How to make a slide rule
(or log-log or semilog graph paper)
- Take an ordinary ruler, and put decimal points before
the numbers marking the inches.
(Ignore the last two inches on the ruler.)
- To position the major (black) divisions on the logarithmic scale,
calculate the base-10 logarithm of each integer from 2 to 9
and plot the integer at that place on the ruler.
log_(10) 2 = .30103,
log_(10) 3 = .47712,
- To get the secondary (red) divisions, calculate the
base-10 logarithm of each integer from 11 to 99, discard the number
before the decimal point (1 in this case), and locate the rest on
log_(10) 11 = .04139,
log_(10) 12 = .07918,
- Continue to the desired precision.
(At the third level, the discarded part of the logarithm will be 2,
and so on.)
Obviously you will plot fewer numbers at the right end of the rule
than on the left, because the points are much closer together
- When you have made two of these logarithmically scaled rulers, you
can position them beside each other so as to multiply numbers by
adding the lengths corresponding to their logarithms.
Yes, before calculators we really did this (using the slide rule on
homework and tests, not the do-it-yourself construction).