Men and Measures

CHAPTER I. General View

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.

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.

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