118 ROYAL SOCIETY OF CANADA 
both kinds. A thèse worked out under general supervision of a 
professor is formally approved by a committee of three professors 
named by the doyen. Birth certificate, diploma as licencié, 148 printed 
copies of the thèse and 145 francs, are deposited with university officials, 
and the day fixed for appearing before the committee to publicly answer 
such general questions on the thèse or other topic which the benevolent 
ingenuity of the examiners may propound. Compared with those in some 
other departments of the university, the examinations of the mathema- 
tician is a very informal affair. It rarely occupies more than three- 
quarters of an hour. The candidate is immediately told whether he 
has got the note “honorable” or “très honorable,” is congratulated 
and dismissed. The amount of help which the candidate for the doctorate 
receives from the professor is much less in France than in Germany. 
In fact he rarely approaches the professor except when he gets his 
subject or is reporting progress. It is expected of the Frenchman 
that the thèse represent his own work and thought. The doctor who 
has presented a remarkable thèse and passed a brilliant examination 
may have the full cost of examination and diploma remitted. A similar 
rule applies to bacheliers. 
THE Écoze NORMALE SUPÉRIEURE. 
This great institution is a part of the Université de Paris and its 
object is to mould the future professors of the secondary schools and 
universities of France by appropriately supplementing the instruction 
they receive at the Sorbonne and the Collège de France. There are 
about 165 pupils, in the departments of science and letters, and prac- 
tically all are internes. We have already remarked that the élèves in 
the department of science are the pick of the boursiers de licence. In 
1909, 22 out of 270 candidates were thus selected and slightly more than 
one half devoted themselves to mathematics. All decided to live as 
internes although it was optional for anyone to attend the École as 
externe—when the amount of the bourse, 1,200 francs, would have been 
paid to him. Most of the pupils were 20 years old, had obtained the 
bourse on second trial and had passed one of the two years military 
service obligatory for every Frenchman by the loi de deux ans of 1905. 
The course for mathematicians is three years, and is arranged as 
follows. During the first year the éléves go to the Sorbonne to hear 
Goursat’s course in calculus and differential equations (3°) and Raffy’s 
applications of analysis to geometry (4°). Instead, however, of follow- 
ing Raffy’s conference (14°), which goes to complete the regular univer- 
sity student’s training for the certificat, calcul différentiel et intégral, 
they are drilled by Borel and Tannery for three hours per week at the 
Ecole Normale. They also take physique générale with Bouty, Lipmann 
