Ancient weights and measures
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Introduction
Many systems of weights and measures have existed throughout history in different civilisations. The definitions of some of these units are often regarded as vague and inaccurate. True enough, although the roots of many of the units were the same, the actual value of a unit differed from civilization to civilization, or epoch to epoch. That fact should not lead to a conclusion that historical units of measure were inaccurate in general. Many units were defined to a high precision, and standards of measurement and tracking were in many cases excellent. As a case in point, the Great Pyramid of Giza was built to a precision of 0.015 m over sides that are 235 meters, over four and a half thousand years ago.
Mesopotamian system
Mesopotamia includes a number of cultures. The Sumerian number system uses a base 60 positional notation, and is the origin for the division of 60 for hours and angles.
Length
- kù
- Cubit (Sumerian). Akkadian ammatu. The copper bar cubit of Nippur, the first known standard bar, defines the Sumerian cubit as about 518.5 mm, widely used in third millennium BC. It was split in 30 digits. The Babylonian (or Salamis) cubit was around 484 mm.
- foot
- Defined as 264.6 mm by Sumerian ruler Gudea of Lagash around 2575 BC, this is the oldest preserved standard of length.
- digit
- 1/16 foot or 1/30 cubit
- stadion
- 148.5 m
- parasang
- Babylonian league is 5.6 km
Area
- sar
- Garden plot (Sumerian)
- iku
- "Plot of land enclosed by a boundary dike/canal", 100 sar. Probably 120 · 120 cubit²
Volume
- log
- 0.54 l
- homer
- 720 log
Weight and monetary
- shekal
- 8.36 g, introduced around 3000 BC
- mina
- 60 shekal
Time
- year
- The Sumerians used a 360 day year by 2100 BC.
- week
- The Babylonians introduced the seven day week, due to the belief that seven brought bad luck, so they did not want to work the seventh day.
- hour
- The 12 hour day and 12 hour night originates from Mesopotamia. The length of these hours changed through the year, being equally spaced over the time of light and dark, respectively.
Persian system
Length
- finger
- ¼ palm
- palm
- ¼ foot
- zereth
- Foot, ½ cubit
- arsani
- Cubit, 52.0 up to 64.0 cm
- cane
- 2 paces, 6 cubits
- chebel
- 40 cubits
- parasang
- The distance a horse would walk for one hour, 250 chebel, approx. 6 km. (6.23 km in mid 19th century. In today's Iran as well as Turkey, a metric farsang of 10 km is commonly used. Forerunner for league.
- mansion
- Equivalent to stathmos, 4 parsang
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 system. The Egyptians based their measurements on the Royal cubit, for which the pharaoh devised a standard (master) cut in granite. From these standards, it is clear that accuracies in measurements of at least 1/16 yeba (1 mm) were possible. The Egyptian system was also noteworthy in having units for volume derived from the standard for length. While the Royal cubit is a very well defined unit, uncertainty is connected to the units for land measurement, especially when the Greek stadion and schoinos units came in use.
Length
- meh nesut
- Royal cubit, 52.3 cm, varied by less than 0.5 cm through the times.
- shesep
- Width of palm, alt. shep, 1/7 Royal cubit. It is speculated that the fraction of 1/7 may have been so that a reasonable pi could be made of 22 shesep over 1 cubit.
- yeba
- Digit, also zebo, ¼ palm, logically enough
- thumb
- 4/3 yeba, or 2.49 cm. Basis for the Roman uncia and later, the inch.
- meh scherer
- Forearm, basically 6 / 7 Royal cubit. Also known as the common cubit, used by commons and not as precise.
- double remen
- Approx. 72.3 cm, the length of the diagonal of a Royal cubit square. (Because the hypotenuse of a square is the side × the square root of 2 (an irrational number), an exact decimal value for the remen in terms of Royal cubits cannot be given.)
- remen
- ½ double remen
- remen digit
- 1/20 remen
- khet, also jet, hayt
- Senus, 100 Royal cubit
- stadion
- 400 Royal cubits, 209.2 m
- parasang
- 10000 Royal cubits
- schoinos
- Presumably the "common atur", 12000 Royal kubits or 6.3 km.
- iter, also atur or ater
- Royal river measure (pl. iteru or itrw). 20000 Royal cubits, or 10.46 km. The units parasang, schoinos and ater seems to be often interchanged. The book of Herodotus clearly states the Egyptian mile as twice a Persian parasang, i.e. 20000 Royal cubits.
Area
- setat, also aura
- 100 × 100 Royal cubit²
- jata
- 100 setat, is said to be used to this day.
- remen
- ½ setat
- hebes
- ½ remen
- sa
- ½ hebes
Volume
- hekat
- 1/30 Royal cubit³, 4.8 l, used for grain. Was divided into fractions of ½, ¼, 1/8, 1/16, 1/32 and 1/64 by an "Eye of Horus" rule.
- oipe, also ipet
- 4 hekat
- jar
- 5 oipe
- hinu
- 1/10 hekat, used for perfume as well as grain.
- ro
- 1/32 hinu
- des
- For liquids, approx. 0.5 l
- secha
- For beer
- hebenet
- For wine
Weight
- deben
- 91 g, normally of copper, but also silver, gold and probably lead. Also used as money.
- qedety
- 1/10 deben
Time
- year
- The 365 day year was introduced by 2773 BC
Miscellaneous
- seked
- Unit of inclination, also seqt. 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°.
- shaty
- 1/6 silver deben or 1/3 lead deben
Indus Valley system
The people of the Indus 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 1.704mm, 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.
Length
- pous
- Foot (pl. podes), 31.6 cm, said to be 3/5 Egyptian Royal cubit. There are variations, from an Ionic foot is 29.6 cm to a Doric foot that is 32.6 cm
- daktulos
- Digit (pl. daktuloi), 1 / 16 pous
- condulos
- 1/8 pous
- palaiste
- Palm, ¼ pous
- dikhas
- ½ pous
- spithame
- Span, ¾ pous
- pugon
- Homeric cubit, 1¼ pous
- pechua
- Cubit, 1½ podes, 47.4 cm
- bema
- Pace, 2½ podes
- khulon
- 4½ podes
- orguia
- Fathom, 6 podes
- akaina
- 10 podes
- plethron
- Cord measure, (pl. plethra), 100 podes
- stadion
- (pl. stadia), 6 plethra, i.e. 600 podes. Usually stated as 185.4 m. 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.
- diaulos
- (pl. diauloi), 2 stadia. Only used for the Olympic footrace introduced in 724 BC.
- dolikhos
- 6 or 12 diauloi. Only used for the Olympic footrace introduced in 720 BC.
- parasanges
- Persian measure, 30 stadia, 5.5 km. Used by Xenophon, for instance.
- skhoinos
- Lit. "reefs" (pl. skhoinoi), based on Egyptian river measure iter or atur. Usually defined as 60 stadia or 11.1 km. There are variants, see Egyptian atur.
- stathmos
- One days journey, roughly 25 km. May have been variable, dependent on terrain.
Volume
- kotule
- Liquid measure, (pl. kotulai), ¼ kheonix
- kheonix, alsp khoinix
- (pl khoenikes), approx. 1.1 l. Initially used for wheat.
- modios
- Bushel, 8 kheonikes
- medimnos
- 48 kheonikes
- kotule
- Dry measure, 6 kuathoi
- khous
- Dry measure, 12 kotulai
- metretes
- Dry measure, 12 choes, approx. 34 l
Weight and monetary
- Medimnos
- ~25 kg
- Talent
- 60 minae
- Mina
- 100 drachmae
- Decadrachm
- Coin only, 10 drachmae
- Tetradrachm
- Coin only, 4 drachmae
- Stater
- Coin only, also didrachmon, 2 drachmae
- Drachma
- Weight of silver coin, 4.5 to 6 g
- Diobolus
- (two oboloi) 1/3 drachmae
- Obolus
- 1/6 drachma, silver
- Chalkos
- 1/8 obolus, copper
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.
Length
| Roman unit | Latin name | Roman Feet | Metric Equivalence | Imperial Equivalence |
|---|---|---|---|---|
| one digit | digitus | 1/16 | 18.525 mm | 0.72933 in |
| one palm | palmus | ¼ | 7.41 cm | 2.92 in |
| one foot | pes | 1 | 29.64 cm | 11.67 in |
| one cubit | cubitus | 1½ | 44.46 cm | 17.50 in |
| one step | gradus | 2½ | 0.741 m | 2 ft 5 in |
| one pace | passus | 5 | 1.482 m | 4 ft 10.3 in |
| one perch | pertica | 10 | 2.964 m | 9 ft 8.7 in |
| one arpent | actus | 120 | 35.568 m | 116 ft 8 in |
| one stadion | stadium | 625 | 185.25 m | 607 ft 9 in |
| one mile | milliarium | 5000 | 1.482 km | 0.9209 mi |
| one league | leuga | 7500 | 2.223 km | 1.381 mi |
In Antiquity the Roman foot was not divided into inches, i.e. twelve shares.
Area
| Roman unit | Latin name | Acres | Equivalence |
|---|---|---|---|
| one square foot | pes quatratus | 1/14 400 | ~ 875 cm² |
| one square perch | scripulum | 1/144 | ~ 8.75 m² |
| one aune of furrows | actus minimus | 1/30 | ~ 42 m² |
| one rood | clima | ¼ | ~ 315 m² |
| one acre | actus quadratus | 1 | ~ 1260 m² |
| one yoke | iugerum | 2 | ~ 2520 m² |
| one morn | heredium | 4 | ~ 5040 m² |
| one centurie | centuria | 400 | ~ 50.4 ha |
| one "quadruplex" | saltus | 1600 | ~ 201.6 ha |
The Roman acre is the squared Roman arpent. This equals 14 400 square feet or about 0.126 hectares, more exactly almost 1264.673 square metres.
Volume
| Roman unit | Latin name | Sesters | Equivalence |
|---|---|---|---|
| one spoonfull | ligula | 1/48 | ~ 11.2 mL |
| one dose | cyathus | 1/12 | ~ 45 mL |
| one sixth-sester | sextans | 1/6 | ~ 90 mL |
| one third-sester | triens | 1/3 | ~ 180 mL |
| one half-sester | hemina | ½ | ~ 270 mL |
| one double third-sester | cheonix | 2/3 | ~ 360 mL |
| one sester | sextarius | 1 | ~ 540 mL |
| one congius | congius | 6 | ~ 3.25 L |
| one urn | urna | 24 | ~ 13 L |
| one jar | amphora | 48 | ~ 26 L |
| one hose | culleus | 960 | ~ 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 unit | Latin name | Pecks | Equivalence |
|---|---|---|---|
| one drawing-spoon | acetabulum | 1/128 | ~ 67.5 mL |
| one quarter-sester | quartarius | 1/64 | ~ 135 mL |
| one half-sester | hemina | 1/32 | ~ 270 mL |
| one sester | sextarius | 1/16 | ~ 540 mL |
| one gallon | semodius | ½ | ~ 4.67; L |
| one peck | modius | 1 | ~ 8.67 L |
| one bushel | quadrantal | 3 | ~ 26 L |
Like the jar, the Roman bushel or "quadrantal" is one cubic foot. It's almost 26.027 liters. The third part of this quadrantal is the Roman peck.
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 AD 296. The earliest bronze coins of Rome 338 BC to 268 BC were 0.273 kg.
| Roman unit | Latin name | Drachms | Equivalence |
|---|---|---|---|
| one chalcus | chalcus | 1/48 | 0.071 g |
| one siliqua | siliqua | 1/18 | 0.189 g |
| one obolus | obolus | 1/6 | 0.57 g |
| one scruple | scrupulum | 1/3 | 1.14 g |
| one drachm | drachma | 1 | 3.4 g |
| one shekel | sicilicus | 2 | 6.8 g |
| one ounce | uncia | 8 | 27.25 g |
| one pound | libra | 96 | 327 g |
| one mine | mina | 128 | 436 g |
All the multiples of the Roman ounce have their proper names.
- uncia
- sextans
- quadrans
- trians
- quincunx
- semis
- septunx
- bes
- dodrans
- dextans
- deunx
- as
One and a half ounce was called by Romans sescuncia.
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, and changed to a divisor of 10 instead of the traditional 16.
- See also: Chinese units
Arabic system
The Arabic system is based on the Persian system.
Length
- assbaa
- Finger, ¼ palm
- cabda
- Palm, ¼ foot
- foot
- Base unit, 0.32 m
- arsh
- Cubit, traditionally 2 feet, new definition 1½ feet
- orgye
- Pace, 6 feet
- qasab
- Cane, 12 feet
- seir
- Stadion, 600 feet
- ghalva
- 720 feet
- farasakh
- League, from parasang, 18000 feet, 5.76 km.
- barid
- 4 farasakh
- marhala
- 8 farasakh
Hebrew
See Hebrew weights
See also
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 (http://www.dubsar.com/nippur/rrannex.html)
Egypt
- Measuring length in Ancient Egypt (http://www.petrie.ucl.ac.uk/digital_egypt/weights/lenght.html)
- Egyptian units (http://gopher.ulb.ac.be/~pcara/hobbies/egypres.pdf)
- Egypt unidades, pesos e medidas (http://www.educ.fc.ul.pt/docentes/opombo/seminario/rhind/medida.htm)
- Las Matemáticas en el Antiguo Egipto (http://www.egiptologia.org/ciencia/matematicas/unidades.htm)
- Irrational numbers and pyramids (http://www.thehallofmaat.com/maat/print.php?sid=39)
- Sekeds and the Geometry of the Egyptian Pyramids (http://www.kch42.dial.pipex.com/sekes.htm)
Greece
- Greek measure (http://www.tulane.edu/~august/H310/handouts/Coinage.htm)
- More on the schoinos (http://www.chufu.de/Strabon/21-25.htm)
General
- Dictionary of Units of Measurement (http://www.unc.edu/~rowlett/units/)
- Units of measure (http://www.sizes.com/)
- Unit systems (http://unicon.netian.com/unitsys_e.html)
- Mile measurements (http://www.kb.nl/kb/resources/frameset_kb.html?/kb/skd/skd/mathemat.html)
- Old units of measure (http://www.du.edu/~jcalvert/tech/oldleng.htm)
- Measures from Antiquity and the Bible (http://members.aol.com/JackProot/met/antbible.html)
- Alte Längenmaße und ihre Bedeutung (http://www.j-lorber.com/Texte/Masse.html)
- Projekt zur Erschliessung historisch wertvoller Altkartenbestände (http://ikar.sbb.spk-berlin.de/werkzeugkasten/sonderregeln/4_3.htm)de:Alte Maße und Gewichte