[ARCHIBALD] MATHEMATICAL INSTRUCTION IN FRANCE 133 
APPENDIX A. 
AGREGATION DES SCIENCES MATHEMATIQUES. 
As there are no mathematical examinations in any other country 
to compare in difficulty with those to which the candidate for a French 
agrégation is required to submit, it has seemed to me that it would be 
a matter of interest if fuller details of what is involved were set forth. I 
therefore subjoin: 
I, The programme for the concours of 1910 (announced 9-11 
months in advance). The examinations will be on topics 
selected from this programme. 
II. The examination papers for 1909. The four written exami- 
nations, it will be observed, occurred on consecutive days. 
The first paper may seem short for the time allowed (seven 
hours); but not when the enormously high standard in pre- 
sentation and detail is taken into consideration. 
III. A Table giving certain data respecting the agrégés named during 
the last twenty-five years, which show that the impressions 
prevailing as to the age of the agrégé, the number of Norma- 
liens who become agrégés, and the number of agrégés who 
became doctors are quite erroneous. 
PART of: 
PROGRAMME. FOR THE CONCOURS OF 1910: 
I.—GENERAL PROGRAMME IN ANALYSIS AND MECHANICS. 
Since the programmes for the certificats d’études supérieures vary 
among the different universities, the jury indicate in the programme 
below the minimum of general knowledge which is supposed acquired 
bythe candidates in differential calculus, integral calculus and mechanics. 
The subjects of the “compositions” in differential calculus, in- 
tegral calculus and mechanics will be chosen from Nos., 1°, 2°, 3°, 4°, 
5°, 7°, 8°, 9°, 14° and 15° of this programme; their scope will not 
exceed the standard set by the subjects of problems proposed for the 
corresponding certificats for the Licence. 
DIFFERENTIAL CALCULUS AND INTEGRAL CALCULUS. 
1°. Fundamental Operations of Differential and Integral Calculus: 
Derivatives and differentials; simple integrals, curvilinear integrals, 
integrals of total differentials, double and triple integrals. 
2°. Applications of the Differential Calculus: Study of functions 
of a real variable (formula of Taylor, maxima and minima, functional 
determinants, implicit functions); Calculation of derivatives and 
differentials; change of variables.—Order of contact and genre of an area. 
