## Definition

The **slide rule** is a mechanical analog computer. The slide rule is used primarily for multiplication and division and for functions such as exponents, roots, logarithms, and trigonometry. They are not designed for addition or subtraction which was usually performed manually, with scientific notation used to keep track of the magnitude of results. Maximum accuracy for standard linear slide rules was about three decimal digits.

At its simplest, each number to be multiplied is represented by a length on a pair of connected rulers that can slide past each other. As the rulers each have a logarithmic scale, it is possible to align them to read the sum of the numbers’ logarithms, and hence calculate the product of the two numbers.

The Reverend William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the electronic 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 as computers were being gradually introduced. The introduction of the handheld electronic scientific calculator around 1974 made them largely obsolete and most suppliers left the business.^{1}

A **slide rule**, also known as a **slide ruler** or a **slipstick**, is an extremely complex ruler that functions as an analog computer. By sliding various components of the ruler to align with one another, a slide rule can compute products, roots, logarithms, and the result of trigonometric functions.

In the mid-1600s, the linear slide rule was invented by Reverend William Oughtred, and the inner slide rule was invented by Robert Bissaker. Until the invention of the pocket calculator in the 1960s, the slide rule was used by virtually every scientist and mathematician in the world.^{3}

## Who

“Dad says that anyone who can’t use a slide rule is a cultural illiterate and should not be allowed to vote. Mine is a beauty – a K&E 20-inch Log-log Duplex Decitrig”

Have Space Suit – Will Travel, 1958. by Robert A. Heinlein (1907-1988)

## What

This page introduces you to the slide rule which use the mathematical magic of logarithms (Mathematical Mysteries).

## Why

See Theoretical Knowledge Vs Practical Application.

## How

The mathematical magic behind the slide rule is logarithms. Logarithms, invented in the 17th century, allow reducing multiplication to addition and division to subtraction. It is very easy to add and subtract by sliding two rulers against one another, so if you use rules whose scales are logarithmic instead of linear, you can multiply and divide without all of the tedious calculation, as long as you’re satisfied with the accuracy you can read off the scale. With even more cleverly defined scales, it is possible to compute the squares of numbers, square roots, cubes and cube roots, trigonometric functions, and logarithms and exponents.

A slide rule does not add or subtract. *Humans* add and subtract, and with a little practice they get very good at it. A slide rule also doesn’t keep track of decimal places. It works only with the significant digits of numbers, and it’s up to you to figure out where the decimal point goes in the result. This sounds tedious, and in the examples that follow it may seem so, but in fact users of slide rules could usually place the decimal by instinct, and if you got it wrong the result was usually so ridiculous you could go back and figure out where you’d goofed.^{2}

Here is how slide rules work for multiplying and dividing. Each number has a logarithm. To multiply two numbers, add their logarithms and find the anti-logarithm of the sum. Division involves subtraction of one logarithm from the other. A slide rule represents logarithms as a distances along a linear scale. Add the distances to multiply. Subtract the distances to divide. The numbers on the scale are the anti-logarithms of the logarithms represented by distances on the scale, so there is no need to consult a table of anti-logarithms.^{4}

Many of the **References** and **Additional Reading** websites and **Videos** will assist you with understanding and the use of slide rules.

As some professors say: “It is intuitively obvious to even the most casual observer.“

## References

^{1} “Slide Rule – Wikipedia”. 2022. *en.wikipedia.org*. https://en.wikipedia.org/wiki/Slide_rule.

^{2} Walker, John. 2022. “Slide Rule”. *fourmilab.ch*. https://www.fourmilab.ch/documents/sliderule/.

^{3} “What Is A Slide Rule?” 2022. *computerhope.com*. https://www.computerhope.com/jargon/s/slide-rule.htm.

^{4} “How to Use a Slide Rule!”. 2022. *instructables.com*. https://www.instructables.com/How-To-Use-A-Slide-Rule-1/.

## Additional Reading

“2.972 How A Slide Rule Works”. 2022. *web.mit.edu*. https://web.mit.edu/2.972/www/reports/slide_rule/slide_rule.html.

“A Seminar On How To Use The Slide Rule”. 2022. *International Slide Rule Museum (ISRM)*. https://www.sliderulemuseum.com/SR_Class/OS-ISRM_SlideRuleSeminar.pdf.

B, Phil. 2022. “A More Complete Slide Rule Tutorial”. *Instructables*. https://www.instructables.com/A-More-Complete-Slide-Rule-Tutorial/.

You do not need your own slide rule because this *Instructable* will make use of a virtual Pickett N600-ES slide rule available for anyone to use at this link. (**RECOMMENDED!**)

“Basic Slide Rule Instructions”. 2022. *hpmuseum.org*. https://www.hpmuseum.org/srinst.htm.

“Illustrated Self-Guided Course On How To Use The Slide Rule”. 2022. *International Slide Rule Museum (ISRM)*. https://www.sliderulemuseum.com/SR_Course.htm.

“Slide Rules”. 2022. *sliderules.info*. http://www.sliderules.info/index.htm.

Ulmann, Bernd. 2017. “Slide Rules: The Early Calculators – Chalkdust”. *chalkdust*. https://chalkdustmagazine.com/features/slide-rules-early-calculators/.

“What Can You Do With A Slide Rule?” 2022. *math.utah.edu*. https://www.math.utah.edu/~pa/sliderules/.