Tuesday, August 16, 2011

The Slide Rule: A Chick Magnet Plus Other Practical Uses

William Oughtred
If you were to place a modern calculator into the hands of famed mathematician Sir Isaac Newton, it is quite likely you would garner much the same quizzical reaction by placing a slide rule into the hands of a present day math student. While they both have the familiarity of numbers printed upon their surfaces and both can be used to multiply and divide large numbers, their mode of operation is quite different.

The invention of the slide rule has widely been accredited to English mathematician William Oughtred. It is believed that Oughtred came up with the idea of the slide rule in 1622 after leaving the University of Cambridge, formerly known as The King's College of Our Lady and St. Nicholas. In truth, had it not been for the prior works of John Napier and Edmund Gunter, the existence of the slide rule would have fallen into the same mind numbing dilemma of “Which came first, the chicken or the egg?”

In 1614 Scottish mathematician and physicist John Napier forged the idea of logarithms (Greek for "ratio-number") as a way to multiply and divide large numbers more easily. However, it was difficult to conceive and apply this new mathematical concept without some form of visual reference as a guide. In 1620, English astronomer Edmund Gunter took Napier’s logarithmic concept a step further by creating a two-foot long scale that mapped out these logs. Then two years later, William came up with the idea of placing two of Gunter’s scales together as a way to calculate large numbers even more quickly. Thus the concept of the slide rule was born. One could argue that English mathematician Henry Briggs also played a key role in the development of the slide rule since it was he who, in 1617, converted Napier’s original logarithmic concept into the base 10 system we know today.


Pickett N500 ES Slide Rule - Photo by: TheKid965

To the untrained eye the slide rule can appear to be quite intimidating; with its tiny numbers and seemingly limitless lines drawn all about its surface. There was a time, not too long ago, when the knowledge of its use and function garnered much admiration and respect from others. In fact, Caltech Math Professor Tom Apostol was once quoted in saying, “‘we all felt macho walking around campus wearing these like guns in holsters.” In 1941, when he was attending college at the University of Utah, Apostol recalled feeling like a stud saying, “…we knew how to use the things, and this made a big impression on the girls." Looks can be deceiving, however, as the operation of the slide rule is quite elementary once you understand the process. 

A slide rule consists of a number of log scales; the more functions it can perform the more log scales it contains. In its simplest form, a slide rule consists of two logarithmic scales that can be used to calculate multiplication and division problems. More advanced models can be used to solve square roots, exponentials, and trigonometric functions. Each scale is assigned an alpha code corresponding to the function that can be performed with it. These codes were first introduced by a French student named Amédée Mannheim in 1850, and have no significant correlation to their function, only that he labeled the scales from top to bottom starting with A and ending with D. For instance to perform basic multiplication or division you would use scales C and D. The final component to the slide rule is an overlapping clear slider, sometimes called a “cursor,” that has a straight vertical line printed or engraved upon it, which is used to line up the scales used in calculations.

Mathematician John Napier   

To illustrate the ease of its use, if you wanted to multiply 2 times 4 you would first start by sliding the cursor to the “2” on the “D” scale, followed by sliding the leftmost “1” on the “C” scale over until lined up with the vertical line on the cursor. Then you would move the cursor so that the vertical line touched the “4” on the “C” scale. Finally, you would read what the cursor lined up with on the “D” scale. If you have done your alignments correctly you should come up with “8”.

As useful as the slide rule is, it has its limitations. For instance, you cannot do simple arithmetic or subtraction with a slide rule, at least not in a manner that we are familiar with. In addition, you have to be very cognizant of your decimal placement during your calculations, as the slide rule will not tell you where that pesky little dot should go. Furthermore, depending on the scale ruler being used, its decimal accuracy is very limited; sometimes only up to a hundredth or thousandth decimal place. 

Despite these limitations, the slide rule has helped mankind spearhead many fantastical advances in math, science, and technology during the years prior to the advent of the modern calculator. We owe a great manner of gratitude to the slide rule and the men responsible for its creation: William, Gunter, Napier and Briggs; for if it were not for the collective works of these brilliant men we might not have ever walked on the moon or given “nerds” of yesterday the means by which to attract the eye of a fine young lady.

Michael A. Walker
Defying Procrastination 


Have you ever used a slide rule? What would you say are the "sexy" tech tools of our day? Share your stories.


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