ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 113 
The first two are written examinations of about four hours each. Theo- 
retical considerations abound in the écrite while numerical calculation 
is characteristic of the pratique. The oral lasts for 15-20 minutes and 
is held before the jury of those professors who have the whole examin- 
ation in charge. It is necessary to get fifty per cent to pass. The first 
certificat and examinations cost 35 francs, the second and third 30 francs 
each and the licence diploma 40 francs. 
The Diplôme d'Etudes Supérieures de Mathématiques. 
This diploma which was instituted by a decree of 1904 has not vet 
been awarded to any one, although its equivalent, 4 certificats (one 
chosen at option), is required of all candidates for the agrégation. It 
may be considered as a little doctarate. The conditions leading to the 
diploma are twofold:— 
(a) That a suitable travail be written on a subject agreed upon by 
the faculty. 
(b) That satisfactory answers be given to questions on the travail 
and on topics given three months in advance and relating to the same 
part of mathematics. The travail may consist either of original re- 
searches, or of the partial or total exposition, of a memoir or of a higher 
mathematical course. In the latter case by “exposition” is meant 
either a simplified résumé of the memoir or of the course, or the detailed 
development, where the result or method that the author or professor 
presents has only been outlined. 
The Agrégation des Sciences Mathématiques. 
This examination, unlike that for the baccalauréat and licence, is a 
concours as in the case for entrance into the Ecole Normale Supérieure and 
the École Polytechnique. The number who become agrégés each year is 
fixed in advance by the Minister of Public Instruction according to the 
needs of the lycées in the country. This number in recent years has 
generally been 14, but in 1897 as few as seven were chosen. The smallest 
number of competitors since 1885 was 54, in 1907; in 1909 there were 81; 
the largest number was in 1893, when there were 134 young men eager for 
13 places.! The candidate for this examination must have four cer- 
tificats; those in calcul différentiel et intégral, mécanique rationnelle, 
physique générale and a fourth chosen at pleasure among the remain- 
ing mathematical subjects. As an equivalent of the fourth certificate 
a diplôme d’études supérieures de mathématiques may be presented. The 
subject of the fourth certificate at Paris is usually Picard’s Analyse Supé- 
rieure et Algèbre Supérieure (2°) or Darboux’s Géométrie Supérieure 

! Compare the analytical table of Appendix A. 
Sec. III., 1910. 8. 
