Bible Encyclopedias
Weights and Measures-2

Image: Square Section of bar.

Image:Slotted Section at points a and b.

 a  b 
 
 --v----------------------------------v--
 
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 / /
 
 FIG. I. - Present Imperial Standard Yard, 1844.
 
 ...............................................................................................
 
 Total length of bronze bar, 38 in.; distance a to  b is 36 in., or the imperial yard; 
 
 a b, are wells sunk to the mid-depth of the bar, at the bottom of each of which is inserted a gold stud, 
 
 having the defining line of the yard engraved on it.
 

National standards of length are not legally now referred to natural standards or to physical constants, but it has been shown by A. A. Michelson that a standard of length might be restored, if necessary, by reference to the measurement of wave-lengths of light. Preliminary experiments have given results correct to ± 0.5 micron, and it appears probable that by further experiments, results correct to to ± 1.0μ may be obtained. That is to say, the metre might be redetermined or restored as to its length within one ten-millionth part, by reference to, e.g., 1553163.5 wave-lengths of the red ray of the spectrum of cadmium, in air at 15° C. and 760 mm. See: Valeur du Metre, A. A. Michelson (Paris, 1894); Units, Everett, Illustrations of C.G.S. System; Unites et Etalons, Guillaume (Paris, 1890); Lupton's Numerical Tables, 1892; Metric Equivalent Cards, 1901; Dictionary of Metric Measures, L. Clark (1891); Glazebrook and Shaw's Physics (1901).

In all countries the national standards of weights and measures are in the custody of the state, or of some authority administering the government of the country. The standards of the British Empire, so far as they relate to the imperial and metric systems, are in the custody of the Board of Trade. Scientific research is not, of course, bound by official standards.

For the care of these national standards the Standards Department was developed, under the direction of a Royal Commission -- See: Report Standards Commission, 1870 -- (of which the late Henry Williams Chisholm was a leading member), to conduct all comparisons and other operations with reference to weights and measures in aid of scientific research or otherwise, which it may be the duty of the state to undertake. Similar standardizing offices are established in other countries (see Standards). Verified " Parliamentary Copies " of the imperial standard are placed at the Royal Mint, with the Royal Society, at the Royal Observatory, and in the Westminster Palace.

 Missing Image: weightsandmeasures-3.jpg
 
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 FIG. 2. - Imperial Standard Pound, 1844.
 
 .
 
 Platinum pound avoirdupois, of cylindrical form, 
 
 with groove at "a" for lifting the weight.
 

The forms of the four primary standards representing the four units of extension and mass are shown in figs. 1 to 4.

A secondary standard measure for dry goods is the bushel of 1824, containing 8 imperial gallons, represented by a hollow bronze cylinder having a plane base, its internal diameter bring double its depth.

The imperial standard measure of capacity is a hollow cylinder (fig. 5) made of brass, with a plane base, of equal height and diameter; which when filled to the brim, as determined by a plane glass disk, contains io lb weight of water at t = 62° F.B. = 30 in., weighed in air against brass weights.

--4. Atmospheric Pressure, and Materials

In the verification of a precise standard of length there may be taken into account the influence of the variation of atmospheric pressure. Taking the range of the barometer in Great Britain from 28 to 31 in., giving a difference of 3 in. (76 millimetres), which denotes a variation of 103 grammes per square centimetre in the pressure of the atmosphere, the change caused thereby in the length of a standard of linear measurement would appear to be as follows: --

For the yard measure of the form shown in fig. 1 a difference of length equal to 0.000002 in. is caused by the variation of atmospheric pressure from 28 to 31 in. For the metre of the form shown in fig. 3, below, the difference in length for a variation of 76 mm. in the barometer would be 0.000048 mm. on the metre.

With reference to the materials of which standards of length are made, it appears that the Matthey alloy iridio-platinum (90% platinum, 10% iridium) is probably of all substances the least affected by time or circumstance, and of this costly alloy, therefore, a new copy of the imperial yard has been made. There appears, however, to be some objection to the use of iridio-platinum for weights, as, owing to its great density (Δ=21.57), the slightest abrasion will make an appreciable difference in a weight; sometimes, therefore, quartz or rock-crystal is used; but to this also there is some objection, as owing to its low density (Δ=2.65) there is a large exposed surface of the mass. For small standard weights platinum (Δ=21.45) and aluminium (Δ=2.67) are used, and also an alloy of palladium (60%) and silver (40%) (Δ=11.00).

For ordinary standards of length Guillaume's alloy (invar ) of nickel (35.7%) and steel (64.3%) is used, as it is a metal that can be highly polished, and is capable of receiving fine graduations. Its coefficient of linear expansion is only 0.0000008 for 1° C. See: Rapport du Yard, Dr Benoit (1896).

 Missing image of Metre Bar, in length A and cross section  b 
 
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 Fig. 3 National Standard Metre, 1897
 

 Iridio-platinum bar of Tresca section as shown at A. The two microscopic lines are engraved on the 
 
 measuring axis of the bar at b, one near to each end of the bar. The standard metre ( metre-traits )
 
 was supplemented by the delivery to Great Britain, in 1898, of an end standard metre (metre-a-bouts ) 
 
 also made of iridio-platinum, and also verified by the C.I.P.M. A comparison of the yard 
 
 with the metre was made by the C.I.P.M. in 1896, and of the pound and kilogram in 1883-1885. 
 
 (See: III. Commercial). 
 

--5. Electrical Standards.

Authoritative standards and instruments for the measurement of electricity, based on the fundamental units of the metric system, have been placed in the Electrical Laboratory of the Board of Trade. (See: Orders in Council (1894)). These include --

Current measuring instruments. The standard ampere, and sub-standards from 1 to 2500 amperes.

Potential measuring instruments. The standard volt, and sub-standards for the measurement of pressure from 25 to 3000 volts.

Resistance measuring instruments. The standard ohm, sub-standards up to 100,000 ohms, and below 1 ohm to = 1/1000 ohm.

--6. Temperature

In the measurement of temperature the Fahrenheit scale is still followed for imperial standards, and the Centigrade scale for metric standards. At the time of the construction of the imperial standards in 1844, Sheepshanks's Fahrenheit thermometers were used; but it is difficult to say now what the true temperature then, of 62° F., may have been as compared with 62° F., or 16.667° C., of the present normal hydrogen scale. For metrological purposes the C.I.P.M. have adopted as a normal thermometric scale the Centigrade scale of the hydrogen thermometer, having for fixed points the temperature of pure melting ice (0°C) and that of the vapour of boiling distilled water (100°C), under a normal atmospheric pressure; hydrogen being taken under an initial manometric pressure of 1 metre, that is to say, at 1000/750 = 1.3158 times the normal atmospheric pressure. This latter is represented by the weight of a column of mercury 760 mm. in height; the specific gravity of mercury being now taken as 13.5950, after Volkmann and Marek, and at the normal intensity followed under this pressure. The value of this intensity is equal to that of the force of gravity at the Bureau International, Paris (at the level of the Bureau), divided by 1.000332; a co-efficient which allows for theoretical reduction to the latitude 45° and to the level of the sea. The length of the metre is independent of the thermometer so far that it has its length at a definite physical point, the temperature of melting ice (0° C.), but there is the practical difficulty that for ordinary purposes measurements cannot be always carried out at 0° C.

The International Geodetic Committee have adopted the metre as their unit of measurement. In geodetic measurements the dimensions of the triangles vary with the temperature of the earth, but these variations in the same region of the earth are smaller than the variations of the temperature of the air, less than 10° C. Adopting as a co-efficient of dilatation of the earth's crust 0.000002, the variations of the distances are smaller than the errors of measurement (see Geodesy).

--7. Standardizing Institutions

Besides the State departments dealing with weights and measures, there are other standardizing institutions of recent date. In Germany, e.g. there is at Charlottenburg (Berlin) a technical institute (Physikalisch - technischeReichsanstalt) established under Dr W. Forster in 1887, which undertakes researches with reference to physics and mechanics, particularly as applied to technical industries. (See: Wissenschaftliche Abhandlungen der physikalischen Reichsanstalt, Band ii. (Berlin, 1900); Denkschrift betreffend die Tdtigkeit der K. Norm.-Aichungs Kommn. (1869-1900).)

In England a National Physical Laboratory (N.P.L.) has been established, based on the German institute, and has its principal laboratory at Bushey House, near Hampton, Middlesex. Here is carried out the work of standardizing measuring instruments of various sorts in use by manufacturers, the determination of physical constants and the testing of materials. The work of the Kew Observatory, at the Old Deer Park, Richmond, has also been placed under the direction of the N.P.L. (See III. Commercial, and Treasury Committee on National Physical Laboratory, Parlimentary Paper, 1898.)

The C.I.P.M. at Paris, the first metrological institution, also undertakes verifications for purely scientific purposes. A descriptive list of the verifying instruments of the Standards Department, London, has been published. (See: Descriptive List of Standards and Instruments. Parlimentary Paper, 1892.)

In the measurement of woollen and other textile fabrics, as to quality, strength, number of threads, &c., there exists at Bradford a voluntary standardizing institution known as the Conditioning House (Bradford Corporation Act 1887), the work of which has been extended to a chemical analysis of fabrics.

FIG. 4. - National Standard Kilogram, 1897.

--8. Ancient Standards of England and Scotland.

A "troy pound " and a new standard yard, as well as secondary standards, were constructed by direction of parliament in 1758-1760, and were deposited with the Clerk of the House of Commons. When the Houses of Parliament were burned down in 1834, the pound was lost and the yard was injured. It may here be mentioned that the expression "imperial" first occurs in the Weights and Measures Act of 1824. The injured standard was then lost sight of, but it was in 1891 brought to light by the Clerk of the Journals, and has now been placed in the lobby of the residence of the Clerk of the House, together with a standard "stone" of 14 lb. (See: Report on Standards deposited in House of Commons, 1st Nov. 1891.)

In the measurement of liquids the old "wine gallon" (231 cub. in.) was in use in England until 1824, when the present imperial gallon (fig. 5) was legalized; and the wine gallon of 1707 is still referred to as a standard in the United States. Together with the more ancient standard of Henry VII. and of Queen Elizabeth, this standard is deposited in the Jewel Tower at Westminster. They are probably of the Norman period, and were kept in the Pyx Chapel at Westminster, now in the custody of the Commissioners of Works. A sketch of these measures is given in fig. 6. (See: S. Fischer, The Arts Journal , August 1900.)

Besides these ancient standards of England (1495, 1588, 1601) there are at the council chambers of Edinburgh

Linlithgow some of the interesting standards of Scotland, as the Stirling jug or Scots pint, 1618; the choppin or half-pint, 1555 (fig. 7); the Lanark troy and tron weights of the same periods (fig. 8). (See: Buchanan, Ancient Scotch Standards. )

FIG. 5 - Present Imperial Standard Gallon, 1824

Weightsandmeasures-5.jpg

FIG 6 - A. Winchester Bushel of Henry VII; B. Standard Hundredweight (112 lbs) of Elizabeth; C. Ale Gallon of Henry VII; D. The old Wine Gallon.

Weightsandmeasures-6.jpg

FIG. 7. - The Scots Choppin, or Half-Pint, 1555.

Weightsandmeasures-7.jpg

FIG. 8. - Lanark Stone. Troy Weight, 1618.

Weightsandmeasures-8.jpg

English Weights and Measures Abolished.

The yard and handful, or 40 in. ell, abolished in 1439. The yard and inch, or 37 in. ell (cloth measure), abolished after 1553; known later as the Scotch ell = 37.06. Cloth ell of 45 in., used till 1600. The yard of Henry VII. = 35.963 in. Saxon moneyers pound, or Tower pound, 5400 grains, abolished in 1527. Mark, 2/3 Tower pound = 3600 grains. Troy pound in use in 1415, established as monetary pound 1527. Troy weight was abolished, from the 1st of January 1879, by the Weights and Measures Act 1878, with the exception only of the Troy ounce, its decimal parts and multiples, legalized in 1853, 16 Vict. c. 29, to be used for the sale of gold and silver articles, platinum and precious stones. Merchant's pound, in 1270 established for all except gold, silver and medicines = 6750 grains, generally superseded by avoirdupois in 1303. Merchant's pound of 7200 grains, from France and Germany, also superseded. ("Avoirdepois" occurs in 1336, and has been thence continued: the Elizabethan standard was probably 7002 grains.) Ale gallon of 1601 = 282 cub. in., and wine gallon of 1707 = 231 cub. in., both abolished in 1824. Winchester corn bushel of 8 x 268.8 cub. in. and gallon of 274+(1/4) are the oldest examples known (Henry VII), gradually modified until fixed in 1826 at 277.274, or 10 pounds of water.

French Weights and Measures Abolished

Often needed in reading older works.

Rhineland foot, much used in Germany, = 12.357 in. = the foot of the Scotch or English cloth ell of 37.06 in., or 3 x 12.353.

(Entry by: Henry James Chaney, I.S.O. 1842, 1906, formerly of the Standards Department of the Board of Trade and Secretary to the Royal Commission on Standards. Represented Great Britain at the International Conference on the Metric System, 1901. Author of Treatise on Weights and Measures. )

II. Ancient Historical

Though no line can be drawn between ancient and modern metrology, yet, owing to neglect, and partly to the scarcity of materials, there is a gap of more than a thousand years over which the connexion of units of measure is mostly guess-work. In the absence of the actual standards of ancient times the units of measure and of weight have to be inferred from the other remains; hence unit in this division is used for any more or less closely defined amount of length or weight in terms of which matter was measured. Except in a few cases, we shall not here consider any units of the middle ages.

A constant difficulty in studying works on metrology is the need of distinguishing the absolute facts of the case from the web of theory into which each writer has woven them -- often the names used, and sometimes the very existence of the units in question, being entirely an assumption of the writer. Again, each writer has his own leaning: A. Böckh, to the study of water-volumes and weights, even deriving linear measures therefrom; V. Queipo, to the connexion with Arabic and Spanish measures; J. Brandis, to the basis of Assyrian standards; Mommsen, to coin weights; and P. Bortolotti to Egyptian units; but F. Hultsch is more general, and appears to give a more equal representation of all sides than do other authors. In this article the tendency will be to trust far more to actual measures and weights than to the statements of ancient writers; and this position seems to be justified by the great increase in materials, and their more accurate means of study. The usual arrangement by countries has been mainly abandoned in favour of following out each unit as a whole, without recurring to it separately for every locality.

The materials for study are of three kinds.

    1: Literary, both in direct statements in works on measures (e.g. Elias of Nisibis), medicine (Galen) and cosmetics (Cleopatra), in ready-reckoners (Didymus), clerk's (katib's) guides, and like handbooks, and in indirect explanations of the equivalents of measures mentioned by authors (e.g. Josephus). But all such sources are liable to the most confounding errors, and some passages relied on have in any case to submit to conjectural emendation. These authors are of great value for connecting the monumental information, but must yield more and more to the increasing evidence of actual weights and measures. Besides this, all their evidence is but approximate, often only stating quantities to a half or quarter of the amount, and seldom nearer than 5 or 10%; hence they are entirely worthless for all the closer questions of the approximation or original identity of standards in different countries; and it is just in this line that the imagination of writers has led them into the greatest speculations, unchecked by accurate evidence of the original standards.

    2: Weights and measures actually remaining. These are the prime sources, and as they increase and are more fully studied, so the subject will be cleared and obtain a fixed basis. A difficulty has been in the paucity of examples, more due to the neglect of collectors than the rarity of specimens. The number of published weights did not exceed 600 of all standards in 1880; but the collections from Naucratis ( 28 ), Defenneh (29 ) and Memphis (44 ) have supplied over six times this quantity, and of an earlier age than most other examples, while existing collections have been more thoroughly examined. (Note: these figures refer to the authorities at the end of this section.) It is above all desirable to make allowances for the changes which weights have undergone; and, as this has only been done for the above Egyptian collections and that of the British Museum, conclusions as to the accurate values of different standards will here be drawn from these rather than continental sources.

    3: Objects which have been made by measure or weight, and from which the unit of construction can be deduced. Buildings will generally yield up their builder's foot or cubit when examined ( Inductive Metrology, p. 9). Vases may also be found bearing such relations to one another as to show their unit of volume. And coins have long been recognized as one of the great sources of metrology -- valuable for their wide and detailed range of information, though most unsatisfactory on account of the constant temptation to diminish their weight, a weakness which seldom allows us to reckon them as of the full standard. Another defect in the evidence of coins is that, when one variety of the unit of weight was once fixed on for the coinage, there was (barring the depreciation) no departure from it, because of the need of a fixed value, and hence coins do not show the range and character of the real variations of units as do buildings, or vases, or the actual commercial weights.

Principles Of Study. --

    1: Limits of Variation in Different Copies, Places and Times. -- Unfortunately, so very little is known of the ages of weights and measures that this datum -- most essential in considering their history -- has been scarcely considered. In measure, Egyptians of Dynasty IV. at Gizeh on an average varied 1 in 350 between different buildings ( 27 ). Buildings at Persepolis, all of nearly the same age, vary in unit 1 in 450 (25 ). Including a greater range of time and place, the Roman foot in Italy varied during two or three centuries on an average 1/400 from the mean. Covering a longer time, we find an average variation of 1/200 in the Attic foot (25 ), 1/150 in the English foot (25 ), 1/170 in the English itinerary foot (25 ). So we may say that an average variation of 1/400 by toleration, extending to double that by change of place and time, is usual in ancient measures. In weights of the same place and age there is a far wider range; at Defenneh (29 ), within a century probably, the average variation of different units is 1/36, 1/60, and 1/67, the range being just the same as in all times and places taken together. Even in a set of weights all found together, the average variation is only reduced to 1/60 in place of 1/36 (29 ). Taking a wider range of place and time, the Roman libra has an average variation of 1/50 in the examples of better period (43 ), and in those of Byzantine age 1/35 (44 ). Altogether, we see that weights have descended from original varieties with so little intercomparison that no rectification of their values has been made, and hence there is as much variety in any one place and time as in all together. Average variation may be said to range from 1/40 to 1/70 in different units, doubtless greatly due to defective balances.

    2: Rate of Variation. -- Though large differences may exist, the rate of general variation is but slow -- excluding, of course, all monetary standards. In Egypt the cubit lengthened 1/170 in some thousands of years ( 25, 44 ) The Italian mile has lengthened 1/170 since Roman times (2 ); the English mile lengthened about 1/300 in four centuries (31 ). The English foot has not appreciably varied in several centuries (25 ). Of weights there are scarce any dated, excepting coins, which nearly all decrease; the Attic tetradrachm, however, increased in three centuries (28 ), owing probably to its being below the average trade weight to begin with. Roughly dividing the Roman weights, there appears a decrease of 1/40 from imperial to Byzantine times (43 ).

    3: Tendency of Variation -- This is, in the above cases of lengths, to an increase in course of time. The Roman foot is also probably 1/300 larger than the earlier form of it, and the later form in Britain and Africa perhaps another 1/300 larger ( 25 ). Probably measures tend to increase and weights to decrease in transmission from time to time or place to place.

    4: Details of Variation --

Having noticed variation in the gross, we must next observe its details. The only way of examining these is by drawing curves (28, 29 ), representing the frequency of occurrence of all the variations of a unit; for instance, in the Egyptian unit -- the kat -- counting in a large number how many occur between 140 and 141 grains, 141 and 142, and so on; such numbers represented by curves show at once where any particular varieties of the unit lie (see Naukratis, i. 83). This method is only applicable where there is a large number of examples; but there is no other way of studying the details. The results from such a study -- of the Egyptian kat, for example -- show that there are several distinct families or types of a unit, which originated in early times, have been perpetuated by copying, and reappear alike in each locality (see Tanis, ii. pl. 1.). Hence we see that if one unit is derived from another it may be possible, by the similarity or difference of the forms of the curves, to discern whether it was derived by general consent and recognition from a standard in the same condition of distribution as that in which we know it, or whether it was derived from it in earlier times before it became so varied, or by some one action forming it from an individual example of the other standard without any variation being transmitted. As our knowledge of the age and locality of weights increases these criteria in curves will prove of greater value; but even now no consideration of the connexion of different units should be made without a graphic representation to compare their relative extent and nature of variation.

    5: Transfer of Units -- The transfer of units from one people to another takes place almost always by trade. Hence the value of such evidence in pointing out the ancient course of trade and commercial connexions ( 17 ). The great spread of the Phoenician weight on the Mediterranean, of the Persian in Asia Minor and of the Assyrian in Egypt are evident cases; and that the decimal weights of the laws of Manu (43 ) are decidedly not Assyrian or Persian, but on exactly the Phoenician standard, is a curious evidence of trade by water and not overland. If, as seems probable, units of length may be traced in prehistoric remains, they are of great value; at Stonehenge, for instance, the earlier parts are laid out by the Phoenician foot, and the later by the Pelasgo-Roman foot (26 ). The earlier foot is continually to be traced in other megalithic remains, whereas the later very seldom occurs (25 ). This bears strongly on the Phoenician origin of our prehistoric civilization. Again, the Belgic foot of the Tungri is the basis of the present English land measures, which we thus see are neither Roman nor British in origin, but Belgic. Generally a unit is transferred from a higher to a less civilized people; but the near resemblance of measures in different countries should always be corroborated by historical considerations of a probable connexion by commerce or origin (Head, Historia Numorum, xxxvii.). It should be borne in mind that in early times the larger values, such as minae, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmae would be the units; and this needs notice, because usually a borrowed unit was multiplied or divided according to the ideas of the borrowers, and strange modifications thus arose.

    6: Connexions of Lengths, Volumes and Weights -- This is the most difficult branch of metrology, owing to the variety of connexions which can be suggested, to the vague information we have, especially on volumes, and to the liability of writers to rationalize connexions which were never intended. To illustrate how easy it is to go astray in this line, observe the continual reference in modern handbooks to the cubic foot as 1000 oz. of water; also the cubic inch is very nearly 250 grains, while the gallon has actually been fixed at 10 lb of water; the first two are certainly mere coincidences, as may very probably be the last also, and yet they offer quite as tempting a base for theorizing as any connexions in ancient metrology. No such theories can be counted as more than coincidences which have been adopted, unless we find a very exact connexion, or some positive statement of origination.

The idea of connecting volume and weight has received an immense impetus through the metric system, but it is not very prominent in ancient times. The Egyptians report the weight of a measure of various articles, amongst others water (6 ), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight. Again, there are many theories of the equivalence of different cubic cubits of water with various multiples of talents (2, 3, 18, 24, 33 ); but connexion by lesser units would be far more probable, as the primary use of weights is not to weigh large cubical vessels of liquid, but rather small portions of precious metals. The Roman amphora being equal to the cubic foot, and containing 80 librae of water, is one of the strongest cases of such relations, being often mentioned by ancient writers. Yet it appears to be only an approximate relation, and therefore probably accidental, as the volume by the examples is too large to agree to the cube of the length or to the weight, differing 1/20, or sometimes even as 1/12.

Relative to the uncertain connexion of length, capacity and weight in the ancient metrological systems of the East, Sir Charles Warren, R.E., has obtained by deductive analysis a new equivalent of the original cubit (Palestine Exploration Fund Quarterly, April, July, October 1899). He shows that the length of the cubit arose through the weights; that is to say, the original cubit of Egypt was based on the cubic double -- cubit of water -- and from this the several nations branched off with their measures and weights. For the length of the building cubit Sir C. Warren has deduced a length equivalent to 20.6169 English inches, which compares with a mean Pyramid cubit of 20.6015 in. as hitherto found. By taking all the ancient cubits, there appears to be a remarkable coincidence throughout with 20.6109 in.

Sir C. Warren has derived a primitive unit from a proportion of the human body, by ascertaining the probable mean height of the ancient people in Egypt, and so thereby has derived a standard from the stature of man. The human body has furnished the earliest measure for many races (H. O. Arnold-Forster, The Coming of the Kilogram, 1898), as the foot, palm, hand, digit, nail, pace, ell ( ulna ), &c. It seems probable, therefore, that a royal cubit may have been derived from some kingly stature, and its length perpetuated in the ancient buildings of Egypt, as the Great Pyramid, &c.

So far this later research appears to confirm the opinion of Böckh (2 ) that fundamental units of measure were at one time derived from weights and capacities. It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.

Another idea which has haunted the older metrologists, but is still less likely, is the connexion of various measures with degrees on the earth's surface. The lameness of the Greeks in angular measurement would alone show that they could not derive itinerary measures from long and accurately determined distances on the earth.

    7: Connexions with Coinage. -- From the 7th century B.C. onward, the relations of units of weight have been complicated by the need of the interrelations of gold, silver and copper coinage; and various standards have been derived theoretically from others through the weight of one metal equal in value to a unit of another. That this mode of originating standards was greatly promoted, if not started, by the use of coinage we may see by the rarity of the Persian silver weight (derived from the Assyrian standard), soon after the introduction of coinage, as shown in the weights of Defenneh ( 29 ).

The relative value of gold and silver (17, 21 ) in Asia is agreed generally to have been 13+1/3 to 1 in the early ages of coinage; at Athens in 434 B.C. it was 14 to 1; in Macedon, 350 B.C., 12+1/2 to 1; in Sicily, 400 B.C., 15 to 1, and 300 B.C., 12 to 1; in Italy in 1st century, it was 12 to 1, in the later empire 13.9 to 1, and under Justinian. 14.4 to 1.

Silver stood to copper in Egypt as 80 to 1 (Brugsch), or 120 to 1 (Revillout); in early Italy and Sicily as 250 to 1 (Mommsen), or 120 to 1 (Soutzo), under the empire 120 to 1, and under Justinian 100 to 1. The distinction of the use of standards for trade in general, or for silver or gold in particular, should be noted. The early observance of the relative values may be inferred from Num. vii. 13, 14, where silver offerings are 13 and 7 times the weight of the gold, or of equal value and one-half value.

    8: Legal Regulations of Measures -- Most states have preserved official standards, usually in temples under priestly custody.

The Hebrew "shekel of the sanctuary" is familiar; the standard volume of the apet was secured in the dromus of Anubis at Memphis (35 ); in Athens, besides the standard weight, twelve copies for public comparison were kept in the city; also standard volume measures in several places (2 ); at Pompeii the block with standard volumes cut in it was found in the portico of the forum (33 ); other such standards are known in Greek cities (Gythium, Panidum and Trajanopolis) (11, 33 ); at Rome the standards were kept in the Capitol, and weights also in the temple of Hercules (2 ); the standard cubit of the Nilometer was before Constantine in the Serapaeum, but was removed by him to the church (2 ).

In England the Saxon standards were kept at Winchester before A.D. 950 and copies were legally compared and stamped; the Normans removed them to Westminster to the custody of the king's chamberlains at the exchequer; and they were preserved in the crypt of Edward the Confessor, while remaining royal property (9 ). The oldest English standards remaining are those of Henry VII. Many weights have been found in the temenos of Demeter at Cnidus, the temple of Artemis at Ephesus, and in a temple of Aphrodite at Byblus (44 ); and the making or sale of weights may have been a business of the custodians of the temple standards.

    9: Names of Units. -- It is needful to observe that most names of measures are generic and not specific, and cover a great variety of units. Thus foot, digit, palm, cubit, stadium, mile, talent, mina, stater, drachm, obol, pound, ounce, grain, metretes, medimrius, modius, hin and many others mean nothing exact unless qualified by the name of their country or city. Also, it should be noted that some ethnic qualifications have been applied to different systems, and such names as Babylonian and Euboic are ambiguous; the normal value of a standard will therefore be used here rather than its name, in order to avoid confusion, unless specific names exist, such as kat and uten. All quantities stated in this article without distinguishing names are in British units of inch, cubic inch or grain.

Standards of Length

Most ancient measures have been derived from one of two great systems, that of the cubit of 20.63 in., or the digit of 0.729 in.; and both these systems are found in the earliest remains.

In. - First known in Dynasty IV. in Egypt, most accurately 20.620 in the Great Pyramid, varying 20.51 to 20.71 in Dyn. IV. to VI. (27 ). Divided decimally in 100ths; but usually marked in Egypt into 7 palms of 28 digits, approximately; a mere juxtaposition. (for convenience) of two incommensurate systems (25, 27 ). The average of several cubit rods remaining is 20.65, age in general about 2500 B.C. (33 ). At Philae, &c., in Roman times 20.76 on the Nilometers (44 ). This unit is also recorded by cubit lengths scratched on a tomb at Beni Hasan (44 ), and by dimensions of the tomb of Ramessu IV. and of Edfu temple (5 ) in papyri. From this cubit, mahi, was formed the xylon of 3 cubits, the usual length of a walking staff; fathom, nent, of 4 cubits, and the khet of 40 cubits ( 18 ); also the schoenus of 12,000 cubits, actually found marked on the Memphis-Faium road ( 44 ).

Babylonia had this unit nearly as early as Egypt. The divided plotting scales lying on the drawing boards of the statues of Gudea (Nature, xxviii. 341) are of 1/2 20.89, or a span of 10.44, which is divided in 16 digits of .653, a fraction of the cubit also found in Egypt.

Buildings in Assyria and Babylonia show 20.5 to 20.6. The Babylonian system was sexagesimal, thus (18 ) --

 uban, 5=qat, 6=ammat, 6=qanu, 60=sos, 30=parasang, 2=kaspu. 
 
 0.69 inch 3.44 20.6 124 7430 223,000 446,000 
 

Asia Minor had this unit in early times-in the temples of Ephesus 20.55, Samos 20.62; Hultsch also claims Priene 20.90, and the stadia of Aphrodisias 20.67 and Laodicea 20.94. Ten buildings in all give 20.63 mean (18, 25 ); but in Armenia it arose to 20.76 in late Roman times, like the late rise in Egypt (25 ). It was specially divided into (1/5)th, the foot of (3/5)ths being as important as the cubit.

In. =(3/5)x20.75. This was especially the Greek derivative of the 20.63 cubit. It originated in Babylonia as the foot of that system (24 ), in accordance with the sexary system applied to the early decimal division of the cubit. In Greece it is the most usual unit, occurring in the Propylaea at Athens 12.44, temple at Aegina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18 ); thirteen buildings giving an average of 12.45, mean variation .06 (25 ), = (3/5)ths of 20.75, m. var. .10. The digit= (1/4) palaeste, = (1/4) foot of 12.4; then the system is --

 |1+(1/2)=cubit, 4=orguia ................................ 100= |
 
 foot, | | stadion. 
 
 |10............................... =acaena, 10=plethron, 6= | 
 
 12.4 in. 18.7 74.7 124.5 1245 7470 
 

In Etruria it probably appears in tombs as 12.45 (25 ); perhaps in Roman Britain; and in medieval England as 12.47 (25 ).

In. This foot is scarcely known monumentally. On three Egyptian cubits there is a prominent mark at the 19th digit or 14 in., which shows the existence of such a measure (33 ). It became prominent when adopted by Philetaerus about 280 B.C. as the standard of Pergamum (42 ), and probably it had been shortly before adopted by the Ptolemies for Egypt. From that time it is one of the principal units in the literature (Didymus, &c.), and is said to occur in the temple of Augustus at Pergamum as 13.8 (18 ). Fixed by the Romans at 16 digits (13+1/3 = Roman foot), or its cubit at 1+4/5 Roman feet, it was legally = 13.94 at 123 B.C. (42 ); and 7+1/2 Philetaerean stadia were = Roman mile (18 ). The multiples of the 20.63 cubit are in late times generally reckoned in these feet of 2/3 cubit. The name "Babylonian foot" used by Böckh (2 ) is only a theory of his, from which to derive volumes and weights; and no evidence for this name, or connexion with Babylon, is to be found. Much has been written (2, 3, 33 ) on supposed cubits of about 17 to 18 in. derived from 20.63--mainly in endeavouring to get a basis for the Greek and Roman feet; but these are really connected with the digit system, and the monumental or literary evidence for such a division of 20.63 will not bear examination.

17.30 = (5/6)x20.76. There is, however, fair evidence for units of 17.30 and 1.730 or (1/12) of 20.76 in Persian buildings ( 25 ) and the same is found in Asia Minor as 17.25 or (5/6)ths of 20.70. On the Egyptian cubits a small cubit is marked as about 17 in., which may well be this unit, as (5/6)ths of 20.6 is 17.2; and, as these marks are placed before the 23rd digit or 17.0, they cannot refer to 6 palms, or 17.7, which is the 24th digit, though they are usually attributed to that (33 ).

We now turn to the second great family based on the digit. This has been so usually confounded with the 20.63 family, owing to the juxtaposition of 28 digits with that cubit in Egypt, that it should be observed how the difficulty of their incommensurability has been felt. For instance, Lepsius (3 ) supposed two primitive cubits of 13.2 and 20.63, to account for 28 digits being only 20.4 when free from the cubit of 20.63--the first 24 digits being in some cases made shorter on the cubits to agree with the true digit standard, while the remaining 4 are lengthened to fill up to 20.6.

In the Dynasties IV. and V. in Egypt the digit is found in tomb sculptures as 0.727 (27 ); while from a dozen examples in the later remains we find the mean, 0.728 (25 ). A length of 10 digits is marked on all the inscribed Egyptian cubits as the "lesser span" (33 ). In Assyria the same digit appears as 0.730, particularly at Nimrud (25 ); and in Persia buildings show the 10-digit length of 7.34 (25 ). In Syria it was about 0.728, but variable; in eastern Asia Minor more like the Persian, being 0.732 (25 ). In these cases the digit itself, or decimal multiples, seem to have been used.

18.23 = 25x0.729. The pre-Greek examples of this cubit in Egypt, mentioned by Böckh ( 2 ), give 18.23 as a mean, which is 25 digits of 0.7292 digits, close to 0.729, but has no relation to the 20.63 cubit. This cubit, or one nearly equal, was used in Judaea in the times of the kings, as the Siloam inscription names a distance of 1758 ft. as roundly 1200 cubits, showing a cubit of about 17.6 in. This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was (1/4)th of the orguia of 100 digits, the series being --

 | 25=cubit, 4= | 
 
 old digit, | | orguia, 10=amma, 10=stadion.
 
 | 100........= |
 
 0.729 inch 18.2 72.9 729 7296.
 

Then, taking (2/3)rds of the cubit, or (1/6)th of the orguia, as a foot, the Greeks arrived at their foot of 12.14; this, though very well known in literature, is but rarely found, and then generally in the form of the cubit, in monumental measures. The Parthenon step, celebrated as 100 ft. wide, and apparently 225 ft. long, gives by Stuart 12.137, by Penrose 12.165, by Paccard 12.148, differences due to scale and not to slips in measuring. Probably 12.16 is the nearest value. There are but few buildings wrought on this foot in Asia Minor, Greece or Roman remains. The Greek system, however, adopted this foot as a basis for decimal multiplication, forming --

 foot, 10=acaena, 10=plethron, 
 
 12.16 inches 121.6 1216 
 

which stand as (1/6)th of the other decimal series based on the digit. This is the agrarian system, in contrast to the orguia system, which was the itinerary series (33 ).

Then a further modification took place, to avoid the inconvenience of dividing the foot in 16+(2/3) digits, and a new digit was formed -- longer than any value of the old digit -- of 1/16 of the foot, or 0.760, so that the series ran --

 | 10=lichas 
 
 digit |
 
 | 96..........=orguia, 10=amma, 10=stadion.
 
 0.76 inch 7.6 72.9 729 7296.
 

This formation of the Greek system (25 ) is only an inference from the facts yet known, for we have not sufficient information to prove it, though it seems much the simplest and most likely history.

11.62 = 16x0.726. Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot. The more so as the half of this foot, or 8 digits, is marked off as a measure on the Egyptian cubit rods ( 33 ). Though Queipo has opposed this connexion (not noticing the Greek link of the digit), he agrees that it is supported by the Egyptian square measure of the plethron, being equal to the Roman actus (33 ). The foot of 11.6 appears probably first in the prehistoric and early Greek remains, and is certainly found in Etrurian tomb dimensions as 11.59 (25 ). Dörpfeld considers this as the Attic foot, and states the foot of the Greek metrological relief at Oxford as 11.65 (or 11.61, Hultsch). Hence we see that it probably passed from the East through Greece to Etruria, and thence became the standard foot of Rome; there, though divided by the Italian duodecimal system into 12 unciae, it always maintained its original 16 digits, which are found marked on some of the foot-measures. The well-known ratio of 25:24 between the 12.16 foot and this we see to have arisen through one being (1/6)th of 100 and the other 16 digits--16+2/3: 16 being as 25: 24, the legal ratio. The mean of a dozen foot-measures (1 ) gives 11.616 ± 0.008, and of long lengths and buildings 11.607 ± 0.01. In Britain and Africa, however, the Romans used a rather longer form (25 ) of about 11.68, or a digit of 0.730. Their series of measures was --

 digitus, 4=palmus, 4=pes, 5=passus, 125=stadium, 8=milliare; 
 
 0.726 inch 2.90 11.62 58.1 7262 58,100 
 

also

 uncia 0.968=(1/12)pes, palmipes 14.52=5 palmi, cubitus 17.43=6 palmi.
 

Either from its Pelasgic or Etrurian use or from Romans, this foot appears to have come into prehistoric remains, as the circle of Stonehenge (26 ) is 100 ft. of 11.68 across, and the same is found in one or two other cases. 11.60 also appears as the foot of some medieval English buildings (25 ).

We now pass to units between which we cannot state any connexion.

25.1 . -The earliest sign of this cubit is in a chamber at Abydos (44 ) about 1400 B.C.; there, below the sculptures, the plain wall is marked out by red designing lines in spaces of 25.13 ± 0.03 in., which have no relation to the size of the chamber or to the sculpture. They must therefore have been marked by a workman using a cubit of 25.13. Apart from medieval and other very uncertain data, such as the Sabbath day's journey being 2000 middling paces for 2000 cubits, it appears that Josephus, using the Greek or Roman cubit, gives half as many more to each dimension of the temple than does the Talmud; this shows the cubit used in the Talmud for temple measures to be certainly not under 25 in. Evidence of the early period is given, moreover, by the statement in I Kings (vii. 26) that the brazen sea held 2000 baths; the bath being about 2300 cub. in., this would show a cubic of 25 in. The corrupt text in Chronicles of 3000 baths would need a still longer cubit; and, if a lesser cubit of 21.6 or 18 in, be taken, the result for the size of the bath would be impossibly small. For other Jewish cubits see 18.2 and 21.6. Oppert (24 ) concludes from inscriptions that there was in Assyria a royal cubit (7/6)ths of the U cubit, or 25.20; and four monuments show (25 ) a cubit averaging 25.28. For Persia Queipo (33 ) relies on, and develops, an Arab statement that the Arab cubit was the royal Persian, thus fixing it at about 25 in.; and the Persian guerze at present is 25, the royal guerze being 1+(1/2) times this, or 371 in. As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit.

21.6. -The circuit of the city wall of Khorsabad ( 24 ) is minutely stated on a tablet as 24,740 ft. (U), and from the actual size the U is therefore 10.806 in. Hence the recorded series of measures on the Senkereh tablet are valued (Oppert) as --

 susi, |20=(palm), 3=U, 6=qanu, 2=sa, 5= (n), 12=us, 30=kasbu. 
 
 |60.............=U, 60....................= (n), 
 
 0.18 inch 3.6 10.80 64.8 129.6 648 7776 223,280
 

Other units are the suklum or (1/2)U=5.4, and cubit of 2U=21.9, which are not named in this tablet. In Persia (24 ) the series on the same base was --

 vitasti, 2=arasni, 360=asparasa, 30=parathañha, 2=gāv; 
 
 10.7 inches 21.4 7704 231,120 462,240 
 

probably

 yava, 6=angusta 10=vitasti; and gama = (3/5)arasni; also bāzu = 2arasni. 
 
 0.18 inch 1.07 10.7 12.8 21.4 42.8 21.4 
 

The values here given are from some Persian buildings (25 ), which indicate 21.4, or slightly less; Oppert's value, on less certain data, is 21.52. The Egyptian cubits have an arm at 15 digits or about 10.9 marked on them, which seems like this same unit (33 ).

This cubit was also much used by the Jews (33 ), and is so often referred to that it has eclipsed the 25.1 cubit in most writers. The Gemara names 3 Jewish cubits (2 ) of 5, 6 and 7 palms; and, as Oppert (24 ) shows that 25.2 was reckoned 7 palms, 21.6 being 5 palms, we may reasonably apply this scale to the Gemara list, and read it as 18, 21.6 and 25.2 in. There is also a great amount of medieval and other data showing this cubit of 21.6 to have been familiar to the Jews after their captivity; but there is no evidence for its earlier date, as there is for the 25 in. cubit (from the brazen sea) and for the 18 in. cubit from the Siloam inscription.

From Assyria also it passed into Asia Minor, being found on the city standard of Ushak in Phrygia (33 ), engraved as 21.8, divided into the Assyrian foot of 10.8, and half and quarter, 5

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