Metrology

E4　—　Count them, and it comes into view

Weighing a single coin is meaningless. But weigh a hundred, and a distribution emerges. The peak of the curve is the standard the mint intended; its spread, the level of technology. Two peaks indicate a mixture of different standards. This collection of numbers speaks of both the mint's craftsmanship and fraud in the marketplace.

Supervised by: Mitsuru Hayama　／　Reading time (main text): About 8 min (3,795 characters of text at 500 chars/min; exercises and readings not included)　／　Beyond the text: 13 exercises · 4 coins · 11 readings · 1 references

What this course teaches you to do

• From the weight and fineness of one coin you can calculate the metal actually present.
• Looking at a distribution of weights, you can judge whether there is one standard or two.
• You can tell worn coins from coins light at issue by the shape of the distribution.
• You can decide how far to trust a figure written as "about 27.7 grams."
• Can explain the process by which the shekel, pound, mark, and peso evolved from units of weight into names of currencies.
• Can read and compare standards from different eras using the formula of "how many coins from a standard weight".

Lessons (8)

1. One multiplication makes the incomparable comparableWeight × fineness = pure metal. Compare by weight alone and you will always be wrong.
2. Weigh a hundred and the shape of the hill begins to speakThe peak of the hill is the mint, its spread the technique, its left tail what happened during circulation.
3. Wear and clipping give different shapesWeight alone is not enough. Pair it with diameter and the causes separate.
4. Reading the "about" in "about 27.7 grams"When you see a number, tell standard from measurement; if measured, ask the sample size.
5. Weight Becomes the Name — From the Shekel to the PesoMany major currency names originate from units of weight. These names carry memories from before the age of coinage.
6. The grammar of standards — "From a standard weight, how many pieces"Standards are written with a single grammar: "from a standard weight, how many pieces." If the number of pieces changes, the content of a single coin changes.
7. The Bimetallic Ratio — A Precarious Balance Between Two MetalsIn a bimetallic system, if the ratio is misjudged, one of the metals will disappear. The king determines the face of a coin, but the market determines its feet.
8. The Protocol for Large Numbers — The Great Buddha and the IndemnityFor huge numbers, convert the units to modern equivalents, add a range, place a yardstick alongside, and report the number along with its range.

Readings (11)

• The Coinage Act of 1792　United States　1792　The text of the Coinage Act
  The scene where a law fixed the weight down to a quarter of a grain. Read it against the failure of paper, to see why such fineness.
• The lion daalder goes out into the world　Netherlands　from 1575　A harbour in the Low Countries
  The source of the figure in §1. Check in the original the passage giving weight and fineness.
• Before the beginning　Overview: 2,700 years of the world　2000 BC　Babylonia
  Before money existed, value was weight itself. It shows that weighing was not a technique that came later.
• Gold and invasion　Japan　1588　Kyoto
  Weight 44 monme = about 165 grams. A case where monme and grams are given side by side. Watch the change of unit.
• Britain　Overview: 2,700 years of the world　the 8th century　King Offa's Penny
  Section 5. Two hundred and forty pieces from one pound of silver—the original text from an era when the pound was a unit of weight.
• Medina del Campo　Spain　1497　A mint of Castile
  Section 6. Sixty-seven pieces from one mark. The most beautiful example of the grammar of standards.
• Britain　Overview: 2,700 years of the world　AD 1717　Newton's Accident
  Section 7. The paragraph on how Newton's ratio accidentally created the gold standard.
• The copper that cast the Great Buddha　Japan　747–752　Tōdai-ji, Yamato Province
  Section 8. How the material described the range when converting 739,000 kin to 500 tons.
• Three Scales　Greece　6th century BC　The Agora of Athens
  The Aeginetan drachma was about 6.1 grams, while the Athenian drachma was about 4.3 grams. Even with the same name, the weight differed from city to city, which is why money changers' tables became a viable business.
• The standard called wu zhu　China　118 BC–AD 8　A desk weighing excavated coins
  When excavated Wuzhu coins are weighed, there is no single answer. The inscribed value, the actual weight, and the value accepted in the market. The task of tracing the discrepancies between these three is described here, in front of the actual artifacts.
• The Year 1897　Russia　1897　The Mint
  The oddly denominated 7 rouble 50 kopeck gold coin has the same weight as the old 5 rouble gold coin. Please try to follow the calculation that reveals the devaluation from its face value.

Assessment

13 exercises in this course (7 check, 0 compare, 6 written). Progress is recorded by self-assessment.

References

• A study on the manufacturing method of the ancient coins, Sangpyeong Tongbo in Korea — npj Heritage Science（2025）　Example of quantitative analysis of composition and manufacturing methods (peer-reviewed journal).

Only works and primary sources whose existence has been verified are listed.