TWEXTY-SIXTII AXNUAL MEETING. 



49 



(9) Here we see that the two diagonals, the central line, and the 



central column, add each 15. It may also be seen that each of the 

 four corners, with the two numbers diagonally across the opposite 

 corner, as indicated in the scheme above (tigs. 1 and 2) separately foot 

 up 15. For example: 1+6 + 8 = 15,3 + 4 + 8 = 15, etc. This 

 gives the clue for the scheme (figs. 1 to 4). 



Square of Four. 



Squares of 16 places have long been considered very difficult, and if by chance 

 a "magic" square were constructed it was heralded as a great accomplishment. 

 Yet, when the principles of their construction are fully understood, the making of 

 these squares by the hundred or the thousand becomes a comfjaratively easy 

 matter. 



I will first construct a square, and we will then proceed to analyze it and 

 study the principles. Take this as a model : 



No. 1. 



Is this square harmonic? Let us see : 



Equal sums are obtained by adding together four numbers in each of the fol- 

 lowing regular ways: 

 1st. — By lines — 



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Each of the columns ( fig. 9 ) . . 



Each of the lines ( fig. 10 ) 



Each of the diagonals ( fig. 11 ) 

 2d. — By squares — 



^^i-_3. 11. 



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Ways. 

 .. 4 

 .. 4 

 .. 2 



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