104 Mr. W. Beverley on the Magic Square 



in column 1, 30 + 52 = 82 

 in column 1, 5 + 43 = 48 



and they will make 130 



Or take the odd numbers in the left division, 1+47 = 48 

 and the even numbers in the right division, 28 + 54 = 82 



and they will make 130 



This will be found the case with all the horizontal columns 1 

 to 8. 



The figure is divided, by the horizontal line cd> and the ver- 

 tical column 16 is also divided by the same line, into two equal 

 parts. Each part consists of four squares, two of whose num- 

 bers are even and the others odd. Take the even numbers 

 above the line cd, and add them to the odd numbers below 

 the line, thus : 



in column 16, 54 + 42 = 96 

 in column 16, 23 + 11 = 34 



and they will produce 130 



Or take the odd numbers above the line, 27 + 7 = 34 

 and the even numbers below the line, 58 + 38 = 96 



and they will also produce 130 



This will be found the case with the columns 10, 12, 13, 

 14, 15, 16; that is to say, all the vertical columns except 

 Nos. 9 and 11, which are different in consequence of a peculiar 

 movement of the knight in these columns. 



Take the odd numbers in the upper half 1 , , Q1 00 

 ot column 9, J 



and the even numbers in the lower half "I 



of column 11, J ' ~~ 



and they will make 130 



Or the even numbers in the upper half^l . , „- _„ 

 c i r> ir >48 + 50 = 98 



of column 9, J 



and the odd numbers in the lower half | , - . , ». „^ 

 e i t i >15+ 1 1 =32 



ot column 11, J 



and they will make 130 



Or the even numbers in the lower half of column 9 

 and the odd numbers in the upper half of column 11 

 Or the odd numbers in the lower half of column 9 \ 

 and the even numbers in the upper half of column 11 [ 



will, added together, produce the same amount, 130 



