The slide rule, or slipstick, is a mechanical analog computer. The slide rule is used mainly for multiplication and division, and also for "scientific" functions such as roots, logarithms and trigonometry, but usually not for addition or subtraction.
There are many different styles of slide rules. They are usually linear or circular. They have a standardised set of markings or scales. These scales are used for mathematical computations. Some slide rules have been made for special use, as for aviation or finance. Those slide rules have special scales for those applications, as well as normal scales.
The slide rule is based on the work on logarithms by John Napier and was invented by William Oughtred. Before electronic calculators were developed, slide rules were the tool used most often in science and engineering. The use of slide rules continued to grow through the 1950s and 1960s even as digital computing devices were gradually introduced; but around 1974 the pocket calculator made the slide rule largely obsolete and most suppliers left the business.
Basic concepts
In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers. These common operations can be time-consuming and error-prone when done on paper. More complex slide rules allow other calculations, such as square roots, exponentials, logarithms, and trigonometric functions.
Mathematical calculations are done by aligning a mark on the sliding central strip with one on one of the fixed strips. The relative position of other marks can then be observed. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result.
The user determines the location of the decimal point in the result, based on mental estimation. Scientific notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.
Most slide rules have three linear strips of the same length. The strips are aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two. The outer two strips are fixed so that their relative positions do not change.
Some slide rules ("duplex" models) have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip, still others on one side only ("simplex" rules). A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not next to each other or, in duplex models, are on the other side of the rule. The cursor can also record an intermediate result on any of the scales.
Using a slide rule for calculation
Multiplication
A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules and . Moving the top scale to the right by a distance of , by matching the beginning of the top scale with the label on the bottom, aligns each number , at position on the top scale, with the number at position on the bottom scale. Because , this position on the bottom scale gives , the product of and . For example, to calculate 3 × 2 (represented as 3*2 on a calculator), the 1 on the top scale is moved to the 2 on the bottom scale. The answer, 6, is read off the bottom scale where 3 is on the top scale. In general, the 1 on the top is moved to a factor on the bottom, and the answer is read off the bottom where the other factor is on the top.
Operations may go "off the scale;" for example, the diagram above shows that the slide rule has not positioned the 7 on the upper scale above any number on the lower scale, so it does not give any answer for 2×7. In such cases, the user may slide the upper scale to the left until its right index aligns with the 2, effectively multiplying by 0.2 instead of by 2, as in the illustration below:
Here the user of the slide rule must remember to adjust the decimal point appropriately to correct the final answer. We wanted to find 2×7, but instead we calculated 0.2×7=1.4. So the true answer is not 1.4 but 14. Resetting the slide is not the only way to handle multiplications that would result in off-scale results, such as 2×7; some other methods are: