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 (tripodin) in diameter, and a pestle three cubits (tripichten), and an axletree seven feet (heptapodin) ... and hew a wheel of three spans (trispithamon) for the plough-carriage of ten palms (dekadoro) length.

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

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

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

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

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

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

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

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.