_ less, we add one to the
lowest figure, which, as we have just shown, will have the same
effect. The terms, however, that are commonly used in performing this
operation, are improper. To say "one that I borrowed, and four"
(meaning the lowest figure in the adjoining column) implies the idea
that what was borrowed is now to be repaid to that lowest figure,
which is not the fact. As to multiplication, we have little to say.
Our pupil should be furnished, in the first instance, with a table
containing the addition of the different units, which form the
different products of the multiplication table: these he should, from
time to time, add up as an exercise in addition; and it should be
frequently pointed out to him, that adding these figures so many times
over, is the same as multiplying them by the number of times that they
are added; as three times 3 means 3 added three times. Here one of the
figures represents a quantity, the other does not represent a
quantity, it denotes nothing but the times, or frequency of
repetition. Young people, as they advance, are apt to confound these
signs, and to imagine, for instance, in the rule of three, &c. that
the sums which they multiply together, mean quantities; that 40 yards
of linen may be multiplied by three and six-pence, &c.--an idea from
which the misstatements in sums that are intricate, frequently arise.

We have heard that the multiplication table has been set, like the
Chapter of Kings, to a cheerful tune. This is a species of technical
memory which we have long practised, and which can do no harm to the
understanding; it prevents the mind from no beneficial exertion, and
may save much irksome labour. It is certainly to be wished, that our
pupil should be expert in the multiplication table; if the cubes which
we have formerly mentioned, be employed for this purpose, the notion
of _squaring_ figures will be introduced at the same time that the
multiplication table is committed to memory.

In division, what is called the Italian method of arranging the
divisor and quotient, appears to be preferable to the common one, as
it places them in such a manner as to be easily multiplied by each
other, and as it agrees with algebraic notation.

The usual method is this:

Divisor
71)83467(1175
Italian method:
Dividend

83467| 71
| ----
| 1175

The rule of th