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- Herausgeber: Science & Technology Publishing
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Men and Measures by Sir Alexander B. W. Kennedy is a fascinating exploration of the evolution of measurement systems and the individuals who shaped them throughout history. The book delves into the origins and development of weights and measures, tracing their journey from ancient civilizations to the modern era. Kennedy examines the practical and scientific challenges faced by early societies in standardizing units for trade, construction, and daily life, highlighting the ingenuity and persistence required to create reliable systems. Through engaging anecdotes and historical accounts, Men and Measures introduces readers to the key figures—scientists, engineers, lawmakers, and visionaries—who contributed to the advancement of measurement. The narrative covers a wide range of topics, including the establishment of the metric system, the evolution of timekeeping, and the quest for universal standards. Kennedy also discusses the social, economic, and political implications of measurement, illustrating how these systems have influenced commerce, industry, and international relations. Rich in detail and insight, Men and Measures offers a unique perspective on the intersection of science, technology, and human progress. It is both a tribute to the pioneers of measurement and a testament to the enduring importance of precision and standardization in society. Whether you are interested in history, science, or the development of civilization, this book provides a comprehensive and engaging account of the men and measures that have shaped our world.
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MEN AND MEASURES
ERRATA.
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“grams”
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“grains.”
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“7925”
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“7625.”
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delete
“to.”
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“ells.”
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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is the development of a short story of the Imperial System of Weights and Measures published eleven years ago, but withdrawn when this fuller work took shape.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.
Feb. 1912.
TABLE OF CONTENTS
CHAPTER I
PAGE
GENERAL VIEW OF THE EVOLUTION OF MEASURES
1
CHAPTER II
THE STORY OF THE CUBITS
1.
The Egyptian common or Olympic cubit
14
The meridian mile
15
Greek itinerary measures
16
The Roman mile
17
2.
The Egyptian royal cubit
18
3.
The great Assyrian or Persian cubit
23
4.
The Beládi cubit
26
The Bereh or equatorial land-mile
27
5.
The Black cubit
28
Comparative lengths of the five ancient cubits
30
CHAPTER III
THE STORY OF THE TALENTS
1.
The Alexandrian talent
33
The Medimnos
34
2.
The lesser Alexandrian or Ptolemaïc talent
35
3.
The Greek-Asiatic talent
36
The Metretes
37
4.
Roman weights and measures of capacity
38
The new Roman pound
40
5.
The Olympic talent
42
6.
Greek coin-weights
43
7.
The Arabic talent
44
Measures of capacity derived from Arabic linear measures
47
CHAPTER IV
THE INVOLUTION OF LINEAR MEASURES FROM WEIGHTS
THE ORIGIN OF THE ENGLISH AND OF THE RHINELAND FOOT
1.
The English foot
49
2.
The Rhineland foot
52
3.
The pán of Marseilles
53
4.
The filiation of the English foot, of the Rhineland foot, and of the pán of Marseilles
55
CHAPTER V
ENGLISH LINEAR MEASURES
1.
The yard, the foot, the inch
58
2.
Standards of the linear measures
59
3.
The hand
61
4.
The ell
62
5.
The rod, furlong, mile, and league
62
CHAPTER VI
LAND-MEASURES
1.
Introduction
65
2.
Evolution of geometric land-measures
66
3.
The story of English land-measures
71
4.
Feudal land-measures
75
5.
Terms used in old land-measures
77
6.
The yard and the verge
82
7.
How the rod came to be 5-1/2 yards
84
8.
How the acre came to be 160 square rods
87
9.
Customs of Lancaster
88
10.
Seed-measures of land
90
CHAPTER VII
ENGLISH COMMERCIAL WEIGHTS
1.
The story of Averdepois
93
2.
The Imperial pound
102
3.
Scientific and medicinal divisions of the pound
104
4.
The long hundredweight
105
5.
Wool and lead weight
109
6.
Trade-units of weight
112
CHAPTER VIII
ENGLISH MEASURES OF CAPACITY
1.
The old wine-measures
114
2.
The ale-gallon
117
3.
Corn-measure
118
4.
The quarter and the chaldron
120
5.
Coal-measure
122
6.
The Imperial gallon
123
7.
Medicinal fluid-measures
126
CHAPTER IX
THE MINT-POUNDS
1.
The Saxon or Tower pound
127
2.
The Troy pound
129
How the averdepois pound was of 7000 grains
133
3.
The pride and fall of Troy
136
The assize of bread
138
The disappearance of the Troy pound
139
CHAPTER X
THE CUBIC FOOT AND THE TON REGISTER
Concordance of capacity, weight, and measurement
145
Volume and weight of water at different temperatures
146
CHAPTER XI
SCOTS, IRISH, AND WELSH MEASURES AND WEIGHTS
1.
Scotland
147
2.
Ireland
155
3.
Wales
156
CHAPTER XII
MEASURES AND WEIGHTS OF SOME BRITISH DOMINIONS
1.
The Channel islands
157
2.
South Africa (Cape Colony)
166
3.
India
167
4.
Burma and the Straits
172
5.
Canada and Mauritius
173
CHAPTER XIII
MEASURES OF VALUE
1.
English money
174
2.
Guernsey currency
183
3.
Indian money
184
4.
Decimal currency
188
CHAPTER XIV
MEASURES OF TIME
The lunar year
194
The compass-card
195
CHAPTER XV
MEASURES OF HEAT AND OF DENSITY
197
Compound industrial units
201
CHAPTER XVI
THE ELLS
202
CHAPTER XVII
FOREIGN LINEAR MEASURES
1.
Teutonic countries
206
2.
Latin countries
208
3.
Russia and the East
212
4.
The Hashimi cubit
214
5.
The Halebi pík or arshīn
215
CHAPTER XVIII
FOREIGN WEIGHTS
1.
Teutonic systems
218
2.
East-European systems
219
3.
Mediterranean systems
220
Summary
224
Original weights of the dirhems
226
CHAPTER XIX
FOREIGN MEASURES OF CAPACITY
1.
The Teutonic system
227
2.
The Mediterranean system
232
3.
Hebrew weights and measures of capacity
237
CHAPTER XX
THE DEVELOPMENT OF MEANING IN THE NAMES OF
WEIGHTS AND MEASURES
1.
General remarks
240
2.
The nail and the clove; the inch and the ounce
242
3.
The carat and the grain
245
4.
The tun and the fother
252
CHAPTER XXI
THE OLD MEASURES AND WEIGHTS OF FRANCE
1.
The Southern system
253
2.
The Northern system
259
CHAPTER XXII
THE METRIC SYSTEM
271
CHAPTER XXIII
HOW THE METRIC SYSTEM WORKS IN FRANCE
284
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.
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.
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—
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—
The Fathom
4
cubits
or
6
feet
or
8
spans
The Reed or Rod
8
„
„
12
„
„
16
„
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
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.
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.
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 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.)
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 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.
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.
18·24
Egyptian
common
cubit
6
palms
of 3·08 in. 24
digits
20·64
„
royal
„
7
„
of 2·95 in. 28
„
25·26
Assyrian
„
8
„
of 3·16 in. 32
„
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.
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.
4. The Beládi Cubit (c. 300 B.C.)
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.
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.
Talmudic
cubit
1/10000
of a
league
1/7200
of the
equator.
Beládi
„
1/9000
„
„
1/8000
„
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.
