Science Fair Project Encyclopedia
Ancient weights and measures
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.
- 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
- sar – Garden plot (Sumerian)
- iku – "Plot of land enclosed by a boundary dike/canal", 100 sar. Probably 120 ·120 cubit²
- log – 0.54 l
- homer – 720 log
Weight and monetary
- shekal – 8.36 g, introduced around 3000 BC
- mina – 60 shekal
- 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.
The Persian system had influence on the Greek system. During the Persian occupation of Egypt, the Persian cubit was sometimes used there, too.
The ghalva (stadion) and parasang were much used as a land measure. There are significant uncertainty, though.
- finger – 1 / 4 palm
- palm – 1 / 4 foot
- zereth – Foot, 1 / 2 cubit
- arsani – Cubit, 52.0 up to 64.0 cm
- cane – 2 paces, 6 cubits
- chebel – 40 cubits
- stadion – Forerunner to Greek and Egyptian stadion, presumably around 264 m
- 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.
- schoinos – Origin of Greek and Egyptian measures
- mansion – Equivalent to "stathmos", 4 parsang
- chenica – 1.32 l, probably basis of the Greek cheonix
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. Note also the cubit and remen which has a ratio that constitutes an irrational number. 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.
- 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, 1 / 4 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
- remen – 1 / 2 double remen
- remen digit – 1 / 20 remen
- khet – Senus, 100 Royal cubit, also jet, hayt
- stadion – 400 Royal cubits, 209.2 m
- parasang – 10000 Royal cubits
- schoinos – Presumably the "common atur", 12000 Royal kubits or 6.3 km.
- iter – Royal river measure (pl. iteru or itrw), also atur or ater. 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.
- setat – 100 · 100 Royal cubit², also aura
- jata – 100 setat, is said to be used to this day.
- remen – 1 / 2 setat
- hebes – 1 / 4 setat
- sa – 1/8 setat
- hekat – 1 / 30 Royal cubit³, 4.8 l, used for grain. Was divided into fractions of 1/2, 1/4, 1/8, 1/16, 1/32 and 1/64 by an "Eye of Horus" rule.
- oipe – Alt. 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
- deben – 91 g, normally of copper, but also silver, gold and probably lead. Also used as money.
- qedety – 1/10 deben
- year – The 365 day year was introduced by 2773 BC
- 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°, 5 1/4 seked is 53.13°, 5 1/2 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.
The Greek system was built mainly upon the Egyptian, and formed the basis of the later Roman system.
- 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, 1 / 4 pous
- dikhas – 1 / 2 pous
- spithame – Span, 3 / 4 pous
- pugon – Homeric cubit, 5 / 4 pous
- pechua – Cubit, 3 / 2 podes, 47.4 cm
- bema – Pace, 5 / 2 podes
- khulon – 9 / 2 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.
- kotule – Liquid measure, (pl. kotulai), 1 / 4 kheonix
- kheonix – Alt. 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 –
- talent – 60 mina
- mina – 100 drachma
- decadrachm – Coin only, 10 drachma
- tetradrachm – Coin only, 4 drachma
- stater – Coin only, also didrachm, 2 drachma
- drachma – Weight of silver coin, 4.5 to 6 g
- diobol – 1 / 3 drachma
- obolo – 1 / 6 drachma, silver
- khalkoi – 1 / 8 obolo, copper
- muriade – 10.000
The Roman system of measurement was built on the Greek system with Egyptian influences. The Roman units were generally accurate and well documented.
|Roman unit||Latin name||Roman Feet||Metric Equivalence||Imperial Equivalence|
|one digit||digitus||1 / 16||18.525 mm||0.72933 in|
|one palm||palmus||1 / 4||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.
one square foot
1 / 14 400
~ 875 cm²
one square perch
1 / 144
~ 8.75 m²
one aune of furrows
1 / 30
~ 42 m²
1 / 4
~ 315 m²
~ 1260 m²
~ 2520 m²
~ 5040 m²
~ 50.4 ha
~ 201.6 ha
The Roman acre is the squared Roman arpent.
This egal 14 400 squared feet or about 0.126 hektar,
more exactly one, almost: 1264.673 square metres.
- Liquid measures :
1 / 48
~ 11.2 mL
1 / 12
~ 45 mL
1 / 6
~ 90 mL
1 / 3
~ 180 mL
1 / 2
~ 270 mL
one double third-sester
2 / 3
~ 360 mL
~ 540 mL
~ 3.25 L
~ 13 L
~ 26 L
~ 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.
- Dry measures :
1 / 128
~ 67.5 mL
1 / 64
~ 135 mL
1 / 32
~ 270 mL
1 / 16
~ 540 mL
1 / 2
~ 4.67; L
~ 8.67 L
~ 26 L
Like the jar, the Roman bushel or "quadrantal" is one cubic foot.
Its almost 26.027 liters. The third part of this quadrantal is the Roman peck.
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.
1 / 48
1 / 18
1 / 6
1 / 3
All the multiples of the Roman ounce have their proper names.
One and a half ounce was called by Romans : "sescuncia".
- See also: Vedic units of time
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
The Arabic system is based on the Persian system.
- assbaa – Finger, 1 / 4 palm
- cabda – Palm, 1 / 4 foot
- foot – Base unit, 0.32 m
- arsh – Cubit, traditionally 2 feet, new definition 3 / 2 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
See Hebrew weights
- 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
- 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
- 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
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