Cubit

<nowiki>Insert non-formatted text here<nowiki>Insert non-formatted text here<nowiki>Insert non-formatted text here<nowiki>Insert non-formatted text here<nowiki>Insert non-formatted text here[[Media:Insert non-formatted text here]][[Media:<math>Example.ogg</math>[ == http://www.example.com link title == [[[http://www.example.com link title]]]]]]</nowiki></nowiki></nowiki></nowiki></nowiki>:For the unit of information, see qubit. For the bone, see ulna. Template:Vitruvian Man Measurements Cubit is the name for any one of many units of measure used by various ancient peoples and is among the first recorded units of length.

The cubit is based on measuring by comparing – especially cords and textiles, but also for timbers and stones – to one's forearm length. The Egyptian hieroglyph for the unit shows this symbol. It was employed consistently through Antiquity, the Middle-Ages up to the Early Modern Times.

The distance between thumb and another finger to the elbow on an average person and measures about 24 digits or 6 palms or 1½ foot. This is about 45 cm or 18 inches. This so-called "natural cubit" of 1½ foot is used in the Roman system of measures and in different Greek systems.

Over time, units similar in type to the cubit have measured: sex From late Antiquity, the Roman ulna, a four-feet-cubit (about 120 cm) is also attested. This length is the measure from a man's hip to the fingers of the outstretched opposite arm.

The English yard could be considered to be a type of cubit, measuring 12 palms, ~90 cm, or 36 inches (3.00 ft). This is the measure from the middle of a man's body to his fingers, always with outstretched arm. The English ell is essentially a kind of great cubit of 15 palms, 114 cm, or 45 inches (3.75 ft).

History of the different cubits

The Egyptian Royal Cubit and Sumerian Nippur cubit

From the Nippur ell to the old royal cubit

The cubit is among the first recorded units of length used by an ancient people.

The earliest attested standard measure was called the Royal Cubit and was 523.5 to 524 mm (20.61 to 20.63 inches) in length, and was subdivided into 7 palms of 4 digits, giving a 28 part measure in total. Secure evidence for this unit is known from architecture, from at least as early as the construction of the Step Pyramid of Djoser from around 2,700 B.C.

This unit was used virtually unchanged throughout the Egyptian dynastic period, and is evidenced into the 1st millennium B.C.

In 1916, during the last years of Ottoman Empire and in the middle of WWI the German assyriologist Eckhard Unger found a copper-alloy bar during excavation at Nippur from c. 2650 BC. which he claimed was a measurement standard. This irregularly formed and irregularly marked graduated rule supposedly defined the Sumerian cubit as about 518.5 mm or 20.4 inches, although this does not agree with more secure evidence from the statues of Guduea from the same region. A 30-digit-cubit known a a kus was nevertheless known from the 2nd millenium B.C., with a digit-length of about 17.28 mm (more than 0.68 inch).

Old Egyptian geometers could calculate the square root of two from the value of the hypotenuse of a Cubit. This well-attested old Egyptian unit was known as the "construction remen" and used a good approximation: 2×20/28 ≥ root 2.

Other important cubits

• The Roman cubitus is a six-palms-cubit of about 444.5 mm. Twenty-four Roman cubits equal thirty-five English feet. So, the Roman cubit is defined to be 17.5 inches exactly one.*

• The Greek pechua (πεχυα) was also a 24-digit-cubit. So, the Greek Kyrenaika Cubit measured about 463.1 mm and the Greek Metrios Cubit about 474.2 mm; respectively 25/24 and 16/15 Roman cubits. Other Greek cubits based on different digit measures of other city-states are less important. The Greek 40-digit-measure, called bema, corresponds to the Latin gradus, the step or half-a-pace.

• The Arabic Hashimi Cubit of about 650.2 mm (25.6 inches) is considered to measure two French feet. Since the established ratio between the French and English foot is 16 to 15 (the small error of about 0.086 % is owed to imperfect standards, not-adjusted mutually), one can give following equation:  5 Hashimi cubits = 10 French feet = 128 English inches. Also the length of 256 Roman cubits and the length of 175 Hashimi cubits are equivalent.

• The Guard Cubit (Arabic: ammatu rabitu) measured about 555.6 mm; 5/4 of the Roman cubit. Therefore:  96 Guard cubits equal 120 Roman cubits equal 175 English feet.

• The Arabic Nil Cubit (or Black Cubit) measured about 540.2 mm. This means 28 (later called) Greek digits of the "Pous of Kyrenaika" equal to 25/24 of a Roman foot or just 308.7 mm. Thus 175 Roman Cubits equal 144 Black Cubits.

• The Mesopotamian cubit measured about 533.4 mm, 6/5 Roman cubit. Thus, 20 Mesopotamian cubits equal 24 Roman cubits equal 35 English feet.

• The Babylonian cubit (or cubit of Lagash) measured about 496.1 mm. Also a Babylonian trade cubit existed, nine tenth of the normal cubit, i.e. 446.5 mm. The Babylonian Cubit is fifteen sixteenths of the Royal cubit. 160 Babylonian trade cubits equal 144 Babylonian cubits equal 135 Egyptian Royal cubits. (The Royal cubit is equal to 529.2 mm. See above).

• The Pergamon cubit 520.9 mm or 75/64 of the Roman cubit.
• The Salamis cubit 484.0 mm or 98/90 of the Roman cubit.
• The Persian cubit of about 500.1 mm or 9/8 of the Roman cubit, which is also 9/10 of the Guard cubit.

• In Izapa, a Precolumbian Mesoamerican city, the measuring unit was equivalent to about 495 mm, very close to the Lagash cubit. This is probably a coincidence, since a diffusion of culture from Mesopotamia to Mesoamerica has not been conclusively demonstrated.
• The different Jewish cubits (אַמָּה ama) are generally borrowed either from Babylonians or Greeks or Romans. In ancient Israel during the First Temple period, the cubit was 428.1 mm (= 26/27 Roman cubit). During the Second Temple period, a cubit of about 444.5 mm (= Roman cubit) was in general use, but in the sacred areas of the temple a special cubit of 437.6 mm seems to have been used instead (= 63/64 Roman cubit).

 *  17.5 inches, with 25.4 mm per inch gives 444.5 mm for the Roman cubit.

Synopsis with 7-smooth values

Please note the information below is highly speculative, and is not included in any mainstream publications on the metrology of antiquity.

Since several years, modern historical metrologists increasingly prefer to use defined, idealistic, 7-smooth values for the old measures of length. This only constitutes a modern, over-all-rounding, clearly inside the scientific coefficient of variation ±0.17% determinated by statistical researches; that give 296.2 ±0.5 mm for the Roman foot. The defined value for the idealistic Roman foot equals 296.352 mm. That gives clear, plain, conventional values. This doesn't assert that old Roman metrologists determinated their measures up to micrometre precisions.

Name of the cubit	Idealistic Length in mm	Type of the cubit	Ratio vs. Roman Digit	Digit Length	Foot Length	Name of the foot (l.c. means later called)
Hashimi Cubit	650.28096	Nibw = 32 digits	192 : 175	20.32128	325.14048	l.c. French Foot
Guard Cubit	555.66000	Kus = 30 digits	1 : 1	18.52200	296.35200	l.c. Roman Foot
Arabic Nil-Cubit	540.22500	Neilos = 28 digits	35 : 36	18.00750	288.12000	l.c. Polnish Foot
Mesopotamian Nil-Cubit	533.43360	Neilos = 28 digits	36 : 35	19.05120	304.81920	l.c. English Foot
Royal Cubit	529.20000	Neilos = 28 digits	50 : 49	18.90000	302.40000	Egyptian Foot
Old Royal Cubit	523.88127	Neilos = 28 digits	10 : 7√2	18.71005	299.36007	Old Egyptian Foot
Nippur cubit	518.61600	Kus = 30 digits	14 : 15	17.28720	276.59520	Nippur Foot
Persian Cubit	500.09400	Persikos = 25 digits	28 : 27	20.00376	320.06016	Arabic Foot
Babylonian Cubit	496.12500	Kus = 30 digits	25 : 28	16.53750	264.60000	Pous Italikos
Old Trade Cubit	449.04109	Pechys = 24 digits	10 : 7√2	18.71005	299.36007	Old Egyptian Foot
Greek pechys metrikos	474.16320	Pechys = 24 digits	16 : 15	19.75680	316.10880	l.c. Austrian Foot
Roman cubit	444.52800	Pechys = 24 digits	1 : 1	18.52200	296.35200	l.c. Roman Foot
Remen cubit	370.44000	Pygon = 20 digits	1 : 1	18.52200	296.35200	l.c. Roman Foot

1. In the table above, solely the irrational Old Royal Cubit and Old Trade Cubit values  – as well as their digit and foot values –  are rounded.
2. The contemporary, legal value of the English foot is doubtless 304.8 mm. The ratio to the 7-smooth idealistic English foot is 15875 : 15876.
   In the context of the ancient measures and their precision, the resulting difference of just about +0.0063% is effectively "of no significance".

See also

• Systems of measurement
• History of measurement
• Units of measurement

References

• Vormetrische Längeneinheiten by Rolf C. A. Rottländer, Rottenburg / Köln (also see Search-Engine).
• Recovery of the Ancient System of Length Units by Dieter Lelgemann, former Director of the Institute for Geodesy and Geo-Information Technology, TU Berlin.
• On the Ancient Determination of Meridian Arc Length by Eratosthenes of Kyrene Dieter Lelgemann, WS – History of Surveying and Measurement, Athens, Greece, May 22-27, 2004.
• Knobloch, Eberhard, Dieter Lelgemann und Andreas Fuls: "Zur hellenistischen Methode der Bestimmung des Erdumfangs und zur Asienkarte des Klaudios Ptolemaios." published in zfv (Zeitschrift für Geodäsie, Geoinformation und Landmanagment) 128. Jahrgang, Heft 3/2003, S. 211-217.

External links

• Measurements of the Nippur Ell, now in a museum in Istanbul (Turkey).