[aRcHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 115 
Blutel a fourth, and Garnier a second. There have been very excep- 
tional cases (in 1885, 1886, 1895), when an agrégé was still in his 
twenty-first year, but the average age for the past twenty-five years is 
a little less than 26. There are also those who do not reach the goal 
of their ambition till after they are 40, and have tried perhaps ten or 
a dozen times. The difference between the salary of those lycée profes- 
sors who are agrégés and of those who are not has been emphasized still 
more by the law just passed, which gives the former an annual bonus 
of 500 francs. 
If the agrégé wishes to become a professor in a university he must 
pass the examination for the doctorate, but only a very small propor- 
tion of the agrégés take this step—during the period 1885-1904, 20 
per cent. If, however, he wishes to teach in a lycée he may demand 
such a position as his right. Among the candidates who are admissible 
but not received are generally selected professeurs chargés de cours (or 
others in positions of inferiority in the lycée), who, however, after 
20 years of service may be named professeurs-titulaires and be the 
academic equals of their luckier comrades of years before. 
Other details concerning the agrégation, such as the programme 
for the concours of 1910, the examination papers for the concours of 
1909, are given in Appendix A. 
The Doctorat. 
What is the relative value of the French and German mathematical 
doctorate? What the relative difficulty of obtaining it? are questions 
which the average American post-graduate studen, who is seeking to de- 
cide between France and Germany for further study is sure to ask. Small 
as is the proportion of students in a German university who present them- 
selves for this degree, the number in France is far smaller. In the two 
years 1906-08 Germany made 87 doctors in mathematics, while France, 
with but 20 per cent. fewer students, created only 13.! This difference 
in numbers is doubtless principally due to the fact that the end in view in 
France is entirely different. The Frenchman usually goes up for his doc- 
torate with the expectation of drawing wide attention to his thése. The 
step is also necessary for everyone who aspires to be appointed a professor 
ina university—unless, perchance, he has become a member of the Institut 
without having the degree. All except three of the French universities 
offer the degree of doctorate in mathematics, but only eleven of them 
have ever conferred it. Again, of the 331 degrees which have been con- 
ferred by the existing universities, 296 have been granted by the Uni- 
versité de Paris. This is, of course, very different from the results in 

1 There is of course no degree of Doctor of Philosophy in France. The equiva- 
lent is explained later. | 
