MAGIC. 



number runs off' at the bottom, carry it to 

 the uppermost cell, that is not occupied, 

 of the same column that it would have full- 

 en in below, and then proceed descending 

 diagonalwise again as far as you can, 

 or till Uie numbers either run oft'at bottom 

 or side, or are interrupted by coming at a 

 cell already filled : now when any number 

 runs off at the right-hand side, then bring 

 it to the furthest ceil on the left-hand of 

 the same row or line it would have fallen 

 in towards the right-hand: and when 

 the progress diagonalwise is interrupted 

 by meeting with a cell already occupied 

 by some other number, then descend di- 

 agonally to the left from this cell till an 

 empty one is met with, where enter it ; 

 and thence proceed as before. Thus, 



To make a magic square of the 49 num. 

 bers 1, 2, 3, 4, &c. 



First place the 1 next below the cen- 

 tre cell, and thence descend to the right 

 till the 4 runs off at the bottom, which 

 therefore carry to the top corner on the 

 same column as it would have fallen in ; 

 but as that runs off at the side, bring it to 

 the beginning of the second line, and 

 thence descend to the right till they ar- 

 rive at the cell occupied by 1 ; carry the 

 8 therefore to the next diagonal cell to 

 the left, and so proceed till 10 runs off at 

 the bottom, which carry therefore to the 

 top of its column, and so proceed till 13 

 runs off at the side, which therefore 

 bring to the beginning- of the same line, 

 and thence proceed till 15 arrives at the 

 cell occupied by 8 ; from this therefore 

 descend diagonally to the left; but as 16 

 runs off at the bottom, carry it to the top 

 of its proper column, and thence descend 

 till 21 runs off at the side, which is there- 

 fore brought to the beginning of its pro- 

 per line ; but as 22 arrives at the cell oc- 



cupied by 15, descend diagonally to the 

 left, which brings it into the first column, 

 but off at the bottom, and therefore it is 

 carried to the top of that column ; thence 

 descending till 29 runs off both at bottom 

 and side, which therefore carry to the 

 highest unoccupied cell in the last co- 

 lumn ; and here, as 30 runs off at the 

 side, bring it to the beginning of its pro- 

 per column, and thence descend till 35 

 runs off at the bottom, which therefore 

 carry to the beginning or top of its own 

 column ; and here, as 36 meets with the 

 cell occupied by 29, it is brought from 

 thence diagonally to the left ; thence de- 

 scending, 38 runs oft' at the side, and 

 therefore it is brought to the beginning 

 of its proper line ; thence descending, 41 

 runs oft' at the bottom, which therefore is 

 carried to the beginning or top of its co- 

 lumn ; from whence descending, 43 ar- 

 rives at the cell occupied by 36, and 

 therefore it is brought down from thence 

 to the left; thence descending, 46 runs 

 off at the side, which therefore is brought 

 to the beginning of its line ; but here, as 

 47 runs off at the bottom, it is carried to 

 the beginning or top of its column, from 

 whence descending with 48 and 49, the 

 square is completed, the sum of every 

 row and column and diagonal making 

 just 175. Dr. Franklin carried this cu- 

 rious speculation further than any of his 

 predecessors in the same way. He con- 

 structed both a magic square of squares, 

 and a magic circle of circles, the descrip- 

 tion of which is as follows. The magic 

 square of squares is formed by dividing 

 the great square into 256 little squares, in 

 which all the numbers from 1 to 256, or 

 the square of 16, are placed, in 16 co- 

 lumns, which may be taken either hori- 

 zontally or vertically. Their chief pro- 

 perties are as follow. 1. The sum of the 

 16 numbers in each column or row, ver- 

 tical or horizontal, is 2056. 2. Every 

 half column, vertical and horizontal, 

 makes 1028, or just one half of the same 

 sum 2056. 3. Haifa diagonal ascending, 

 added to half a diagonal descending, 

 makes also the same sum 2056 ; taking 

 these half diagonals from the ends of any- 

 side of the square to the middle of it ; and 

 so reckoning them either upward or 

 downward, or sideways from right to left, 

 or from left to right. 4. The same with 

 all the parallels to the half diagonals, as 

 many as can be drawn in the great 

 square : for any two of them being di- 

 rected upward and downward, from the 

 place where they begin, to that where 

 they end, their sums still make the same 



