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