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The slide rule

Chapter 8: THE PRIMITIVE SLIDE RULE.
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 PRIMITIVE SLIDE RULE.

The application of the foregoing principles to the slide rule can be shown most conveniently by describing the construction of a simple form of slide rule:—Take a strip of card about 11 in. long and 2 in. wide; draw a line down the centre of its width, and mark off two points, 10 in. apart. Draw cross lines at these points and figure them 1 and 10 on each side, as in Fig. 3. Next mark off lengths of 3·01, 4·77, 6·02, 6·99, 7·78, 8·45, 9·03 and 9·54 inches, from the line marked 1. Draw cross lines as before, and figure these lines, 2, 3, 4, 5, 6, 7, 8 and 9. To fill in the intermediate divisions of the scale, take the logs, of 1·1, 1·2, 1·3, etc. (from a table), multiply each by 10, and thus obtain the distances from 1, at which the several subdivisions are to be placed. Mark these 1·2, 1·3, 1·4, etc., and complete the scale, making the interpolated division marks shorter to facilitate reading, as with an ordinary measuring rule. Cutting the card cleanly down the centre line, we have the essentials of the slide rule.

Fig. 3.

The fundamental principle of the slide rule is now evident:—Each scale is graduated in such a manner that the distance of any number from 1 is proportional to the logarithm of that number.

Fig. 4.

“We know that to find the product of 2 × 3 by logarithms, we add 0·301, or log. 2, to 0·477, the log. of 3, obtaining 0·778, or log. 6. With our primitive slide rule we place 1 on the lower scale to 3·01 in. (which we have marked 2) on the upper scale (Fig. 4). Then over 4·77 in. on the lower scale (which we marked 3), we have 7·78 in. (which we marked 6) on the upper scale. Conversely, to divide 6 by 3, we place 3 on the lower scale in agreement with 6 on the upper, and over 1 on the lower scale read 2 on the upper scale. This method of adding and subtracting scale lengths will be seen to be identical with that used in the simple case shown in Fig. 1.