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The slide rule

Chapter 14: THE USE OF THE UPPER SCALES FOR MULTIPLICATION AND DIVISION.
By Charles N. Pickworth
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About This Book

The manual defines the slide rule as an instrument for performing calculations by means of logarithms and provides a concise primer on common logarithms, mantissa and characteristic. It explains the mathematical principle that adding and subtracting logarithms yields products and quotients, and extends this to powers, roots, and trigonometric and algebraic operations. Practical instruction covers the layout and use of scales, slide and cursor, magnifying cursors and special rule types, with examples of routine procedures such as multiplication, division, square and root extraction, and proportional calculations. Descriptions of specialized instruments and applications include engineering tasks like screw-cutting and gear calculations, together with advice on accuracy and practice.

THE USE OF THE UPPER SCALES FOR MULTIPLICATION AND DIVISION.

Many prefer to use the upper scales A and B, in preference to C and D. The disadvantage is that as the scales are only one-half the length of C or D, the graduation does not permit of the same degree of accuracy being obtained as when working with the lower scales. But the result can always be read directly from the rule without ever having to change the position of the slide after it has been initially set. Hence, it obviates the uncertainty as to the direction in which the slide is to be moved in making a setting.

When the A and B scales are employed, it is understood that the left-hand pair of scales are to be used in the same manner as C and D, and so far the rules relating to the latter are entirely applicable. But in this case the slide is always moved to the right, so that in multiplication the product is found either upon the left or right scales of A. If it is found on the left A scale, the rule for the number of digits in the product is found as for the C and D scales, and is equal to the sum of the digits in the two factors, minus 1; but if found on the right-hand A scale, the number of digits in the product is equal to the sum of the digits in the two factors.

In division, similar modifications are necessary. If when moving the slide to the right the division can be completely effected by using the L.H. scale of A, the quotient (read on A above the L.H. of index B) has a number of digits equal to the number in the dividend, less the number in the divisor, plus 1. But if the division necessitates the use of both the A scales, the number of digits in the quotient equals the number in the dividend, less the number in the divisor.