To multiply 8,679 by 8, look at the eighth line of squares from the top, and on that line will be found the product of each of the integers 8, 6, 7, 9, when multiplied by 8. We have then to write down the 2 as the first figure of the product, add 7 and 6 together = 13; write 3 as the next figure, carry 1 to add to the sum of 8 and 5, and so on.
The reason for dividing the figures in each square by a diagonal line, and for placing the left-hand figure higher than the right is, that the eye may be thus assisted in adding the carried figure of one slip to the unit of the next.
To provide for the occurrence of more than one of the same figures in the multiplicand, there should be several slips or rods for each of the digits.
In practice the rods are placed on a flat piece of wood, with two ridges at right angles, by which they are preserved in a proper position.
This instrument can be made useful in "divisions," by making by means of it a table of the product of the divisor, multiplied by each of the numbers 1 to 9.
THE ARITHMETICAL BOOMERANG.
The boomerang is an instrument of peculiar form, used by the natives of New South Wales, for the purpose of killing wild fowl and other small animals. If projected forwards, it at first proceeds in a straight line, but afterwards rises in the air, and after performing sundry peculiar gyrations, returns in the direction of the place where it was thrown.
The term is applied to those arithmetical processes by which you can divine a number thought of by another. You throw forwards the number by means of addition and multiplication, and then, by means of subtraction and division, you bring it back to the original starting point, making it proceed in a track so circuitous as to evade the superficial notice of the tyro.
TO FIND A NUMBER THOUGHT OF.
First Method.