How to use a Slide Rule (HPR Show 2166)

Dave Morriss


Table of Contents

Introduction

In my show 1664, “Life and Times of a Geek part 1”, I spoke about using a slide rule as a schoolboy. As a consequence, I was asked if I would do a show on slide rules, and this is it (after a rather long delay).

What is a Slide Rule?

A slide rule is an analogue computer which can be used to do multiplication and division (amongst other mathematical operations). Most slide rules consist of a fixed portion with a central slot into which a sliding part fits. The top and bottom areas of the fixed part hold various different scales, and the slider is marked with its own scales. A transparent cursor slides over the top of the other parts and can be used to read from one scale to another.

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Slide Rule (Wikimedia)

I still have my slide rule from my schooldays, a plastic Faber-Castell version from the 1960’s.

My old slide rule
My old school slide rule looking very much worse for wear

Recently, while contemplating this HPR episode, I checked eBay to see whether slide rules were still available. Within the hour I had found an interesting-looking example, had placed a bid on it for £9.99, and won. It is also a Faber-Castell but mainly made of wood (possibly boxwood or mahogany) with ivory-like (celluloid) facings. It seems quite a bit older than my other one. It is a model 1/60/360, made in Bavaria, apparently from some time after 1935 when this style of model numbering began to be used.

Faber-Castell 1/60/360 picture 1 Faber-Castell 1/60/360 picture 2 Faber-Castell 1/60/360 picture 3
My newly acquired Faber-Castell 1/60/360

In researching it I found that the slide rule is actually split in two, with a spring steel spine which keeps the two halves together, and tensions the slot in which the slider runs. You can see some of this in the pictures.

How does a Slide Rule work?

Slide rules use logarithmic scales to perform multiplication and division.

What is a logarithm?

A logarithm of a number is the exponent to which a base must be raised to produce the number.

So, if the base is 10 (known as a common logarithm, written as ‘log10’) then 100 is 102, so the log10 of it is 2, and the log10 of 1000 (103) is 3. The Wikipedia page on the logarithm does a better job of explaining this than I can do.

At the time I was using a slide rule, back in the 1960’s, we were expected to know how to use logarithms and were each allocated a book of log tables. This allowed you to look up the common logarithm of a number, or to convert a logarithm back to a number.

The great advantage of logarithms is that multiplication can be achieved by addition, and division by subtraction. In other words, the following rules apply for any base b:

logb(xy)=logb(x)+logb(y)

logb(x/y)=logb(x)−logb(y)

Provided b, x and y are positive and b is not 1.

So, at school when multiplying two numbers, the process was to take the first multiplicand, look up its log10, write it down, then do the same for the second multiplicand and add the two logarithms together. The result could then be looked up in an “anti-log” table to get the product of the two original numbers.

If you want to go further with this look at the wikiHow article below for details of how to use logarithmic tables.

John Napier

As an aside, the inventor of logarithms, John Napier, lived in Edinburgh and was born in 1550 in Merchiston Tower, otherwise known as Merchiston Castle. The original grounds of the tower is now the site of Edinburgh Napier University, and the tower is part of their Merchiston Campus. I live in Edinburgh, and have visited this site on many occasions.

Merchiston Castle
Merchiston Castle (Wikimedia)

The slide rule as a short-cut to using logarithms

With a slide rule the process uses logarithmic scales but short-circuits the table look-ups.

The operation of a slide rule is covered quite well on the Wikipedia page referenced in the Links section below.

Multiplication

We have already seen that the process of multiplication using logarithms is transformed into a process of addition. So the example shows the multiplication of 3 by 2. The sliding scale is positioned so that the 1 is positioned over the 2 on the scale below it. Looking at the 3 on the sliding scale the answer of 6 can be seen below it.

On my Faber Castell 1/60/360 I used the upper scale to achieve the same result (since it’s a little bit easier to see):

Faber-Castell 1/60/360 picture 4
Calculating 3 times 2

The same can of course be achieved by placing the 1 on the sliding scale against the 3 on the upper scale and reading from the 2 on the sliding scale:

Faber-Castell 1/60/360 picture 5
Calculating 2 times 3

Division

Taking the Wikipedia example of 5.5 divided by 2, on my Faber Castell 1/60/360 again, the 5.5 mark on the slider is aligned with the 2 mark on the upper scale and the result, 2.75 read off the slider under the 1 on the upper scale.

Faber-Castell 1/60/360 picture 6
Calculating 5.5 divided by 2

Further Study

The International Slide Rule Museum offers many resources for the slide rule enthusiast. If you are interested in learning more about how to use a slide rule then they have a self-guided course with a virtual slide rule.

In addition, you could consider obtaining a real slide rule. There are many to be had for not very much money on eBay. Apart from the Faber-Castell I bought myself for £10, and have been demonstrating here, I bought two more Faber-Castell models, costing less than £20 for both.