You proceed in this manner to fill all the empty cases in the angle where the 15 is placed: and as there is no space for the 16 in the same diagonal, descending, you must place it in the part it would hold in another square, and continue the same plan till all the spaces are filled. This method will serve equally for all sorts of arithmetical progressions composed of odd numbers; even numbers being too complicated to afford any amusement.
To find the Difference between two Numbers, the greatest of which is unknown.
Take as many nines as there are figures in the smallest number, and subtract that sum from the number of nines. Let another person add that difference to the largest number, and, taking away the first figure of the amount, add it to the last figure, and that sum will be the difference of the two numbers.
For example: Robert, who is 22, tells George, who is older, that he can discover the difference of their ages; he therefore privately deducts 22 from 99, and the difference, which is 77, he tells George to add to his age, and to take away the first figure from the amount, and add it to the last figure, and that last sum will be the difference of their ages. Thus, the difference between
| Robert's age and 99, is | 77 |
| To which George adding his age | 35 |
| ———— | |
| The sum will be | 112 |
| ———— | |
| 12 | |
| 1 | |
| ———— | |
| Then by taking away the first figure, 1, and adding it to the last figure, 2, the sum is | 13 |
| Which added to Robert's age | 22 |
| ———— | |
| Gives George's age, which is | 35 |
The Boundless Prospect.
Take a square box, about six inches long and twelve high, or of any other proportionate dimensions. Cover the inside with four flat pieces of looking-glass placed perpendicular to the bottom of the box. Place at the bottom any objects you please, as a piece of fortification, a castle, tents, soldiers, &c. On the top, place a frame of glass shaped like the bottom of a pyramid, as in Fig. 8, and so formed as to fit on the box like a cover. The four sides of this cover are to be composed of ground glass, or covered inside with gauze, so that the light may enter, and yet the inside be invisible, except at the top, which must be covered with transparent glass: when you look through this glass, the inside will present a pleasing prospect of a boundless extent; and, if managed with care, will afford a deal of amusement.
Fig. 8.
