112 ROYAL SOCIETY OF CANADA 
12°. Although there is nothing in the mathematical departments 
of the universities of France which exactly corresponds to the German 
Seminar,’ the method of conducting the conferences at travaux pratiques 
is, | believe, a French specialty. We also find it used in the lycées at the 
Ecole Normale Supérieure, at the Ecole Polytechnique, etc. Each week 
the instructor gives out exercises which the students solve and hand in; 
these are returned with written comment and correction. The hour is 
employed by calling some student to the board and leading him by means 
of suggestive questioning to work out, generally in great detail, a piece 
of analysis or a problem or a theorem—either arising from, or nearly 
related to, the main course. The manner in which this is carried through, 
with its exacting demands as to form in statement and black board 
presentation, is in the highest degree instructive. 
The above list does not display all the mathematical courses offered 
at the Sorbonne this year. Cartan had a special problem course for 
candidates for the agrégation and Bachelier, gave a cours libre of 20 
lectures on the calculus of probabilities and its application to financial 
operations. The number of cours libres varies from year to year.? 
The Licence. 
When a student has finished any one of the groups of studies 
such as (3°, 4°, 14°) or (10°, 18°), he may pass an examination and 
receive a certificat d’études supérieures. With the third certificat is 
given the diploma licence ès science. The choice of subjects is not 
necessarily limited to those given above but may be selected (at 
the Sorbonne) from a list of 23* which includes general chemistry, 
zoology, geology, ete. If, however, the student expects to teach in the 
secondary schools his choice is greatly limited. The mathematician 
must have certificuts in calcul différentiel et intégral, in mécanique 
rationnelle and in physique générale, or a third certificat in mathematies, 
excepting (11°, 19°). The physicist must have certificats in physique 
générale (12°, 20°), in chémie générale and in minéralogie or mathéma- 
tiques générales (11°, 19°), or another subject of mathematical or physi- 
cal science. The natural scientist must have certificats in zoology or 
general physiology, in botany and in geology. The examination for 
certificats may be taken twice in a vear, in July or in November. It 
consists of three parts, épreuve écrite, épreuve pratique, épreuve orale. 
! Other subjects are treated in Seminar style at the École des Hautes Études 
which is an off-shoot of the Collège de France. 
*In July, 1910, the University of Paris accepted the offer of M. Albert Kahn 
to bear the expense, for a period of five years, of a course on “The Theory of 
Numbers.”’ 
# This number varies with the university; at Dijon it is 12. 
