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Many of the '''ancient weights and measures''' used throughout history are variations on a common theme sharing the same system. Despite a number of different civilisations making adjustments to serve their own purposes the accuracy and agreement of definitions improved over time. | |||
{{R with history}} | |||
Measurements that are used to define property are often used to impose taxes or tithes resulting in there being one measure for ordinary transactions and another for royal or religious transactions. Though throughout history people and their various representatives in guilds and lobbys, have been very scrupulous in defending the value of their possessions, governments and religions are even more scrupulous about getting their cut. | |||
The first measures were the lengths of the ditches that bordered and defined the fields. Since people tend to pace off a distance differently, knotted cords were used to measure their sides and cord stretchers became the first surveyors. | |||
== Mesopotamian system == | |||
] gradually developed as a number of associated city states. The ] number system uses a ] ], and is the origin for the division of 60 for ]s and angular ]s. The Akkadian system adopts the Sumerian. Over a period of several millenia international trade and commerce spread the idea of standards of measure based on definitions of land and property throughout the ancient near east. For a timeline of ANE civilizations, and who did business with who in the Jemdet Nasr see "The Cambridge Atlas of Mesopotamia" Michael Roaf. | |||
=== Sumerian lengths === | |||
* As a collection of city states organized like the Greeks | |||
* by gene, oinkos and phratre the Sumerians had a plethora of | |||
* multiple standards | |||
*; digits | |||
* 1 ''šusi'' little finger: 15 mm = .59" | |||
* 1 ''shusi'' ring finger: = 16.67 mm = .65" | |||
* 1 ''sheshi''index finger: = 17.67 mm = .70" | |||
* 1 ''uban'' thumb: = 20 mm (6 ''shusi'' = 5 ''uban'') | |||
*; ell of three digits | |||
* 1 short ''šusi ell'' 45 mm = 1.77" | |||
* 1 median ''shusi ell'' : = 50.01 mm = 1.97" | |||
* 1 long ''sheshi ell''= 53.01 mm 2.09" | |||
* 1 ''uban ell'' := 60 mm = 2.36 " (18 ''shusi'' = 15 ''uban'')ell | |||
*; palm of four digits | |||
* 1 short ''šusi palm'' 60 mm = 2.36" | |||
* 1 median ''shusi palm'' : = 66.68 mm = 2.63" | |||
* 1 long ''sheshi palm''= 70.68 mm 2.78" | |||
* 1 palm ''uban palm'' := 80 mm = 3.15" (24 ''shusi'' = 20 ''uban'')palm | |||
*; hand of five digits | |||
* 1 short ''šusi qat'' 75 mm = 2.95" | |||
* 1 median ''shusi qat'' : = 83.85 mm = 3.30" | |||
* 1 long ''sheshi qat'': = 88.35 mm = 3.48" | |||
* 1 thumb ''uban gat'' := 100 mm 3.94" (30 ''shusi'' = 25 ''uban'')hand | |||
*; fist of six digits | |||
* 1 short ''šusi fist'' 90 mm = 3.54" | |||
* 1 median ''shusi fist'' : = 100.02 mm | |||
* 1 long ''sheshi fist'': = 106.02 mm | |||
* 1 thumb ''uban fist'' := 120 mm 3.94" (36 ''shusi'' = 30 ''uban'')fist | |||
*; span | |||
* 1 šu-dù-a: 10 ''šusi''= 150 mm = 5.90" ('hands' + 'to stack'). | |||
* 1 ''zipaþ'' mm 10 shusi = 166.66 mm. = 6.56" | |||
* 1''zapaþ ŠU.BAD'': 10 sheshi = 176 mm. = 6.90" | |||
* 1 zipaþ = 10 uban = 200 mm = 7.87 mm | |||
*; quarter | |||
* span of outstretched thumb (uban) and little finger (šusi). | |||
* 1 '' ñušur'' = 15 ''šusi'' = 220.5 mm = 8.86" | |||
* 1 ''šu-dù-a'': 12 ''shusi'' = 250 mm = 9.84" | |||
*; foot | |||
* 1 '' ñušur'' = 20 ''šusi'' = 300 mm = 11.81" | |||
* 1 ''šu-dù-a'': 18''shusi'' = 304.8 mm = 12.14" | |||
* 1 ''šu-dù-a'': 18.5 ''shusi'' = 308.4 mm = 12.14" | |||
* 1 ''ñiš'': tool rod = 17 ''sheshi'' = 300 mm = 11.81" | |||
* 1 ''ñìri'' : foot, feet = 15 uban = 3 gat= 1/2 cubit =300 mm =11.81" | |||
* cubit | |||
* 1 ordinary cubit, ''kù'' := 6 ordinary ''qat'' = 5 long ''qat'' | |||
* 1 ''ku'' := 30 ''shusi'' = 25 ''uban'' = 500 mm | |||
* 1 ''kus'' := 36 ''shusi'' = 30 ''uban'' = 600 mm | |||
* 1 ''kùš '': 'hand' + 'arm'. | |||
*; hand and forearm, as a unit of measurement, ell/cubit | |||
* 1 ''šu-da'': 2 gat of a cubit of 5 gat divided into 30 ''shusi'' | |||
*; double remen | |||
* 1 ''ñìr'': step; way, path = 60 ''shusi'' = 50 ''uban'' =1 m | |||
* 1 kùš-numun: = 2 ÑIŠ-BAD, = 1 m | |||
* 1 ''ñidri''+ uru9, 'support'; úr, 'leg(s)';pace = 1500 mm | |||
* 1 ''ñìri...gub'': to step on 'foot' + 'to stand'= 3000 mm | |||
* 1 ''qanu'' := 6 ''ammat'' = 3600 mm ≈12 ft | |||
* 1 ''še ñiš-è-a'': harvested grain that has just been threshed and | |||
* only roughly measured with a stick | |||
* 'grain + 'stick' + 'to exit from' + nominative. | |||
* 1 ''gi'': reed; = 6 cubits = 3 meters circular + to sprout | |||
* 1 éše, éš: rope; measuring tape/cord; length measure, | |||
* 1 rope = 10 nindan rods = 20 reeds = 120 cubits | |||
* side of the ordinary ''iku'' := 60 ordinary ''kù'' = 30 m ≈ 100 ft | |||
* side of the ordinary ''iku'' := 60 ''qanu'' = 1/6 ''sos'' | |||
* side of the great ''iku'' := 60 ''qanu'' = 36 m ≈ 120 ft | |||
* 1 ''sos'' := 360 ''ganu'' = 180 m ≈ =590.55 ft | |||
* 1 ''parasang'' := 30 ''sos'' ≈ 5.4 km (≈ 3.36 miles) | |||
* 1 ''kapsu'' := 2 ''parasang'' ≈ 10.8 km (≈ 6.7 miles) | |||
=== Sumerian Area Measure === | |||
* 1 ''uzalag'' | |||
* 1 ''uzalak'': = 1/4 of an iku = 25 sar | |||
* 1 ''še'': barley; grain; = 432 square linear barleycorns = 12 square uban | |||
* 1 ''ubu'' : = 1/2 of an iku (= 50 sar). | |||
* 1 ''sar'': | |||
* 1 ''šar'': 'garden plot' = 1 square ninda | |||
* 1 square ''ninda'' = 60 surface shekels = 1/100 iku | |||
* 1 square ''ninda'' = 4 square reeds = 144 square cubits | |||
* 1 iku: = 3600 meters2 = 100 sar = 1 square 'rope' = 1/18 bùr | |||
* (plural Akk. form of ég, ék, 'levee'). | |||
* 1 éše, = 120 1/2 cubits or feet = the side of 1 square iku in area | |||
* éš: = 6 iku; leash (can be an adverbial suffix like eš) | |||
* (eš, 'much', + eš, 'much') . | |||
* nindan, | |||
* ninda: rod = 12 cubits (kùš) = 6 meters; one side of a sar | |||
* šar, 'garden plot' square measure | |||
* from Akk. middatu, mindatu, 'to measure' | |||
=== Volume Measure === | |||
* 1 gur = 1 square ninda times 1 kùš = 144 kùš3 | |||
* 1 gur = 18 cubic meters | |||
* 1 bariga = 60 gur PI or UL in Old Sumerian period | |||
* 1 bariga = 36 sìla in the Old Sumerian period | |||
* 1 bán-rig-a = 6 bán. 'the bán from picking, gleaning' | |||
* 1 èše: = 6 iku. | |||
* 1 bùr: = 18 iku = 3 éše = 1800 sar | |||
* the amount of land that supported a family | |||
* 1 bùru from Akkadian buuru IV, "hunger", | |||
* bii/eeru IV, "space, distance" | |||
* gána, gán: tract of land, field parcel; | |||
* (flat) surface, plane; measure of surface; shape, outline; | |||
* cultivation = iku = gan- field" GAN2 | |||
* 1 ma-na-tur: little mina = 1/3 shekel = 60 surface še = 720 square uban | |||
* 1 a-ñá-ri-in: a flat area measured in sar | |||
* 1 ñarim | |||
* 1 A-ñar: | |||
* 1 e5-ñar | |||
* 1 gín-tur: little shekel = 1/60 shekel = 1/3600 square nindan | |||
* 1 sar = 3 surface še = 36 square fingers | |||
* 1 sar = surface of the side of a cube of 1 sìla capacity. | |||
=== Akkadian length === | |||
* 1 ''ŠU.BAD'': 'open hand' = 12 ''šusi'' = 220 mm = 8.66" | |||
* 1 ''ammat'' cubit of 530 mm - 20.87 a unit of wheat or barley measure | |||
* 1 ''ammatu'' := 6 long ''qat''= 600 mm | |||
* 1 ''ÑIŠ-BAD'': =1 kùš. 600 mm | |||
* 1 ''UŠ'': = 6 ropes = 60 nindan rods. | |||
===Akkadian Area === | |||
* 2 ''AŠ'': = 1/2 of an iku (= 50 sar). | |||
* 1 iku: = 3600 meters2 = 100 sar = 1 square 'rope' | |||
* 1 iku = 1/18 bùr plural Akk. form of ég, ék, 'levee' | |||
* 1 éš: = 120 cubits = the side of 1 square iku in area | |||
=== Akkadian Volume === | |||
* 1 bariga = 60 sìla in the Old Akkadian and Neo-Sumerian periods. | |||
=== Mesopotamian Standards ==== | |||
* the Greek root of stadios means to stand or have standing, | |||
* to establish a standard | |||
* The Problem was that there were several different standards | |||
* In Mesopotamia there was the sos = 180 m | |||
* In Egypt the khet was 100 royal cubits | |||
* In Egypt 210 khet were an itrw or hour of travel on the river | |||
* In Egypt 300 Royal cubits were the stadia of Eratosthenes = 157.5 m | |||
* 700 to a degree at Alexandria, | |||
* In Egypt 350 Royal cubits were a Minute of March = 183.75 m | |||
* In Egypt 60 Minutes of March were an atur or Hour of March | |||
* In Persia there were stadia of 700 feet = 222 m | |||
* 500 to a degree on the equator or | |||
* This was the geographic stadia of Marianus of Tyre and Ptolomy | |||
* In Attic Greece a Milos was 8 Stadions of 600 pous = 185 m | |||
* 600 to a degree of 111 km | |||
* In Attic Greece a Milos was 8 Stadions of 600 pous = 185 m | |||
* 600 to a degree of 111 km | |||
* In Ionic Greece a Milos was 8 Stadions of 625 pous = 185 m | |||
* 600 to a degree to a degree of 111 km | |||
* In Rome a Milliare of 8 Stadiums of 625 pes = 185 m | |||
* 600 to a degree to a degree of 111 km | |||
* In England a Myle of 8 Furlongs of 625 fote = 185 m | |||
* 600 to a degree to a degree of 111 km | |||
* The ] bar ''cubit of ]'', | |||
* the oldest preserved standard bar, defines the Sumerian cubit (''kù'') | |||
* as half a ]. | |||
* This was widely used in ]. | |||
* The ]ian (or ]) cubit | |||
* was about the same size and is portrayed in a rule | |||
* on the statue of ] (], around ]) which | |||
* according to sources measures from 496 to 500 mm | |||
* 360 ordinary ''kù''= 180 m in the same range as | |||
* 1 ''stadios'', 1 Roman ''stadium'' 1/10 ] (185 m), | |||
* i.e. 1/216000 or 1/60³ the circumference of Earth. | |||
=== Mesopotamian area === | |||
* ''sar'': Garden plot (Sumerian) | |||
* 1 ''iku'':= 100 ''sar'', | |||
* 1 ''iku'' = 120 × 120 cubit² | |||
* plot of land enclosed by a boundary dike/canal”. | |||
* 1 ''bùr'':= 18 ''iku'' = 3 area ''éše'' = 1800 ''sar'' | |||
* the amount of land that supported a family | |||
=== Mesopotamian volume === | |||
* 1 ''log'':= 0.54 l | |||
* 1 ''homer'':= 720 ''log'' ≈ 390 l | |||
=== Mesopotamian weight and monetary === | |||
* 1 ''shekal'':= 8.36 g, introduced around ] | |||
* 1 ''mina'':= 60 ''shekal'' ≈ 232 g | |||
=== Mesopotamian time === | |||
* year: The Sumerians used a 360 day year by ]. | |||
* week: The ]ians introduced the seven day week, due to the belief that ] brought bad luck, so they did not want to work the seventh day. | |||
* hour: The ] 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 == | |||
=== Persian length === | |||
; 1 finger:= ¼ palm | |||
; 1 palm:= ¼ foot | |||
; 1 foot, ''zereth'':= ½ cubit | |||
; 1 cubit, ''arsani'':= 520–640 mm | |||
; 1 pace: | |||
; 1 cane:= 2 paces, 6 cubits<!--does that comma mean 'and' or 'or'?--> | |||
; 1 ''chebel'':= 40 cubits | |||
; 1 ''parasang'':= 250 ''chebel'' ≈ 6 km (6.23 km in mid-]) | |||
; 1 ''mansion'', ''stathmos''<!--Greek?-->:= 4 ''parsang'' | |||
The parasang is the distance a horse would walk in one hour. A ] ''farsang'' of ] is commonly used today in ] and ]. It is the forerunner for ]. | |||
=== Persian volume === | |||
; ''chenica'': 1.32 l, probably derived from the ]. | |||
== Egyptian system == | |||
* Much of the ]ian 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 ] and | |||
* converted it to a ] Egyptian system. | |||
* They did this by taking an ordinary ] 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). | |||
<!--This sounds like 5/6 = 6/7.--><!--The fingers change from 20 mm to 18.75 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). | |||
<!--Picture?--><!--what?--> | |||
* | |||
* | |||
* | |||
* | |||
* | |||
* 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). | |||
<!--This sounds like ''rmn'' == ''nibw''.--><!-- Yes.--> | |||
* The Romans whose uncia became the English oynch | |||
* made their remen 15" or 381 mm. | |||
<!--The Romans used the English inch? | |||
<!--No, the Egyprtians used the English Inch--> | |||
<!-- the Romans used the Uncia of 1/12 pes --> | |||
* 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, | |||
<!--(I think this is meant, but did they actually use a ''pes uncia''?)--> | |||
* 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. | |||
<!--Just showing that the sentence as is is rubbish and this is only one example. --> | |||
<!-- aren't you embarassed now that I explained it to you--> | |||
* 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. | |||
<!--and are almost useless for non-Egyptologists--> | |||
<--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 ]” rule, were also in use for breead and beer. | |||
=== Egyptian weight === | |||
* 1 ''deben'' :≈ 91 ], 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 ] | |||
=== 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 ] (ca. ]) 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 ], was approximately 1.704 mm, the smallest division ever recorded on a scale of the ]. The ] system was used. ]n ]s 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 ] or ]<!--Greek or Roman?-->, and smaller objects were weighed in similar ratios with the units of 0.871. | |||
== Greek system == | |||
The ] system was built mainly upon the Egyptian, and formed the basis of the later ]. | |||
=== Greek length === | |||
Like the ], 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. | |||
{| | |||
|+ Greek length measures and other, alledgedly related ones for comparison | |||
! Unit !! Daktylos !! Metre !! feet or podes | |||
|- | |||
! (1 "shusi"<!--Mesopotamian-->) = | |||
| 1 (little finger) ||= 14.49 mm ||= 0.05 feet or podes | |||
|- | |||
! 1 ''daktylos'' = | |||
| 1 (ring finger) ||= 19.275 mm ||= 0.06 feet or podes | |||
|- | |||
! 1 ''uncia''<!--Roman?--> ≈ | |||
|1.33 (thumb or inch)||= 25.64 mm ||= 0.08 feet or podes | |||
|- | |||
! 1 ''condylos'' = | |||
| 2 (daktylos) ||= 38.55 mm ||= 0.13 feet or podes | |||
|- | |||
! 1 ''palaiste'', palm = | |||
| 4 (daktylos) ||= 77.1 mm ||= 0.25 feet or podes (= 1 palm) | |||
|- | |||
! 1 ''dichas'' = | |||
| 8 (daktylos) ||= 154.2 mm ||= 0.51 feet or podes (= 2 palms) | |||
|- | |||
! 1 ''spithame'' = | |||
| 12 (daktylos) ||= 231.3 mm ||= 0.76 feet or podes (= 3 palms) | |||
|- | |||
! 1 ''pous'', foot = | |||
| 16 (daktylos) ||= 308.4 mm ||= 1.01 feet or podes (= 4 palms) | |||
|- | |||
! 1 ''pygon'', remen = | |||
| 20 (daktylos) ||= 385.5 mm ||= 1.26 feet or podes (= 5 palms) | |||
|- | |||
! 1 ''pechya'', cubit = | |||
| 24 (daktylos) ||= 462.6 mm ||= 1.52 feet or podes (= 6 palms) | |||
|- | |||
! 1 English cubit<!--? common 18 or alleged 19.2 inches?--> ≈ | |||
| 25 (daktylos) ||= 493.44 mm ||= 1.62 feet or podes | |||
|- | |||
! 1 Egyptian royal cubit<!--?--> ≈ | |||
| 28 (daktylos) ||= 539.7 mm ||= 1.77 feet or podes (= 7 palms) | |||
|- | |||
! 1 ''bema'' = | |||
| 40 (daktylos) ||= 771 mm ||= 2.53 feet or podes (= 10 palms = 1 double remen) | |||
|- | |||
! 1 yard<!--English?--> ≈ | |||
| 48 (daktylos) ||= 925.2 mm ||= 3.04 feet or podes (= 12 palms) | |||
|- | |||
! 1 ''xylon'' = | |||
| 72 (daktylos) ||= 1.3878 m ||= 4.55 feet or podes (= 18 palms) | |||
|- | |||
! 1 ''passus''<!--Roman?--> = | |||
| 80 (daktylos) ||= 1.542 m ||= 5 feet or podes (= 20 palms = 1 Roman Pace) | |||
|- | |||
! 1 ''orguia'' = | |||
| 96 (daktylos) ||= 1.8504 m ||= 6 feet or podes (= 24 palms = 1 fathom) | |||
|- | |||
! 1 ''akaina'' = | |||
| 160 (daktylos) ||= 3.084 m ||= 10 feet or podes (= 40 palms) | |||
|- | |||
! 1 English rod ≈ | |||
| 264 (daktylos) ||= 5.0886 m ||= 17 feet or podes (= 66 palms) | |||
|- | |||
! 1 ''hayt'' = | |||
| 280 (daktylos) ||= 5.397 m ||= 18 feet or podes (= 70 palms = 10 royal cubits) | |||
|- | |||
! 1 perch<!--English?--> ≈ | |||
| 1056 (daktylos) ||= 20.3544 m ||= 66 feet or podes (= 264 palms) | |||
|- | |||
! 1 ''plethron'' = | |||
| 1600 (daktylos) ||= 30.84 m ||= 100 feet or podes (= 400 palms) | |||
|- | |||
! 1 ''actus''<!--Roman?--> = | |||
| 1920 (daktylos) ||= 37.008 m ||= 120 feet or podes (= 480 palms) | |||
|- | |||
! ''khet'' side<!--Egyptian?--> = | |||
| 2800 (daktylos) ||= 53.97 m ||= 175 feet or podes (= 700 palms = 100 royal cubits) | |||
|- | |||
! English acre side = | |||
| 3333 (daktylos) ||= 64.359 m ||= 208.71 feet or podes (= 835 palms) | |||
|- | |||
! 1 Persian stade = | |||
| 8400 (daktylos) ||= 161.9 m ||= 525 feet or podes (= 2100 palms) | |||
|- | |||
! 1 minute<!--Roman?--> = | |||
| 9336 (daktylos) ||= 180 m ||= 300 great cubits (= 2334 palms) | |||
|- | |||
! 1 minute of march<!--Egyptian?--> = | |||
| 9500 (daktylos) ||= 183.3 m ||= 350 royal cubits (= 2450 palms) | |||
|- | |||
! 1 ''stadion'' = | |||
| 9600 (daktylos) ||= 185 m ||= 600 Greek pous (= 2400 palms) | |||
|- | |||
! 1 Roman ''stadium'' = | |||
| 9600 (daktylos) ||= 185 m ||= 625 Roman pes (= 2400 palms) | |||
|- | |||
! 1 ] ''stadios'' = | |||
| 10000 (daktylos) ||= 192.8 m ||= 625 Greek pous (= 2500 palms) | |||
|- | |||
! 1 English furlong = | |||
| 10560 (daktylos) ||= 203.544 m ||= 660 Greek pous (= 2640 palms) | |||
|- | |||
! 1 ] ''stade'', cable<!--English?--> = | |||
| 11520 (daktylos) ||= 222 m ||= 720 Greek pous (= 2880 palms) | |||
|- | |||
! 1 ''stade'' of ] = | |||
| 12000 (daktylos) ||= 231 m ||= 750 Greek pous (= 3000 palms) | |||
|- | |||
! 1 ''diaulos'' = | |||
| 19200 (daktylos) ||= 370 m ||= 1200 Greek pous (= 4800 palms) | |||
|- | |||
! 1 ''millos'' = | |||
| 80000 (daktylos) ||= 1.542 km ||= 5000 Greek pous (= 20000 palms) | |||
|- | |||
! 1 English mile ≈ | |||
| 84480 (daktylos) ||= 1.628352 km ||= 5280 English feet (= 21120 palms) | |||
|- | |||
! 1 ''dolichos'' = | |||
| 115200 (daktylos) ||= 2.221056 km ||= 7200 Greek pous (= 28800 palms) | |||
|- | |||
! 1 ''stadia'' of ] = | |||
| 280000 (daktylos) ||= 5.397 km ||= 17500 Greek pous (= 70000 palms) | |||
|- | |||
! 1/10 degree = | |||
| 560000 (daktylos) ||= 10.797 km ||= 35000 Greek pous (= 140000 palms) | |||
|- | |||
! 1 ''schœnus'' = | |||
| 576000 (daktylos) ||= 11.1024 km ||= 36000 Greek pous (= 144000 palms) | |||
|- | |||
! 1 ''stathmos'' = | |||
| 1280000 (daktylos) ||= 24.672 km ||= 80000 Greek pous (= 320000 palms) | |||
|- | |||
! 1 degree = | |||
| 5760000 (daktylos) ||= 111 km ||= 360000 Greek pous (= 1440000 palms) | |||
|} | |||
; 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 ]. There are variations, from 296 mm (]) to 326 mm (]) | |||
; 1 ''pugon'', ]ic 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 '']'' (pl. ''stadia'') := 6 ''plethra'' = 600 ''podes'' ≈ 185.4 ]. | |||
; 1 ''diaulos'' (pl. ''diauloi'') := 2 ''stadia'', only used for the Olympic footrace introduced in ]. | |||
; 1 ''dolikhos'' := 6 or 12 ''diauloi''. Only used for the Olympic footrace introduced in ]. | |||
; 1 ''parasanges'' := 30 ''stadia'' ≈ 5.5 km. Persian measure used by ], for instance. | |||
; 1 ''skhoinos'' (pl. ''skhoinoi''), lit. “reefs” : 60 ''stadia'' ≈ 11.1 km (usually), based on ] ''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 ] 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 '']'' := 60 ''minae'' | |||
; 1 '']'' := 100 ''drachmae'' | |||
; 1 ''decadrachm'' := 10 ''drachmae'', coin only | |||
; 1 ''tetradrachm'' := 4 ''drachmae'', coin only | |||
; 1 ''stater'', ''didrachmon'' := 2 ''drachmae'', coin only | |||
; 1 '']'' := 4.5–6 g, weight of silver coin | |||
; 1 ''diobolus'' := 2 ''oboloi'' = 1/3 ''drachmae'' | |||
; 1 '']'' := 1/6 ''drachma'', silver | |||
; 1 '']'' := 1/8 ''obolus'', copper | |||
=== Greek miscellaneous === | |||
; ''muriade'': 10.000 | |||
== Roman system == | |||
The ] 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 ] ≈ 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 ]). | |||
=== 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 ''pes''³ = 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 ''pes''³ = 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 ]. | |||
=== 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 ] which were in use from ] to ]. The earliest bronze coins of Rome ] to ] 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. | |||
# uncia | |||
# sextans | |||
# quadrans | |||
# trians | |||
# quincunx | |||
# semis | |||
# septunx | |||
# bes | |||
# dodrans | |||
# dextans | |||
# deunx | |||
# as | |||
One and a half ounce was called ''sescuncia''. | |||
=== Roman time === | |||
; year: The ] 365¼ day year was introduced in ]. | |||
== Vedic system == | |||
Vedic measures were first used by the ]n ], and are still in use today – primarily for religious purposes in ] and ]. | |||
''See also:'' ] | |||
== Chinese system == | |||
The traditional units used in Imperial ] (市制 ]: Shìzhì, “city standard”) are used to this day, albeit now rounded and bound to ] units. | |||
''See also:'' ] | |||
== Arabic system == | |||
The ]ic 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 ]'' | |||
== 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=== | |||
* | |||
===Egypt=== | |||
* | |||
* | |||
* | |||
* | |||
* | |||
* | |||
===Greece=== | |||
* | |||
* | |||
===General=== | |||
* | |||
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* | |||
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] | |||
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] | |||
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] |
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