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.
Numeration teaches us to estimate or properly value the numbers and divisions on the rule in an arithmetical form.
Their values are all entirely governed by the value set upon the first figure, and being decimally reckoned, advance tenfold from the commencement to the termination of each radius: thus, suppose 1 at the joint be one, the 1 in the middle of the rule is ten, and 1 at the end, one hundred: again, suppose 1 at the joint ten, 1 in the middle is 100, and 1 or 10 at the end is 1000, etc, the intermediate divisions on which complete the whole system of its notation.
Set 1 on B opposite to the multiplier on A; and against the number to be multiplied on B is the product on a.
Multiply 6 by 4.
Set 1 on B to 4 on A; and against 6 on B is 24 on A.
The slide thus set, against 7 on B is 28 on A.
Set the divisor on B to 1 on a; and against the number to be divided on B is the quotient on A. Divide 63 by 3.
Set 3 on B to 1 on A; and against 63 on B is 21 on A.