with a purpose, whose pupils are stimulated to learn in the spirit of inquiry, and who consequently exercise a personal influence that is profound and enduring. I am deeply conscious how much I owe to some such teachers with whom I have studied and to others whom I have known. But still it does remain true that is not yet the atmosphere of ordinary university education, that it does not yet invigorate the ordinary university student, and that to him the passage from school to the university does not necessarily mean a transition from mental discipline and preparation to mental activity and performance.
The distinction that I have in my mind between university and school teaching may be expressed in this way. At school no subject should be taught to a class as though it were intended to be their life work; to take an example, it too often happens at present, owing really to excessive zeal on the part of school teachers, that mathematics is taught as though each member of the class were destined to become a mathematician; consequently only the few scholars with a real aptitude for mathematics become interested, and the remainder are left behind. On the other hand, at the university each subject should be studied as though it really were the life-work both of teacher and of student. Thus, to take the same subject as an illustration, the mathematical student will attend the full courses of his professors and will follow them with the interest of a mathematician; whereas for the scientific student it will only be in those branches of mathematics which concern him that the interest of his special science will put him on terms of equality with the mathematical student. If I may choose an illustration which is familiar to myself, any student of mineralogy can easily be interested in and benefit by a course in spherical trigonometry, because it is one of the tools of his trade, but to send him to lectures on differential equations would be only to discourage him. On the other hand, the student of chemistry would rather be interested in the latter. To each of them certain branches of mathematics as taught by an ardent teacher afford a real intellectual training, but neither would gain much if compelled to follow a general university course of mathematics designed for mathematicians.
It will be observed that I have endeavored to confine myself to the subject of university education and not to say much, except by way of contrast, concerning school teaching.
I must, however, return to it for a moment, if only to emphasize the danger of that specialization which, since it takes place at school and not at the university, is bound to be narrow, and which is often encouraged in pupils of special aptitude preparing for university scholarships.
That a boy or girl should for a year or even two years before leaving school be practically confined to one subject, and should before entering the university be examined in that alone, appears to me to be contrary
