To John Canton
ms not found; facsimile: Royal Society; also draft: American Philosophical Society.
[Extract of a letter to John Canton, May 29, 1765]

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 concentric 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.

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