166 MATHEMATICS 



Although APPELL has long been dean of the Faculty 

 of Sciences at the Sorbonne, he has continued to give a 

 course there each year. His contributions to analysis 

 and applied mathematics are indicated by his well-known 

 volumes on algebraic functions and their integrals (in 

 collaboration with GOURSAT), on elliptic functions, 

 (jointly with LACOUR), and especially by his three-volume 

 "Traite de mecanique rationnelle." He has been espe- 

 cially distinguished as a teacher, and for a number of 

 years gave a most successful course in the Sorbonne on 

 general mathematics for students of other sciences; this 

 is now accessible in published form. In 1915-16 he 

 lectured on analytic mechanics and celestial mechanics. 



GOURSAT has long covered the field of differential and 

 integral calculus at the Sorbonne. His lectures have 

 formed the basis of his celebrated "Cours d'analyse," 

 one of the most widely used modern texts in its field. 

 Only less well-known are his works on partial differential 

 equations and on algebraic functions, while his frequent 

 contributions have made his name familiar to readers 

 of mathematical periodicals. 



BOREL bears the title of professor at the Sorbonne, and 

 in some years has given public lectures there. In the 

 year 1915-16, however, his work was confined to the 

 Ecole Normale Superieure, and was open to visiting stu- 

 dents only by special arrangement. He may be con- 

 sidered, perhaps jointly with HADAMARD, as the leader 

 in a younger group of French analysts. He is probably 

 best known by the series of monographs (on the theory 

 of functions) of which he is the editor, and of a number 

 of which he is the author. 



In 1915-16, GUICHARD and CAHEN gave courses in 

 the Sorbonne on rational mechanics. Both these men 

 have done important work also in other fields, the former 

 in geometry, the latter in the theory of numbers. Their 



