Standard weight
Give every market a balance whose readings can be checked and a set of reference weights within published tolerances, held to a master by an office that verifies, stamps and re-inspects them.
Everything for this step
- Field guide
- Institutions: what to found, and how to run them → 32 sections
- Builds
- None yet.
- Reference sheets
- None.
- Sciences it rests on
- Physics · Mathematics
- Track
- Money, credit and capital, level 2 of 5 · next: Double entry and the auditable enterprise
Why this matters
Before coins, value is weighed: grain, salt, metal. A trade is fair only if the balance and the weights agree everywhere, so the balance and a set of reference weights come before money. Modern legal metrology still works this way. The OIML's international recommendation sets the largest error each class of weight may carry: a 1 kg trade weight of class M1 may be off by at most ±50 mg, of class M2 by ±160 mg and of class M3 by ±500 mg (OIML R 111-1).
The frauds are as old as the market — a light weight, a second set for buying, a bent beam — and each has a rule against it: a master standard, verification and a stamp, and inspection without warning.
The shape of it
- Build an equal-arm balance and test it: a load must be balanced by the same weights whichever pan it is in.
- Make weights in a fixed series, such as 1, 2, 2, 5 × 10ⁿ, with an adjusting cavity sealed after adjustment.
- Adjust each weight against the master to its class: a 1 kg M2 weight within ±160 mg.
- Keep a master set that is never used for trade, and compare the working sets with it on a schedule.
- Verify and stamp every trade weight and balance, and record the stamp in a register.
- Re-verify every year and inspect markets without warning.
- Name the frauds in the law — light weights, double sets, false balances — with the penalty for each.
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 · Build an equal-arm balance and test it by transposition
An equal-arm balance is a straight beam on a hard, sharp pivot at its centre, with a pan hanging from each end at equal distances and a pointer over a scale. Make the pivot and the pan hangers from the hardest metal the smith can give, and the beam stiff enough not to bend under full load.
Test it by transposition, the procedure NIST still publishes for equal-arm balances (NIST SOP 6): weigh a standard against the test weight and read the pointer; swap the two loads between the pans and read again; then add a small known weight to one pan and read a third time to find how far one unit of mass moves the pointer. Unequal arms move both readings the same way, while a difference between the weights moves them in opposite directions; half the difference of the two readings therefore cancels the arms and leaves the difference between the weights. It does not cancel a steady drift of the balance, so make the readings promptly.
2 · Make the weights in a fixed series
A weight set covers every load with few pieces. OIML R 111-1 allows sets built from these sequences of nominal values, each repeated for every power of ten:
- 1, 1, 2, 5
- 1, 1, 1, 2, 5
- 1, 2, 2, 5
- 1, 1, 2, 2, 5
With 1, 2, 2, 5 g, any whole number of grams from 1 to 10 can be made up. R 111 names the materials for class M: brass for the small weights (below 100 g, or below 5 kg in class M1) and grey cast iron for the larger ones up to 50 kg. Give each a shape that sits steadily and is easy to grip, with the nominal value cast or struck into the face.
3 · Adjust each weight against the master
Cast each weight slightly light, then add to it. For trade weights of classes M1–M3 from 100 g to 50 kg, R 111-1 requires an adjusting cavity — a hole closed by a plug — no larger than one quarter of the weight's volume, and about half empty after the first adjustment, so later adjustments are possible. Weights of 1–10 g are solid with no cavity.
Adjust by adding lead shot or filings to the cavity, comparing with the master by transposition after each addition, until the weight is within its class (R 111-1, Table 1):
| Nominal value | M1 | M2 | M3 | |---|---|---|---| | 10 kg | ±500 mg | ±1,600 mg | ±5,000 mg | | 1 kg | ±50 mg | ±160 mg | ±500 mg | | 100 g | ±5 mg | ±16 mg | ±50 mg | | 10 g | ±2 mg | ±6 mg | ±20 mg | | 1 g | ±1 mg | ±3 mg | ±10 mg |
Below 100 g the tolerance no longer shrinks in step with the weight: a 1 g weight is allowed a far larger share of its mass than a 1 kg one. Close the cavity with its plug and seal it with lead driven into the groove round the plug.
4 · Keep a master set, and compare down the chain
Three levels, each checked against the one above: a master set held by the office and used only to check working standards; working standards used to verify traders' weights; and the traders' weights themselves. R 111-1 requires the uncertainty of each calibration to be no more than one third of the weight's tolerance, so the checking weight must be markedly better than the weight it checks.
Store the master sealed, dry and at steady temperature, as standard units does for the national kilogram, and record every comparison with its date and result.
5 · Verify, stamp and register
No balance or weight is used in trade until the office has verified it. On verification:
- Stamp the weight's control mark into the lead seal of its adjusting cavity — on the base of a weight with no cavity — so it cannot be re-adjusted without destroying the mark (R 111-1, clause 16.4). Stamp the balance too, with the office's mark and the year.
- Register each item: owner, nominal value, class, result and stamp.
- Refuse anything outside tolerance until it is adjusted and resubmitted.
Write the classes, tolerances and stamping rules into the published law, so every trader and buyer can know them.
6 · Inspect without warning, and name the frauds
Re-verify every trade weight and balance every year, and send inspectors into the markets unannounced with working standards, to check a sample on the spot.
Name each fraud in the law with its penalty and the rule against it:
- Light weights: stamped, sealed cavities and spot checks.
- Two sets (heavy for buying, light for selling): only stamped weights may be in a trader's possession.
- A false balance (unequal arms, a weighted pan): the transposition test at every inspection.
Pay inspectors from public funds, never from the traders they inspect, and rotate them between markets.