American Journal of Mathematics, vol. xvii. No. i. (January, 1895).—Sur one transformation de mouvements, P. Appell, is a treatment of Elliot's problem (Comptes rendus, 1893), and of a question solved by Mestschersky, in the Bulletin des Sciences Math. 1894, as a particular case of transformation of movements.—An extract from a letter addressed to Dr. Craig by M. Hermite, gives the result of an investigation of the asymptotic value of log Г(a) when α is large.—On the first and second logarithmic derivatives of hyperelliptic? functions;, by Orkar Bolza, opens with a statement of certain well-known theorems of the theory of elliptic functions, and then extends these and some allied theorems to hyperel?ptic functions.—Sur la definition de la limite d'une fonction. Exercice de logique mathématique, by Prof. Peano. The definition is one previously used by the writer, and also by two or three previous writers. It is practically given by Abel (Works ii. p. 199), in the form. “Pour qu'une série Σun soit convergente, il faut que la plus petite des limites de Σun soit zéro.” The same general idea of a limit is given in Cauchy's “Cours d'Analyse algébrique”(1821, p. 13), “quelquefois... une expression converge à-la-fo sversplusieurs limites différentes les unes des autres.” Prof. Peano works on this definition, and demonstrates at "ome length its principal properties.