programmes, none is more interesting than that of the relative number of hours devoted to mathematics in the French and American courses. The figures are as follows: French lycée, 740 hours; Boston Latin School, 1,387 hours. The French boyarrives at the end of his classical preparatory course of study, having been subjected on an average to less than two hours of recitation per week in mathematical subjects. The average American pedagogue would certainly rise with protests deep, and disgust profound, if ever it were proposed to him to fit a boy for college with an allowance of only 8·7 per cent of the whole school course for his arithmetic, algebra, and geometry. Yet this is precisely what the French do—in their classical course. In the Boston representative course the percentage is 17·8 per cent.
As the treatment of mathematics in the French classical course, with the limited time allotted to this study, is of general interest, a résumé of it is given here. In the preparatory class of the lycée, as well as in the classe de huitième following, the allotted time is devoted to simple arithmetical work in whole numbers, mental work, and to the solving of easy problems. In septième (third year of the course) are added decimal numbers and the metric system, with drawing of geometrical figures. In the next year there is a review of work oh whole numbers, a continuation of mental exercises and problems, and decimals; work on fractions is entered upon, and elementary geometry is begun. In the succeeding year arithmetic is continued, with the study of the rule of three, interest, discount, with simple problems in alligation, a detailed review of the metric system, and with further very elementary geometrical exercises. In quatrième, theoretical geometry is begun, with one recitation per week. In troisième, the two hours per week are devoted to a review of arithmetical subjects,
- The percentage of hours devoted to recitations in mathematics, in such typical fitting schools of the United States as have supplied data to the writer, is as follows: Boston Latin School (with four years' grammar-school course added), 17·8 per cent. Boston English High School (with two years' grammar-school course added), 16·6 per cent. Phillips Academy Exeter, N. H., classical course, 26·5 per cent; scientific course, 26·9 per cent. Williston Seminary, Easthampton, Mass., classical course, 26·7 per cent; scientific course, 25·7 per cent. Phillips Academy, Andover, Mass., classical course, 25·7 per cent; scientific course, 28·8 per cent. St. Paul's School, Concord, N. H., classical course, 24·9 per cent; scientific course, 27·8 per cent. Lawrenceville School, Lawrenceville, N. J., classical course, 17 per cent; scientific course, 22·7 per cent. St. Mark's School, Southborough, Mass., exclusively classical, 21·6 per cent. Doubtless these percentages may, in some of the schools cited, be increased or decreased in the case of certain pupils; but they represent the mathematical courses as prescribed for the major portion of them. How strikingly the figures illustrate the different methods of treatment of the mathematical question, in the United States and France, will be understood when it is further stated that the percentage allowed to mathematics in the French lycée course is only 8·7 per cent, and in the secondary special course, where mathematical studies are considered by the French to be especially prominent, only 17 per cent.