# Introduction

The history of the slide rule spans roughly 350 years from beginning to end. The earliest slide rules were simple physical rulers but marked with special scales based upon the concept of the logarithm and were used to quickly perform multiplication and division calculations to several digit accuracy. Invented in the early 17th century using two sliding scales, by the start of the 19th century additional scales had been added to slide rules to provide access to squares, roots, and values of trigonometric functions. By the middle of the 20th century many slide rules were double-sided with highly-accurate scales and manufactured from a variety of materials. Models could be found that had incorporated one or two dozen different scales on a single slide rule for performing a wide variety of calculations; the slide rule had become a standard tool used by students and professionals for computations typical of mathematics, science, engineering, and many business practices. Then in the 1970s, seemingly overnight, electronic calculators became easily attainable by the general public and the production and sales of slide rules vanished.

The slide rules in the collection presented here mostly have been found in antique shops, flea markets, and through local dealers in the Midwestern United States, typically within a few hours drive from Chicago. With many early American slide rule manufacturers and retailers having been based in Chicago, the search has been a very fruitful activity for this enthusiastic hobbyist. Other slide rules in the collection have been found during various trips around the U.S. and some have been obtained from overseas, via online vendors.

The original motivation for creating this online book was to help me in keeping track of the items in the collection and to be able to share the collection with other slide rule connoisseurs. As time went on, however, it became clear that many young people are starting to collect slide rules and are interested in learning how to use them. And while I was actually trained in their use and the mathematics behind them, anyone under the age of about 60 likely never had that experience. Hence this book has evolved to include introductory material in the opening chapters in addition to a selection of special groupings and stories about various subgroups of the collection.

The first few chapters provide introductory material written for someone unfamiliar with the slide rule, although a certain level of basic math skill is assumed. Chapter 1 describes the mathematical framework that governs the use of slide rules in computations – the logarithm. While a deep understanding of the logarithm is not necessary to learn how to perform the basic operations of a slide rule, it is certainly of great help when trying to master them.

In Chapter 2, a calculus-based discussion of how values of logarithms can be computed numerically is presented. Again, knowing how to compute values of logarithms is not required before using such values to perform calculations. This chapter is included for completeness of the topic, and some of the results within this chapter may be of interest to the reader, even if the steps involved to arrive at those results may not be completely comprehensible to those not proficient in the mathematics being used.

Next, in Chapter 3, the various standard logarithmic scales found on the most common slide rules are described, as well as their use in performing calculations – multiplication and division; squares and square roots; trigonometric calculations; raising a number to an arbitrary power, and so on.

With a basic understanding of logarithms, how they are used in calculations, and how they are utilized on a slide rule, the following chapters delve into the slide rule collection itself. After a brief summary of the collection contents, Chapter 4 presents the entire collection organized by major slide rule maker or groups of related makers. The lists provided here have further details of each rule and some information for each major slide rule maker. Links to photos of the rules are also included in the lists found in this chapter. On the other hand, Chapter 5 also has the entire collection, but is presented in approximate chronological order. The format of this chapter provides a quick, easy-to-navigate visual overview of all the slide rules.

In addition to the style and precision of the various makers, the large variety of slide rule types and models is indicative of the variety of scales and scale arrangements that can be found on them; Chapter 6 provides lists of the scale sets found on all of the rules in the collection.

Special groupings of items in the collection can be found in the various sections of Chapter 7. Here, one can quickly find the 25 oldest rules, the youngest rules, “beginner’s” rules, rules with the most number of scales, and other special listings. And Chapter 8 presents a number of historical books, manuals, and slide sheets that are also part of the collection.

Finally, in Chapter 9, a growing series of short vignettes can be found that provides special insights and details of portions of the slide rule collection. This chapter is often expanded and updated, and the vignettes are not necessarily listed in the order in which they were written. The latest updates are listed at the beginning of the chapter.

Appendices are included which provide a brief time-line of the history of the slide rule, a listing of common slide rule scales, some statistics of the current collection, and a synopsis of the database used to create this document. References for each of the items in the collection are also available, as well as links to other important introductory materials.

Tips for best navigating and viewing the site, including the use of its search tool and other features, are also provided.

The state of the collection is kept up to date through the use of a database maintained and processed using the R programming language . A few details about the database can be found in Data Frame Properties. When changes to the database are made, the present document is automatically updated through the bookdown package (Xie 2016) in R and re-posted.

 Photographic images, figures, tables, and other graphics found throughout the text have been produced by the author unless otherwise noted.

Errors, of course, are expected and acknowledged, as I am still learning while long-time devotees of the subject have much more knowledge than I about the slide rules and their history. I am deeply thankful for their tutelage and encouragement.

Since the electronics revolution of the late 1970’s quick numerical calculations have been performed with pocket calculators or, in today’s 21st century environment, perhaps through “calculator” apps on one’s laptop, phone or mobile device. A basic modern calculator will have keys for entering numbers and for performing functions such as addition and subtraction, multiplication and division, and perhaps squares and square roots and percentages. Some of the more sophisticated calculators and applications have functions such as cubes and cube roots, reciprocals, exponentials and numbers raised to arbitrary powers or arbitrary roots, logarithms, trigonometric functions such as sine, cosine, and tangent, and maybe more. With the exception of basic addition and subtraction, which the user was assumed to be able to readily perform, all of these other functions just mentioned were accessible using slide rules. And, like the electronic calculators, there were simple slide rules for the basic functions above, and more sophisticated slide rules for performing the more advanced functions.

 Simple Slide Rule Advanced Slide Rule

The earliest pocket calculators that became affordable to the general public were sometimes named “slide rule calculators” to emphasize that they performed most of the same functions.

Early electronic calculators of the 1970’s were capable of performing numerical calculations with multi-digit (usually 10-13) precision; but for many computations, only 2-3 digit accuracy – or 4 at most – is sufficient for the project at hand. Note that an error in the last digit in a three-digit number is an error on the scale of 1 out of a few hundred, say 1 out of 500 as an example; this amounts to an error of about 0.2% or so for a typical calculation. Computations necessary for the building of buildings and sidewalks, bridges and automobiles, even airplanes and rocket ships could be performed through the use of slide rules for many of the relevant calculations. Mechanical computing machines and other techniques could be used sparingly in special cases where more accuracy was critical.

As mentioned at the beginning of this introduction, it was the invention of the concept of a logarithm that paved the way for the invention of a logarithmic scale, with which one could perform the multiplication of arbitrary numbers by adding or subtracting lengths along a physical rule. Following this invention in the early 17th century, additional scales were gradually created over time and added to the slide rules produced over the centuries so that more complex calculations could take place on these relatively simple and easy to carry devices.

The following two chapters will first introduce the concept of the logarithm and its use in performing multiplication and division calculations, and then will discuss a modern method for how logarithms of numbers can be obtained. With this information at hand, the third chapter will discuss how logarithmic scales on slide rules allow for a wide variety of calculations, and will present some of the diverse mathematical functionality found on many of the popular slide rule models from the last past two centuries.

Continue to a Review of the Logarithm
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