This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.

The manner in which the foregoing Table of Circumferences is found is as follows: Taking the diameter at unity, we have by decimal proportion

in. | in. | |

As l : 8.1416 : | : 1. | : 3.1416, |

and the decimal 1416 multiplied by 8, gives the circumference for 1 inch of diameter 3 1.8 inches.

In these Tables the number 3.1416 is divided by 8, which gives 3927 This decimal proportion has been used as a constant, and the sum multiplied by 8 gives the excess above the decimal value in eighths of an inch

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