566 



SCIENCE. 



Science, 



Curiosities 



in. 



Preparation of the Natural Square. 



Rules for 

 transferring 

 the minors 

 from the 

 natural to 

 the magic 

 circle. 



(5. Mark all the corner cells on the left of the upper 1 ^ 



quarter . j 



The corner cells on the right of do. . . b 



The middle cells of the upper quarter . rn 



The cells on the left quarter opposite the centre c 



In the even belts alone, 



Mark a cell in each, in the upper 7 on the left s 



quarter, next the corner cells, 3 on the right r 



Mark the cells in the left quarter immediately under a, n 



And the cells on the right quarter immediately 1 ^ 



above those which are opposite the centre, j 



Rules for transferring the Minors from the Natural to 

 the Magic Square. 



1. General rules. These numbers, when carried from 

 any belt in the natural square, must be placed in a si- 

 milar belt in the magic square. 



8. They must never be placed opposite, either dia- 

 gonally, or facing each other. 



9. Particular rules. For the odd belts. 



In the left corner cells of the upper quarter, place c 

 In the right corner cells of do. place . . m 



In any cells out of the corner sin the lower quarter place a 

 In any cells out of do. in the left quarter . b 



10. For the even belts. 



In the left corner cells of the upper quarter, place a 

 In the right corner cells of do. ... m 



In any cells on the left quarter between the diago- 1 . 



nals, place . . . . . . j 



In any cells on the right quarter do. and not? j j 



/* j . \ . f Ct tlilt I Tl 



facing b, place J 



ate belts. Thus, suppose there are four unlettered in Science, 

 any belt, the numbers in which are 2, 3, 5, and 6, Curiosities 

 place No. 2 and 6 in the upper, and 3 and 5 in the in> 

 lower quarter and similar belt of the magic square. *~~Y""" 

 Or the extremes may be carried to the lower, and 

 the means to the upper quarter, no matter which. 



12. In the right and left quarters, the cells unmark- 

 ed in each belt are always in pairs, as 2, 4, 6, 8, &c. 

 Carry the numbers in one half, say the upper half of 

 those on the left quarter to the left quarter of the magic 

 square, and the lower half to the right quarter. Do 

 the same with those which are unlettered on" the right 

 quarter, but in the reverse order ; so that the amount 

 of the numbers so transferred shall be the same in each 

 of these quarters. 



13. The minors being all transposed, will each of 

 them, if properly placed, have a corresponding empty 

 cell in its own belt, either diagonally opposite, if it is 

 in a corner, or facing it, if in any cell between the di- 

 agonals. 



14. These empty cells are now to be filled with the 

 majors, which is done without any reference to the na- 

 tural square. Each minor must have its proper major, 

 which is that number which the minor wants of the 

 amount of the first and last number of the progression. 

 Thus, if the series runs from 1 to 25, the amount of 

 these is 26 ; and if the minor in question be 7, its ma- 

 jor of course must be J9, &c. Inserting the majors, 

 therefore, diagonally opposite those numbers which 

 are in the corner cells, and facing those which are 

 situated between the diagonals, each in the same 

 belt with its minor, the magic square will be com- 

 pleted. 



Example in the Square oj 11. 

 NATURAL SQUARE. 



In any cells in the lower quarter, between the dia- 

 gonals place *, c, and r. The minors, which are let- 

 tered, being thus inserted in the magic square, the re- 

 mainder must be transferred by the following general 

 rules : 



11. In the upper quarter, the cells remaining un- 

 marked, are either in number 4 or its multiples, as 8, 

 12, 16, in each belt. Of the numbers in these then, 

 place the extremes in the upper, and the means in the 

 tower quarter of the magic square, in their appropri- 



