124 ROYAL SOCIETY OF CANADA 
easier requirements. We prefer to retain the genial, sympathetic re- 
lations between the student and professor, to encourage the emotional 
and sentimental life of the students with one another. 
We may, however, still learn from France the advantages of in- 
timate relation, in standards and scheme, of secondary and higher 
education. How much of the first year in American universities is 
wasted by getting freshmen into form, in teaching them how to work 
and how to think for themselves! The French university professors 
are in constant intercourse with the lycées, are the examiners of all 
their graduates, are the authors of many of the text-books employed. 
The mathematical training and equipment of the average writer of 
secondary texts in France is of far higher order than that of the average 
American author. 
TEACHING OF MATHEMATICS AS A PROFESSION IN FRANCE. 
We have now seen how the mathematician is trained in France. 
It remains to discuss the nature of the inducements which are offered 
to young men to prepare themselves for giving mathematical instruc- 
tion, and to see whether the inducements offered are sufficient to attract 
the best talent of the nation. 
The agrégés are those specially prepared by the State for the 
positions as professeurs titulaires in the lycées. Although this title is 
not conferred regularly till the agrégé has completed his twenty-fifth 
year, those who are younger receive temporary appointment. The 
salaries vary according to the classe of the professor. At Paris the lowest 
salary is 6,000 franes per year, and the highest, 9,500. In this range 
seven classes are represented; six, each differing from the one before 
by 500 francs, and the hors classe, for which the salary is 9,500 francs. 
Promotion from one class to another takes place by selection and by 
seniority. From the sixth (the lowest classe) to the third, the number 
of those who can be advanced each year by selection is equal to the 
number which can be advanced by seniority. In the second and first 
classes two advancements may be made by selection to one by seniority. 
In choosing those for the hors classe, selection alone is taken into ac- 
count. The promotions are made at the end of each calendar year, 
and take place so that there are always 20 per cent. of them in the 
sixth class, 18 in the fifth, 18 in the fourth, 16 in the third, 14 in the 
second, and 14 in the first. This arrangement is obviously a happy 
one, both by way of recognition of the merits of the unusually success- 
ful teacher, as well as those of him whose service is rather characterized 
by faithfulness. 

1 Compare Appendix D. 
