One metre, one kilogram, everywhere
Fix the units, hold the standards, and make every measurement comparable to every other.
Everything for this step
- Field guide
- Navigation and the sky → 7 sections The sciences → 15 sections Mathematics → 9 sections Physics → 12 sections
- Builds
- None yet.
- Reference sheets
- None.
- Sciences it rests on
- Physics · Mathematics
- Track
- Science and measurement, level 1 of 3 · next: Controlled comparison and the negative result
Why this matters
This is the least glamorous step on the ladder and one of the highest-leverage. Interchangeable parts, which the factory depends on entirely, are not a manufacturing achievement — they are a metrological one. Two workshops can only make parts that fit each other's assemblies if they are measuring against the same standard, physically traceable to the same object. Without that, precision is local: every workshop is internally consistent and mutually useless. The same applies to a dose, a charge, a bearing and a temperature. Fixing units is what lets work be divided across people who never meet.
The shape of it
- Choose decimal, and choose it once. Any coherent system works; a decimal one removes an entire class of arithmetic error and makes conversion trivial. Mixed traditional units are the single largest source of avoidable calculation mistakes on record.
- Make the primary standards from the most stable material you can work and keep them in conditions that do not change — temperature above all, since everything you can make expands.
- Make working copies and never use the primary. The standard that gets handled is the standard that drifts.
- Establish a comparison procedure and a schedule, and record every comparison. A standard nobody re-checks is a belief, not a measurement.
- Define temperature and time as well as length and mass. Every process step on this ladder above tier 2 is gated by one of the four.
- Publish the definitions. A standard held privately is a monopoly on being able to make things fit.
Doing it, step by step
The summary above says what has to happen. This says how, with the numbers that decide whether it works.
1 · Choose a decimal system, and define the base units
Any coherent system works; a decimal one removes an entire class of arithmetic error. Mixed traditional units are the single largest source of avoidable calculation mistakes on record.
Define four base units and write the definitions down: length (the metre), mass (the kilogram), time (the second) and temperature (degrees Celsius). Derive the rest from them: 1 litre is a 10 cm cube, 1 kg is about the mass of a litre of water, 1 m³ is 1,000 litres. Every process above tier 2 is gated by one of the four.
2 · Make the primary length standard stable and support it correctly
Make it from the most stable material you can work — a hard, well-annealed metal — as a bar with fine marks near each end, and a cross-section shaped like an H or an X so it resists bending.
Support it at its Airy points — about 0.211 of its length in from each end — which keeps the end marks level as the bar sags under its own weight. Store it where the temperature does not change — a deep cellar — and record the temperature at every use. Everything you can make expands with heat.
3 · Realise the kilogram and store it sealed
Fill a vessel whose inside is exactly a 10 cm cube with pure, air-free water at about 4 °C — its densest — and weigh it against a metal block, filing the block until they balance. That block is the primary kilogram.
Make it from a dense metal that does not corrode easily, polish it, and never touch it with bare hands — use tongs or a clean cloth. Store it sealed against dust and moisture, which add mass.
4 · Make working copies, and never use the primary
The standard that gets handled is the standard that drifts. Build a chain:
- Primary — compared only with secondaries, rarely.
- Secondary — compared with working standards.
- Working standards — used every day in workshops.
Each copy is numbered, and its comparison with the level above is recorded. The primary never leaves its store.
5 · Compare on a schedule, and withdraw anything that drifts
A standard nobody re-checks is a belief, not a measurement. Set a schedule and keep it:
- Secondaries against the primary: yearly.
- Working standards against secondaries: monthly, or more often in heavy use.
Compare side by side, at the same temperature, with the best comparator you have. Record every result with the date and temperature in a register. Set a drift limit; any standard outside it is withdrawn and remade.
6 · Define time and temperature too
- Time: the second is 1/86,400 of a mean solar day. Keep a regulated clock and check it against local noon — the moment of the shortest shadow — averaged across the year, since noon moves by up to about a quarter of an hour through the seasons.
- Temperature: 0 °C in melting ice, 100 °C in steam from water boiling at sea level, with a correction for altitude. Calibrate every thermometer against both points.
Publish both definitions with the length and mass standards.
7 · Publish the definitions and retire the old units
A standard held privately is a monopoly on being able to make things fit. Print the definitions, the comparison procedure and the drift limits, and distribute calibrated working standards to every workshop.
Set a date after which only standard units may be used in contracts, drawings, recipes and records. Until then, allow conversion only through one printed conversion table. Local units kept alongside "for convenience" guarantee conversion errors in exactly the calculations that matter.