Cubit

For the unit of information, see qubit. For the bone, see ulna.

Cubit is the name for any one of many units of measure used by various ancient peoples. The natural cubit is based on the distance between thumb and another finger to the elbow on an average person. It was employed consistently (for example, to measure originally cords and textiles) through the Middle-Ages up to the Early Modern Times. The natural cubit measures 24 digits or 6 palms. This is about 45 cm or 18 inches (1.50 ft).

Over time, other units similar in concept to the cubit have measured:

7 palms, ~52.5 cm, or 21 inches (1.75 ft)
8 palms, ~60 cm, or 24 inches (2.00 ft)
9 palms, ~67.5 cm, or 27 inches (2.25 ft)

From late Antiquity, a Roman cubit of 16 palms (approximating the ulna, which is about 120 cm) was also used. This length is the measure from a man's hip to his fingers of the other side with a stretched arm, which was considered highly practical for quickly measuring textiles or cords over the elbow.

The English yard could be considered to be a type of cubit, measuring 12 palms, ~90 cm, or 36 inches (3.00 ft). This would be the measure from the middle of a man's body to his fingers, always with outstretched arm. (To conceive this measure as being the distance between the tip of his nose and the end of the thumb of Henry I of England is at best anecdotal and likely legendary.) The English Ell is essentially a kind of great cubit of 15 palms, 114 cm, or 45 inches (3.75 ft).

Contents

1 History of the different cubits

1.1 The Egyptian royal cubit and The Sumerian Nippur Cubit
1.2 Other important cubits

2 See also
3 External links
4 References

History of the different cubits

The Egyptian royal cubit and The 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 Egyptian royal cubit: It has been securely estabished from multiple cross referenced sources and surviving architectural evidence that a standard measure was employed as early as c. 2750 BC (Dynasty III) at Saqqara (J.P.Lauer). From the evidence this is widely accepted to have been 523.5 to 524 mm (20.61 to 20.63 in) in length, and was subdivided into 7 palms of 4 digits, giving a 28 part measure in total. This unit was used virtually unchanged for 3000 years, although some variations were seen.

The copper bar cubit of Nippur from c. 2650 BC is possibly a 'graduated rule' found by archaeologist and defines the Sumerian cubit as about 518.5 mm or 20.4 inches. It was published by Eckhard Unger in 1916, after studying the weights of the Museum of Constantinople. He interpreted it as a standard of length indicating 30-part standard of 518mm, and despite its irregularity, and the lack of any supporting textual evidence, this was, and still is, considered to be the earliest extant unit of measurement ever in existence, supposedly predating even units widely attested in Old Kingdom Egypt. The period in which this was published is notable for political and diffusionist arguments between Assyriologists and Egyptologists, so that the status of this item as a standard rule is highly questionable.

From c.2150 B.C. are two now famous statues of the Sumerian regent Gudea c.2150 B.C. found in 1880 in the excavation of Lagash by Ernest de Sarzec, which Gudea holding on his knees a rectangular writing tablet bordered with a graduated measuring rule. The two rules appear identical and indicate a 16-part measure of around 250mm, similar to a typical but short foot.

Old Egyptian geometers could not calculate the square root of two but they needed the value of the hypotenuse. The well-attested old Egyptian set square called the "construction remen" used a good approximation: 20√2 ≥ 28. The sides of this surveying instrument measured 20 digits of the Nippur cubit (about 518.5 mm) divided into 28 equal parts, that's about 20 × 18.5 mm = 370 mm, the remen measure. The digit of the sides is identical to the later Roman digit. The hypotenuse of this set square gives the old royal cubit of about 523.5 mm. (See schema image: From the Nippur ell to the old royal cubit.)

So, the old Egyptian geometers found a very good approximation for land survey. It is obvious they knew that the two digits were not identical, but a difference of only one percent is satisfactory in practice.

A shorter Egyptian rule of 6 palms may also have been employed, but based on the same 7 part standard. During Dynasty XII (1900 BC) the length of the royal cubit grew to about 529.2 mm (+1% more than the former old royal cubit). Since these times for the sides of the construction remen, the digits of the old Royal cubit were used. Therefore the ratio between the digits of the Royal cubit and the later called Roman digits is 100 to 98 exactly one. After the Egyptian length standard did not change anymore.

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.

Many other cultures used cubits as well:

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). (Cf. Biblical Archaeology Review, March-April 1983, and Newsletter and Proceedings of the Society for Early Historical Archaeology, issue 159.)

* 17.5 inches, with 25.4 mm per inch gives 444.5 mm for the Roman cubit.
Some modern metrologists consider that the English inch should be redefined officially to be hence 25.4016 mm, because an inch of 7² x 5² x 3⁴ x 2⁸ nanometres better matches with the omnipresent simple primary factors of the ancient system of measure than the current 127 x 5⁵ x 2⁶ nanometres. Just 1.6 µm more per inch, that is 8/127,000 or about 0.0063 %. That is nothing even for high-level technical precision. In practice nothing changes, but this would simplify all the theoretical values for all the ancient measures in a considerable manner.

External links

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

References

[Vormetrische Längeneinheiten] by [Rolf C. A. Rottländer], Rottenburg / Köln (also see [Search-Engine]).
[Recovery of the Ancient System Foot/Cubit/Stadion — Length Units] by [Dieter Lelgemann], acting 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."
zfv (Zeitschrift für Geodäsie, Geoinformation und Landmanagment) 128. Jahrgang, Heft 3/2003, S. 211-217.

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