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Paid in gold dust of 360 Babylonian talents (= 468 Attic talents). At a gold - silver ratio of 1-13 this yields an equivalent in silver of 4,680 Babylonian talents.

Source: Herodotus III. 90-96 and cf.

A. R. Burn, Persia & the Greeks (New York, 1962), pp. 123-126.

Persian volume

chenica

1.32 l, probably derived from the Greek cheonix.

Egyptian system

• Much of the Egyptian system of measurement is based on the Mesopotamian.
• The Egyptian system in its turn formed the basis of the later Greek and Roman systems while
• those in turn influenced later European systems.

• The Egyptians took a sexagesimal Mesopotamian system and
• converted it to a septenary Egyptian system.
• They did this by taking an ordinary cubit of five gat,
• measuring 30 šusi or 25 uban (ca. 500 mm),
• and a great cubit of 6 gat, measuring 36 šusi or 30 uban (ca. 600 mm), and
• making the former 6 šsp (6 palms with 24 db = 450 mm) and
• making the latter 7 šsp (7 palms with 28 db = 525 mm).

<--! Yes.-->

• The best and clearest evidence is found on Egptian ceremonial rulers
• where it is carved in stone and where
• even those not fluent in reading hieroglyphic writing
• can observe the mh or foot cubit glyph
• spanning 15 fingers (3 hands) and 16 fingers (four palms = 300 mm).
• fingers, palms, hands, fists, feet, remen
• cubit divided into fingers and hands
• modern replica
• wooden ruler
• Egyptian cubit rods

• In the first image the ceremonial ruler identifies the foot cubit mh
• across 15 and 16 fingers allowing a foot to be measured in palms or hands
• the remen the nibw glyph above 20 fingers (5 palms = 1 remen = 375 mm).
• The Romans whose uncia became the English oynch
• made their remen 15" or 381 mm.

• 1 digitus = 1/16 pes ≈ 18.5 mm,
• 1 pes = 1 Ionic pous ≈ 296 mm,
• 15/16 pes = 15 digiti ≈ 278 mm,
• 15/12 pes = 20 digiti ≈ 370 mm,
• 381 mm ≈ 1.29 pes ≈ 20.6 digiti because the remen is the hypotenuse of a 3:4:5 triangle
• The Egyptians solved seked problems using rise and run to define the angle of a slope
• and in at least one case at saqqara to define the arc of a circle.

• The cubit of the inscription grids foot holds a stylus and that of the nibw
• is shown spanning 18 fingers (three fists) and 19 fingers on this ruler.

Egyptian length

• 1 ro := ½ db
• 1 rwy := 2/3 db
• 1 hmt rw := ¾ db
• Egyptian measures are systematic to this standard but
• on actual measuring rods and artifacts may vary ≈ +/- 1 mm per cubit
• 1 finger, db: = 18¾ mm
• 1 palm, šsp := 4 db = 75 mm
• 1 hand, drt := 5 db = 93¾ mm
• 1 fist, amm := 6 db = 112½ mm
• 1 span, spd := 12 db = 225 mm
• 1 foot, bw := 16 db = 300 mm
• 1 remen, rmn := 20 db = 375 mm
• 1 ordinary cubit, mh := 6 šsp = 450 mm
• 1 royal cubit, mh := 7 šsp = 525 mm
• 1 nibw := 8 šsp = 600 mm
• 1 double remen := 2 rmn = 750 mm
• 1 rod, h3yt := 10 mh (royal) = 5.25 m
• 1 ht, ht n nhw := 10 h3yt = 52.5 m
• 1 minute of march := 350 mh (royal) = 183.75 m
• 1 hour of march, atur, itrw := 21,000 mh (royal) ≈ 11 km

• Egyptian rulers vary from rough wooden sticks scored in fingers or palms
• to elaborate stone rulers.

• On the later rulers the db or finger units of 18.75 mm
• are individually named and divided into both unit fractions or ro.
• On the lower register a few special fractions like the rwy or 2/3 and
• the hmt rw or ¾, which are the only two non unit Egyptian fractions, are also shown.
• Other divisions are named as well.

• The lengths are from measures of surviving rulers with the caveat that
• the Egyptians of the 3rd millenium were not working to an accuracy of 2 decimal places.

• The bw or foot is marked with the glyph mh for forearm or cubit spaced across the
• division between 15 and 16 fingers with 15 fingers being 3 hands and 16 fingers 4 palms.

• The remen (5 palms) is interesting in that if it is the hypotenuse of a triangle (3:4:5) * and one of the sides is a foot (4 palms or 3 hands), then the other side is a span (3 palms), * similarly if the ordinary cubit is used as the short side (3)
• then the double remen (10 palms) can be the long side (5) and
• the nibw (8 palms) becomes the middle side (4).

• The next multiple used by the Egyptians was the h3yt or rod
• of 10 royal cubits as in the Mesopotamian system.
• 10 h3yt were used as a ht of 100 cubits or ht n nhw
• a rod of cord to mark the side of an 3ht or field
• the Greek aroura or area is literally h3 t3 or a thousand of land.

• For longer distances the Egyptians used a minute of march of 350 royal cubits and
• an atur (hour of march) or itrw (river journey) of 21,000 royal cubits.

• Horus Eye fractions were used for bread and beer.

Egyptian area

• 1 st3t spd := 1/5 st3t, a field of sides 100 spd ≈ 500 m²
• 550 m², 5625 ft²
• 1 st3t mh bw := 1/3 st3t, a field of sides 100 mh bw ≈ 900 m²
• 916_2/3 m², 10,000ft²
• 1 st3t remen := 1/2 st3t, a field of sides 100 remen ≈ 1400 m²
• 1375 m², 15,000 ft²
• 1 st3t khet : a field of sides 100 ordinary cubits 2000 m² 21,000 ft²
• 1 st3t : a field (3ht) of sides
• 100 royal cubits or 1 ht n nhw ≈ 2750 m² 30000 ft²

• The unit names come from “Gardiner Egyptian Grammar” § 266 and
• are informed by Gillings Mathematics in the time of the Pharoahs chapter 20.

<--Egyptian standards of measure are our standards of measure in an early form-->

Egyptian volume

• 1 hekat, hk3t := 1/30 royal cubit³ ≈ 4.8 l, used for grain
• 1 oipe, ipet := 4 hekat ≈ 19 l
• 1 jar := 5 oipe ≈ 96 l
• 1 hinu := 1/10 hekat ≈ 0.48 l, used for perfume as well as grain
• 1 ro := 1/32 hinu ≈ 0.015 l
• 1 des :≈ 0.5 l, for liquids
• secha : for beer
• hebenet : for wine
• Fractions of ½, ¼, 1/8, 1/16, 1/32 and 1/64 hekat,
• by an “Eye of Horus” rule, were also in use for breead and beer.

Egyptian weight

• 1 deben :≈ 91 g, normally of copper, but also silver, gold and probably lead.
• Also used as money.
• 1 qedety := 1/10 deben
• shaty: 1/6 silver deben or 1/3 lead deben

Egyptian time

• year: The 365 day year was introduced by 2773 BC

Egyptian calculation of slope by unit rise and run

• seked, seqt: Unit of inclination. Indicates horizontal dimension
• measured in palms (and digits fractions as necessary) per vertical Royal cubit rise,
• e.g. 5 seked is 54.46°, 5¼ seked is 53.13°, 5½ seked is 51.84°.

Indus Valley system

The people of the Indus Valley Civilization (ca. 2600 BC) achieved great accuracy in measuring length, mass, and time. They were among the first to develop a system of uniform weights and measures. Their measurements were extremely precise. Their smallest division, which is marked on an ivory scale found in Lothal, was approximately 1.704 mm, the smallest division ever recorded on a scale of the Bronze Age. The decimal system was used. Harappan engineers followed the decimal division of measurement for all practical purposes, including the measurement of mass as revealed by their hexahedron weights. Weights were based on units of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with each unit weighing approximately 28 grams, similar to the English ounce or Greek uncia, and smaller objects were weighed in similar ratios with the units of 0.871.

Greek system

The Greek system was built mainly upon the Egyptian, and formed the basis of the later Roman system.

Greek length

Like the Mesopotamian units, where the cubit or ku was divided into two different digits (shusi of about 17 mm or uban of about 20 mm) and hands (qat), the Greek units also have long, median and short forms.

Generally the sexagesimal or decimal multiples have Mesopotamian origins while the septenary multiples have Egyptian origins.

1 daktulos (pl. daktuloi), digit

= 1/16 pous

1 condulos

= 1/8 pous

1 palaiste, palm

= ¼ pous

1 dikhas

= ½ pous

1 spithame, span

= ¾ pous

1 pous (pl. podes), foot

≈ 316 mm, said to be 3/5 Egyptian royal cubit. There are variations, from 296 mm (Ionic) to 326 mm (Doric)

1 pugon, Homeric cubit

= 1¼ podes

1 pechua, cubit

= 1½ podes ≈ 47.4 cm

1 bema, pace

= 2½ podes

1 khulon

= 4½ podes

1 orguia, fathom

= 6 podes

1 akaina

= 10 podes

1 plethron (pl. plethra)

= 100 podes, a cord measure

1 stadion (pl. stadia)

= 6 plethra = 600 podes ≈ 185.4 m.

1 diaulos (pl. diauloi)

= 2 stadia, only used for the Olympic footrace introduced in 724 BC.

1 dolikhos

= 6 or 12 diauloi. Only used for the Olympic footrace introduced in 720 BC.

1 parasanges

= 30 stadia ≈ 5.5 km. Persian measure used by Xenophon, for instance.

1 skhoinos (pl. skhoinoi), lit. “reefs”

60 stadia ≈ 11.1 km (usually), based on Egyptian river measure iter or atur, for variants see there.

1 stathmos

≈ 25 km, one day’s journey. May have been variable, dependent on terrain.

For reference, the stadion at Olympus measures 192.3 m. With a widespread use throughout antiquity, there were many variants of a stadion, from as low as 157 m up to 211 m, but it is usually stated as 185.4 m.

Greek volume

1 kotule (pl. kotulai)

= ¼ kheonix, liquid measure

1 khœnix (pl khœnikes), khoinix

≈ 1.1 l, initially used for wheat

1 modios, bushel

= 8 kheonikes

1 medimnos

= 48 kheonikes

Dry measures:

1 kotule

= 6 kuathoi

1 khous

= 12 kotulai

1 metretes

= 12 choes ≈ 34 l

Greek weight and monetary

1 medimnos

≈ 25 kg

1 talent

= 60 minae

1 mina

= 100 drachmae

1 decadrachm

= 10 drachmae, coin only

1 tetradrachm

= 4 drachmae, coin only

1 stater, didrachmon

= 2 drachmae, coin only

1 drachma

= 4.5–6 g, weight of silver coin

1 diobolus

= 2 oboloi = 1/3 drachmae

1 obolus

= 1/6 drachma, silver

1 chalkos

= 1/8 obolus, copper

Greek miscellaneous

muriade

10.000

Roman system

The Roman system of measurement was built on the Greek system with Egyptian influences. The Roman units were generally accurate and well documented.

Roman length

1 digit, digitus

= 1/16 pedes ≈ 18.5 mm

1 palm, palmus

= ¼ pedes = 4 digiti ≈ 74 mm

1 foot, pes

= 1 Ionic pous ≈ 296 mm

1 cubit, cubitus

= 1½ pedes = 24 digiti ≈ 444 mm

1 step, gradus

= 2½ pedes ≈ 740 mm

1 pace, passus

= 5 pedes = 2 gradi ≈ 1.480 m

1 perch, pertica

= 10 pedes = 2 passūs ≈ 2.960 m

1 arpent, actus

= 120 pedes = 12 perticæ ≈ 35.52 m

1 stadion, stadium

= 625 pedes = 125 passūs ≈ 185 m = 1 Greek stadion

1 mile, milliarus

= 5000 pedes = 1000 passūs = 8 stadii ≈ 1.480 km

1 league, leuga

= 7500 pedes = 1½ milliari ≈ 2.22 km

The Roman pes (foot) was first divided into 12 uncia (inches) or 16 digiti (fingers) by the Ionian Greeks (see Greek orders of architecture).

Roman area

1 pes = 296 mm

1 square foot, pes quatratus ≈ 876.16 mm²

1 square perch, scripulum = 1 pertica quadrata ≈ 8.76 m²

1 aune of furrows, actus minimus = 1/30 actus quadratus ≈ 42 m²

1 rood, clima = ¼ actus quadratus = 36 scripuli ≈ 315.42 m²

1 acre, actus quadratus ≈ 1261.67 m²

1 yoke, iugerum = 2 actūs quadratus ≈ 2523.34 m²

1 morn, heredium= 2 iugera ≈ 5,046.64 m²

1 centurie, centuria = 100 heredia ≈ 504,664 m²

1 “quadruplex”, saltus = 4 centuriæ ≈ 2,018,656 m²

Roman volume

Roman liquid volume

1 spoonfull, ligula

= ¼ cyathus ≈ 11.2 ml

1 dose, cyathus

= ½ sextans ≈ 45 ml

1 sixth-sester, sextans

= 1/6 sextarius ≈ 90 ml

1 third-sester, triens

= 1/3 sextarius ≈ 180 ml

1 half-sester, hemina

= ½ sextarius ≈ 270 ml

1 double third-sester, cheonix

2/3 sextarius ≈ 360 ml

1 sester, sextarius

≈ 540 ml

1 congius

= 6 sextaria = (½ pes)³ ≈ 3.25 l

1 urn, urna

= 4 congii = ½ amphora ≈ 13 l

1 jar, amphora

= 1 pes³ = 8 congii ≈ 26 l

1 hose, culleus

= 20 amphoræ ≈ 520 l

The Roman jar, so-called “amphora quadrantal” is the cubic foot. The congius is half-a-foot cube. The Roman sester is the sixth of a congius.

Roman dry volume

1 drawing-spoon, acetabulum

= ½ quartarius ≈ 67.5 ml

1 quarter-sester, quartarius

= ¼ sextarius ≈ 135 ml

1 half-sester, hemina

= ½ sextarius ≈ 270 ml

1 sester, sextarius

= 1/16 modius ≈ 540 ml

1 gallon, semodius

= ½ modius ≈ 4.67 l

1 peck, modius

= 1 ≈ 8.67 l

1 bushel, quadrantal

= 1 pes³ = 3 modia ≈ 26 l

Like the jar, the Roman bushel or “quadrantal” is one cubic foot. It is almost 26.027 liters. The third part of this quadrantal is the Roman peck.

Roman weight

The Roman units of weight varied significantly throughout the times, since most of the standards were obtained from the weight of particular coins. The values listed are based on the gold aureus of Augustus which were in use from 27 BC to 296 AD. The earliest bronze coins of Rome 338 BC to 268 BC were 273 g.

1 chalcus

= 1/8 obolus ≈ 0.071 g

1 siliqua

= 1/3 obolus ≈ 0.189 g

1 obolus

= ½ scrupulum ≈ 0.57 g

1 scruple, scrupulum

= 1/3 ≈ 1.14 g

1 drachm, drachma

≈ 3.4 g

1 shekel, sicilicus

= 2 drachmæ ≈ 6.8 g

1 ounce, uncia

= 4 sicilici ≈ 27.25 g

1 pound, libra

= 12 unciæ ≈ 327 g

1 mine, mina

= 16 unciæ ≈ 436 g

All the multiples of the Roman ounce have their proper names.

1. uncia
2. sextans
3. quadrans
4. trians
5. quincunx
6. semis
7. septunx
8. bes
9. dodrans
10. dextans
11. deunx
12. as

One and a half ounce was called sescuncia.

Roman time

year

The Julian calendar 365¼ day year was introduced in 45 BC.

Vedic system

Vedic measures were first used by the Indian Vedic civilization, and are still in use today – primarily for religious purposes in Hinduism and Jainism.

See also: Vedic units of time

Chinese system

The traditional units used in Imperial China (市制 Pinyin: Shìzhì, “city standard”) are used to this day, albeit now rounded and bound to SI units.

See also: Chinese units

Arabic system

The Arabic system is based on the Persian system.

Arabic lLength

1 finger, assbaa

= ¼ palm

1 palm, cabda

= ¼ foot

1 foot

≈ 0.32 m

1 cubit, arsh

= 2 feet traditionally, 1½ feet later

1 pace, orgye

= 6 feet

1 cane, qasab

= 12 feet

1 stadion, seir

= 600 feet

1 ghalva

= 720 feet

1 league, farasakh

= 18000 feet ≈ 5.76 km, from parasang

1 barid

= 4 farasakh

1 marhala

= 8 farasakh

Hebrew

See Hebrew weights

See also

• Megalithic yard
• Weights and measures
• Medieval weights and measures

References

• Measure for Measure, Richard Young and Thomas Glover, ISBN 1-889796-00-X.
• Masse und Gewichte, Marvin A. Powell
• The Civilisation of Ancient Egypt, Paul Johnson

External links

Mesopotamia

• Mesopotation bibliograpy

Egypt

• Measuring length in Ancient Egypt
• Egyptian units
• Egypt unidades, pesos e medidas
• Las Matemáticas en el Antiguo Egipto
• Irrational numbers and pyramids
• Sekeds and the Geometry of the Egyptian Pyramids

Greece

• Greek measure
• More on the schoinos

General

• Dictionary of Units of Measurement
• Units of measure
• Unit systems
• Mile measurements
• Old units of measure
• Measures from Antiquity and the Bible
• Alte Längenmaße und ihre Bedeutung
• Projekt zur Erschließung historisch wertvoller Altkartenbestände