mathematical teaching. Professor Perry, in his opening address to the
Engineering Section of the British Association at Belfast, expressed an
opinion that the average boy of fifteen might be got to the
infinitesimal calculus. As a matter of fact the average English boy of
fifteen has only just looked at elementary algebra. But every one who
knows anything of educational science knows, that by the simple
expedient of throwing overboard all that non-educational, mind-
sickening and complex rubbish about money and weights and measures,
practice, interest, "rule of three," and all the rest of the solemn
clap-trap invented by the masters of the old Academy for Young
Gentlemen to fool the foolish predecessors of those who clamour for
commercial education to-day, and by setting aside the pretence in
teaching geometry, that algebraic formulae and the decimal notation are
not yet invented, little boys of nine may be got to apply quadratic
equations to problems, plot endless problems upon squared paper, and
master and apply the geometry covered by the earlier books of Euclid
with the utmost ease. But to do this with a class of boys at present
demands so much special thought, so much private planning, so much
sheer toil on the part of the teacher, that it becomes practically
impossible. The teacher must arrange the whole course himself, invent
his examples, or hunt them laboriously through a dozen books; he must
be not only teacher, but text-book. I know of no School Arithmetic
which does not groan under a weight of sham practical work, and that
does not, with an absurd priggishness, exclude the use of algebraic
symbols. Except for one little volume, I know of no sane book which
deals with arithmetic and elementary algebra under one cover or gives
any helpful exercises or examples in squared paper calculations. Such
books, I am told, exist in the seclusion of publishers' stock-rooms,
but if I, enjoying as I do much more leisure and opportunity of inquiry
than the average mathematical master, cannot get at them, how can we