[ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 119 
and Leduc (12°, 20°), and at the end of the year pass the examinations 
for the certificats in these two subjects. In the second year they take 
up mécanique rationnelle with Painlevé (10°) at the Sorbonne, and with 
Hadamard in conference at the Ecole. They also “assist” at such a 
course as Darboux’s and Cartan’s in géométrie supérieure (1°, 13°), 
pass the examinations and receive two more certificats. During the 
third year the éléves follow their own inclination in the selection of 
courses at the Sorbonne or Collége de France, while they are well 
grounded at the École, in descriptive geometry by Roubaudi, and in 
pedagogy, of algebra and analysis by Tannery, of geometry by Borel. 
Nearly all those of the first and second year also follow Picard’s course 
(2°), at the Sorbonne, and those of the third year that of Borel (15°). 
The drill in conferences (14 hours each), at the École Normale is 
unequalled. In addition to the good points of those at the Sorbonne, 
we here find in much smaller classes a great degree of intimacy between 
students and professor, and a freedom of question and discussion. 
When, then, at the end of the third year these élite in intellect present 
themselves in the terrific competition of the agrégation, we are not sur- 
prised that they give a good account of themselves. Some do not succeed 
at the first trial or for ten, or twelve years afterwards, but 60 per cent. 
of the 300 agrégés named during the last 25 years were École Normalians; 
in 1890 there were only 4 out of 12, but of the 96 competitors in 1898, 
the 8 chosen were from this famous school. ' 
But as the whole end and aim of the Ecole Normale are not only to 
prepare its éléves for the agrégation and hence for professorships in 
the lycées, but also to prepare them as university professors, we find 
many who have been encouraged to take up certain fields of research 
and who have made good progress toward a thése for doctorate. Not 
only this, but from those who have succeeded in the agrégation, are 
chosen agrégé préparateurs who are taken back to the Ecole for still 
another two years (sometimes three), while they prepare finally for their 
doctorate with all the attendant advantages, of the counsels from their 
former masters, and of the great library collections of the city. The 
agrégé-préparateur de mathématiques is officially chargé de la biblio- 
thèque of the school. 
The life in the Ecole is singularly pleasant and inspiring. Here 
alone of all the institutions we have considered do we find among the 
éléves anything approaching the comradeship, so characteristic of the 
student relations in American colleges. Nor in after years are friend- 
ships and interests thus formed easily changed, as the Association 
Amicale des Anciens Elèves serves as a strong bond of sympathy and 
1 Cf. Appendix A. 
