Mr. Logan then shewed me an old arithmetical book, in quarto, wrote, I think, by one Stifelius,' which contained a square of 16, that he said he should imagine must have been a work of great labour; but if I forget not, it had only the common properties of making the same sum, viz. 2056, in every row, horizontal, vertical, and diagonal. Not willing to be out-done by Mr. Stifelius, even in the size of my square, I went home, and made, that evening, the following magical square of 16, which, besides having all the properties of the foregoing square of eight, i.e. it would make the 2056 in all the same rows and diagonals, had this added, that a four square hole being cut in a piece of paper of such a size as to take in and shew through it, just 16 of the little squares, when laid on the greater square, the sum of the 16 numbers so appearing through the hole, wherever it was placed on the greater square, should likewise make 2056. This I sent to our friend the next morning, who, after some days, sent it back in a letter with these words; "I return to thee thy astonishing or most stupendous piece of the magical square, in which" but the compliment is too extravagant, and therefore, for his sake, as well as my own, I ought not to repeat it. Nor is it necessary; for I make no question but you will readily allow this square of 16 to be the most magically magical of any magic square ever made by any magician. (See Plate VII. Fig. 2.) I did not, however, end with squares, but composed also a magick circle, consisting of 8 concentric circles, and 8 radial rows, filled with a series of numbers, from 12 to 75, inclusive, so disposed as that the numbers of each circle, 1 Mich. Stifelius, "Arithmetica integra cum praefatione Phil. Melanchthonis (Novimb. 1544)." — Ed. or each radial row, being added to the central number 12, they made exactly 360, the number of degrees in a circle; and this circle had, moreover, all the properties of the square of 8. If you desire it, I will send it; but at present, I believe, you have enough on this subject. I am, &c. B. FRANKLIN. SIR, 100. TO PETER COLLINSON 1 1 I am glad the perusal of the magical squares afforded you any amusement. I now send you the magical circle. (See Plate VIII.) Its properties, besides those mentioned in my former, are these. Half the numbers in any radial row, added with half the central number, make 180, equal to the number of degrees in a semicircle. Also half the numbers in any one of the concentric circles, taken either above or below the horizontal double line, with half the central number, make 180. And, if any four adjoining numbers, standing nearly in a square, be taken from any part, and added with half the central number, they make 180. There are, moreover, included four other sets of circular spaces, excentric with respect to the first, each of these sets containing five spaces. The centers of the circles that bound them, are at A, B, C, and D. Each set, for the more easy 1 From "Experiments and Observations on Electricity," London, 1769, P. 354. |