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Slide rule

Mechanical analog computer

  • 26 min read
  • 7 chapters
w:Slide rule , Pickett model N902-T simplex trig. This is a typical student model. The back has instructions for use and a table of fractional powers of 2, to the 64th, and their decimal equivalents.
ArnoldReinhold · CC BY 2.5

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Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form. Slide rules manufactured for specialized fields such as aviation or finance feature scales that aid in specialized calculations particular to those fields. The slide rule is closely related to nomograms used for application-specific computations. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while scientific notation is used to keep track of the order of magnitude of results.

English mathematician and clergyman Reverend William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. It made calculations faster and less error-prone than evaluating on paper. Before the advent of the scientific pocket calculator, it was the most commonly used calculation tool in science and engineering. The slide rule's ease of use, ready availability, and low cost caused its use to continue to grow through the 1950s and 1960s even with the introduction of mainframe digital electronic computers. But after the handheld HP-35 scientific calculator was introduced in 1972 and became inexpensive in the mid-1970s, slide rules became largely obsolete and no longer were in use by the advent of personal desktop computers in the 1980s.

In the United States, the slide rule is colloquially called a slipstick.

Basic concepts

Each ruler's scale has graduations labeled with precomputed outputs of various mathematical functions, acting as a lookup table that maps from position on the ruler as each function's input. Calculations that can be reduced to simple addition or subtraction using those precomputed functions can be solved by aligning the two rulers and reading the result.

For example, a number to be multiplied on one logarithmic-scale ruler can be aligned with the start of another such ruler to sum their logarithms. Then by applying the law of the logarithm of a product, the product of the two numbers can be read. More elaborate slide rules can perform other calculations, such as square roots, exponentials, and trigonometric functions.

The user may estimate the location of the decimal point in the result by mentally interpolating between labeled graduations. Scientific notation is used to track the decimal point for more precise calculations. Addition and subtraction steps in a calculation are generally done mentally or on paper, not on the slide rule.

Components

Most slide rules consist of three parts:

  • Frame or base – two strips of the same length held parallel to form a frame.
  • Slide – a center strip that can move lengthwise relative to the frame.
  • Cursor, runner or glass – an exterior sliding piece with a hairline for accurately reading and aligning numbers.

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 (which can usually be pulled out, flipped over and reinserted for convenience), 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 adjacent 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.

Decades

Scales may be grouped in decades, where each decade corresponds to a range of numbers that spans a ratio of 10 (i.e. a range from 10n to 10n+1). For example, the range 1 to 10 is a single decade, and the range from 10 to 100 is another decade. Thus, single-decade scales (named C and D) range from 1 to 10 across the entire length of the slide rule, while double-decade scales (named A and B) range from 1 to 100 over the length of the slide rule.

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