_A Natural Square._ _A Magical Square._ A G B A B +--+--+--+--+--+ +--+--+--+--+--+ | 1| 2| 3| 4| 5| |11|24| 7|20| 3| +--+--+--+--+--+ +--+--+--+--+--+ | 6| 7| 8| 9|10| | 4|12|25| 8|16| +--+--+--+--+--+ +--+--+--+--+--+ E |11|12|13|14|15| F |17| 5|13|21| 9| +--+--+--+--+--+ +--+--+--+--+--+ |16|17|18|19|20| |10|18| 1|14|22| +--+--+--+--+--+ +--+--+--+--+--+ |21|22|23|24|25| |23| 6|19| 2|15| +--+--+--+--+--+ +--+--+--+--+--+ C H D C D To form a magical square, first transpose the two ranks in the natural square to the diagonals of the magical square; then place the number 1 under the central number 13, and the number 2 in the next diagonal downward. The number 3 should be placed in the same diagonal line; but as there is no room in the square, you are to place it in that part it would occupy if another square were placed under this. For the same reason, the number 4, by following the diagonal direction, falling out of the square, it is to be put into the part it would hold in another square, placed by the side of this. You then proceed to numbers 5 and 6, still descending; but as the place 6 should hold is already filled, you then go back to the diagonal, and consequently place the 6 in the second place under the 5, so that there may remain an empty space between the two numbers. The same rule is to observed, whenever you find a space already filled. 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