POINCARE, pwaN'Idt'riV, JULES HENRY (1854— ). A French mathematician and phys icist, born at Nancy. He entered the Eeole Poly technique in 1873. but left two years later to take up work in the School of .),lines. He became an engineer in 1S79, and in the same year doctor of sciences. In 1881 he was called to Paris. where in 1886 he became professor of mathematical phyises and calculus of probabilities in the Faculty of Sciences. At the death of Tis serand (1896) he changed this chair for that of celestial mechanics. In 1887 he was made member of the Academy of Sciences at Paris, and after 1S93 was a member of the Bu reau of Longitudes (after 1898 its president). In 1889 he obtained the prize awarded by King Oscar of Sweden for a work on the problem of the three bodies (q.v.). Poincare has become known as one of the greatest mathematicians pro duced by France in the last century. A disciple of Cauchy, he has carried out the investigations of the latter along the various lines of the theory of functions, and he has also applied his remarkable mathematical powers to profound researches in the domain of physics. He has introduced into mathematics a new class of transcendents, analogous to. but more general than, the elliptic functions, which he has named the Fuehsian func tions in honor of Immanuel Fuchs (q.v.). lle has also introduced in connection with these func tions a new class of groups, also called Fuehsian.

He has contributed to the theory of non-Euclidean geometry, to the theory of differential equa tions, and to various branches of higher algebra.

His works include: Les methodes nourelles de la meehanique celeste (3 vols., 1892-99) : CiIeul des probabilites (ed. by Quiquet, 1S96) ; Incite (ed. by Biondi'', 1895) : ('inentatique et potentiels et mecanique des flu ides ed. by Guillet, 1899) : Elretrieite et optique (2 vols., 1890-91) : Therm ody na ique ( ed. by Blon din, 1S92) Lecons sum la theorie mathentatique de In lumif'-re (2 vols., 1889-92) ; Lerons sum In theorie de relastirite (ed. by Borel and Drach, 1892) ; Les oscillations electriques (ed. by Maur rain, 1894) ; Theorie anulytique de la propaga tion de la. chuleur (ed. by Rouyer and Baire, 1895) ; Theorie des tourbillons( 1893) ; Theorie du potentiel Newtonien (ed. by Le Roy and Vincent, 1899). Part of these works form his /'ours de physique (13 vols., 1890). He has also published important memoirs on mathematics and physics in the Journal des inathematiques pares et appli quees, the Journal de rEcolc Polytechnique, the Transactions of the Philosophical society of Cam bridge, Scientia, the Acta .11athentatica, the Mathematische Annalen, and many other leading mathematical journals.