To John Canton
MS not available: facsimile of ALS: The Royal Society
Cravenstreet, May 29. 1765
Dear Sir,
As you seem’d desirous of seeing the magic
Circle I mention’d to you, I have revis’d the one I made many Years
since, and with some Improvements, send it you.
I have made it as distinct as I could, by using
Inks of different Colours for the several Sets of interwoven
Circles; and yet the whole makes so perplext an Appearance, that I
doubted whether the Eye could in all Cases easily trace the Circle
of Numbers one would examine, through all the Maze of Circles
intersected by it: I have therefore, in the middle Circle, mark’d
the Centers of the Green, Red, Yellow, and Blue Sets; so that when
you would cast up the Numbers in any Circle of either of those
Colours, if you fix one Foot of the Compasses in the Center of the
same Colour, and extend the other to any Number in that Circle, it
will pass round over all the rest successively.
This magic Circle has more Properties than are
mention’d in the Description of it, some of them curious and even
surprizing; but I could not mark them all without occasioning more
Confusion in the Figure, nor easily describe them without too much
Writing. When I have next the Pleasure of seeing you, I will point
them out. I am, Dear Sir, Your most obedient humble Servant
p.s. You have my curious Square of 8, and
the great perfect one of 16; I enclose one of 6, and one of 4,
which I assure you I found more difficult to make, (particularly
that of 6) tho nothing near so good. Mr Canton
A Magical circle of circles. By B:F.
It is compos’d of a Series of Numbers from 12 to 75 inclusive,
divided in 8 concentric Circles of Numbers, and rang’d in 8 Radii
of Numbers, with the Number 12 in the Center, which Number, like
the Center, is common to all the Circles and to all the Radii. The
Numbers are so dispos’d, as that all the Numbers in any one of the
Circles, added together, make, with the central Number, just 360,
the Number of Degrees in a Circle. The Numbers in each Radius also,
with the central Number, make just 360. Also Half of any of the
said 8 Circles, taken above or under the horizontal double Line
with Half the Central Number, make 180, or half the Degrees in a
Circle. So likewise do the Numbers in each Half Radius, with half
the Central Number. There are moreover included 4 other Sets of
concetric Circles, 5 in each Set, the several Sets distinguish’d by
Green, Yellow, Red, and Blue Ink, and each Set drawn round a Center
of the same Colour. These Sets of Circles intersect the first 8 and
each other; and the Numbers contain’d in each of these 20 Circles,
do also, with the Central Number, make 360. Their Halves also,
taken above or under the horizontal Line, do, with half the central
Number make 180. Observe, That there is no one of the
Numbers but what belongs to at least two different Circles, some to
three, some to four, and some to five; and yet all so plac’d (with
the central Number which belongs to all) as never to break the
requir’d Number 360 in any one of the 28 Circles. The Diagonals are
to be reckon’d by Halves, not crossing but turning at right Angles
from the Center, by which 4 Varieties are made instead of two. By
Doctor Benj. Franklin
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