THE CONFLICT OF THE IMPERIAL AND METRIC SYSTEMS
1. General view of the Imperial system 295
2. The propaganda of the Metric system 300
3. The reform of the Metric system 306
CONVERSION-TABLES OF METRIC AND IMPERIAL MEASURES 310
INDEX 311
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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]
Footnote 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)
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.
------------------------------------------------------------------------
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—
At degrees 1 to 3 = 68·704 statute miles; 1/60 = 6046 ft.
„ 88 to 90 = 69·409 „ „ ; 1/60 = 6108 ft.
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.
6 Olympic feet = 1 fathom (orgyia)
60 „ „ = 1 rod (kalamos)
60 rods or 600 feet = 1 stadion
60 stadia (6 meridian miles) = 1 schoinos
60 schoinoi = 6 meridian degrees
60 × 6 degrees = circumference of the globe.
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.
Footnote 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.
Footnote 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.
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.
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 „
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]
Footnote 4:
Διάφραγμα τῆς ὀικουμένης. Instituted by Dicæarchus 310 B.C., corrected
by Eratosthenes 276-196.
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.
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.
Under Al-Mamūn, son of Harūn al-Rashid, science was flourishing in the
East, while the West was in the dark ages, at least in all the countries
unenlightened by the civilisation of the Moors of Spain. Of Christian
Europe, Provence and the other Occitanian countries alone had that
light, a light that shone over other countries until extinguished by the
Albigensian crusade.
‘Mahmd Ibn Mesoud says that in the time of Almamon (the learned Calife
of Babylon) by the elevation of the pole of the equator, they measured
the quantity of the degree upon the globe of the earth, and found it to
be 56-2/3 miles, every mile containing 4000 cubits, and each cubit 24
digits, and every digit 6 barleycorns, and every barleycorn 6 hairs of a
camel’ (‘A Discourse of the Romane Foot and Denarius,’ by John Greaves,
Professor of Astronomy in the University of Oxford, 1647).
From this determination of 56-2/3 meridian miles to the degree of
longitude it would appear, (1) that the measurement was made at about
20·1°; south of Mecca, (2) that the meridian mile was still of 4000
Egyptian common cubits or 1000 Egyptian fathoms.
It was then probably after this measurement that Al-Mamūn instituted his
new Cubit, sometimes known as the Black cubit, so named from the black
banner and dress adopted by the Abbaside caliphs.
This new cubit was not, directly at least, of geodesic basis. The caliph
was probably inspired by the idea of making in a reasonable manner the
alteration which the ancient Egyptians had done badly in making their
seven-palm cubit out of simple proportion to the common cubit. So the
new cubit had palms and digits of the same length as the common cubit.
But it had all the inconveniences of the factor seven. Perhaps Al-Mamūn
may have thought that the addition of a seventh palm was not only a
homage to the seven planets but that it was satisfactory to lengthen the
common cubit in the ratio of the degree of latitude to that of longitude
in a part of his dominions where the ratio was exactly 7 to 6. This is
the ratio at Alexandria, in 31° N.
The Common cubit being = 18·24 inches = 6 × 3·04 in.
The Black cubit was = 21·28 „ = 7 × 3·04 in.
Two-thirds of this cubit were taken for
The Black foot = 14·186 inches, divided into 16 digits of
the 24 digits or qiráts of the cubit.
This cubit and foot are still in use. The old nilometer on the island of
Al-Rauzah (Rode) near Cairo has its scale in cubits of this standard,
and measurement of the worn scale gives 21·29 inches for the cubit.
The cubit and foot of Al-Mamūn are the basis of measures and of weights
which spread from Egypt to every country in Europe.
The story of the five cubits, ancient and medieval, has shown that they
were all derived, directly or indirectly, from the meridian measurement
of the earth, some of them being probably instituted with the desire to
make them representative of the relation of latitude and longitude.
I venture to say that every measure and weight used throughout the world
has been developed from one of these cubits and thus, more or less
directly, from the Egyptian meridian cubit. The Republican system of
France is but a decimal imitation of the system based on the common
Egyptian meridian cubit; its basis being the kilometre, 1/10000 of the
quarter-meridian, instead of the Egyptian meridian mile, 1/(90 × 60) of
the quarter-meridian.
There were some other cubits of minor importance; one of them is the
Hashími cubit described in Chapter XVII.
COMPARATIVE LENGTHS OF THE FIVE ANCIENT CUBITS
Egyptian common cubit = 18·24 in.; its foot 2/3 = 12·16 in.
„ royal „ = 20·64 „ „ 2/3 = 13·76 „
Great Assyrian „ = 25·26 „ „ 1/2 = 12·63 „
Beládi „ = 21·888 „ „ 1/2 = 10·944 „
Black „ = 20·28 „ „ 2/3 = 14·186 „
------------------------------------------------------------------------
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]
Footnote 5:
The Imperial pound = 27·727 cubic inches of water, 7000 grains: the
gallon 10 lb. or 277·274 c.i.
The actual weight was 93·65 lb. = 655·550 grains; 655550/3000 = 218·5
grains was the weight of the shekel, nearly our half-ounce—exactly the
half-ounce of Plantagenet times, and very near to the weight of our
half-crown, which weighs 218·18 grains.
The difference between calculated weight and the actual weight
determined from coin or other standards, from trustworthy historical
statements and other sources of information or of evidence, is generally
due to the great difficulty in constructing accurately the cubical
vessel used to ascertain the weight of a cubed measure of water. A
difference of 2/100 of an inch in the sides of the vessel made to hold a
royal cubic foot of water would make a difference of about 3 parts in
1000, of 4-1/2 of the 1500 ounces or double-shekels of water it
contained. And we do not know the temperature of the water used.
From the ancient and medieval cubits were derived all the weights and
measures of medieval and modern civilisation, largely through the medium
of the talents derived from these standards.
From the Egyptian common foot came the Olympic Talent
„ „ „ royal „ „ „ Alexandrian „
„ „ Great Assyrian „ „ „ Greek-Asiatic „
„ „ Arabic „ „ „ Arabic „
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.
Footnote 6:
_Essai sur les Systèmes Métriques_ (1859).
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; 12·63^3 = 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]
Footnote 7:
The Metretes was one-tenth more than our firkin. In the story of the
Marriage at Cana (John ii.) the Greek has ‘two or three metretes.’
This term is kept in Wycliff’s version (1388) and in the modern Dutch
version.
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]
Footnote 8:
5050 grs.—Smith’s _Dict. of Antiquities_. 5047 grs.—Daremberg and
Scaglio’s _Dict. of Antiquities_.
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—
11·67^3 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)
As = 5040 grs. 12 unciæ
Deunx 11 „
Dextans 10 „
Dodrans 9 „
Bessis 8 „
Septunx 7 „
Semissis 6 „
Quincunx 5 „
Triens 4 „
Quadrans 3 „
Sextans 2 „
Uncia = 420 grs. 1 „
NEW WEIGHTS (MEDICINAL SERIES)
Libra = 5244 grs.
Uncia = 437 „
Sextula = 72·8 „ = 1/6 uncia
Denarius = 62·45 „ = 1/7 uncia
Drachma = 54·6 „ = 1/8 uncia
Scrupulus = 18·2 „ = 1/3 drachma
Obolus = 9·1 „
Siliqua = 3·03 „
Chalcus = 1 „ = 1/3 siliqua
Lens (Sitarion) = 3/4 „ = 1/4 siliqua
MEASURES
WINE
Metretes (Gr.) = 8·8 gall.
Quadrantal 80 As = 5·77 „
Urna 40 „
Congius 10 „ = 5·77 pints
Sextarius 20 unciæ = 0·96 „
Hemina 8 „
Acetabulum 2 „
Cyathus 1 „
Ligula 1/4 „
CORN
Medimnos = 11·45 gall. = 2 quadrantal
Modius = 1·92 gall. = 1/3 quadrantal
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—
12·16^3 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
OLYMPIC IMPERIAL
Foot = 12·16 in. 12 in.
Cubic foot = 1798 c. in. 1728 c. in.
Talent = 64·81 lb. 62·3 lb.
1/1000 of talent = 453·6 grs. 437·5 grs.
│ Orig. Wine gallon 7·83 lb.
1/8 = Bath = 8·1 lb. water │ Modern „ „ 8·33 „
│ Imperial „ „ 10 „
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.
Miná Talent
Drachma of of
100 drachmæ 60 miná
Egypt 109-1/4 grs. 10,926 grs. 93·65 lb.
Ægina, early 105 „ 10,560 „ 90·5 „
„ before 700 103·7 „ 10,370 „ 88·9 „
„ after 700 95·68 „ 9,568 „ 81·76 „
Athens, 600 B.C. 93·08 „ 9,308 „ 79·78 „
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—
Drachma Didrachma Miná Talent
67·37 grs. 125·74 grs. 6737 grs. 57·75 lb.
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]
Footnote 9:
There was a custom of _rhōpi_, turn of the scale, or long weight,
which increased the legal commercial weight to a customary weight
tending towards that of the Alexandrian talent series.
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—
14·1868^3 = 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.
Both these dirhems became, like the drachma coin-weights of Greece, the
bases of other systems of weight, either at their original weight or at
the lower weights to which coins might fall.
The Lesser Rotl—
1. With its ounce of 480-1/4 grains would seem to have given rise to the
Troy pounds, but it is much more probable that their variable ounces
were 10 dirhems of about 48 grains.
2. From 8 of its drachms came the Venetian pound and the German
apothecaries’ pound with an ounce of 8 × 57·63 = 461 grains.
From the Greater Rotl came—
1. Eight of its ounces of 450-1/4 grains = the Marc of Cologne, its
double being the German Imperial pound = 7218 grains; our royal
Tower-pound of Plantagenet times being 12 ounces = 5400 grains.
The 100 lb. centner of North Germany = 103·1 lb. was almost exactly the
same weight as Al-Mamūn’s Cantar.
2. WEIGHTS OF EASTERN EUROPE (see Chap. XV)
The Polish pound 16 × 8 dirhems of 48·9 grains
„ Russian „ „ „ 49·37 „
„ Austrian „ „ „ 50·6 „
From 8 dirhems of 50 to 47 grains came the ounces of the pounds of
Southern France.
From 10 dirhems of 48 grains, more or less, came the ounces of the Troy
pounds.
The weight of the dirhem is now: Turkey 49·6 grains, Greece 49·4 grains,
Morocco 49 grains, Egypt 47·6 grains, Tripoli 47·07 grains. In Tripoli
there is a small weight = 12·55 grains called a dirhem, which seems to
be 1/4 of an original weight dirhem = 50·1 grains.
The fall of the dirhem weight, and consequently of the weights which are
multiples of it, accounts for the Egyptian Cantar having fallen from its
original weight to somewhat over 98 lb.
The quarter-Cantar gave its Arabic name to other quarter-hundredweights,
the Arroba of Spain, the Rubbio of Italy, the Rub of Southern France
(from Ar. _rouba_, four; cf. Rubaiyát, quatrain).
_Measures of Capacity derived from Arabic Linear
Measures_
Al-Mamūn’s cubit cubed became the medieval standard of grain measure on
the Mediterranean coasts—
21·28 in. cubed = 9639 c.i. = 347·314 lb. water,
which is equal to 34·73 gallons or 4·34 bushels.
This measure subsists in Egypt as the Rebekeh = 4·32 bushels. It passed
to Marseilles as the Cargo, and to Paris as the Setier.
These developments of the Arabic cubit and foot will be more fully
explained in the chapters on foreign systems. They are sketched in order
to show how the Eastern caliphate took up the system begun by the great
monarchies of many centuries before, and elaborated by Greece and Rome.
Thus, from Moslem Egypt as from Pharaonic Egypt have come virtually all
the weights and measures of the Western world.
------------------------------------------------------------------------
CHAPTER IV
THE INVOLUTION OF LINEAR MEASURES FROM
WEIGHTS
THE SOURCES OF THE ENGLISH AND OF THE RHINELAND
FOOT
Commerce is the great conservator of standards. These may become altered
by the ill-advised action of rulers, by municipal or parochial
carelessness, even by the desire of profit on short measure, or
occasionally, as seen to a slight extent in our old Bushel, by the
faulty dimensions of a standard; but wholesale trade, supported, in
weights at least, by the goldsmith and the apothecary, preserved the
integrity of many standards during the Middle Ages and up to modern
times. Commerce conveyed to the West the standards that had developed in
the great Oriental Kingdoms, sometimes with the modifications due to
Roman influence. Masons and architects also preserved the standards of
length and, allowing for variations inevitable under the feudal system,
the principal linear measures can generally be traced to their sources
as surely as weights. But there are two, yea three, striking exceptions
among the linear standards of the West: the English foot, and the
Rhineland foot, and also the Pán of Marseilles. These are quite
unconnected with any ancient measures, and there is no record of their
origin. The only clue to it is found in the simple relation of each to
the corresponding weights and measures of capacity, the origin of which
can be satisfactorily traced. This leads to the hypothesis that these
linear measures were ‘involved,’ that is produced by a method of
involution the inverse of that which had evolved the measures of weight
and capacity.
1. THE ENGLISH FOOT
There seem three hypotheses for the origin of the English foot.
1. That it was the Olympic foot = 12·16 inches, its standard diminished
by the accidents of time.
But we know that the Romans established their measures in Britain, and
our mile of 8 stadia and of 5000 feet (first Roman, then English) up to
Tudor times, shows that it was originally 1000 Roman paces of 5 feet;
and our early wine-bushel, of which the wine-gallon was 1/8, is
referable to the cube of the English foot, not to that of the Olympic
foot.
There is no trace of the Olympic foot in Northern Europe except the
possibility (mentioned under Foreign Linear Measures) of the Amsterdam
local foot, = 11·146 inches, being 11 inches of the Olympic foot.
2. It happens that the mean of the Roman foot = 11·67 inches, and of the
Rhineland foot = 12·356 inches, gives 12·013 inches. But there is no
instance of a new standard being formed from the mean of two older ones;
moreover this hypothesis begs the question of the Rhineland foot.
3. The hypothesis which I consider the most likely is that the foot is
the measure of the side of a cubical vessel containing 1000 Roman ounces
of water. It seems likely that in early times, possibly under King
Alfred by the advice of Italian moneyers or Jewish merchants, this
measurement was effected in order to establish a foot and a cubic foot
measure of capacity corresponding to a new talent of 1000 Roman ounces.
There is no record of this, any more than there is a record of the
standard taken for the Tower pound of the Norman and Plantagenet kings.
All we know is that, during the times of these kings, the relation of
Averdepois or Roman weight to our measures of capacity was utterly
ignored until at last, in 1685, ‘some Gentlemen at Oxford determined the
weight of a cubic foot of spring water, or 1728 solid inches, to be 1000
ounces averdepois.’ That the correct weight is not 1000 but about 998
ounces at 62° does not militate against the connexion of the weight and
measure any more than the fact that a cubic decimetre of water, supposed
to weigh 1000 grammes, only weighs about 998-1/2 grammes would disprove
a connexion between the cubic decimetre and the gramme.
The difficulty of making a ‘quadrantal,’[10] a vessel of exactly cubical
form inside, is so great that the wardens of the Metric System abandoned
the cubic decimetre of water as giving the standard, either of the litre
for capacity, or of the kilogramme for weight. Even approximate accuracy
was unattainable, and they were obliged to make the kilogramme an
arbitrary standard of mass and the litre a vessel containing a
kilogramme of water.
Footnote 10:
Quadrantal, the Roman standard of capacity, a cubic vessel measuring
one foot on each of its inside panels.
When it is seen that a difference of 1 in 2500 in the length of the foot
taken as the inside measure of a quadrantal makes a difference of 3
cubic inches out of 1728 in its capacity, the material difficulties of
constructing a vessel exactly cubical will be understood. However, a
quadrantal being constructed, perhaps after many trials of sides as
exactly equal as possible, and holding 1000 ounces of Roman ounces (=
437 grains) of water, the mean measure of its panels was taken as a
foot, and the quadrantal as a cubic foot—the wine-bushel.
Let us take 1000 Roman ounces and divide the total number of grains
weight by the statute number of grains in a cubic inch of water as
determined by Captain Kater in 1824.
The dividend will be the number of cubic inches, and its cube root will
be the foot—
437,000/252,458 = 1729·8 cubic inches,
of which the cube root is 12·0042 inches, a length differing by only
1/2400 from the actual Imperial foot.
I took the idea of this hypothesis from that by which Don V. V. Queipo
inferred the Beládi cubit to be the double measure of the side of a
cubical vessel containing a Ptolemaïc talent of water. Certainly it
solves the question of the origin of our foot, and it happens that,
applied to the equally obscure origin of the Rhineland foot, the results
are equally satisfactory.
2. THE RHINELAND FOOT
Let the same process of involution be applied to the side of a cubical
vessel containing 1000 Troy ounces of water.
The standard of Troy weight varied very much, from the Danish value of a
little over 481 grains in the ounce, to the French Troy value of 472·13
grains.
The Scots Troy weight, = 476·09 grains to the ounce, is nearly the same
as the Amsterdam weight, = 476·68 grains.
These Troy weights may be taken at three main standards, high, medium,
and low, represented by:
English Troy, its ounce = 480 grains
Amsterdam „ „ „ = 476·68 „
French „ „ „ = 472·13 „
Let us apply to 1000 ounces of water, at the medium Amsterdam standard,
= 10 Egyptian dirhems of 47·6 grains, the same measurement of a
quadrantal made to contain them as exactly as possible.
476·687/252·458 = 1886·9 cubic inches
and the cube root of the dividend gives 12·357 inches, exactly, to 1 in
20,000, the Rhineland foot as established in Prussia = 12·3564 inches.
The Prussian standard of the Cologne pound (its ounce = 451·1 grains)
was 1/66 of a Rhineland cubic foot of water at 65·75 F., and was fixed
at 7217·9 grains. This was exactly 1/66 of 1000 Troy ounces of water at
the standard of 476·38 grains. So 66 Prussian pounds were equal to 1000
Troy ounces, or to 62·5 Troy pounds at that standard.
The Rhineland cubic foot had, like the English cubic foot, long been the
bushel standard of North Germany. The Himt, now, or until quite
recently, the unit of corn-measure in Hanover and Brunswick, contained
6·852 gallons, or 68·52 lb. of water. It is probable that the Himt,
which passed to Scotland in the fifteenth century as the firlot of that
time, had risen slightly, and that it was originally = 68·05 lb., the
true Rhineland cubic foot of water.
3. THE PÁN OF MARSEILLES
Marseilles, a city of Greek origin, always in extensive commercial
relations with the Mediterranean countries using the Arabic system of
weights and measures, had an almost perfect system of its own, entirely
sexdecimal, and dating from about the tenth century. This system is
still extant, so far as the French law can be evaded (see Chap. XXI: Old
Weights and Measures of France). Wine and corn measures were in the
usual Southern water-wheat ratio of 1 to 1·22, and the principal of
these was the Escandau for wine and oil, and the Panau for corn. Now
Escandau means ‘standard’; and this measure was 1/4 of the Mieirolo, the
half wine-load or ‘wey’ which corresponded in water-wheat ratio to the
half-load or wey of wheat. The load of wheat, the _cargo_, was the cubic
cubit of Al-Mamūn, brought from Egypt by the corn-trade. The unit of
length was the Pan (pronounced páng), a word apparently similar to the
palmo of Italy and Spain, but really different. Palmo becomes _paume_ in
Provençal, while Pan is from L. _pannus_, a side, pane or panel;[11] and
the Marseilles Pan = 9·9 inches is exactly the measure of the side or
pan of an Escandau of cubical form. The filiation of the Escandau is
evident, while the Pan is not derived from any antecedent measure. That
the Pan was the measure of the pan or panel of a cubical Escandau is
supported by the name of the corn-standard, the Panau, corresponding to
the fluid standard of the Escandau, and of the land-measure, L.
_Panalata_, the peck-land, originally the extent usually sown with a
Panau of wheat.
Footnote 11:
The French word _pan_ has the same meaning, while Fr. _empan_, a span,
is a corruption of _espan_.
Escandau = 16·096 litres = 3·54 gallons.
∛16096 = 25·24 centimetres, the Pan = 9·9 inches.
The evidence of the Pan seems to me to remove any doubt as to the
medieval evolution of linear measures from imported standards of weight
or capacity. The meaning of Pan as ‘side, panel’ is conclusive,
especially when supported by the Panau measure and by other Provençal
derivatives:
_Panard_, a limping man, leaning to one side as he walks.
_Lou Panard_, the star Antares which, rising late and setting early, not
appearing much above the horizon, is visible only on one side of it.
4. THE FILIATION OF THE ENGLISH FOOT, OF THE
RHINELAND FOOT, AND OF THE MARSEILLES PAN
In the description of the ancient cubits and talents and of the Roman
system derived from them, the filiation of the English system of weights
and measures, and of the Scots and other cognate systems, is clearly
seen. There was no taking of a King’s heel-to-toe as a foot, no pound
imported from some unknown country at an unknown period, no
wheat-quarter preserved in the dimensions of an Egyptian sarcophagus,
not even a pint from the Roman sextarius; legend disappears, the course
of evolution, and, at one point, of involution, is clear, and as
thoroughly scientific as in any system invented by an Academy of
Sciences. Here are the links of filiation of the English foot:
1. The Egyptian meridian cubit.
2. The royal cubit, increased from the meridian cubit.
3. The royal foot, two-thirds of the royal cubit.
4. The cubic royal foot.
5. The Alexandrian talent, the weight of a royal cubic foot of
water.
6. The Roman ounce, 1/1500 of the Alexandrian talent.
7. The English talent, 1000 Roman ounces.
8. The volume of 1000 Roman ounces of water, the original
wine-bushel.
9. The 1000-ounce Quadrantal becomes the cubic foot, its side
giving the English foot.
For the Rhineland and Scots system we have:
1. The Egyptian meridian cubit.
2. The Arabic or Black cubit, 7 palms of the meridian cubit’s 6
palms.
3. The Arabic foot, two-thirds of the Arabic cubit.
4. The Arabic talent or Cantar, the weight of an Arabic cubic
foot of water.
5. The Troy ounce, 1/1500 of the Cantar, and coinciding with 10
lesser dirhems of about 48 grains.
6. The Rhineland talent of 1000 Troy ounces Amsterdam standard.
7. The Quadrantal containing 1000 Troy ounces of water becomes
the cubic Rhineland foot, its side giving the measure of the
Rhineland foot.
For the Provençal system we have:
1. The Egyptian meridian cubit.
2. The Arabic cubit, 7 palms of the meridian cubit’s 6 palms.
3. The Arabic cubit cubed, in the corn-measure of medieval
Egypt, the Cargo of Marseilles, the Setier of Paris.
4. The half-cargo reduced to wine-measure in wheat-water ratio
becomes the Mieirolo; of which one-fourth is the Escandau or
Standard measure.
5. The Quadrantal containing an Escandau gives, as the measure
of its side or panel, the Pán of Marseilles.
The evolution of the English foot, of the Rhineland or Scots foot, of
the Pán of Marseilles, being now made clear, we can proceed to English
and other linear measures. The origin of the Ounce, the foot, the cubic
foot or wine-bushel is explained. That of Troy weight has been seen, and
its predecessor, Tower weight, came from another ounce of the Arabic
cantar. The origin of every measure and weight used in the civilised
world will be found in the stories of the ancient cubits and talents.
------------------------------------------------------------------------
CHAPTER V
ENGLISH LINEAR MEASURES
1. THE YARD, THE FOOT, THE INCH
The term Yard, the Old English ‘gerde’ or ‘yerde,’ a wand or rod, became
specially applied to a wand of 3 feet, or 4 spans; from this double mode
of division and from its convenient length the cloth-yard of 3 feet
became generally used. It has the convenience of being a half-fathom,
and of being divisible not only into feet and inches, but also
sexdecimally into units which are familiar as limb-lengths of the cubit
and span system.
The half-yard corresponds to the Cubit.
The quarter-yard is a Span.[12]
Footnote 12:
The usual dimensions of bricks are a span by a half-span, by a nail.
The eighth is a Finger; women constantly measure linen approximately by
the length of the bent middle finger.
The sixteenth is a Nail; this is the length of the half-finger, the last
two joints of the middle finger.[13]
Footnote 13:
The story of the Nail will be found in Chap. XX.
While the yard is lawfully divided into halves, quarters, eighths, and
nails, it may also, as a measure of 3 feet, be divided into 36 inches.
Yard-measures are usually divided in both ways, on one side into 16
nails, on the other into inches.
It is customary to say either a yard and a quarter, or 45 inches, or 3
feet 9 inches. Or to say either 58 inches or 4 feet 10 inches; but it is
not customary to say a yard and 22 inches. We cease to use the yard as
unit when we cannot express its fractions sexdecimally.
The Foot is lawfully divided into 12 inches; but there is nothing to
prevent it being divided decimally, or otherwise, as convenient.
The Inch is divided according to convenience, either
Sexdecimally, into halves, quarters, &c., down to sixty-fourths.
This is the usual division.
Duodecimally, into 12 lines.
Decimally, into tenths and hundredths.
Steel foot-rules usually show all three of these scales.
Some trades may have special scales. Thus type-founders divide the Inch
into 6 ‘picas’ each = 2 lines, and the ‘pica’ into 12 points each = 1/6
line or 1/72 inch. Nonpareil type is 6 points; Brevier is 8 points.
2. STANDARDS OF THE LINEAR MEASURES
Tables of measures, from the earliest, about 1500, down to quite recent
times, usually began by stating that ‘Three barley-corns make an inch’
or that ‘Geographical measures begin at a barley-corn and increase
upward to a league,’ &c.
King David I of Scotland (_c._ 1150) is credited with the pronouncement
that the Scots inch was to be the mean measure of ‘the thowmys of iij
men, that is to say an mekill man and a man of messurabil statur and of
a lytell man. The thoums are to be messurit at the rut of the nayll.’
But no more in Scotland than in England, or elsewhere, has the inch ever
been anything but a division of the foot.
A standard of the English foot was fixed in Old St. Paul’s Church,
London, and was known as Paul’s foot, all measures being referred to the
standard ‘qui insculpitur super basim columpnæ in ecclesia Sancti
Pauli.’ In 1273 a deed gave the measurement of land ‘according to the
iron ell [yard] of the King’s palace.’
The present standard yard is a bronze bar kept in London, the length of
which agrees exactly with the yard, still extant, of Tudor times. A set
of standard measures of length is fixed along the base of the northern
wall of Trafalgar Square,[14] and another set is in the flooring of the
Guildhall. Sets are also fixed to public buildings in several chief
towns of the United Kingdom.
Footnote 14:
The Standards Commission in 1870 advised that the public standards of
length should be placed so as to be readily accessible to the public
without their use ‘being disturbed by passers or idle gazers.’ Anyone
who has tried to get access to those in Trafalgar Square may regret
that there seems to be no provision made against their site being made
the usual lounge of often very objectionable persons.
As metal rods vary in length according to temperature, comparisons with
a standard measure should be made at the normal temperature of 62°. But
there is an alloy of steel and nickel (42 per cent.), named Invar, which
is not perceptibly affected by temperature.
A pendulum beating seconds at sea-level and at normal temperature
measures 39·1393 inches at Greenwich (Act of Parliament, 1824). This
length varies in different places from the variations of gravity due to
the ellipticity of the earth and local causes of deviation.
3. THE HAND
The popular ‘hand’ was the ‘palm’ of ancient times, four digits or
finger-breadths.
_Pes habet palmos iv, palmus habet digitos iv_ (Frontinus).
‘Foure graines of barlye make a finger; foure fingers a hande; foure
handes a foote’ (Eden, 1566).
But the present Hand for horse-measurement is ‘the measure called a
Handful used in measuring the height of horses, by 27 Hen. 8, Chap. 6,
ordained to be 4 inches’ (Sam. Leake, 1701). This is part of an old
popular duodecimal division of the foot into 3 hands of 4 inches, then
of the inch into 3 barleycorns (lengthwise) each of 4 poppy-seeds, and
of these again into 12 hairbreadths.
In Austria this horse-measure is the Faust or fist.
Another very widely spread limb-measure is that of the fist with the
thumb projecting, roughly = 6 inches. It is the Shaftment of some parts
of England, _scæft-mund_ (shaft-hand) in Old English, _bawd_ in Wales;
the _somesso_ of Italy, the _kubdeh_ of Egypt, the _taim_ of Burma.
In the Laws of Æthelstan (1000) a measurement is given as 9 feet, 9
shaftments, and 9 barleycorns, i.e. 9 feet + 9 half-feet + 3 inches.
4. THE ELL
The yard, being 4 spans, was formerly one of the Ells, measures of 3, 4,
5 or more spans, related to the cubit of 2 spans. The Scots yard, of 37
inches, was always known as an Ell, and it was only gradually that our
yard took the place, for cloth measure, of the Ell of 5 spans = 45
inches, which was long maintained by statute. The yard and the ell were
usually distinguished as _virga_ and _ulna_ in statutes, but sometimes
_ulna_ meant a yard.
Both yard and ell were divided into halves, quarters, and nails
(sixteenths).
See Chap. XVI (The Ells), and Chap. XX (section on the Nail and the
Clove).
5. THE ROD, FURLONG, MILE, AND LEAGUE
The earliest table of English linear measures is probably that in
Arnold’s ‘Customs of London,’ _c._ 1500.
The lengith of a barly corne iij tymes make an ynche
and xij ynches make a fote
and iij fote make a yerde
and v quatirs of the yarde make an elle
v fote make a pace
cxxv pace make a furlong
and viij furlong make an English myle.
Thus, in 1500, the furlong was 125 × 5 = 625 feet, and the mile = 5000
feet = 1666·6 yards.
The mile was originally the Roman mile, 1000 paces or 5000 Roman feet,
and = (5000 × 11·67)/(3 × 12) in. = 1621-1/3 yards. So in course of time
our mile had become 5000 English feet.
But the linear unit for land measurement was not, as in the Roman
system, a _pertica_ or rod of 10 or 12 feet; it became very early, on
the Teutonic system, a rod of 16 feet, with varieties, under French
influence later on, of 18, of 21 and 24 feet.
In early Plantagenet times, not later than Edward I, the statute rod was
fixed at 5-1/2 yards or 16-1/2 feet. Thus, while the rood, that is the
field-furlong, was 40 rods or perches of 16-1/2 feet = 660 feet, the
itinerary furlong, 1/8 mile, remained 625 feet, ‘xxxviij perchis sauf ij
fote’ (Arnold’s ‘Chronicle’). This clashing of the new statute rod, and
its multiple the rood or field-furlong of 40 rods, with the ancient
itinerary furlong now only = 37·87 rods, was rectified in Tudor times,
probably temp. Henry VII, but definitely by a statute of Elizabeth which
raised the furlong to coincide with the rood. The mile thus became of
its present length, 8 furlongs of 40 rods of 5-1/2 yards = 1760 yards =
5280 feet. The mile has then successively been:
1.—Roman mile of 5000 Roman feet = 1621·3 yards.
2.—Old English mile „ 5000 English „ = 1666·6 „
3.—New „ „ „ 5280 „ „ = 1760 „
For long measurements chains came into use, and shortly after 1600
Edward Gunter introduced, for surveying purposes, measurement by a chain
of 4 rods, i.e. a ‘brede’ or ‘acre-brede,’ the breadth of an acre of 40
× 4 rods, divided into 100 links.
So the multiples of the yard are now:
5-1/2 yards = 1 rod
22 „ or 4 rods, or 100 links = 1 chain
220 „ „ 40 „ „ 10 chains = 1 furlong (rood)
1760 „ „ 320 „ „ 80 „ or 8 furlongs = 1 mile
The Scots mile and the Irish mile were equally 8 furlongs of 40 rods,
but Scots and Irish rods (see Chap. XIV).
Scots mile 320 rods of 6 ells (6·1766 yards) = 1976 yards
Irish „ „ „ 7 yards = 2240 „
The term Yard has been used for certain large land-measures. These, with
the evolution of the Rod, will be given in the next chapter.
_The League_
It has been seen that the Persian Parasang was three meridian miles, or
3000 Olympic fathoms. France retains this as the _lieue marine_ of 20 to
the degree, and Southern France long retained a league of 3 miles each
of 1000 toises or cannes. But in Roman times the Leuca or Leuga of Gaul
was 1-1/2 Roman miles. It passed to medieval England at about the same
length, being defined as _duodecim quaranteinis_, 12 furlongs or roods
of 40 rods.
------------------------------------------------------------------------
CHAPTER VI
LAND-MEASURES
1. INTRODUCTION
The first measures of land were seed-measures. They are found in every
country; they become fixed in course of time as the idea of geometric
measurement arises; they survive in name giving the peasant a concrete
idea of the extent of his fields.
Then came the estimation of land by the amount of ploughing, or
sometimes of hand-digging, that could be done in a day, and by the
extent that could be cultivated with a pair of oxen. Then came a system
of geometric measurement, fixing the former seed-units or labour-units
by measures of length and breadth, and finally the abstract idea of
superficial area. These different systems have succeeded one another
everywhere and in all time.
1. Seed-units.—The land that could be sown with a certain measure of
seed-corn, wheat being the usual standard: Fr. _seterée_, _estrée_,
_boisselée_, &c.; It. _moggio_; Sp. _fanega_; G. _scheffel_; Nor.
_tunn-land_. These names correspond to corn-measures.
2. Day’s hand-labour units.—The land that could be tilled with spade or
hoe in a day: the ‘Daieswork,’ about 10 square rods; Fr. _hommée_,
_ouvrée_—20 square rods of vineyard.
3. Day’s ploughing units.—L. _jugerum_; It. _giornata_; Fr. _journal_,
_arpent_; G. _morgen_, _joch_, _acker_; Du. _bouw_; Hind. _bigha_; Ar.
_feddan_; Ir. _ardagh_. All about an English acre more or less.
4. Oxgang units.—The land that a boor with a yoke of oxen could keep in
husbandry; about 7 acres of arable, about 30 acres including wood and
pasture:
Yard-land; Du. _hoeve_. A group of oxgangs, generally of four yoke, made
a Ploughland; Prov. _un mas de quatre couble_, a four-yoke farm.
5. Geometric units.—First, units of a certain shape based on the
customary length of the furrow: Rood, 40 rods by 1 rod broad; Fr.
_vergée_, _seillon_. Then small units of a square rod, the rod being of
customary length; with large units, usually groups of roods, vergées,
&c. Four roods side by side make the English or the Norman acre. A rood
square or square furlong is the ‘acreme’ or 10-acre field.
Legal units of land were usually abstract, of so many square rods or
fathoms, independently of any customary shape.
2. EVOLUTION OF GEOMETRIC LAND-MEASURES
While smaller units, such as the superficial rod, can easily be
conceived as square, the larger arable units have, or have had, a
peculiar form which still attaches to them. The peasant, whose mind’s
eye can perceive the square rod or toise or verge, refers the rood or
the acre, the vergée or the arpent, to the familiar length of the furrow
and to the breadth of the rod or of the four-rod acre-breadth equal to a
cricket-pitch. These lengths and breadths will long be his essentially
concrete standards of field-measurement.
While some legal units of surface have recognised the customary
furrow-length as an element of this form, others have always been
undefined as to form.
In ancient Egypt the land was surveyed by the state, not only for
revenue purposes, but because of the Nile overflow effacing the
land-marks usual in other countries.
‘Hence land-measuring appears to me to have had its beginning, and to
have passed over to Greece’ (Herodotus). The agrarian unit of Egypt,
called by the Greeks _aroura_, a plough-land, was a square, each side
being a Khet or cord, of 100 royal cubits = 172 feet or 57-1/3 yards.
The square khet is represented by the present Egyptian feddan al risach
of 20 lesser qasáb (each 20 × 4 Hashími cubits) = 170·4 feet square =
2/3 acre.
Ten square khet made the usual land-holding. This unit, = 6·79 acres,
corresponds closely to 10 modern feddan, to the véli or oxgang unit of
Southern India, and to the 7 acres of arable in the medieval English
boor’s yard-land. That the ancient Egyptian oxgang was 10 khets in a
line, giving if required a furrow of 573 yards easy in muddy alluvial
soil, seems certain, for its hieroglyphic is a line of ten small
squares. This is exactly the primitive form of the English acre, 10 × 1
chains.
In ancient Greece the unit of land-measure was the plethron of 10 rods
(kalamoi) each of 10 Olympic feet, = 101·33 English feet. Had it a
concrete agrarian form? Evidently the square plethron (= 0·235 acre or
nearly a rood) was much too short for a plough-unit; but the larger unit
was the tetragyon, i.e. a four-rood field, and with the four square
plethra end-on-end, this Greek acre afforded a furrow-length of 135
yards. So it is probable that the tetragyon, 135 × 33-3/4 yards, = 0·94
acre, was the usual concrete agrarian unit.
A common size of land-holding was 12 × 12 = 144 plethra, = about 34
acres, a size corresponding to our medieval oxgang.
In ancient Italy land was measured by the Roman decempeda or pertica,
the 10-foot perch or rod, = 9·725 feet.
A strip of land 120 × 4 Roman feet made an Actus, probably the breadth
of a double furrow, up and down. The square actus, actus quadratus, = 30
acti = 120 × 120 feet, about 50 square rods.
Two square acti made a Jugerum, the day’s work for a yoke of oxen, =
0·623 acre.
Four square acti, bina jugera, made the Heredium, = 1·246 acre.
How were the four square acti arranged? Were they in a square 240 × 240
feet? No doubt that would be the official form of the heredium; but it
is probable that, as I have assumed for the Greek tetragyon of 4 square
plethra, the 4 Roman acti would be, when convenient, practically
arranged in a line, thus giving an agrarian unit of 480 × 120 feet and a
furrow of about 160 yards, which is nearly one-tenth of the 5000 feet
Roman mile.[15]
Footnote 15:
For evidence on the form of agrarian units see Notes in section 5 of
this chapter.
The official division of the field was based on the jugerum; this being
divided, on the duodecimal or uncial system, into 12 unciæ, each of 24
square perticæ, the latter being the scruples, the qiráts, of the Roman
land-ounce. Here we see the uncial system overshadowing the decempeda;
for if the jugerum could be divided into 12 ounces of 240 × 10 feet and
these into 24 scruples of 10 feet square, each of its two acti might
also be divided into 100 sections of 12 feet square, or the double
jugerum into 100 sections of 24 feet square. It is probable that this
would be a more popular division than that based on the decempeda; for
it is certain that a rod of 16 spans = 12 feet was used; it was the
Græco-Roman _akena_ (from _akis_, goad), a gad or rod.
The Heredium passed to Gaul, where it established itself in the north,
becoming the French arpent, 100 square perches, each of 6 aunes (= 24
Roman feet) square, so that the arpent is identical with the heredium,
and was divided on the plan I have suggested as that of the Roman
land-measure. But the arpent rarely coincided with the standard of the
Paris government, and both seed-measures and work-measures, of fixed
area, were often preferred. Where the _coutumes de Normandie_ are still
in almost full force and are cherished by the people, the principal unit
of land-measure was, and is still, the Acre de Normandie, containing 160
perches of 24 feet square. The standard of the foot varies; sometimes it
is the royal foot, sometimes the Roman foot, retained by the device of
taking 11 royal inches for a foot. The ancient standard of this acre is
thus expressed in law-Latin: Pertica terræ fecit 24 passus seu soleas
pedis; 40 perticæ faciunt virgatam; duæ virgatæ faciunt arpentum; 4
virgatæ faciunt acram. ‘Passus’ is here a foot; but sometimes it meant a
pace, half of the Roman pace which is here represented by the brasse of
5 royal feet = 1·624 metre. So in Normandy land-measure the _pas_ = 32
inches and the Caux peasant reckons his vergée as 100 × 20 paces = 88·8
× 17·76 yards. These concrete forms of land-unit are dying out, yet
everywhere traces of it can be found in conversation with old peasants.
From the South of France to England and Scotland there is a concrete
shape recognisable in the large unit of land-measure. The Provençal
Saumado of 1600 square cano or toises, the Normandy acre of 160 square
rods of 4 toises, the English acre of 160 square rods of 5-1/2 yards,
the Scots acre of 160 square rods of 6 ells = 18·53 feet, are all
connected by a common tradition of concrete form, and are all made up of
four minor units: sesteirado, vergées, roods, &c. Looking back to the
land-measures of Greece and Rome we find this same group of four lesser
units in the tetragyon and heredium. The law may only recognise abstract
superficial standards, but the peasant holds to the concrete units of
form convenient for cultivation.
3. ENGLISH LAND-MEASURES
Notwithstanding Homer’s recommendation of mules as ‘better far than kine
to drag the jointed plough,’ oxen are still used in the greater part of
the world. In light soils one yoke of oxen is sufficient, but in heavy
fallows, with deep-working ploughs, two, three or more yoke were used;
and in feudal times it would appear that the four tenants of a hide or
ploughland co-operated with their oxen. A furrow of 40 rods could thus
be made easily in one breath, and as this length of a rood coincided
approximately with the eighth of a mile, that division of the mile was
also called a furrow-long or furlong. When ploughing up fallow-land the
oxen, on getting to the end of the ‘shot,’ turned and took breath. The
ploughman measured a rod-breadth from the first furrow by means of his
goad, Scottice by the ‘fall’ of it, and this rod-breadth down which the
oxen turned, the _tornatura_ of Italy, was a rood.
Sometimes between the roods a narrow unploughed strip, a balk of land,
was left, marking the roods or ‘selions,’ four of which, side by side,
made an acre, and forty of which made the square furlong, the ten-acre
field.
Ploughing in roods, selions, square furlongs, is still far from extinct.
In Brittany land is still reckoned by _seillons_ of so many furrows
wide, or of so many _gaules_ or 12-foot rods. In Southern France fields
are estimated in breadths of a _destre_, of the 12-foot rod
corresponding roughly to the width cleared by a couple of mowers. In our
Isle of Axholme, in North Lincolnshire, land is reckoned in selions of a
rod wide and usually of a furlong in length; these selions or roods
being grouped into furlongs, that is, actually or originally, into
greater units of a square furlong = 40 roods or 10 acres.
Simple country-folk, whose only ideas of land-measure were taken from
the length of the ox-goad and of the furrow, and from the breadth of the
long acre-strip of land, came slowly to understand that the surface of a
field of irregular shape might be reckoned in acres and rods. A statute
of Edward II gave a table of the different breadths of the acre when it
was less than forty rods or perches in length:
‘When an acre of land containeth ten perches in length, then it shall be
in breadth sixteen perches; when it containeth eleven perches in length,
then it shall be in breadth fourteen and a half and three-quarters of a
foot’—and so on through the different lengths an acre might be.
So people came gradually to abstract the idea of superficial measure
from shape and to apply it to land of any figure, however different from
a square or a rectangle. Thus measures, always _concrete_ at first and
taken from some known object of comparison, became _abstract_ in men’s
minds for purposes of calculation. Then came the land-surveyor
introducing arithmetic and geometry into the art of measurement, and
using the cord or chain instead of the measuring rod; and it was also
found that decimal calculation would be an improvement in this art.
For purposes of accurate measurement and calculation, Edward Gunter
introduced, nearly three centuries ago, measurement by a chain of a
hundred links and twenty-two yards or four rods in length. Its adoption
decimalised the land-measures without disturbing them. Ten chains go to
a furlong and ten square chains to an acre.
Norden (‘Surveior’s Dialogue,’ 1610) mentions the ‘standard chaine, that
is by the chaine of 16-1/2 foote.’ It was soon after this that the chain
was increased to 66 feet or 4 rods, which length was a current unit, the
‘brede’ or acre-brede, the breadth of an acre.
MEASURES OF LENGTH AND OF SURFACE
In the following table each superficial unit is placed opposite the
lineal unit of which it is the square:
─────────────────────────┬───────────────────────────────────────────────
LINEAL MEASURES │ SUPERFICIAL MEASURES
─────────────────────────┼───────────────────────────────────────────────
12 inches 1 foot │ 144 square inches 1 sq. foot.
3 feet 1 yard │ 9 square feet 1 sq. yard.
5-1/2 yards 1 rod │ 30-1/4 square yards 1 sq. rod.
│⎧ 40 square rods 1 rood
40 rods 1 furlong │⎨ (4 roods or 160 square rods 1 acre).
│⎩ 40 roods (10 acres) 1 sq. furlong.
8 furlongs 1 mile │ 64 square furlongs (640 acres) 1 sq. mile.
─────────────────────────┴───────────────────────────────────────────────
SURVEYOR’S MEASURE
─────────────────────────────────┬─────────────────────────────────────────────
1 link (7·8 inches) ·22 yards.│1 square link ·048 sq. yds.
10 links 2·2 „ │100 square links 4·84 „
100 links (1 chain) 22 „ │10,000 sq links (1 sq. chain) 484 „
10 chains (1 furlong) 220 „ │10 sq. chains (1 acre) 4840 „
─────────────────────────────────┴─────────────────────────────────────────────
It must be remembered that _the length of the rod determined the length
of the mile and the area of the acre_. This is shown in the table on the
following page.
BRITISH MILES AND ACRES DERIVED FROM DIFFERENT RODS IN LOCAL USAGE
────────────────────────┬─────────────────────┬─────────────────────
LENGTH │ STATUTE │ SCOTTISH
────────────────────────┼─────────────────────┼─────────────────────
1 rod │ 5-1/2 yards │ 6·1766 yards
40 rods = 1 furlong │ 220 „ │ 247 „
8 furlongs = 1 mile │ 1760 „ │ 1976 „
│ │= 1·123 statute miles
│ │
SURFACE │ │
1 square rod │ 30-1/4 square yards│ 38·15 square yards
40 square rods = 1 rood │ 1210 „ „ │ 1526 „ „
4 roods = 1 acre │ 4840 „ „ │ 6104 „ „
│ │ = 1·26 statute acre
────────────────────────┼─────────────────────┼─────────────────────
LENGTH │ IRISH │ CHESHIRE
────────────────────────┼─────────────────────┼─────────────────────
1 rod │ 7 yards │ 8 yards
40 rods = 1 furlong │ 280 „ │
8 furlongs = 1 mile │ 2240 „ │
│= 1·278 statute miles│
│ │
SURFACE │ │
1 square rod │ 49 square yards│ 64 square yards
40 square rods = 1 rood │ 1960 „ „ │ 2560 „ „
4 roods = 1 acre │ 7840 „ „ │ 10240 „ „
│ = 1·62 statute acre │= 2·116 statute acre
────────────────────────┴─────────────────────┴─────────────────────
_Note._—The Scottish rod or ‘fall’ is six Scottish ells or yards. The
Scottish and Irish miles have long been practically obsolete. The
Lancashire rod and acre, also the Guernsey perch and acre, are the same
as the Irish. The Guernsey land-measures are statute locally; the rood
or vergée is the customary unit.[16]
Footnote 16:
It is worth remark that the 160 square rods of the Irish, Lancashire
or Guernsey acre being equal to 1·62 statute acres, 100 of these
square rods would make almost exactly a statute acre. A rod of 6·957
yards would give a decimal square rod of 48·4 square yards equal
1-10th square chain, or 1-100th acre, or 1-1000th square furlong. A
square-shape acre is 69·57 yards square.
A SQUARE FURLONG OR TEN-ACRE FIELD
1 2 3 4 5 6 7 8 9 10
┌┬┬┬┬────┬────┬────┬────┬────┬────┬────┬────┬────┐
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ ├────┤
│││││ │ │ │ │ │ │ │ │ │
│││││ │ │ │ │ │ │ │ │ │
└┴┴┴┴────┴────┴────┴────┴────┴────┴────┴────┴────┘
Acre No. 1 is divided, according to the ancient custom, into 4
roods, each 40 rods long and 1 rod broad.
Acre No. 10 is divided, according to Gunter’s decimal system,
into 10 square chains, each 4 rods square.
4. FEUDAL LAND-MEASURES
In ancient Egypt land was surveyed by a State department, but other
Eastern Kingdoms, even of the present time, are less advanced. There is
a simple system of taxing each plough. This was approximately the
medieval system, as we see in the Domesday revenue-survey, the great
record of the plough-lands and rental of England. Estates are thus
described:
2-1/2 hides; land for 1-1/2 ploughs. There is 1 plough with 4
bordars and 4 serfs. Worth 30_s._
2 hides, land for 2 ploughs, 30 acres meadow. Worth 60_s._
4 hides, 1-1/2 virgates; land for 10 ploughs. Now worth 14 li.,
formerly at 17 li.
In some parts the ‘knight’s fee’ was reckoned at 480 acres (4 hides)
worth 40 shillings a year. On this valuation—
The pound-land, librata terræ, was 240 acres.
The shilling-land, solidata terræ, was 12 acres.
The penny-land, denariata terræ, was 1 acre.
The farthing-land, 1/2 obolata terræ, was 1 rood.
_Cent livrées de terre à l’esterlin_ (Froissart) a hundred pound-lands,
reckoned of the annual value of 100 pounds sterling. This is sometimes
taken as the amount of ‘relief,’ another feudal estimate, often taken at
one year’s value.
In Edward I’s time a son and heir paid £18 for relief of his land which
was worth £18 a year. In Henry II’s time £5 appears to be the usual
relief paid for a knight’s fee on succession to it. By Magna Charta the
relief of a whole barony (10 to 40 knight’s fees) was fixed at 100
marks; in Henry III’s time it was £100.
I may here give a fifteenth-century record of English linear
measures.[17]
Nota, for to mesure and mete lande.
It is to mete that iij Early Cornys in the myddis of the Ere
makyth one ynche, And xij enchis makyth a foote
And sixteyne foote and a halfe makyth a perche; And in sum
cuntre a perche ys xviij foote.
Fourty perchys in lengyth makyth a Rode of Lande; put iiij
therto in brede, and that makyth an Acre.
And xiiij Acrys makyth a yerde of lande;
And v yerdis makyth an hyde of lande, which ys lxx Acrys.
And viij hydis makyth a knyghtis fee, which is vC.lx Acrys of
lande.
Footnote 17:
I insert this note (sent to the _Academy_ in August 1896 by the late
Mr. F. J. Furnivall, who found it in a Bodleian MS.) because it
happened to direct my attention to our measures, and was thus the seed
whence this book has sprung. The yardland and hide are here of less
than half the usual extent.
5. TERMS USED IN LAND-MEASURES
ROD.—Pole, Perch, Goad, Lug, L. _pertica_, Fr. _perche_, _verge_, G.
_ruthe_, Du. _roede_.
The equivalent words, L. _virga_, Fr. _verge_, A.S. _geard_, Eng.
‘yard,’ originally any long straight twig or rod, came to mean: (1) a
yard or ell-measure, (2) a rod measure of land, lineal or superficial.
The French verge is still thus used in Normandy and the Channel Islands.
Our ‘yard’ acquired this extended sense, and others still more extended.
In Cornwall 2 staves (of 9 feet) make a yard of land. In Somerset the
lineal rod is the ‘land-yard,’ and the yard of land is a square rod.
Thus the rood is ‘forty yard o’ ground’ and the acre is ‘eight score
yard o’ ground.’
ROOD.—A differentiated form of ‘rod’ applied in a lineal sense to 40
rods, and also to the area of a quarter-acre 40 × 1 rods.
In Normandy and the Channel Islands our rod and rood are verge and
vergée, and as the first sense of verge was ‘yard’ so vergée became in
English a ‘yard of lande.’ So here we have a third sense of the
triple-form word virga-verge-yard.
‘A rodde of land which some call a roode, some a yarde lande, and some a
farthendale’ (Recorde, 1542).
The latter term, meaning a ‘fourth part,’ as in the farthing to the
penny, may also have referred to the rood as being a farthing-land in
rental. It appears as L. _furendellus_, _farundel_, _ferling_.
The rood was also divided into 4 day’s-work, each of 10 square rods.
ACRE.—As the rood was sometimes lineal, though usually superficial, so
also the ‘acre’ was sometimes a rough lineal measure, generally an
acre-breadth, or 4 rods (a cricket-pitch). But it might also be an
acre-length = a rood length. The verse in 1 Samuel xiv.: ‘And that first
slaughter which Jonathan and his armour bearer made was about twenty men
within as it were an half-acre of land which a yoke of oxen might plow,’
is in Coverdale’s version (1535) ‘within the length of halve an aker of
londe,’ that is, in a length of 20 rods. In French ‘arpent’ was likewise
used for a French acre-length, reckoned, not of the official square
arpent, but of the furrow-long arpent, nearly a furlong. Thus in the
Chanson de Roland
_Einz qu ’hum alast un sul arpent de camp_
(Before one (he) went a single acre of ground)
evidently means about a furlong, just as in Iliad x., ‘when he was as
far off as the length of the furrow made by mules’ has the same meaning.
Similarly the _sesteirado_ of Provence was used as an itinerary measure,
probably of 100 cano = about 220 yards, the same as the centenié.
The _sesteirado_, the rood of Southern France, corresponding to the
_boisselée_, the bushel-land of Mid-France, was, like the latter,
originally a seed-unit, the extent sown with a _sestié_ of seed-corn.
Its extent is 0·4 acre, = our rood. Now if this were square, each side
would measure 40 yards, a length too small for itinerary measure.
Neither Northern nor Southern France had any official itinerary measure
under the league, so field-units were necessarily used; in the north the
arpent-length, in the south the sesteirado-length; both corresponding to
our rood-length, furrow-length or furlong. There seems little doubt that
the _centenié_, the popular itinerary measure of the south, 100 cano or
fathoms, was the same as the sesteirado-length. And the sesteirado being
400 square cano, it seems that its dimensions were 100 × 4 cano. It was
moreover the rood, or quarter of the greater land-unit, the _saumado_,
the ‘seam’ of land, which would thus be 100 × 16 cano just as our rood
was 40 × 1 rods, and our acre 40 × 4 rods. Ten sesteirado-lengths, 10
centenié, made the _milo_, a mile of 1000 local fathoms, one-third of
the league of Southern France.
YARDLAND.—L. _quatrona terræ_, _virgata_. Fr. _bouvée_. Bovate, Oxgang.
About 30 acres more or less, including pasture and perhaps some
woodland. Before the Norman conquest the gebur-geriht (boor’s right) was
6 sheep and 7 acres arable on his yard-land. This corresponds roughly to
the German _hufe_ = about 20 acres, and to the Netherlands _hoeve_, the
unit of small holding. Almost everywhere and always, 6 or 7 acres of
arable have been all that the boor’s yoke of oxen can till. There was
other work for the oxen besides ploughing, and at least five ploughings
were usually necessary for proper tillage; then there was cartage and
feudal duties in consideration of the small rent.
In the Roll of Battel Abbey (tenth and eleventh centuries) the perch is
16 feet; the acre is 40 perches long and 4 broad and pays a penny a
year; 3 shillings for the virgate or wist, the price of which was about
20 shillings. In this case 8 virgates made a hide, but this ‘eighth’ is
exceptional, for the term ‘virgate’ brought a fourth sense to the virga
= yard series of words, giving rise to the term yard-land as a quarter
of the plough-land or hide. As the vergée in France (sometimes
ambiguously called verge, as it has been seen that Recorde spoke of ‘a
rodde of lande which some call a roode’) and the rood in England were a
quarter-acre, and as this quarter-acre was sometimes called a ‘yard of
land,’ so virga-verge-yard acquired the general sense of
‘quarter’—either of an acre or of a ploughland or carucate. Thus in
‘Quant une homme est feffe dune verge de terre et dun autre de un carue
du terre’ (Statute of Wards, 1300), the term ‘verge de terre’ means not
a rod, a verge, but a yardland or virgate.
‘Farthing’ or ‘ferling’ as a quarter was used in the same double sense:
a quarter-acre or a quarter-hide, indeed, as will presently be seen, a
quarter-virgate.
ACREME.—This old law-term for 10 acres of land points to a tradition
that our original unit of land-measurement was a rood or furlong square,
that is 40 × 40 rods: it was called a Ferlingata or Ferdelh.
A document temp. Edw. II describes the virgate (of which 4 made a hide;
5 hides being a knight’s fee) as of 4 (square) furlongs, each of 10
acres.
X acræ terræ faciunt unam fardellam.
Decem acræ faciunt ferlingatam; quatuor ferlingatæ faciunt
virgatam, et quatuor virgatæ faciunt hidam; quinque hidæ faciunt
feodum militis.
So it appears conclusive (1) that the hide was 16 square furlongs, a
quarter of a square mile = the quarter section of America; (2) that the
acre was originally a slice of land off the square furlong, a rood, or
furlong in length, a tenth of this in breadth.
FURLONG AND FERLING.—The square furlong is the same as the Acreme = 10
acres. The square furlong or furrow-long tends to become confused with
ferling, G. _vierling_, with fardel, G. _viertel_, with farthendale, Du.
_vierendeel_, all meaning a fourth. This confusion arises from the
square furlong, similar in sound to ferling, being approximately the
fourth, or farthing, of the virgate or yardland, itself Ferlingus terræ,
a fourth of the hide or ploughland. So a ferling may be a fourth of an
acre, or of a virgate, or of a hide. Similarly it may be, as farthendale
or farendel, a quarter-bushel.
Another cause of confusion in feudal land-measures is the
money-estimation of land. Bishop Fleetwood (‘Chronicon,’ 1707) thought
the acre was a marc-land of 160 pence and the rod a penny-land,
denariatus terræ, so that the quarter-rod was a farthing-land. He was
deceived by the coincidence of the 160 rods of the acre with the 160
pence, 13_s._ 4_d._, 8 ounces of silver, of the monetary marc, and he
mistook the Farthingdale or Farendel, a quarter-acre or rood, for a
quarter-rod. The acre was distinctly a penny-land, and the hide of 160
acres was a marc-land, paying 160 pence.