114 ROYAL SOCIETY OF CANADA 
(1°, 13° and an épure). Poincaré’s course is chosen less frequently and 
at present Borel’s course may not be selected independently of others. It 
is usually four years after leaving the Classe de Mathématiques Spéciales 
that the young mathematician first presents himself for the agrégation, 
1.e., when he is about 21 years of age. In this interval he has probably 
spent a year in military service, worked off the examinations for the first 
and third of the above mentioned certificates during the second year, for 
the second and fourth during the third, while the fourth year was spent 
in general review, study of teaching methods or other special direct 
preparation for the agrégation. This examination, which is unique 
in its difficulty and exactions, is organized for selecting the most ef- 
ficient young men in the country, to take charge of the mathematical 
classes in the lycées. It consists of épreuves préparatoires and épreuves 
définitives. The former are four written examinations, each of seven 
consecutive hours in length! The first two of these are on subjects 
chosen from the programme of the lycées in mathématiques élémen- 
taires and mathématiques spéciales. The last two, based on the work 
of the candidates in the universities, are a composition sur l’analyse et 
ses applications géométriques and a composition de mécanique rationnelle. 
These épreuves are held at the seats of the various académies of France. 
Those who have reached a sufficiently high standard are declared 
admissible. Their number is usually a little less than twice the possible 
number to be finally received. In 1909 it was 27, but in 1905, 20; 
while in 1887 there were only 15, from which 13 were selected. They 
must present themselves at the Sorbonne for the épreuves définitives. 
These consist of two written examinations and two lecons. The writ- 
ten tests are an épreuve de géométrie descriptive, and a calcul numérique. 
Their duration is fixed by the jury, but it is usually four hours for 
each. The leçons, which are supposed to be such as a professor might 
give (during 3-1 hour) in a lycée, are on subjects from (a) mathéma- 
tiques spéciales, (b) the programmes of the classes, Secondes, Première, 
C, D, and Mathématiques A,B. The subjects are drawn by lot, and for 
each lesson the candidate has four hours to think over what he is going 
to say. No help from any book or other source is permitted. The 
unfortunate who has little to say is speedily adjourned. As a salve 
for disappointment and as encouragement to try again, he receives 
300 francs a year for three years because he had won a place among 
those admitted to the second examination. 
The names in the list of agrégés are published in order of merit, 
and those who head the list are likely to get the better positions. Many 
of the instructors at the Sorbonne were first agrégés. Appell, Picard 
and Goursat were successively first agrégés, 1876-78; Cartan and Borel 
1891-92; Andoyer in 1884. Painlevé was, however, a ninth agrégé; 
