MEN AND MEASURES

MEN AND MEASURES

A HISTORY OF

WEIGHTS AND MEASURES

ANCIENT AND MODERN

BY

EDWARD NICHOLSON, F.I.C., F.C.S.

SURGEON LIEUT.-COLONEL ARMY MEDICAL DEPARTMENT

AUTHOR OF ‘A MANUAL OF INDIAN OPHIOLOGY’

‘THE STORY OF OUR WEIGHTS AND MEASURES’ ‘FLOURETO DE PROUVÈNÇO’ ETC.

LONDON

SMITH, ELDER & CO., 15 WATERLOO PLACE

1912

[All rights reserved]

ERRATA.

PREFACE

This history is the development of a short story of the Imperial System of Weights and Measures published eleven years ago, but withdrawn when this fuller work took shape. To have made it at all complete would have required a long lifetime of research; to give and discuss every authority, to trace, even to acknowledge, every source of information would have unduly swollen the volume and slackened the interest of the narrative. I offer it with all its shortcomings as an attempt to show the metric instincts of man everywhere and in all time, to trace the origins and evolution of the main national systems, to explain the apparently arbitrary changes which have affected them, to show how the ancient system used by the English-speaking peoples of the world has been able, not only to survive dangerous perturbations in the past, but also to resist the modern revolutionary system which has destroyed so many others less homogeneous, less capable of adaptation to circumstances.

E. N.

Feb. 1912.

TABLE OF CONTENTS

MEN AND MEASURES

CHAPTER I
GENERAL VIEW

The earliest measures were those of length, and they were derived from the rough-and-ready standard afforded by the limbs of man.

The readiest of these measures were those offered by the length of the forearm, and by parts of the hand; these formed a natural series of far-reaching importance.

These arm-measures were—

1. The Cubit, the length of the bent forearm from elbow-point to finger-tip, about 18 to 19 inches.

2. The Span, the length that can be spanned between the thumb-tip and little finger-tip of the outstretched hand. It is nearly half of the cubit, about 9 inches.

3. The Palm, the breadth of the four fingers, one-third of the span, one-sixth of the cubit, about 3 inches.

4. The Digit or finger-breadth at about the middle of the middle finger, one-twelfth of the span, one-twenty-fourth of the cubit = 3/4 inch.

From this division of the cubit into 6 palms and 24 digits, and of its half, the span, into 12 digits, came the division of the day into watches and hours, of the year into months; came also the consecration of the number 12 in legend, history, and social institutions—came in short duodecimalism wherever we find it.

Add to the above measures the outstretch of the arms, the fathom, we have the five primitive limb-lengths.

A time came when civilisation required the fixing of a standard cubit. It was perhaps at first an arbitrary standard, but it became fixed by law in the most ancient Eastern Kingdoms and, about the fortieth century before the Christian era, perhaps much earlier, certainly by the time of the Egyptian fourth dynasty, it had been fixed at a length known for certain to be equal to 18·24 English inches.

This was no arbitrary standard, any more than that of the English yard or the French metre. I may say that, apart from parochial varieties and convenient trade-units, always referable to some recognised standard, there are no arbitrary standards in any country; all have a directly scientific basis or a lineage reaching, perhaps far back, to a scientific basis. They may have deviated, by carelessness, or even by petty fraud, from some accepted standard, but wholesale trade has always been a conservator of standards.

There is not the slightest doubt that the common cubit of ancient Egypt, brought probably from Chaldæa, was deduced from the measurement of the earth, from the quarter-meridian distance between the pole and the equator. There are no written records of this measurement; but an imperishable monument remained to record it, and other ancient monuments still remain to corroborate this testimony. The base of the Great Pyramid was, from ancient times, always known to be 500 cubits long on each side, and it is found to be exactly half a meridian mile, or 500 Egyptian fathoms, in perimeter.

There is no doubt that the wise men of the ancient Eastern Kingdoms had great astronomical knowledge and were capable of making the necessary meridian measurement.

Bailly (author of ‘Histoire de l’Astronomie,’ 1775-1787) wrote:

The measurement of the earth was undertaken a vast number of ages ago in the times of primitive astronomy.... We pass contemptuously by the results of ancient astronomical observations; we substitute others and, as we perfect these, we find the same results that we had despised.

It will be seen that these ancient observations were of great accuracy, and that modern science cannot improve much on the measurements of the meridian that were made on the plains of Chaldæa, or along the Nile, at least sixty centuries ago.

The unit of distance used at the present day by seamen of all nations, the meridian mile, one-sixtieth of a degree, is exactly 1000 Egyptian fathoms, or 4000 Egyptian meridian cubits, and the Great Pyramid was built with a base measuring exactly 500 of these cubits along each side and 500 of these fathoms in perimeter.

It had probably been found convenient before that time to take a shorter unit than the cubit for use in many everyday measurements. It was two-thirds of the cubit, one-sixth of the fathom, and was called a Foot from its being roughly about the length of a long human foot. Apparently one of the primitive limb-measures, it is really an outcome of the cubit, ‘foot’ being merely a convenient name for it. The foot of the meridian cubit was of 4 palms or 16 digits and was = 12·16 English inches.

The Egyptian standards of linear measure, thus adjusted to the meridian mile, passed to Greece, and under the name of ‘Olympic’ became the Greek standards of length.

The use of the cubit and foot series of measures is seen in Hesiod (ninth century B.C.):

Hew a mortar three feet (tripodīn) in diameter, and a pestle three cubits (tripichtēn), and an axletree seven feet (heptapodīn) ... and hew a wheel of three spans (trispithamon) for the plough-carriage of ten palms (dekadōro) length.

Besides the original division of the foot into 16 finger-breadths or digits, there arose an alternative division into 12 thumb-breadths or inches. So for the Roman foot, of shorter standard than the Egyptian or Olympic foot from which it was derived—

Pes habet palmos iv, uncias xij, digitos xvi,

Palmus habet digitos iv, uncias iij.

It may be said that with the foot originated the sexdecimal system, as with the span the duodecimal system. But the foot had as many inches, twelve, as the span had of digits; and this division was the same in other feet or spans not differing much from the Olympic standard.

The popularity of the foot, its general adoption for the common purposes of life, are due to its being divided into either 12 inches or 16 digits, the familiar thumb-breadths and finger-breadths. Every popular system meeting the convenience and the ways of thought of men and women, must have its measures of length approximately coinciding with the familiar units of limb-lengths, and it must be divided sexdecimally or duodecimally to enable people, men, women and children, to calculate mentally in the everyday business of life.

The octonary or semi-sexdecimal mode of division seen in our Pint-Gallon-Bushel series is also very convenient, especially for measures of capacity and for land-measures, admitting extensive halving and quartering with subordinate units at each division. Duodecimal division having the convenience of thirding is convenient for the coinage series. A combination of the score and dozen series, as in our money-pound of 20 × 12 pence, combines the advantages of extensive halving and thirding.

But never has man taken to a decimal series of weights and measures; he may use them on compulsion, and then will evade them whenever he can. He has ten fingers, whence decimal numeration from the earliest times; but he has always rejected decimal measures.[^[1]]

If to the inconvenience of not being able to halve a unit more than once (and that only as a concession to unscientific weakness of mind), so that there is an interval of ten units between each named unit of the series, be added that the familiar units of common life, the thumb-breadth, the span, the foot, the pound, the pint, have no representatives in a decimal system, then no cajolery of science or patriotism will persuade men and women to use the system, except under police compulsion, and every trick will be used to evade it. Such are the ways of the human mind. Systems that are suited to popular convenience, both in wholesale and retail trade; systems that admit of modification and improvement—these will live. Systems imposed by police-force in which the people must fit themselves to the system—these are bound to fail.

The convenient foot being taken as subsidiary to the cubit, it afforded, for long measurements, larger units which harmonised with the cubit, and with its half, the span. The most usual long unit has been the Fathom and its double—

This Rod, varying according to the local standard of the foot or the span, is that nearly always used in countries round the Mediterranean. In northern countries where the foot has superseded the span for measures of any length, 16 feet instead of 16 spans is a usual length for the rod-measure.

It is a curious fact in the history of human nature that neither ancient Egypt nor the other Eastern monarchies kept to the meridian cubit and the measures based on it. While it survived in Greece, it was abandoned, officially at least, in Egypt, Assyria, and Persia. Influences in which science was mixed with astrolatry caused a second cubit to arise, even at the time of the building of the Great Pyramid, and this cubit superseded the meridian cubit as the official standard of the Eastern Kingdoms. Centuries passed and other cubits, not many, five or six at the most, arose through analogous influences. From these Eastern cubits, and from the Roman linear measures based on a mile eight-tenths of the meridian mile, all the various systems of the civilised world have been evolved.

From linear measures, the fathom and the rod, came measures of surface which, quickly in some countries, slowly in others, superseded more primitive estimates of cultivated area. A very usual unit of land-length and of road-distance was the customary length of the furrow. In all times and countries the peasant has found that a certain length of furrow, often about 100 fathoms or 50 rods, was convenient for himself and his plough-cattle. A strip of land of this length, and of one or more rods in breadth, would become a unit of field-measurement, and in time this superficial extent, in some shape or other, would become a geometrical standard.

Commerce, even of the most primitive kind, led to two other forms of measure—to Weight and Capacity. The capacity of the two hands, that of a customary basket or pot, that of the bottomed cylinder obtained from a segment of well-grown bamboo, would be superseded by that of a vessel containing a certain weight of corn, oil or wine, as soon as the goldsmith had devised the balance. Seeds of generally constant weight such as those of the locust-tree, used for weighing the precious metals, would soon be supplemented by a larger standard for heavier weighing; and the weight of a cubic span or a cubic foot of water would afford a suitable unit. A vessel containing a cubic foot of water thus afforded a standard, the Eastern Talent, both for weight and for capacity. The cubic foot would become a standard for the measure of oil or wine, while this measure increased, usually by 22 or 25 per cent., so as to contain a talent-weight of corn, generally of wheat, would become the Bushel or otherwise-named standard of capacity, for the peasant and for corn-dealers.

The peasant would use his bushel not only to measure his corn, but also to estimate his land according to the measure of seed-corn it required. He would also take a day’s ploughing on a customary length of furrow, as a rough measure of surface, and the landlord would estimate the extent of his property by the number of yoke of plough-cattle required to work it. These seed-units and plough-units would in time be fixed, and thus become the basis of agrarian measures.

In the meantime coinage would have arisen. A subdivision of the talent would become the pound or common unit of weight in the retail market, and a subdivision of the pound would be fixed as the weight of silver which, impressed with signs guaranteeing its fineness, if not its actual weight, would be the currency of the merchants.

Then arose, by involution, another system of weights in which the pound was usually of 12 or 16 ounces, and the ounce was the weight of so many standard coins. Every modern pound was based on this system. But again, the pound of silver would yield a certain number of coins, giving rise to a new monetary system under which the coin-origin of the pound would in time be forgotten.

The necessary state-privilege of coining money sometimes led to differences between mint-weight and commercial weight. Just as there arose in the ancient East a royal or sacred cubit different from that in vulgar use, so there arose in many countries a royal pound used in the mint and different from the vulgar commercial weight. In many countries, ancient and modern, the mint has kept up systems of weight consecrated by tradition but obsolete for all other uses, and out of harmony with commercial weight.

The scientific measurement of time had early been established by the astronomers who had measured the meridian.

The skilled artisans who constructed astronomical instruments and the standard measures of capacity and weight must have observed that the water contained in the standard measure of capacity weighed more when it was as cold as possible than when at the temperature of an Eastern summer; they could not fail to develop the idea of thermometry thus made evident to them. Nor could anyone fail to see that oil was lighter than water, strong wine than unfermented, and spring-water than brine or sweet juices. Some means of aræometry, by an immersed rod or bead, would be devised to avoid the trouble of finding their density by the balance.

It may thus be said that the scientists and skilled artisans of very ancient Eastern lands were fully as capable of constructing a scientific system of weights and measures as Western Europeans in our eighteenth century.

Good systems were carried by commerce to less advanced countries; if convenient they took root, partially or entirely, and, with such modifications as circumstances caused or required, they spread and were in due time given legal sanction.

Such is the usual course of evolution in the formation of a system of weights and measures from a linear measure.

A modification of the original linear standard may lead to the evolution of a new system. Thus, when the Romans took as their foot 1/5000 of a short mile of 8 Olympic stadia instead of 1/6000 of the meridian mile of 10 stadia, this new foot was the starting point of a new system.

Another process of evolution, or rather of involution, may occur from an imported standard of capacity. Supposing that trade has carried a certain measure to a country which it supplies with corn, and that this measure has been adopted, with divisions convenient to the people: from this corn-measure another measure, about 4/5 of it, may be constructed, containing the same weight of wine or water that the former contains of corn; here will be a standard fluid measure, and perhaps some fraction of it filled with water may be taken as a standard of weight. Let now some cubical vessel be constructed to hold exactly the standard measure of water; the length or breadth of each side will give a linear unit which, if it approximate sufficiently with a foot or span to which the people are accustomed, will offer a fixed linear standard in harmony with the other standards. Thus, from a convenient foreign unit of capacity or of weight, a new and complete system of national measures may be constructed by involution.

It will be seen that several cases of such involution have happened. There is indeed no documentary evidence for them, and often very little for the more usual processes of evolution. But the evidence for the origin of most weights and measures is entirely circumstantial; it is by the study of metrology, founded on research into the systems of different countries, that the student is able to weigh circumstantial evidence, to use it prudently, to guard himself against mere coincidence, to clear away legend, to examine documentary evidence carefully, to read between the lines of records, often very deceptive if he come to them unprepared.

The various systems which have developed by these processes, generally of evolution, but sometimes of involution, lose the appearance of Babel-confusion they had before their development could be explained otherwise than by fanciful legend or despotic caprice. But once the right point of view is found, unity is seen in the hitherto bewildering variety, and the trend of the human mind is seen to be regular in the systems that it evolves, in its way of meeting difficulties, in its acceptance of changes which are real improvements, in its aversion to arbitrary changes, in its devices for evading despotic interference with what it has found convenient.

[1]. Even in numeration he often prefers to count by the score. The Welshman says dega-dugain (10 and 2-score), the Breton quarante et dix, other Frenchmen quatre-vingt-dix (4 score and 10)

CHAPTER II
THE STORY OF THE CUBITS

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.

1. The Egyptian Common, or Olympic Cubit

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—

69·091 statute miles; 1/60 = 6080 feet.

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—

8/10 of 6080 ft. = 4864 ft. = 1621-1/3 yards.

The pace was divided into 5 feet.

1/5 of 4·864 ft. (or 58·368 inches) = 11·673 inches.

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 schœnus 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-Mamūn.

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—

1 : 1·224 :: 20·64 : 25·26.

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—

1/8000 of 2029·11 yards × 60 × 360 = 5478·6 yards.

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.

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.

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

[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.

1. The Alexandrian Talent

The standard of this talent has been already given as 93·65 lb., which × 7000 = 655,550 grains.

It was divided on different systems:

1. By the Chaldæans and Egyptians into 60 minás, divided—

(a) On the Chaldæan system into 60 shekels of 182 grains, with a quarter-shekel = 45-1/2 grains.

(b) On the Phœnician, and Hebrew, system into 50 shekels of 218-1/2 grains, with a quarter-shekel = 54·6 grains.

2. By the Greek-Egyptians into 120 minás (or the half or lesser talent into 60 minás) of 100 drachmæ = 54·6 grains.

3. By the Romans into 125 libræ of 12 unciæ (1500 ounces) further divided by the Greeks into 8 drachmæ = 54·6 grains.

Three of these modes of division give a drachma of 54·6 grains. So a Phœnician or Hebrew shekel, a Ptolemaïc tetradrachm and a Roman half-ounce, are of the same weight, differing by only 1/4 grain from our half-ounce, and by only 1/2 grain from our half-crown.

The Alexandrian talent was the Hebrew Kikkar or talent of the sanctuary. In the Chaldæan kingdom the standard measure was the Egyptian royal cubit, and the standard weight was the talent derived from its foot; but the miná appears to have been divided into 60 instead 50 shekels.

The words which Belshazzar saw written on the wall referred to the miná and shekel, or tekel, of this talent. Their meaning may be thus rendered:

Mene, a miná—the great King Nabupalasur, founder of the new Chaldæan Kingdom.

Mene, a miná—the great King Nabukudurusur, son of the preceding.

Tekel, a shekel (of 4 quarters)—Nabunahid (Belshazzar) and his three predecessors, all of small account.

Upharsin, a division, perhaps 2 half-shekels, the Medes and Persians. Or it may simply be the Parsīs or Persians, the enemies at the gate.

This talent is still extant at Bássora (in Chaldæa) as the mánd sofi = 93·22 lb.

The Medimnos.

This was the measure made to hold an Alexandrian talent of wheat. The cubed Egyptian royal foot (probably used as a fluid measure) was increased in the Southern water-wheat ratio of 1 : 1·22. Thus 2605 c.i. × 1·22 = 3176 c.i. and 3176/277·4 = 11·45 gallons as the contents of the Medimnos.

This measure was adopted by the Romans, as well as by the Greeks, as the basis of their corn-measures, doubtless in consequence of the corn-trade from Egypt. A sixth part of it was the Roman Modius.

The Medimnos was divided by the Greeks into 48 Choinix, or into 96 Xestes (L. sextarius) = 0·95 Imperial pint or 19 fluid ounces.

2. The Lesser Alexandrian or Ptolemaïc Talent

This was half of the ordinary or greater talent.

Half the calculated weight of the greater talent gives 46·956 lb. for the lesser. But the actual weight was somewhat less, 46·82 lb.

It was divided into 60 Ptolemaïc miná = 5462 grains, and the miná into 100 drachms. The drachm = 54·62 grains and the tetradrachm = 218·5 grains coincide as coin-weights with the quarter-shekel and shekel of the greater talent.

The miná was divided also on the Roman uncial system:

1/12 = an ounce = 455·28 grs.; of this

1/12 = a double-scruple = 37·94 grs.; of this

1/12 = a carat of 3·1616 grs.

The carat 1/144 ounce, is exactly, to 1/100 grain, the jeweller’s carat of to-day in European countries.

What could be the reason for this talent?

Its miná was half an Alexandrian miná; its drachm was a quarter-shekel.

Don V. V. Queipo[^[6]] considered that the half Beládi cubit had been produced from it by involution, taking the side of a cubical vessel containing half an Alexandrian talent of water and then doubling this new foot to make a new cubit. Its water-volume = 1302·5 c.i. gives as cube root 10·9207 inches, almost exactly half the Beládi cubit = 21·888 inches. But the Beládi cubit being 1/7200 of a Parasang is sufficient evidence of its origin. I consider that the close coincidence of the half-cubit with the side of a cubic vessel containing an Alexandrian half-talent of water led the Ptolemies to institute this smaller talent, as if it had been evolved from the Beládi foot in the same way that the Greek-Asiatic talent had been evolved from the Persian foot or half-cubit.

3. The Greek-Asiatic Talent

After the institution of the great Assyrian or Persian cubit a new talent was necessarily evolved from it.

The Persian foot, half of the cubit, was cubed, and the weight of this cubic foot of water was the Persian or Greek-Asiatic talent—

25·26/2 = 12·63 inches; 12·63³ = 2014 c.i. = 72·61 lb.

The actual weight of this talent (as in the case of the Alexandrian talent) was somewhat less. It corresponded to a cubic foot of 2000 c.i., giving 72·13 lb. = 504,910 grains. This was divided into 60 minás—

(72·13 lb. × 1000)/60 = 8415 grams = 1·2 lb.

The miná was divided by the Persians into 100 darics = 84·15 grains. The actual weight of silver darics found, 83·73 grains, corresponds almost exactly to this weight.

This is the talent Herodotus used when estimating the revenue of the Persian empire. Its miná has survived as the Attári or Assyrian rotl = 8426 grains, extant in Algeria. Another Attári pound = 8320 grains is still used at Bássora, near the Persian gulf. The ounce of this rotl, 8426/16 = 526·6 grains, is exactly the Russian ounce.

The Persian coins weighing 129-130 grains usually called darics are staters or Greek didrachms.

The Metretes

The second Greek standard of capacity was the Metretes.

While the Medimnos contained an Alexandrian talent of wheat, the Metretes contained a Greek-Asiatic talent of it.

The capacity of the Persian cubic foot was 2000 c.i. = 72·13 lb. = 7·213 gallons.

This cubic foot, increased in water-wheat ratio, gives 7·213 × 1·22 = 8·8 gallons or 70·4 pints, as the capacity of the Amphoreus metretes.[^[7]]

Some archæologists have given it as = 8·68 gallons, a very slight difference.

The Metretes was divided into 36 Choinix or 72 Xestes, which contained O·977 pint as against the O·955 pint of the Xestes, which was 1/96 Medimnos. A mean figure, 0·96 pint, is usually taken as the common capacity of the two Xestes.

The Greeks had thus two standards of capacity, the Metretes and the Medimnos, both cubic feet increased in water-wheat ratio to make them corn-measures. It is very likely that, having these two measures from different sources, the one of 72 Xestes, the other of 96, they would use the smaller as a fluid measure. In modern measures there are several instances of corn-measures having become wine-measures. Our Imperial gallon used for fluids is a slightly altered corn-gallon; at present the multiples above the gallon are used for corn, the gallon and its divisions for fluids.

4. Roman Weights and Measures of Capacity

Used by the Greek colonies in Asia, the Greek-Asiatic talent passed to the Greek or Trojan colonies in South Italy, and became the source of the old Roman pound, the As libralis = 5049 grains, 1/100 of the talent; (72·13 × 7000)/100 = 5049 grains.[^[8]]

The Aes or As, the bronze or copper pound of the Roman republic in its earlier times, was divided into 12 ounces, each = 420·75 grains.

It remained the mint-pound of both Republic and Empire.

The Aurei of Julius Caesar, 1/40 As, weigh 127 grains, those of Augustus 125 grains. The mean weight appears to be about 126 grains, which gives 5040 grains for the As.

The Aurei of the later Empire were struck at 1/72 As, and weigh 70 grains, giving the same weight, 5040 grains, for the As. At 70·1 grains they would give 5049 grains, the calculated weight of the As.

The evolution of the As from the Greek-Asiatic talent leads to consideration of the measures connected with it, and with the Alexandrian talent.

It has been seen that the Roman foot, 1/5000 of the Roman mile, 8 Olympic stadia, was 11·67 inches. This foot being cubed, the weight of the cubic foot of water was made the basis of the Roman measures of capacity—

11·67³ inches = 1589 c.i. = 57·32 lb. water

= 401,240 grains.

This calculated measure, 57·32 lb. = 5·732 gallons = 45·8 pints, was the Amphora Quadrantal, supposed to weigh, of wine, 80 As or primitive pounds. Quadrantal vinei octoginta pondo sit. The correspondence was only approximate. The Quadrantal should have been = 57·7 lb. for its 1/80 part (= 5049 grains) to correspond with the As. Its capacity was probably adjusted so as to make it half a Medimnos and = 3 Modii.

There are specimens extant of the Quadrantal, of cubical shape, showing that it was named from its being a cubic foot in measure.

The Quadrantal, being equal to 45·8 pints, was almost exactly half the Greek Medimnos, equal to 91·5 pints; so that, divided into 8 congii, each of 6 sextarii, the Sextarius, 1/48 Quadrantal, was practically the same as the Xestes, 1/96 of the Medimnos.

And the Quadrantal being also very nearly two-thirds of the Greek Metretes, equal to 70·4 pints, the Sextarius was also nearly the same as the other Xestes, 1/72 of the Metretes.

So the Sextarius was 1/48 Quadrantal, 1/72 Metretes, and 1/96 Medimnos.

The relation of the Roman Modius to the Alexandrian-Greek medimnos appears to be only a coincidence, as the former is one-third of a Roman cubic foot, and the latter an Alexandrian cubic foot increased in water-wheat ratio.

The New Roman Pound

Trade with Egypt led the Romans, not only to use the Alexandrian medimnos, but also to put aside the As for commercial purposes and adopt a standard taken from the Alexandrian talent. Its 1500 double-shekels made 125 libræ each of 12 unciæ = 437 grains. The libra was thus = 5244 grains as compared with the As = 5049 grains.

A further uncial division of the libra made the Uncia either of 6 sextulæ, 24 scrupuli, 48 oboli, 144 siliquæ, or of 12 semi-sextulæ, 144 siliquæ.

The siliqua was a little less than the Eastern qirát, being 3·03 grains instead of the 3·1616 grain carat of the Ptolemaïc series of weights.

Table of Roman Weights and Measures of Capacity

Weights

OLD WEIGHTS (MINT SERIES)

NEW WEIGHTS (MEDICINAL SERIES)

Measures

WINE

CORN

5. The Olympic Talent

From the Olympic foot, two-thirds of that most ancient linear standard the common cubit of Egypt and the other Eastern monarchies, a talent was also constructed—

12·16³ in. = 1798 c.i. = 64·81 lb. water = 453,670 grs.

and in practice its actual weight was the same as that calculated.

It was divided in two ways:

1. On the Bosphoric system, which prevailed in Asia Minor, in the Phœnician colonies, and in some parts of Greece, it was divided into 80 miná, each = 5670 grains, and these into 100 drachms of 56·7 grains. Or the Bosphoric miná was divided uncially into 12 ounces of 472·5 grains.

2. On the Euboic system, frequently used in Greek commerce, this talent was divided into 50 minás of 100 drachms.

The drachm = 90·73 grains.

There was also a Euboic talent which coincided with the weight of the Roman Quadrantal, nominally of 80 As weight = 57·7 lb., and in transactions with the East the Romans appear to have called their Quadrantal-weight of water a Euboic talent. But it will presently be seen that this was the Attic monetary talent.

The volume of an Olympic talent of water was 8 times the Hebrew Bath or, for dry goods, Epha.

Comparison of Olympic and Imperial Measures

6. Greek Coin-weights

In ancient Greece as in medieval Europe, financial difficulties led rulers to lower the weight of the coinage. But while in Europe, in England for instance, more pennies were coined from the mint-pound of silver, this remaining fixed, although nominally based on the weight of the sterling, the weights of Greece were actually based on that of the drachma.

When the drachma was diminished in weight, the miná and the talent both dropped proportionately. Thus the standard of the Alexandrian talent, carefully preserved in Egypt, dropped in Greece.

So in Athens, where the Ægina standard was in use, the drachma stood at 93·08 grains when, in 594 B.C., Solon’s Seisachthia law ‘unburdened’ the State and other debtors by decreeing that 73 (or more accurately 72-1/2) drachmæ should now be equal to 100 drachmæ, and altering the coinage accordingly.

This reduced the coin-weights of Athens to—

But commercial weight remained the same. The miná emporikí, the trade miná, was fixed at 138 of the new drachmæ, so that it continued to be 100 of the old drachmæ: 138 × 67·37 = 100 × 93·08 grains.

The commercial miná thus remained at the 600 B.C. standard of 9308 grains = 1·33 lb. and the talent at 79·78 lb.[^[9]]

In settling the reduction of the Attic money-weight at 100 new drachmæ = 73 old drachmæ, Solon probably fixed on the latter figure in order to make the new talent, = 57·74 lb., have approximately the simple ratio of 4 : 5 with the Greek-Asiatic talent—

4/5 × 72·13 lb. = 57·704 lb.

Thus the Roman As being = 5049 grains, 1/100 of the Greek-Asiatic talent, 80 As, = 403,920 grains = 57·7 lb., came to coincide with the Attic monetary talent.

7. The Arabic Talent

To the talents and measures of capacity evolved from the feet of the three principal cubits of antiquity, must be added the talent and other measures evolved from the Black foot of Al-Mamūn’s cubit. They have had great influence on the weights and measures of Europe.

Al-Mamūn’s cubit was = 21·28 inches, the foot = 14·186 inches.

The foot cubed gave a measure of water, the weight of which was the Egyptian Cantar or Cental—

14·1868³ = 2855 c.i. = 102·92 lb. water = 720,441 grs.

This talent was divided in two ways:

1. As the Romans had divided the Alexandrian talent into 125 pounds of 12 ounces, so the new talent was divided into 125 parts each = 5763 grains. This was the Arabic lesser Rotl, its ounce = 480·25 grains. The rotl was also divided in the Greek way into 100 drachms or dirhems = 57·63 grains.

2. Another mode of division was into 100 greater Rotl, thus becoming a Cental of 100 lb. each = 7204·4 grains.

This greater rotl was divided, commercially into 16 ounces (Ar. ukyé, Gr. oggia, L. uncia) of 450,275 grains, and uncially for coin-weight into 12 × 12 dirhems of 50·03 grains.