5. The Black Cubit (Ninth Century)
Many centuries after the institution of the Assyrian great cubit and of the Persian Beládi cubit, another important cubit became a standard of measure in the Moslem caliphate which reigned over the lands of the Eastern great kingdoms.
Under Al-Mamūn, son of Harūn al-Rashid, science was flourishing in the East, while the West was in the dark ages, at least in all the countries unenlightened by the civilisation of the Moors of Spain. Of Christian Europe, Provence and the other Occitanian countries alone had that light, a light that shone over other countries until extinguished by the Albigensian crusade.
‘Mahmd Ibn Mesoud says that in the time of Almamon (the learned Calife of Babylon) by the elevation of the pole of the equator, they measured the quantity of the degree upon the globe of the earth, and found it to be 56-2/3 miles, every mile containing 4000 cubits, and each cubit 24 digits, and every digit 6 barleycorns, and every barleycorn 6 hairs of a camel’ (‘A Discourse of the Romane Foot and Denarius,’ by John Greaves, Professor of Astronomy in the University of Oxford, 1647).
From this determination of 56-2/3 meridian miles to the degree of longitude it would appear, (1) that the measurement was made at about 20·1°; south of Mecca, (2) that the meridian mile was still of 4000 Egyptian common cubits or 1000 Egyptian fathoms.
It was then probably after this measurement that Al-Mamūn instituted his new Cubit, sometimes known as the Black cubit, so named from the black banner and dress adopted by the Abbaside caliphs.
This new cubit was not, directly at least, of geodesic basis. The caliph was probably inspired by the idea of making in a reasonable manner the alteration which the ancient Egyptians had done badly in making their seven-palm cubit out of simple proportion to the common cubit. So the new cubit had palms and digits of the same length as the common cubit. But it had all the inconveniences of the factor seven. Perhaps Al-Mamūn may have thought that the addition of a seventh palm was not only a homage to the seven planets but that it was satisfactory to lengthen the common cubit in the ratio of the degree of latitude to that of longitude in a part of his dominions where the ratio was exactly 7 to 6. This is the ratio at Alexandria, in 31° N.
| The Common cubit being | = 18·24 | inches | = 6 × 3·04 in. |
| The Black cubit was | = 21·28 | „ | = 7 × 3·04 in. |
Two-thirds of this cubit were taken for
The Black foot = 14·186 inches, divided into 16 digits of the 24 digits or qiráts of the cubit.
This cubit and foot are still in use. The old nilometer on the island of Al-Rauzah (Rode) near Cairo has its scale in cubits of this standard, and measurement of the worn scale gives 21·29 inches for the cubit.
The cubit and foot of Al-Mamūn are the basis of measures and of weights which spread from Egypt to every country in Europe.
The story of the five cubits, ancient and medieval, has shown that they were all derived, directly or indirectly, from the meridian measurement of the earth, some of them being probably instituted with the desire to make them representative of the relation of latitude and longitude.
I venture to say that every measure and weight used throughout the world has been developed from one of these cubits and thus, more or less directly, from the Egyptian meridian cubit. The Republican system of France is but a decimal imitation of the system based on the common Egyptian meridian cubit; its basis being the kilometre, 1/10000 of the quarter-meridian, instead of the Egyptian meridian mile, 1/(90 × 60) of the quarter-meridian.
There were some other cubits of minor importance; one of them is the Hashími cubit described in [Chapter XVII].
Comparative Lengths of the Five Ancient Cubits
| Egyptian | common | cubit | = 18·24 | in.; | its foot | 2/3 = 12·16 | in. |
| „ | royal | „ | = 20·64 | „ | „ | 2/3 = 13·76 | „ |
| Great Assyrian | „ | = 25·26 | „ | „ | 1/2 = 12·63 | „ | |
| Beládi | „ | = 21·888 | „ | „ | 1/2 = 10·944 | „ | |
| Black | „ | = 20·28 | „ | „ | 2/3 = 14·186 | „ | |
[2]. Plutarch speaks of the mystic connexion assumed by the Egyptians between the 28 cubits maximum rise of the Nile and the same number of days in the lunar month.
[3]. The royal cubit is sometimes called the Philiterian cubit; this name (apparently meaning ‘royal’) is used by the later Hero of Alexandria, who wrote about 430. But Herodotus says, ‘They call the pyramids after a herdsman Philition who at that time grazed his herds about that place’; so it is probable that the name came from some legend.
[4]. Διάφραγμα τῆς ὀικουμένης. Instituted by Dicæarchus 310 B.C., corrected by Eratosthenes 276-196.
CHAPTER III
THE STORY OF THE TALENTS
It has been seen that throughout the ancient Eastern Kingdoms, from soon after 5000 B.C. to some centuries after our era, there was general unity in the system of linear measures. It will now be seen that there was similar unity in the system of weights and measures, all derived from some well-known linear standard cubed. In modern times this unity is much less apparent, but yet it can be traced, and it survives with little change in the great part of the world where the English system of weights and measures remains as an inheritance from the most ancient epochs of civilisation.
The 400 shekels of silver, currency of the merchants, that Abraham weighed to Ephron about 1900 years B.C. were probably of about the same weight as 400 half-crowns of the present day.
When Moses levied 100 talents and 1775 shekels, at the rate of half a shekel on each of the 603,550 men who were numbered (Exod. xxxviii.), the weight of the silver shekels can be precisely ascertained.
603550/2 = 301,775 shekels = 100 talents and 1775 shekels.
The Talent was the weight of an Egyptian royal cubic foot of water and was divided into 3000 shekels.
The royal foot, 2/3 of the cubit, = 13·76 inches.
The foot cubed = 2605 cubic inches; 2605/27·73 = 93·9 lb. as the calculated weight of the standard afterwards known as the Alexandrian talent.[[5]]
The actual weight was 93·65 lb. = 655·550 grains; 655550/3000 = 218·5 grains was the weight of the shekel, nearly our half-ounce—exactly the half-ounce of Plantagenet times, and very near to the weight of our half-crown, which weighs 218·18 grains.
The difference between calculated weight and the actual weight determined from coin or other standards, from trustworthy historical statements and other sources of information or of evidence, is generally due to the great difficulty in constructing accurately the cubical vessel used to ascertain the weight of a cubed measure of water. A difference of 2/100 of an inch in the sides of the vessel made to hold a royal cubic foot of water would make a difference of about 3 parts in 1000, of 4-1/2 of the 1500 ounces or double-shekels of water it contained. And we do not know the temperature of the water used.
From the ancient and medieval cubits were derived all the weights and measures of medieval and modern civilisation, largely through the medium of the talents derived from these standards.
| From | the | Egyptian | common | foot | came | the | Olympic Talent | |
| „ | „ | „ | royal | „ | „ | „ | Alexandrian | „ |
| „ | „ | Great Assyrian | „ | „ | „ | Greek-Asiatic | „ | |
| „ | „ | Arabic | „ | „ | „ | Arabic | „ | |