To make an addition before the Figures are set, by knowing only how many Figures are in each Row; as likewise how many Rows compose the whole; and then adding yourself some Figures equal to those that had been set.

Suppose the person had set five rows of figures, each row containing five figures.

Say in your mind, as you are making the addition beforehand, 9 times 5 make 45; set down 5 and carry 4: repeat the same thing for each of the five figures, as if they all counted 9; therefore for the second, say again, 9 times 5 make 45, and 4 carried over make 49; set down 9 and carry 4: in the same manner for the third, say 9 times 5 are 45, and 4 carried over are 49; set down 9 and carry 4: for the fourth do the same; and set down 9 and carry 4: for the fifth repeat the same, by setting down 9 and carrying 4.

Thus your addition being made before-hand will produce the sum of 499995: then shew this addition to every body in the company; and beg some one to do you the favour of laying on a paper 5 rows of numbers, containing five figures in each row.

EXAMPLE.

The first figure being 2, you must set 7; the second being 9, (which completes the number wanted) you must set a cypher (0); the third being the same, operate as before; the fourth being 7, set down 2; the fifth being 1, set down 8.

The second row beginning by 1, your first figure will be 8; the second number being 4, set down 5; the third being 5, put down 4; the fourth being 6, you must set down 3; the fifth being 3, set down 6.

As the third row begins by 7, begin yours by 2; under the 6 lay 3, then 1 under the 8, and 7 under the 2.

For the fourth row, set 6 under the 3, 2 under the first 7, and another 2 under the other 7; a 0 under the 9, and 2 under the 7, which complete this row.

You are to do the same for the fifth row, putting 1 under the 8, 9 under the 0, 8 under the 1, 6 under the 3, and 9 under the 0.

Then desire some of the company to cast up these ten sums, and it will be found that the product of the whole addition will form the sum of 499995.

In order to come to this combination, you need only fix the number of figures that will compose each row, and determine the number of rows; then to reckon each row for 9, as has been shewn above.

You may likewise present this addition, by saying, that it is the total amount of ten rows, composed of five figures each; out of which five rows will be set by the person who chuses to do it; then multiply secretly as many times 9 as you are to set rows of five figures; therefore multiply 5 times 9 by 5, which will give you the sum of 499995.

The person having set his numbers, you are to add your five rows, taking care that every number you set will make 9 with that to which it corresponds; which being done, you are to ask any one to cast the whole sum up, and the product will be the same as the sum you set down before-hand.

If it were requisite to employ other numbers instead of that of 9, you should, in order to succeed, warn the persons who chuse to set the figures, to be attentive that their numbers do not exceed that agreed upon.