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.
As l : 8.1416 :
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