slide_rule
Narration transcript
Generated from the narration in the Voiceover app. To change the script, edit it there — edits made directly to this file are replaced on the next build.

Slide 1 — How to Use a Slide Rule
For three and a half centuries, every bridge, every engine, and every rocket was designed on one of these. It is a ruler that multiplies. There is no battery, no display, and nothing happening inside it that could be called a calculation — only two pieces of wood, marked in a particular way, sliding past one another. Understanding the marking is the whole of it, and it takes about five minutes.

Slide 2 — Three Parts and a Hairline
The mechanism has three parts and no more. The outer body is fixed, and you hold it. The slide runs in a groove down the middle and is the only thing that moves. Riding over both is the cursor, a glass window carrying a single hairline scratched down it, which does nothing except let you carry a reading from a scale on the slide across to a scale on the body without losing your place. The rule photographed here is a special-purpose one for humidity, so its scales are unfamiliar, but the anatomy is universal.

Slide 3 — Why It Works
The trick is in the spacing. Numbers along the scale are not evenly placed; each sits at a distance proportional to its logarithm. One is at the far left, at distance zero. Two sits about thirty percent of the way along, because the logarithm of two is roughly three tenths. What that buys you is the identity underneath the whole instrument: log two plus log three equals log six. Distances add when you lay them end to end, and because these distances are logarithms, adding them multiplies the numbers they stand for.

Slide 4 — Multiplying 2 x 3
Two scales are all it takes, labelled C and D — C on the slide, D on the body, marked identically. To multiply two by three, move C until the one at its left end, the left index, sits directly over the two on D. That lays down the distance for two. Then run the cursor along to the three on C, which lays the distance for three on the end of it, and read whatever the hairline crosses on D underneath. It reads six. Notice that both ends of every scale are labelled one: the scale covers a single decade and then begins again.

Slide 5 — Compound Interest
Powers work the same way. A thousand dollars at six percent for twelve years means one point oh six raised to the twelfth, and the LL scales exist for exactly that. They are spaced by the logarithm of a logarithm, which lets an ordinary C scale do the arithmetic in the exponent. Set the index of C over one point oh six on LL1, run the cursor to one point two on C — that is the twelve, since stepping from LL1 up to LL2 supplies the factor of ten — and read two point oh one on LL2. The money has doubled: two thousand and twelve dollars. Twelve years at six percent is seventy-two over six, so the Rule of 72 is really a fact about where these scales land.

Slide 6 — What You Actually Get
What comes back is three significant figures, from an instrument about ten inches long, in a design William Oughtred first assembled around 1622. Three figures sounds thin against a calculator's ten, until you ask how many of those ten were ever justified by the inputs. The Empire State Building, the Boeing 747, and the Saturn V were all sized this way, and the astronauts who flew to the Moon carried slide rules as backup. Precision was never the binding constraint. Knowing which quantities mattered was.

Slide 7 — What Killed It
It ended abruptly. Hewlett-Packard put the HP-35 in a shirt pocket in 1972 — ten digits, no estimating, no hairline — and within about four years an industry that had run for three centuries was finished. Something did go with it. The rule gave you the digits but never the decimal point; you supplied the magnitude yourself, every single time, which meant you always knew roughly what the answer should be before you read it. That habit of checking your own order of magnitude left along with the wood.
