106 ROYAL SOCIETY OF CANADA 
interrogés en classe, exercés aux calculs numériques, habitués à 
raisonner directement sur les cas particuliers et non à appliquer des 
formules. En résumé, on devra développer leur jugement et leur 
initiative, non leur mémoire.” 
In France, as everywhere else, the success of the system depends 
much on the personality of the professor. A Paris lycée instructor 
who had a genius for getting hold of his boys has recently died. No 
less than 35 of his pupils were admitted to the École Polytechnique in 
a single year. The ordinary professor has to be content with a half 
or a third of this number. But the success of a class is, by happy ar- 
rangement, not left to depend wholly upon a single man. Take, for 
example, lycée Saint Louis, which is the greatest preparatory school 
in France for the École Normale Supérieure and the École Polytech- 
nique. There are four Classes de Mathématiques Spéciales and for all 
the members of these classes, conferences, interrogations and individual 
examination are organized. These exercises, which complete the daily 
instruction, are conducted by one of the professors in the lycée itself, 
or by one of those from the Collège de France, the Sorbonne, the École 
Polytechnique, the École Normale, from other lycées or from the 
collèges. Incapables are thus speedily weeded out. Of perhaps greater 
value than the solidity of the training got in this way is the fact that 
the interest of the éléve is sustained. 
Just a word about the calculus course. This is practically equiv- 
alent to the first course in the best American universities. The integ- 
ration of differential equations of the first order in the cases where 
(1) the variables separate immediately, (2) the equation is linear, as 
well as of linear differential equations of the second order, constant 
coefficients, (a) without second member, (b) when the second member 
is a polynomial or a sum of exponentials of the form Ae**—, is taken up. 
With the end of the year the éléve has his first experience of a 
concours. Previously he has found that it was necessary only to make 
a certain percentage in order to mount to the next stage in his scholastic 
career; but now it is quite different. In 1908, 1,078 pupils tried for 
admission into the École Polytechnique, but only 200, or 19.5 per cent., 
were received; for the department of science in the École Normale 
Supérieure, 22 out of 274, or 8 per cent., succeeded. In each case the 
number was fixed in advance by the Government according to the 
capacity of the school; the fortunate ones were those who stood 
highest in the examinations, written and oral. In the case of the 
École Polytechnique, the written examinations were held in all the 
lycées which had a Classe de Mathématiques Spéciales. The 387 can- 
didates declared admissible were then examined orally at Paris, and 
from them the 200 were chosen. Similarly for the École Normale, the 
