Logarithm Scales and Slide Rules

A logarithm scale is any scale in which equal distances on the scale represent equal ratios. Here is such a scale.

The marks on the scale are equally separated but the values double. If you want to think of this is a normal scale then just take logarithms. The base 2 logarithms of the numbers on the scale are 0, 1, 2, 3, 4, etc. Here is the same scale, but with the usual markings.

It looks strange doesn't it, but note that the distance between 1 and 10 is the same as that between 10 and 100.

Logarithm scales are used for graphing in scientific work.

Slide Rules

In the old days, before calculators were invented (pretty well any time before 1975), logarithm scales were used to do calculations. This was done by sliding one scale over the other.

If you look at the bottom scale the number 1 is lined up with the 8 on the top scale. This is set up to multiply by 8. Notice that 8 times the bottom number equals the top number. This works because of the laws of logarithms. To multiply numbers you add the logarithms. A slide rule like this is really only adding lengths. But this is enough to multiply the numbers.

Here is a genuine slide rule. See if you can do the same multiplications that the simple slide rule above shows, then try something more complicated.

Working Slide Rule