Uses of a Slide Rule

Slide rules are essentially analog computers, once widely used for the same purpose as modern digital calculators. These mechanical devices are composed of sliding scales that allow users to perform various mathematical operations accurately. From its invention by the Rev. William Oughtred in 1630 until the spread of computers in the 1970's, slide rules were widely used by students and scientists to avoid mistakes. Their basic operations are multiplication and division, with more elaborate slide rules also providing help with exponentiation, logarithms and other calculations.
  1. Multiplication

    • Using the so-called C and D scales, you can find the result of two single-digit factors, by one factor to the number 1 of the other scale. For example, if you want to calculate 2 --- 4, align the numbers 2 of scale C and 1 of scale D and look for what number 4 on scale D is aligned to. It will be 8. For multiplications going off scale, like 3 --- 4 for example, you can use the double-decade scales A and B.

    Division

    • Division on slide rules is similar to multiplication. Align the divisor on the upper scale to the dividend on the lower one. For example, to divide 9 by 3, align the number 9 to the number three and look under the upper scale's number 1 to find the quotient: 3. Slide rules could not give accurate results for all divisions, such as 7.3 divided by 2.75; users had to come up with a result, typically by estimation.

    Squares and Square Roots

    • Scales A and B are used to calculate the square roots of scales C and D. All you have to do is align the number 1 of both scales -- A and C or B and D -- and search for the the number you want to square on scale C or D. Its squared value will be aligned to it, on scale A or B respectively. Finding the square root is equally straightforward: search for the squared number on scale A or B and find their corresponding roots on scale C or D.

    Other Operations

    • Advanced slide rulers also feature scales to find cube numbers and routes (K), as well as scales CF and DF, which resemble the C and D scales, but they start from π, multiplication with which is common in engineering and science. In addition, scales such as T, T1, T2, ST and SRT are used for trigonometrical operations, to find tangents and cotangents, while scale L, or linear scale, is used to calculate powers of 10 and base-10 logarithms.

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