenty-three to thirty-four years, the average for each of these years being twelve ; there were thirteen at twenty-three, eighteen (the maximum) attwenty-