Multiplication is easily attained by this method: and the use which is made of the Multiplication table in general, as an auxiliary to the memory in acquiring this rule, is a cogent reason in favour of the method I suggest to public notice.

In the instance of dictating the figures 27,935, and any other variations after the same example, the scholars, by writing, acquire a thorough knowledge of Numeration, expressed both in words and figures, without paying any attention to it as a separate rule. In fact, Numeration is most effectually learned by the scholars in my institution, not from the study, but by the practice of it; and I may add, almost every other branch of knowledge, taught in the different classes, is acquired in the same easy and expeditious way.

The boys vie with each other in writing their sums neatly on the slate, and their practice and improvement in writing is greatly increased by this

means.

Before the introduction of this method, I had found it needful to employ the senior boys as teachers of arithmetic: and, when their improvement in the lower rules was desirable, a more honourable and efficacious mode could not be adopted; but when proficiency was such as rendered

it

it. needless, it was time not so usefully employed as it might be. This I saw with regret, and have the pleasure of seeing the difficulty removed by this improvement.

It must be obvious, that if a boy had studied and attained a quickness in addition, and was to repeat it before me, in the usual way, to show his improvement, the key to the preceding sum comprises the substance of what he would express; and if I were to take a scholar, unacquainted with arithmetic, and show him minutely how he was to work the sum, the key contains not only the substance of what I should express, but also the same of any other teacher in like case.

By this means, any boy of eight years old, who can barely read writing, and numerate well, is, by means of the guide containing the sums, and the key thereto, qualified to teach the first four rules of arithmetic, simple and compound, if the key is correct, with as much accuracy as mathematicians who may have kept school for twenty years.

Perhaps it is not reasonable to expect much invention and intellectual exertion from boys, whose talents are yet in embryo; but, when the line is drawn, they can abide by it. Boys in general are excellent agents, in whatever they are equal to; and,

in

in this case, nothing is left to their discretion, and they cannot err, without they go to sleep, or do it for the purpose.

Here is a positive certainty to the teacher, that every boy in the class is employed, and detection + follows a disposition to idleness as soon as it exists; that none sit idle while others are waiting the master's partial instructions; and that three times the usual quota of sums are done and repeated by every boy.

Some examples of sums, in the succeeding classes, are added. I propose soon to publish a collection of sums, with appropriate keys, for the use of schools.

and

FARTHINGS.

make, and makes 1d. and make 12,

and make 2-set down under the farthings

and carry 2 to the next.

PENCE.

PENCE.

7 and 8 make 15, and 9 make 24, and 1 makes 25,

37 pence

and 10 make 35, and 2 I carry make 37. are 3 shillings and 1 penny.-Set down 1 under pence, and carry 3 to the next.

the

SHILLINGS.

7 and 9 make 16, and 6 make 22, and 1 makes 23, and 10 make 33, and 10 make 43, and 10 make 53, and 10 make 63, and 3 I carry make 66. 66 shillings are 3 pounds 6 shillings.-Set down 6 under the shillings, and carry 3 to the next.

POUNDS, FIRST COLUMN.

8 and 8 make 16, and 2 make 18, and 7 make 25, and 9 make 34, and 3 I carry make 37.-Set down 7 under the 8, and carry 3 to the next.

SECOND COLUMN.

3 and 1 make 4, and 8 make 12, and 3 make 15, and 3 make 18, and 3 I carry make 21.-Set down 1 under the 3 and carry 2 to the next.

THIRD COLUMN.

6 and 1 make 7, and 4 make 11, and 2 make 13, and 6 make 19, and 2 I carry make 21.-Set down 21.

Total, in figures, 2117 6- 11/

Total,

Total, in words, two thousand one hundred and seventeen pounds, six shillings, and one penny farthing.

SUBTRACTION.

67843789

16754899

51088890

Take 9 from 9, 0 remains-9 from 8 I cannot, borrow 10 and say, 9 from 18 and 9 remaincarry 1 to the 8 is 99 from 7 I cannot; borrow 10 and say, 9 from 17 and 8 remain-carry 1 to the 4 is 55 from 8 I cannot; borrow 10 and say, 5 from 13 and 8 remain-carry 1 to the 5 is 6 6 from 4 I cannot; borrow 10 and say 6 from 14 and 8 remain-carry 1 to the 7 is 8-8 from 8 and 0 remains-6 from 7 and 1 remains-1 from 6 and 5 remains.

Remainder, in figures, 51088890.

Remainder, in words, fifty-one million, eightyeight thousand, eight hundred and ninety.