502 THE POPULAR SCIENCH MONTHLY 
with a purpose, whose pupils are stimulated to learn in the spirit of 
inquiry, and who consequently exercise a personal influence that 1s pro- 
found 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 ordi- 
nary 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. ‘T'o 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 
