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nals, had this added, that a four-square hole being cut in a piece of paper of such a size as to take in and show through it just sixteen of the little squares, when laid on the greater square, the sum of the sixteen 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 sixteen 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 magic circle, consisting of eight concentric circles, and eight radial rows, filled with a series of numbers from 12 to 75 inclusive, so disposed as that the numbers of each circle, or each radial row, being added to the central number 12, they make exactly 360, the number of degrees in a circle; and this circle had, moreover, all the properties of the square of eight. If you desire it, I will send it; but at present, I believe, you have enough on this subject. I am, &c.
TO PETER COLLINSON.
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, eccentric with respect to the first, each of these sets containing five spaces. The centres of the circles that bound them, are at A, B, C, and D. Each set, for the more easy distinguishing them from the first, are drawn with a different colored ink, red, blue, green, and yellow.*
These sets of eccentric circular spaces intersect those of the concentric, and each other; and yet the numbers contained in each of the twenty eccentric spaces, taken all around, make, with the central number, the same sum as those in each of the eight concentric, viz. 360. The halves, also of those drawn from the centres A and C, taken above or below the double horizontal line, and of those drawn from centres, B and D, taken to the right or left of the vertical line, do, with half the central number, make just 180.
* In the plate they are distinguished by dashed or dotted lines, as different as the engraver could well make them.
It may be observed, that there is not one of the numbers but what belongs at least to two of the different circular spaces; some to three, some to four, some to five; and yet they are all so placed as never to break the required number 360, in any of the twenty-eight circular spaces within the primitive circle.
These interwoven circles make so perplexed an appearance, that it is not easy for the eye to trace every circle of numbers one would examine, through all the maze of circles intersected by it; but, if you fix one foot of the compasses in either of the centres, and extend the other to any number in the circle you would examine belonging to that centre, the moving foot will point the others out, by passing round over all the numbers of that circle successively. I am, &c.
TO JARED ELIOT.
Northeast Storms begin at the South. — Account of a Copper Mine. — Subscriptions for an Academy in Philadelphia.
Philadelphia, 13 February, 174950.
You desire to know my thoughts about the northeast storms beginning to leeward. Some years since, there was an eclipse of the moon at nine o'clock in the evening, which I intended to observe; but before night a storm blew up at northeast, and continued violent all
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night and all next day; the sky thick-clouded, dark, and rainy, so that neither moon nor stars could be seen. The storm did a greal deal of damage all along the coast, for we had accounts of it in the newspapers from Boston, Newport, New York, Maryland, and Virginia; but what surprised me was, to find in the Boston newspapers an account of an observation of that eclipse made there; for I thought, as the storm came from the northeast, it must have begun sooner at Boston than with us, and consequently have prevented such observation. I wrote to my brother about it, and he informed me, that the eclipse was over there an hour before the storm began. Since which I have made inquiries from time to time of travellers, and of my correspondents northeastward and southwestward, and observed the accounts in the newspapers from New England, New York, Maryland, Virginia, and South Carolina; and I find it to be a constant fact, that northeast storms begin to leeward; and are often more violent there than farther to windward. Thus the last October storm, which with you was on the 8th, begun on the 7th in Virginia and North Carolina, and was most violent there.*
As to the reason of this, I can only give you my conjectures. Suppose a great tract of country, land and sea, to wit, Florida and the Bay of Mexico, to have clear weather for several days, and to be heated by the sun, and its air thereby exceedingly rarefied. Suppose the country northeastward, as Pennsylvania, New Eng* Professor Bache, of the University of Pennsylvania, has shown, that the eclipse of the moon, here alluded to, happened in the evening of the 21st of October, 1743; as may be seen in his tract entitled, "An Attempt to fix the Date of the Observation of Dr. Franklin, in Relation to the Northeast Storms of the Atlantic Coast of the United States," published in the Journal of the Franklin Institute, in the year 1833. It appears that Dr. Franklin was the first discoverer of the above facts respecting northeast storms. — Editor..