ation.
When once he clearly comprehends that the third place, counting from
the right, contains only figures which represent hundreds, &c. he will
have conquered one of the greatest difficulties of arithmetic. If a
paper ruled with several perpendicular lines, a quarter of an inch
asunder, be shown to him, he will see that the spaces or columns
between these lines would distinguish the value of figures written in
them, without the use of the sign (0) and he will see that (0) or
zero, serves only to mark the place or situation of the neighbouring
figures.

An idea of decimal arithmetic, but without detail, may now be given to
him, as it will not appear extraordinary to _him_ that a unit should
represent ten by having its place, or column changed; and nothing more
is necessary in decimal arithmetic, than to consider that figure which
represented, at one time, an integer, or whole, as representing at
another time the number of _tenth parts_ into which that whole may
have been broken.

Our pupil may next be taught what is called numeration, which he
cannot fail to understand, and in which he should be frequently
exercised. Common addition will be easily understood by a child who
distinctly perceives that the perpendicular columns, or places in
which figures are written, may distinguish their value under various
different denominations, as gallons, furlongs, shillings, &c. We
should not tease children with long sums in avoirdupois weight, or
load their frail memories with tables of long-measure, and
dry-measure, and ale-measure in the country, and ale-measure in
London; only let them cast up a few sums in different denominations,
with the tables before them, and let the practice of addition be
preserved in their minds by short sums every day, and when they are
between six and seven years old, they will be sufficiently masters of
the first and most useful rule of arithmetic.

To children who have been trained in this manner, subtraction will be
quite easy; care, however, should be taken to give them a clear notion
of the mystery of _borrowing_ and _paying_, which is inculcated in
teaching subtraction.

From 94
Subtract 46

"Six from four I can't, but six from ten, and four remains; four and
four _is_ eight."

And then, "One that I borrowed and four are five, five from nine, and
four remains."

This is the formula; but is it ever explained--or can it be? Certainly
not without some alteration. A child se