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92 METHODS OF SOCIAL REFORM.
makes mathematical science the most powerful training-gound
thoughts excited. In some subjects mental exertion in the
pupil is called forth by tho working of problems and exercises.
Thoso form a kind of continuous examination, which should
accompany every lecture. Arithmetic is only to be learnt by
sums upon the schoolboy’s slate, and it is the infinite variety
of mathematical tasks from common addition upwards which
of the intellect. ’The Into Professor De Morgan +as probably
the greatest tcacher of mathematics who ever lived. He con-
Bidered it requisite that students should attend his expository
lccturcs for an hour and n quarter every clay ; but he always
gave an abundance of exercises as well, which, if fully worked
out, would tuko at least as long, and often tmico as long a, time.
l??rtrciscs are the sheet-anchor of the teacher, and in this way
oxlly can me explain thc? cxtraordinary propensity of classical
teachers towards Latin verses. As I have heard such teachers
explain, verses, though useless in every other way, afford a
definite measurable amount of exercise-a manageable classical
treadmill. For many years past it was my duty to teach several
subjects-Logic, Mental and Iforal Philosophy, and Political
Economy. Experience made me acutely aware of the very
different educational values of these diverse subjects. Logic is
by far tho best, because when properly taught it admits of the
samo activo training by exercises and problems that we find in
mathematics. It is no doubt necessary that some instruction
should also bo given to scnior studcnts in philosophy and
political economy; but it is difficult in these subjects to make
tho student think for himself. Examination, then, represents
the active as opposed to the passive part of education, and in
answer to Mr. Cross’s statement that examination is not
ednwtion, I venture to repeat that, in some form or other,
examination is the most powerful and essential means of
training the intellect.
I now pass on to the wholly different question whether
open competitive examinations ape the best means of selecting
men for important appointments. In this view of examinations
the educational results are merely incidental, and the
main object is to find an impartial mode of putting the right