10 



ON THE CONSTRUCTION AND DIFFERENT FORMS 



the descending diagonal rows of which were made the leading vertical rows of two simi- 

 lar squares, (h), (It); and from the reverse combinations (9, 8), (10, 7), (ll, 6), (12, 5), 

 I constructed two additional squares (/), (*')• It is obvious that I had it in my power to 

 form other analogous squares, by taking in a different order the combinations here given. 

 From the squares thus made, I obtained the fundamental squares (G), (H), (G 1 ), (H); and 

 from these, as before, the compound perfect arrangements (G //), (HG), &c. To serve as 

 a comparison with Mr. Dalby's, and to notice its remarkable properties in my own way, 

 I shall present the second combination, (HG). 



New perfect magic square, including sixteen perfect magic squares, formed of the 

 scries of 256 numbers, 1, 2, 3 ... . 256. 



(HG) 



Besides the properties expressed in the title of this new perfect magic square; every 

 four numbers round the centre of any component square, or at the two opposite sides, or 

 at the four angles, always give the same amount 514, which is also the result of each 

 corresponding row, whether horizontal, vertical, or diagonal. Every four adjacent num- 

 bers round any point, wherever taken, amount to 514. The properties of the whole square 

 remain when its component squares are removed in vertical or horizontal rows from one 

 side to the other; and it will continue perfectly magical, when any number of its single 

 vertical, or horizontal rows are subjected to a like displacement, as already explained in 

 case of the smaller square (AB), to which it bears constant analogy, but with increased 

 variety in respect to the number and possible location of its magic components. 



It will be observed that Mr. Dalby has left no theoretical construction of his magic square; 

 and that the mode by which Dr. Ilutton obtains it in his Dictionary is indirect and limited. 



