John Cook:

Suppose you have two sticks. The length of one is log x, and the length of the other is log y. If you put the two sticks end to end, the combined length is

log x + log y = log xy.

That’s the basic idea behind a slide rule.

The simplest slide rule consists of two bars with numbers marked on each bar on a logarithmic scale, running from 1 to 10 or maybe 1 to 100.

To multiply x by y, line the 1 on the left end of the bottom bar with x on the top bar. Then the number above y on the bottom bar is xy on the top bar.

This works because the 1 of the bottom bar is positioned a distance log x from the 1 on the top bar. The y on the bottom bar is a distance log yfurther to the right, and so it is a distance log x + log y from the 1 on the top, which is marked with log xy.

Here’s an example. Suppose you want to find the circumference of a circle 5000 ft in diameter. The image below shows how you would multiply π times 5000.