Page:Carroll - Euclid and His Modern Rivals.djvu/265

Rh hitherto used, accompanied with more or less desire to adopt ours, we are urged by many persons to exchange our system for one which is falling out of favour on the continent.

Many assertions have been made in discussion which rest entirely on the authority of the individual advocate, and thus it is necessary to be somewhat critical in our estimate of the value of the testimony. Two witnesses who are put prominently forward are MM. Demogeot and Montucci, who drew up a report on English education for the French Government. Now I have no doubt that these gentlemen were suited in some respects to report on English education, as they were selected for that purpose; but I have searched in vain for any evidence of their special mathematical qualifications. No list of mathematical publications that I have consulted has ever presented either of these names, and I am totally at a loss to conceive on what grounds an extravagant respect has been claimed for their opinions. The following sentence has been quoted with approbation from these writers: "Le trait distinctif de l'enseignement des mathématiques en Angleterre c'est qu'on y fait appel plutôt à la mémoire qu'à l'intelligence de l'élève." In the first place we ought to know on what evidence this wide generalisation is constructed. Did the writers visit some of the humbler schools in England in which the elements of arithmetic and mensuration were rudely taught, and draw from this narrow experience an inference as to the range of mathematical instruction throughout England? Or did they find on inspecting some of our larger public schools that the mathematical condition was unsatisfactory? In the latter case this might have arisen from exclusive devotion to classics, or from preference for some of the fashionable novelties of the day, or from want of attention and patience in the teachers. On the most unfavourable supposition the condemnation pronounced on the general mathematical training in England cannot be justified. But take some kind of experimental test. Let an inquirer carefully collect the mathematical examination papers