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Supplementary Note on th Construction and different Forms qftht V . Cyclovohite, 

 By E. Nulty. Read Dec* mbt r 6, 1844. 



The arrangement of numbers, denominated a Magic Cyclovohite, wad published in the 



filth volume of the Society's Transactions, 1835, has fur in Im-i- a perfect magic 

 square, formed of the sixty-four integral numbers, 1, 2, 3 . . . 64. Tin- pet uliai square 

 essentially diners, in its construction, from the basis of the magic circle, which nm-i !»• 

 viewed a- imperfect, so far as respects an inequality which subsists betwi i a the rami "i 

 the numbers along its horizontal and vertical row-, and those constituting H- principal 

 diagonals. The perfect form winch we here propose to construct ma] I" regarded aa 

 compound, and as generated from two others: one consisting of binary combinations 

 taken from the series of eight numbers, 1, 2, 3 . . . 8; the other, of multiples bj eight of 

 the ditl'erent terms of the corresponding series, (), 1, 2 ... 7, .and which, being joined bj 

 addition to tin; preceding, "ill evidently give the several terms of the tir-i series, 

 1,2,3 . . . <>t. In order to exhibit these; component squares in n ference to the particular 

 arrangement published, let US take the two binary combinations (1,8) and -. 7), "huh 

 being placed in vertical and horizontal rows, will form the two following elemental 1 ] 

 magic squares: 



(«) 



■ 



In like manner from the two binarj combinations (3, 6) and I, 5), let tu form the 

 analogous perfect squan 



(*) 





in which, ami the pn i eding, the upper row oi the 6nl i- made the <h to nding diagonal "i 

 the second; and the upper row of the second it the leading n meal row oi the t 



VOL. X. 5 



