Slide Rule

Pick a working length — 250 mm is a good size. Every mark on every scale is measured from this one number, so decide it now.

The mark for a number n sits at L × log₁₀(n) from the left end. For n = 2 on a 250 mm scale that is 250 × 0.301 = 75.3 mm.

Work out and write down all the main positions before marking anything. Note that 1 lands at 0 mm and 10 at the full length — the scale is one decade.

The gap from 1 to 2 is huge; from 9 to 10 it is tiny. That uneven spacing IS the logarithm, drawn to scale, and it is the whole reason the device works.

Add intermediate marks — tenths between 1 and 2, coarser divisions higher up. Each subdivision also goes at L × log of its value, never evenly spaced.

Cut two outer strips and one slider, all the same length, with the slider a snug running fit between the outer two.

Cut a shallow rebate along each outer strip so the slider is held but moves freely. Tight enough not to rattle, loose enough not to bind.

Transfer the same scale onto the fixed body (the D scale) and onto the slider (the C scale), aligned along the meeting edge.

Mark 1 at each end — the left index and the right index. You will need both, and knowing which you used decides the answer.

To find 2 × 3, put the slider's left index against 2 on the body scale.

Find 3 on the slider and read what lies beneath it on the body: 6. You have physically added log 2 and log 3.

For 4 × 6 the answer falls past the right end. Slide the RIGHT index to 4 instead and read under 6 — you get 2.4, meaning 24.

The rule gives digits, never magnitude — 2.4, 24 and 240 look identical on it. Estimate the size in your head; this is the discipline every engineer who used one had to keep.

Set the divisor on the slider against the dividend on the body, then read the quotient at the slider's index. Subtracting lengths divides.

The identity underneath. log(a × b) = log(a) + log(b). Napier published logarithms in 1614 precisely to convert multiplication into addition, because addition is enormously easier by hand. Edmund Gunter turned that into a physical scale around 1620 — a logarithmic line you worked with dividers. The step to two sliding scales, so no dividers are needed, is credited to William Oughtred around 1622.

The priority quarrel is real. Oughtred's pupil Richard Delamain published a description of a circular slide rule in 1630, before Oughtred published his own in 1632, and the two accused each other of theft in print for years. Oughtred is generally credited on the strength of earlier unpublished work; Delamain published first. Presenting either as the sole undisputed inventor misrepresents the record.

Precision, and its cost. A slide rule gives about three significant figures — you read between the marks by eye. That was accepted because engineering inputs are rarely known better than that, and because the alternative was hours with log tables. The blind spot is the decimal point: the device tracks ratios and not magnitudes, so the user must keep the order of magnitude in their head. Engineers of the era were consequently very good at estimation, a skill the pocket calculator quietly removed.

How it ended. The slide rule ran the technical world for three and a half centuries and died in about five years. HP's HP-35 pocket scientific calculator arrived in 1972, and by 1975 slide rule production had essentially stopped. Keuffel & Esser reportedly donated its last rule to the Smithsonian. Few technologies with that long a run have been displaced that abruptly.