Science, 

 Curiosities 



in. 



SCIENCE. 





Magic Squares of Even Numbers. 



These are generally subdivided into two kinds, 

 squares of j gtj oddly even squares, which are those whose roots 

 m num- w j lgn na ] ve( j p ro duce odd numbers, as the squares of 

 6, 10, 14, 18, &c. 



2d, Evenly even squares, are the squares of 4 and its 

 multiples, as 8, 12, 16', &c. 



The 6rst kind, though possessing fewer properties, 

 is more difficult of construction than the second. We 

 have seen no method superior to the following one, 

 which embraces both kinds, and at the same time the ad- 

 ditional property of being bordered, so that the exterior 

 surrounding row or rows may be removed, and the 

 square remaining still continue magic. 



This method is similar to the one immediately pre- 

 ceding for squares of odd numbers, and the description 

 and rules there given will enable us to shorten what 

 follows for even numbers. 



Preparation of the Natural Square. 



Preparation 1. The first strong line is to be drawn round the 



of the natu- central square of 4, and the circumscribing lines are to 



ral square. ^ e cont j nue d f rom that to the extremity of the square. 



The belts are then to be numbered 1, 2, 3, &c. and 



named odd and even belts as in the odd squares. 



2. The numbers above the middle horizontal line 

 are the minors, those below it are the majors, and the 

 square is supposed to be divided into four quarters by 

 the diagonals. 



3. The square of 4 in the middle is excluded from 

 the following directions, and is to be filled up in the 

 magic square after the other numbers are inserted, by 

 a rule to be given afterwards. 



4. In the odd belts, 



Mark all the corner cells on the left of the upper 

 quarter a 



The corner celli on the right of do. 

 The cell* in the upper quarter 

 next the corner, 



The cells in do. next c and d, 

 The cells in the lowest range of 



on the Wt 

 on the right 

 on the left 

 on the n'ffht 



on the left 



minor*, . . . | on the right 

 The cell* on the left immediately under a, 

 The cells on the right immediately above *, 

 5. In the even belt*, 



Mark the corner cells in the up- Jon the left 

 per quarter, 



The cells next./ and g in do. 

 The cells in the lowest range of 



minors, 



on the right 

 on the le 

 on the right 

 on the left 



MM g 



rft h 



' on the right 



f.-o:n t!ie 



P 



s and b 

 c and d 



a and r 



m and n 



f 



g 

 h and i 



themigk 

 quart- 



Rules for transferring the Minortfrom the Natural to 

 the Magic Square. 



6. The general rules, 7 and 8 for odd squares are to Rules for 

 be followed here. 



7- Particular rules for the odd belts. 

 In the corners of the upper f on the left place 



quarter, . . on the right 

 In any cells between o and p place 

 In any cells in the lower quarter between") 



the corners, and not facing * or h, place s ' 

 In any cells on the left quarter between ' 



the diagonals place . . . 

 In any cells on the right quarter, between , 



the diagonals, and not facing a orr, place J 



8. For the even belts. 

 In the corners of the upper ") on the left place 



quarter . . . J on the right 

 In any cells in the lower quarter, between 



the diagonals, place 

 In any cells on the left quarter, between 



the diagonals, place 

 In any cells on the left quarter between " 



do. not facing v, place 



They will then appear in the following order : 



The lettered numbers being now transferred, the 

 remainder of the minors must be placed, and the ma- 

 jors added exactly in the same way as ordered for 

 the odd squares, in the general rules 11, 12, 13, and 

 14. 



The square of 4 in the middle of the natural quart, 

 being now made magic, by the rules given in the next 

 section, and inserted in the middle of the magic square, 

 the whole will be completed. 



