Associated Topics || Dr. Math Home || Search Dr. Math

### Slide Rules

```
Date: 03/13/99 at 01:38:51
From: Ben Eller
Subject: Slide Rules

I recently received a slide rule from my grandfather's estate. I would
like to know what the different scales are for. I know that they are
outdated, but he was an engineer (mechanical) and used it all the time.
Of course, there were no instructions.

Thank you.
```

```
Date: 03/13/99 at 06:55:56
From: Doctor Mitteldorf
Subject: Re: Slide Rules

If you had two rulers, you could put one against another and use them
to add: for example, lining up the zero of one ruler with the 2 of the
other, then going 3 inches out on the first, you would find 5 inches
(3 + 2) opposite on the second. The idea behind a slide rule is
similar, except that the distance scale on the slide rule is
proportional to the log of the numbers, not the numbers themselves.
When you line numbers up, it is like adding logs, and, as you know,
that is like multiplying numbers. You cannot add on a slide rule, but
you can multiply and divide.

First exercise: Line up the 1 on the C scale with the 2 on the D scale.
Then, opposite the 3 on the C scale, you will find 2 TIMES 3 on the D
scale.

Second exercise: You can divide 12 by 4 on the slide rule, just by
putting 1.2 on the C scale opposite 4 on the D scale. Opposite 1 on the
D scale, you will find the answer, 3 on the C scale.

There is a lesson here: another thing slide rules cannot do is tell you
where to put the decimal point. You have to do that yourself, in your
head. On a slide rule, 1.2 and 12 or .012 and 12000 are all the same
number.

Third exercise: Figure out how to multiply x times y and divide by z,
all in one step.
------------------------

The A and B scales are exactly half as big as C and D scales. If you
line up a number on the A scale, using the cross hair, with the
corresponding number on the C scale, the number on the C scale will be
the square root of the number on the A scale. The principle is the same
as dividing the log of a number by 2.
--------------------

All this is more interesting if you have already had a little
introduction to logarithms, in school or elsewhere. If you do not
an hour explaining to you what a logarithm is and giving you some
exercises to illustrate the properties of logarithms. The L scale on
your slide rule has numbers arranged in regular linear fashion, like a
ruler, and it can be used with the C scale to calculate logarithms
directly.

Hope this gives you a start.

- Doctor Mitteldorf, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logs