Slide Rule, (Mathematics)

Slide Rule, mechanical device formerly used by engineers and scientists for rapid and approximate multiplication, division, extraction of roots, raising to powers, and other simple computations. The slide rule has been almost totally superseded by the small hand-held electronic calculator. The principle of the slide rule is the translation of all computations to equivalent additions or subtractions that can be carried out on a set of scales sliding over each other. Thus, two uniformly graduated marked scales can be used for addition or subtraction as shown in Fig. 1 for 2 + 4 = 6. If 2 and 3 are to be multiplied, it follows from the definition of logarithm that log 2 + log 3 = log 6. Accordingly, a scale which is laid out logarithmically (Fig. 2) can be used to add (or subtract) logarithms and therefore to multiply or divide. Powers or roots (fractional powers) can be represented on a set of scales by a further extension of logarithms. Thus, 42 = 16 becomes 2 × log 4 = log 16. If the logarithm is taken once more, log 2 + log (log 4) = log (log 16). Thus, the combination of the normal (logarithmic) slide-rule scale with a so-called log-log scale leads to the evaluation of powers and roots. Other scales, such as for sine, cosine, and tangent, and logarithm and for calculations involving p (pi) are also found on the usual rectilinear slide rule. This consists of an upper and lower fixed part with various imprinted scales and a movable center slide on which further scales are given (see illustration). A glass runner or cursor with a finely engraved vertical line is provided for easier alignment of the scales.
The computational accuracy possible depends on the size of the slide rule and on the care with which the scales are printed. The commonly used 10-in. slide rule permits multiplications and divisions to be made with an accuracy of about 1/10th percent, which suffices for many engineering calculations. Both the rectilinear and the less commonly used circular slide rule were invented by the English mathematician William Oughtred shortly after the discovery of logarithms. Various special slide rules have been devised for the solution of widely applicable engineering formulas, or for business calculations, such as the determination of interest, compound interest accumulation, and depreciation.