The story of the cubits and of the talents, the great units of weight evolved from the cubits, is part of the history of the ancient and medieval Eastern Kingdoms, so intimately is it connected with their mutual relations, with their astrolatric ideas, and with the influence of those ideas on their science and art. This story, extending over more than fifty centuries, from long before the building of the Great Pyramid to near the tenth century of our era, explains the evolution of all weights and measures, ancient and modern.

The standard of the cubits has come down to us in great monuments, the measurements of which show undoubted unity of standard, and ancient histories and records often state the dimensions in the original cubits or in other cubits. Sometimes the actual wooden measures used by architects or masons are still extant; sometimes weights known to have been derived from these cubits either survive or can be ascertained. Thus in various ways the original length of the ancient cubits is known more accurately than that of many modern standards of length.

A certain record of this cubit remains in the Great Pyramid. It is known to have measured 500 cubits along each side of the base, 2000 cubits or 500 fathoms being the perimeter of the base. The measurement made by our Ordnance Surveyors gave 760 feet for the side. The latest measurement, by Mr. Flinders Petrie, is not quite 6 inches longer. Taking the Ordnance Survey figure we have (760 × 12)/500 = 18·24 inches as the length of the common cubit, and two-thirds of this gives 12·16 inches for the common foot, or the Olympic foot as it is called from the adoption of this standard by the Greeks.

This length, supported by measurements of other ancient monuments, may be regarded as certain. Four cubits or six Olympic feet were contained in the Egypto-Greek orgyia or fathom, and this measure = 72·96 inches or 6·08 feet, is exactly one-thousandth of the 6080 feet length of the Meridian or Nautical Mile.

This cubit, common to the three great ancient kingdoms, Babylonia, Egypt, and afterwards Assyria, originated probably in ChaldÆa, passing to Egypt with the earliest civilisation of that country, and thence to Greece. The name of Olympic thence attached to this standard must not make us forget its origin. The saying of Sir Henry Maine, ‘Except the blind forces of nature, nothing moves in the world which was not Greek in its origin,’ is not exact unless we include as Greek the great kingdoms conquered by Alexander, and which, under the Roman empire and afterwards under the Saracen caliphates, continued to have great influence over the civilisation of the West.

The Meridian Mile

At least sixty centuries ago the ChaldÆan astronomers had divided the circumference of the earth, and of circles generally, into 360 degrees (that is 6 × 60) each of 60 parts. There is good reason to believe that they, before the Egyptians, who had the same scientific ideas, had already measured the terrestrial meridian and determined the length of the mean degree and of its sixtieth part, the meridian mile.

Owing to the flattening of the globe towards its poles, meridian degrees are not of equal lengths; they increase in length from the equator, so that their sixtieth parts are—

The mean length is at about 49° N. where the degree and mile are—

The perimeter of the base of the Great Pyramid is exactly half of that length, i.e. 3040 feet.

The length of the meridian mile, 1000 Olympic fathoms = 4000 Olympic feet, was divided by the Greek geometers (and probably by the Egyptians and ChaldÆans long before them) into 10 stadia, each of 100 fathoms = 600 Olympic feet = 608 feet, which is about our present cable length. And the meridian or nautical mile, used by seamen of all nations, is this same Egypto-Greek mile of 6080 feet = 2026-2/3 yards = 1013-1/3 fathoms = 1·1515 statute miles. It is sometimes put at 6082-2/3 feet. French geometers estimate it at 1852·227 metres = 6076-3/4 feet, one ten-millionth of the quarter-meridian being = 1·0002 metre. The nautical mile is sometimes called a knot, in the sense of a ship going so many nautical miles in an hour, as ascertained by the number of knots of the log-line, each 1/120 of a nautical mile or 50-2/3 feet, run out in half a minute, 1/120 of an hour.

The meridian mile must not be confounded with the geographical or equatorial mile, 1/60 degree along the equatorial circumference = 6087-1/3 feet.

Greek Itinerary Measures

Though a length of 10 stadia is a meridian mile, neither the Egyptians nor the Greeks appear to have used this mile as an itinerary measure. Herodotus says:

All men who are short of land measure it by Fathoms; but those who are less short of it, by Stadia; and those who have much, by Parasangs; and such as have a very great extent, by Schoinoi. Now a Parasang is equal to 30 stadia, and each Schoinos, which is an Egyptian measure, is equal to 60 stadia.

The Parasang of 30 stadia was then 3 meridian miles, the modern marine league, 1/20 of a degree.

The Schoinos was probably common to Egypt and to ChaldÆa. The ChaldÆans venerated the numbers 6, 60, 600, &c., and their sexagesimal scale, making the year 6 × 60 + 5 days and the circle 6 × 60 degrees each of 60 minutes, has prevailed. The Olympic or Egyptian-Greek measures of distance were on this scale, though land-measures were, officially at least, on a decimal scale.

Between the Stadion and the Schoinos there is a long gap, but the Greeks, for whose small country the Stadion was a convenient unit, used, when abroad, the Persian Parasang of 3 meridian miles, = 1/7200 of the meridian circumference.

The rise of other cubits obscured the Olympic series of measures. The Schoinos became absorbed in the Parasang, and under the Roman domination it became a measure of 32 stadia or 4 Roman miles. The Stadion also came to vary; it was nearly always of 100 fathoms, but these might be fathoms of systems varying from the Olympic. The slightly different term Schoinion, meaning a rope or chain, was applied to a measure of 10 fathoms.

The Roman Mile

The Romans took for their itinerary unit a length of 8 Olympic stadia and, dividing it into 1000 paces or double steps, called it a mille (mille passus) or mile. The Roman mile and pace are therefore respectively four-fifths of the meridian mile and the Olympic fathom—

The pace was divided into 5 feet.

There was in course of time some slight variation in the length of the Roman foot. It has been calculated at between 11·65 and 11·67 inches. The best value appears to be that of Greaves at 11·664 inches, but 11·67 seems to me sufficiently accurate, and corresponding better to other Roman measures.

The pace was also divided into quarters (palmipes) of a foot and a palm.

The foot was divided into 16 digits or into 12 inches (pollices). Roman dominion over Greece and Egypt led to some modifications, probably local, in measures of distance. There was a Roman schoenus of 4 miles, and the mile was divided, sometimes into 10 Olympic stadia, sometimes into 8 Pythic stadia of 500 feet or 100 paces.

It will be seen that the English mile was originally 5000 Roman feet, and then 5000 English feet, before being fixed at its present length of 5280 feet or 1760 yards.

2. The Egyptian Royal Cubit (c. 4000 B.C.)

The possession of a geodesic cubit, 1/4 of the fathom which was 1/1000 of the meridian mile, did not satisfy the astrolatric priesthood of Egypt. Under their influence another cubit, of 7 palms = 20·64 inches, became the official measure of Egypt, and it was used in the planning of the monuments, always excepting the outside plan of the Great Pyramid.

What could have been the reason for this change, from the scientifically excellent and fairly convenient common cubit to this less convenient length, and for bringing the inconvenient number seven into the divisions and making both palms and digits different in length from those of the common cubit?

No valid reason can be found other than the desire to institute, by the side of the common cubit in which the 6 palms and 24 digits corresponded to the watches and hours of the day, a sacred cubit in which the 7 palms would correspond to the seven planets or to the week of seven days, and the 28 digits to the vulgar lunar month of four weeks of seven days.^[2] Among us, at the present day, astrology is far from being dead; the days still bear the names of the seven planets ruling successively the first hour of the days named respectively after them; we call, however unconsciously, men’s temperaments or characters according to the mercurial, jovial, saturnine and other influences of the planets which rule the hour of birth. It is not for us then to criticise severely the pious desire of a learned priesthood or of a theocratic king to institute a sacred standard of linear measure with divisions corresponding in number to the seven planets which ruled the destinies of man, whose influence ruled them through the Christian middle ages, which at the present day still rule the world in the minds of the great majority of mankind. The royal or sacred cubit became the official cubit of the Eastern great kingdoms, the common or meridian cubit being also used, not only for ordinary purposes, but sometimes along with it. Thus, the external dimensions of the Great Pyramid are in common cubits, while the unit of its internal dimensions is the royal cubit, perhaps recently established at the time of the building.^[3] And centuries after the institution of the royal cubit, the meridian cubit became the standard of the Greeks.

The question naturally arises—Why was the royal cubit not formed by simply adding a seventh palm to the common cubit, a palm of the same length, = 3·04 inches, as the six others? This would have given a new cubit of 18·24 × 7/6 = 21·28 inches, instead of 20·64 inches in 7 palms of 2·95 inches. And it will be seen that this was actually done, fifty centuries later, by the caliph Al-Mamun.

The answer I venture to give is, that the royal cubit was intended to be, not only by its division a homage to the seven planets, but also, by its increase of length, a symbol of the proportion of latitude to longitude at some Egyptian observatory.

Possibly it was a practical commemoration of the art of determining longitude. On this hypothesis the new cubit was made as much longer than the old cubit as the mean degree of latitude is longer than the degree of longitude in 29° N., at an observatory about 50 meridian miles south of the Pyramids. In that parallel, the proportion of the degree of longitude to the degree of latitude is 1:1·13, or as 18·24 to 20·64.

Measurements of monuments, both in Egypt and in the Babylonian and Assyrian Kingdoms, show that 20·64 inches was the length of the royal cubit, and actual cubit measures now extant do not vary from it more than one-or two-hundredths of an inch. There are at least ten of these cubits in museums and in other collections. One, a double cubit, is in the British Museum; another, very perfect, is in the Louvre; another, of rough graduation, but accurate length, is in the Liverpool Museum. There may be others, generally unknown. I found one, apparently unrecorded, in the museum of Avignon.

As the Pyramids are very nearly in the same parallel of latitude as the southern limits of Babylonia, near Ur of the Chaldees, it is possible that the length of the royal or sacred cubit may have been as acceptable to the priesthood of Babylonia as that of Egypt. This would account for the prevalence of the seven-palm cubit throughout the Eastern great monarchies. Perhaps the new cubit may have been instituted internationally between the Bureau des Longitudes of Egypt and that of Babylonia.

As in the case of the common cubit, two-thirds of the royal cubit were taken for the royal foot = 13·76 inches, a measure which when cubed will be seen to be the source of our Imperial system of weights and measures.

The inconvenience of a cubit of 7 palms is increased when two-thirds of it are taken for the foot; this foot, being 4-2/3 palms or 18-2/3 digits, was possibly divided for popular use into 16 digits, if it were ever in popular use. For scientific and probably for popular use it appears to have been divided into 2 feet = 10·32 inches. This may be inferred from the division of the degrees, attributed to Eratosthenes (third century B.C.), into 700 stadia, each 600 of these feet. Probably 700 is a round number, for, on the basis of this foot, the degree would be 706·8 stadia.

Three centuries later Pliny gave the base of the Great Pyramid a length of 883 feet. The modern measurement being 760 feet = 9120 inches, we have 9120/883 = 10·328 as the length of the foot in Pliny’s account, a length differing by less than 1/100 inch from that of the half-cubit.

The investigations of FrÉret, Jomard, Letronne and other mathematicians led them to the conclusion that the ancient Egyptians had surveyed their land so exactly as to know its dimensions to a cubit near, and that certainly at some unknown time they had measured an arc of the meridian and established their measures on the basis of the meridian degree with no less exactness than has been done in modern times.

I have put aside all attempts, often connected with theology, to show that the base of the Great Pyramid was 220 double cubits (of 2 × 20·61 inches), the same number as the yards in an Elizabethan furlong, or that its other dimensions were intended to hand down the English inch, or the gallon, or the squaring of the circle, or the laws of harmonic progression.

3. The Great Assyrian or Persian Cubit
(c. 700 B.C.)

The Egyptian idea of increasing the cubit appears to have also seized the Assyrian monarchy many centuries later. It was increased to 8 palms, as different from those of the Egyptian royal cubit as these were from those of the meridian cubit.

This new measure is the cubit of Ezekiel, the ‘great cubit,’ the ‘cubit and a handbreadth,’ = 25·26 inches.

The same question as that presented by the increased cubit of Egypt arises in the case of the Assyrian cubit. What reason can be suggested for an increase such as to again disturb the palm and the digit? The advantage of having a standard of 8 palms divisible into 2 feet of 4 palms, could have been obtained far more simply and conveniently by adding an eighth palm equal to the others, making it 23·6 inches, with a half giving a foot = 11·8 inches. Or two palms might have been added to the common cubit, making a new cubit = 24·32 inches, with the Olympic foot as its half.

I again venture a similar explanation. The increase from the length of the Egyptian royal cubit corresponds to the ratio of the degree of longitude to the degree of latitude in 35·5° N., i.e. 1:1·224—

This position was only 30 meridian miles from the parallel of 36° N., a line which, passing through Rhodes and Malta to the Straits of Gibraltar, was considered by the ancient geographers as the first parallel and was the base-line of their maps. It was called by the Greek geographers the ‘diaphragm of the world.’^[4]

This line passing also a few miles south of Nineveh, it is possible that some observatory near that capital city, a few miles south of 36°, may have been the point at which the difference in the lengths of the degrees of longitude and of latitude was determined for the standard length of the new cubit.

There is an alternate hypothesis. The Egyptian royal cubit was increased by 1·224 to make the Great Assyrian cubit. Now this is about the proportion in which a measure containing a certain weight of water must be increased in height to contain the same weight of wheat. This proportion, the water-wheat ratio, is something between 1·22 and 1·25, the former being the usual ratio with the heavier wheat of Southern countries. Supposing a cubical vessel measuring a royal cubit of 20·64 inches in each side, therefore containing 8792 cubic inches = 317 lb. of water (which was the Great Artaba) to be increased in height so as to hold the same weight of wheat, its height would now be 1·224 × 20·64 = 25·26 inches. This might have been taken for a new cubit.

This would not prevent the new cubit, the Great Assyrian cubit, being itself in course of time cubed to form the Den measure, as its half, the foot, was cubed for its weight of water to make the Greek-Asiatic talent.

However this be, the great Assyrian cubit, which continued to be used in the Persian empire, had the advantage of being divided into 8 palms and of making a good two-foot rule, though its half, the foot, was rather too long for popular use. This cubit exists to this day in Egypt, being the basis of the Reed or QasÁb. This is the ‘full reed of six great cubits’ (Ezek. xli.), the ‘measuring rod of six cubits by the cubit and a handbreadth,’ that is the old seven-palm cubit with a palm added. The QasÁb = 151·16 inches is = 12 Assyrian feet.

Yet, for the common purposes of life, a foot = 12·63 inches was too long to be popular; everywhere the people like a short foot, especially in the South and the East. Moreover the cubit was a departure from the simple geodesic standard of the meridian cubit. Accordingly there was devised in Persia a cubit satisfactory both to the scientific class and to the people, with a simple geodesic standard for scientific purposes and a convenient short foot for the common purposes of life. This was the BelÁdi cubit. It is perhaps the best of the cubits.

4. The BelÁdi Cubit (c. 300 B.C.)

The new Persian cubit, known as the BelÁdi (from belÁd, country), had the advantage, first, of a simple relation to the Parasang or meridian league of 30 stadia = 1/20 degree; secondly, of it being divisible into two feet of convenient length.

The meridian mile being = 6080 feet or 72,960 inches the parasang is therefore 3 × 72,960 = 218,880 inches; and the BelÁdi cubit, 1/10000 of the parasang, was therefore = 21·880 inches. This is the length that John Greaves gave in 1645 as his measurement of what he called the Cairo cubit, one of the different standards that have accumulated in Egypt during sixty centuries.

The BelÁdi cubit is still to be found in the East. A half BelÁdi cubit = 10·944 inches, a convenient foot for Eastern use, passed to Spain with the Moors and became the Burgos foot, the standard of which was allowed to go astray after the fall of the Moorish dominion. But the Spanish shore-cubit (Covado di ribera) still exists at the standard of 21·9157 inches.

The BelÁdi cubit is that used by Posidonius (131-53 B.C.). He gave the circumference of the globe as 240,000 stadia, which = 666·66 to the degree, or 11·111 to the meridian mile of 6080 feet or 72,960 inches, 72,960/11.111 = 6566 inches or 10 fathoms of 65·66465 inches, exactly 3 BelÁdi cubits or 6 half-cubits.

It is interesting to find this Greek philosopher, settled in Rome, reckoning the circumference of the globe accurately on the basis of the BelÁdi cubit of Persia. Coupling this with the use by the Hebrews of the Bereh equatorial cubit brought back from the Captivity, the date of the BelÁdi meridional cubit is evidently at some centuries before the Christian era.

The Bereh or Equatorial Land-mile.

The Jews brought back from the Captivity a measure known as the Cubit of the Talmud. It was 1/3000 of a mile, called the Bereh, which was said to be 1/24000 the circumference of the earth. Now this latter fraction corresponds to one-thousandth of an hour of longitude, or of 15 degrees on the equator, and thus points to the Bereh being an equatorial, not a meridian mile. It is still extant in the Turkish dominions in Asia. While the modern, as the ancient, Persian Parasang is 1/7200 of the meridian, the Turkish Farsang of 3 Bereh should be 3/24000 = 1/8000 of the equatorial circumference—

This corresponds very closely to the length of the farsang, which is 5483·9 yards. The Bereh, by calculation, is 1826 yards and the Talmudic cubit, 1/3000 of it, = 21·914 inches.

Each then was one 72-millionth of the terrestrial circumference, but the Talmudic cubit was measured on the equator, the BelÁdi cubit on the meridian.

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-Mamun, son of Harun 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-Mamun 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-Mamun 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.

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-Mamun 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.