# Encyclopædia Britannica, Ninth Edition/Weights and Measures

Weights and Measures

WEIGHTS AND MEASURES

THIS subject may be best divided for convenience of reference into three parts:— including the facts and data usually needed for scientific reference; including the principles of research and results in ancient metrology; and including the weights and measures of modern countries as used in commerce.

I. Scientific.

A unit of length is the distance between two points defined by some natural or artificial standard, or a multiple of that. For instance, in Britain the unit of the yard is defined by the distance between two parallel lines on gold studs sunk in a bar of bronze, when at 62° F., which bar is preserved in the Standards Office. There are other units, such as the inch, foot, mile, &c.; but, as these are aliquot parts or multiples of the yard, there is no separate standard provided for them. A unit is an abstract quantity, represented by a certain standard, and more or less perfectly by copies of the standard.

A unit of mass is the matter of a standard of mass, or a multiple of that. For instance, in Britain the unit of the pound is defined by a piece of platinum preserved in the Standards Office.

A unit of weight is the attractive force exerted between a unit of mass and some given body at a fixed distance,—this force being the weight of the unit in relation to the given body, or any other body of equal mass.[1] Usually the given body is the earth, and the distance a radius of the earth. For instance, the unit of weight in Britain is the attraction between the earth and the standard pound when that is placed at sea-level at London, in a vacuum. For astronomical comparisons the unit of mass is the sun, and a unit of weight is not needed.

Standards of length are all defined on metal bars at present in civilized countries. Various natural standards have been proposed, such as the length of the polar diameter of the earth (inch), the circumference of the earth (metre) in a given longitude, a pendulum vibrating in one second at a fixed distance from the earth, a wave of light emitted by an incandescent gas, &c. But the difficulty of ascertaining the exact value of these lengths prevents any material standard being based upon them with the amount of accuracy that actual measurements, to be taken from the standard, require. A natural standard is therefore only a matter of sentiment.

Standards of length are of two types, the defining points being either at a certain part of two parallel lines engraven in one plane (a line-standard), or else points on two parallel surfaces, which can only be observed by contact (an end-standard). The first type is always used for accurate purposes. Units of surface are always directly related to standards of length, without any separate standards. Volume is either determined by the lineal dimensions of a space or a solid, or, for accurate purposes, by the mass of water contained in a volume at a given temperature, which again is measured either by liquid measure, or, more accurately, by weight. The standard of volume in Britain is a hollow cylinder of bronze, with a plate glass cover, when at 62° (gallon), legally defined as 277·274 cubic inches, or containing 10 pounds of water at 62°F.

Comparisons.—Lengths nearly equal are compared accurately by fixing two micrometer microscopes with their axes parallel, and at the required distance apart, on a massive support which will not quickly vary with temperature; then the two lengths to be compared, e.g., the standard yard and another, are alternately placed beneath the microscopes, and their lengths observed several times. The error of a single observation in the Standards Department is stated to be a 100,000th of an inch. For fractional lengths a divided bar is required, the accuracy of which is ascertained by a shorter measure, which can be compared with successive sections of the whole length by micrometers. For ordinary purposes, where not less than ·001 inch is to be observed, measures may be placed in contact if one is divided on the edge, and the comparison made with a magnifier. In large field-work the ends of a measure are transferred vertically to the ground by a small transit instrument or theodolite. End-measures between surfaces are read by means of a pair of contact pieces bearing line marks, the value of which is ascertained separately, or by a second end-measure; if both measures bear a line for observation, reversals then give the value of each measure.

Volumes are always most accurately defined by their weight of water, as weighing can be more accurately done than measuring. If the volume is hollow, it may be filled with water and closed with a sheet of plate glass, or if solid the body may be weighed in water and out, the difference giving the weight of its volume of water. Unfortunately the relation between water-weight and absolute volume is not yet accurately known. Volumes of liquid are similarly ascertained by their weight. Volumes of gas are measured in a graduated glass vessel inverted over a liquid, or for commercial purposes by some form of registering flow-meter.

Masses are compared by the Balance (q.v.), which may be made to indicate a 100,000,000th of the mass. They may also be estimated, not by their attractive force being balanced by an equal mass, but by the elasticity of a spring; this, which is the only true weighing-machine showing weight and not mass, is useful for rough purposes, owing to its quick indication; the most accurate form probably is that with angular readings.[2]

Temperature and the Atmosphere.—All the serious difficulties of weighing and measuring result from these causes, the effects of which and their corrections we will briefly notice. In measurement, since all bodies expand by heat, the temperature at which any measure or standard bar represents the abstract unit requires to be accurately stated and observed, the accuracy of optical observation being about equal to 1100 of a degree F. of expansion in a standard. Great accuracy is therefore needed in the manufacture and reading of thermometers, and care that the standard and the thermometer shall be at the same temperature. Another method is to attach a parallel bar of very expansible metal to one end of the standard, and read its length on the standard at the other end; this ensures a more thorough uniformity of mean temperature between the standard and the heat-measurer. The most accurate method is by immersing the measures in a liquid, of which the temperature is read by several thermometers; but this is scarcely needful unless high or low temperatures are required to ascertain the rate of expansion. A room with thick walls, double windows, and the temperature regulated by a gas stove is practically sufficiently equable for comparisons.

The temperature adopted for the standards is not the same in different countries. In Britain 62° F. has been adopted since the revision of the standards in 1822, as being a convenient average temperature for work; but, as it is purely a temperature of convenience, the rather higher point of 68° F. would be better. In any case an aliquot part of the thermal unit from freezing to boiling of water should be adopted; 62° is 16 and 68° is 15 of this interval. Whether a much higher temperature would not be more conducive to accuracy is a question; 92°, or 13 of the thermal unit, would be so near the temperature of the observer's skin and breath that measures and balances could be approached with less production of error; and such a heat does not at all hinder accurate observing. The French temperature of 32° F. for standards has abandoned all other considerations in favour of readily fixing the temperature in practice by melting ice. This is a ready means of regulation, but a point so far from ordinary working temperatures has two great disadvantages: the observer's warmth produces more error, and the corrections for all observations not iced are so large that the rates of expansion require to be known very accurately for every substance employed. For water their standard temperature is 39°.2 F., when it is at its maximum density; this has the advantage that the density varies less with temperature than at any other point, but it is very doubtful if this is much used for actual work.

No substance expands uniformly with temperature, most materials expanding more rapidly at higher temperatures. The expansion of rods of the following metals, of 100 inches long, is given in decimals of an inch for the 90° from 32° to 122° F. (0 to 50° C.), and from 122° to 212° F. (50° to 100° C.):[3]

 Platinum. Platino-iridium. Steel. Iron. Bronze. Brass. Zinc. 32° to 122° .0445 .0435 .0536 .0591 .0876 .0915 .1469 122° to 212° .0471 .0454 .0574 .0637 .0927 .0964 .1437

But variations of 3 or 4 per cent. may easily be found in the rates of different specimens apparently alike; hence the individual expansion of every important measure needs to be ascertained.

Weighing is complicated by being done in a dense and variable atmosphere, unless—as in the most refined work—the whole balance is placed in a vacuum. When in the air all bodies placed in the balance must, for accurate purposes, have their volume known; and the weight of an equal volume of such air as they are weighed in must be added to their apparent weight to get their true weight. The weight of air displaced by a pound of the following materials is given in grains, at temperature 62° F., barometer 30 inches,—also with barometer 29 inches (temperature 62°), and with temperature 32° (barometer 30 inches), to illustrate the variation[4] (allowing for contraction of the material as well):—

 Platinum. Brass. GiltBronze. Iron, with LeadAdjustment. Quartz. Glass. Water. Sp. Gr. 21.157 8.143 8.283 7.127 2.650 2.518 1.000 62°, 30 .403 1.047 1.029 1.196 3.217 3.385 8.523 62°, 29 .390 1.012 .995 1.156 3.110 3.272 8.240 32°, 30 .429 1.112 1.093 1.271 3.422 3.600 9.056

The above is for London at sea-level; but where the force of gravity is less 30 inches height of mercury will weigh less, and will therefore balance a less weight of air; the air allowance must therefore be less for 30 inches of mercury barometer in lower latitudes and greater heights over sea-level. The change, for instance, in the allowance of air equal to the brass pound will make it, instead of 1.047 grains, become 1.046 when 15,000 feet above the sea, or 10° S. of London. Hence this reduction need rarely be noticed. The composition of the air also varies, and most seriously in the amount of aqueous vapour; the above is ordinary air, but if quite dry the 1.047 grains would become 1.052 grains; the change in carbonic acid is quite immaterial, unless in very close rooms, so that it may be concluded that the moisture of the air is the main point to be noted, after its temperature and pressure,—small errors in any of these three data making far more difference than any other compensation that can be made in the weight of air.

The more complex allowances for the expansion of water in glass, brass, or other vessels we need not enter on here; the principles are simple, but the data require to be accurately determined for the material in question. The expansion of water is, however, so often in question, especially for taking specific gravities, that it is here given. A constant volume which contains or displaces 10,000 grains of water at 62° will contain[5]

 At 32° F. (0° C.), 10,009.84 grains. At 62° F. (1623° C.), 10,000.00 grains. .mw-parser-output .__ditto{display:inline-block;position:relative;text-indent:0}.mw-parser-output .__ditto_hidden{visibility:hidden;color:transparent;white-space:nowrap}.mw-parser-output .__ditto_text{display:inline-block;position:absolute;left:0;width:100%;white-space:nowrap}At„ 39°.2 F. (4° C.), 10,011.20 grains.„ At„ 68° F. (20° C.), 9,993.76 grains.„ At„ 50° F. (10° C.), 10,008.89 grains.„ At„ 86° F. (30° C.), 9,968.76 grains.„

Hence if a specific gravity is observed at any of these temperatures it must be × the corresponding weight ÷ 10,000 to reduce it to a comparison with water at 62°; the expansion of the body observed is another question altogether, and must be compensated also.

The weight of a cubic inch, or other linearly measured volume, of water is not yet very accurately known. The observations have been made by weighing closed hollow metal cases in and out of water (thus obtaining the weight of an equal volume of water), and then gauging the size of the case with exactitude. Cubes, cylinders, and spheres have been employed. The results are:[6]

Cubic
Inch at
62° F.
Cubic
Foot at
62° F.
Cubic
Decimetre
at 4° C.
Grains. Ounces. Grammes.
1795
1.  In France, by Lefevre-Gineau (legal French)................................................................................................................................................................................................................................................................................................................................................................................................
252.603 997.70 1000.000
1797 ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$
1.  In England, by Shuckburgh and Kater (legal British)................................................................................................................................................................................................................................................................................................................................................................................................
${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ 252.724 998.18 1000.480
1821
1825 ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$
1.  In Sweden, by Berzelius, Svanberg, and Akermann................................................................................................................................................................................................................................................................................................................................................................................................
${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ 252.678 998.00 1000.296
1830
1.  In Austria, by Stampfer................................................................................................................................................................................................................................................................................................................................................................................................
252.515 997.35 999.653
1841
1.  In Russia, by Kupffer................................................................................................................................................................................................................................................................................................................................................................................................
252.600 997.69 999.989

National Standards and Copies.—Having now noticed the principles and constants involved, we will consider the British and metric standards, the only ones now used in scientific work.

The imperial standard yard is a bronze bar 38 inches long, 1 inch square; the defining lines, 36 inches apart, are cut on gold studs, sunk in holes, so that their surface passes through the axis of the bar. Thus flexure does not tend to tip the engraved surfaces nearer or farther apart. This bar when in use rests on a lever frame, which supports it at 8 points, 4.78 inches apart, on rollers which divide the pressure exactly equally.[7] This standard is in actual use for all important comparisons at the Standards Office. Four copies, which are all equal to it, within 16° of temperature, are deposited in other places in case of injury or loss of the standard. The standard pound is a thick disk of platinum about 116 inches across, and 1 inch high, with a shallow groove around it near the top. Four copies are deposited with the above copies of the yard. For public use there are a series of end-standards exposed on the outer wall of Greenwich observatory; and a length of 100 feet, and another of 66 feet (1 chain), marked on brass plates let into the granite step along the back of Trafalgar Square. As this is a practically invariable earth-fast standard, and most convenient for reference, it is important to know the minute errors of it, as determined by the Standards Department.[8] Starting from 0 the errors are in inches—

 at 0 10 20 30 40 50 60 70 80 90 100 feet. error 0 − 0.007 − 0.019 − 0.022 − 0.015 − 0.008 − 0.007 + 0.011 + 0.021 + 0.17 − 0.008 inches.

The mean uncertainty in these values is .003, and the greatest uncertainty .01. The total length of the chain standard is − .019 inch from the truth. There is also a public balance provided at Greenwich observatory, which shows the accuracy of any pound weight placed upon it, For important scientific standards comparisons are made gratuitously, as a matter of courtesy, by the officials of the Standards Office, 7 Old Palace Yard, Westminster. The most delicate weighings are all performed in a vacuum case with glass sides, which is so constructed that the weights can be exchanged from one arm to the other without opening the case, so as to obtain double weighings.

The toleration of error in copies for scientific purposes, by the Standards Department, is .0005 inch on the yard or lesser lengths, about equal to 15 divisions of the micrometer; on the pound .0025 grain, about 12 a division of the official balances; on the ounce .001 grain; on the gallon 1 grain; and on the cubic foot 4 grains. The toleration for commercial copies is .005 on the yard, .001 on the foot and under, and .1 grain on weights of 1 ounce to 1 pound.[9] The Standards Commission of 1851 recommended a limit of 1 in 20,000.

For practical work of moderate accuracy the most convenient forms of measures are—for lengths under a foot, feather-edge metal scales divided to 150 inch (finer divisions are only confusing, and 11000 of an inch can be safely read by estimation); for lengths of 1 to 10 feet, metal tubes or deep bars bearing line-divisions, and with permanent feet attached at 21 per cent. from either end, so that the deformation by flexure is always the same; for long distances a steel tape with fine divisions scratched across it and numbered by etching. The most accurate way of using such a tape is not to prepare a flat bed for it, but to support it at points not more than 50 feet apart; then by observing the distances and levels of these points, and knowing the weight of the tape, the correction for the sloping distance between the points and the difference of the catenary length of the tape from the straight distance can be precisely calculated; the corrections for stretching of the tape (best done by a lever arm with fixed weight), and for temperature, are all that are needful besides.

The first French standard metre (of 1799) is a platinum bar end-standard of about 1 inch wide and 17 inch thick; the new standard of the International Metric Commission is a line-standard of platino-iridium, 40 inches long and .8 inches square, grooved out on all four sides so that its section is between × and ʜ form; this provides the greatest rigidity, and also a surface in the axis of the bar to bear the lines of the standard. The new standard kilogramme, like the old one, is a cylinder of platinum of equal diameter and height. These new standards are preserved in the International Metric Bureau at Paris, to which seventeen nations contribute in support and direction, and in which the most refined methods of comparison are adopted. For lineal comparisons the alternate substitution of the measures on a sliding bed beneath fixed micrometer microscopes is provided as in the British office, and a bath for the heating of one measure in a liquid to ascertain its expansion. For weighing four balances are provided, each with mechanism for the transposition of the weights, and the lowering of the balance into play on its bearings, so that weighings can be performed at 13 feet distance from the balance, thus avoiding the disturbance caused by the warmth of the observer. The readings of the balance scale are made by a fixed telescope, the motion being observed by the reflexion of a fixed scale from a mirror attached to the beam of the balance. In this bureau are also an equally fine hydrostatic balance for taking specific gravities by water weighing, a standard barometer, and an air thermometer, with all subsidiary apparatus. The special work of the bureau is the construction and comparison of metric standards for all the countries supporting it, and for scientific work of all kinds.

The legal theory of the British system of weights and measuresis—(A) the standard yard, with all lineal measures and their squares and cubes based upon that; (B) the standard pound of 7000 grains, with all weights based upon that, with the troy pound of 5760 grains for trade purposes; (C) the standard gallon (and multiples and fractions of it), declared to contain 10  of water at 62° F., being in volume 277.274 cubic inches, which contain each 252.724 grains of water in a vacuum at 62°, or 252.458 grains of water weighed with brass weights in air of 62° with the barometer at 30 inches.

The legal theory of the metric system of weights and measures is—(A) the standard metre, with decimal fractions and multiples thereof; (B) the standard kilogramme, with decimal fractions and multiples thereof; (C) the litre (with decimal fractions and multiples), declared to be a cube of 116 metre, and to contain a kilogramme of water at 4° C. in a vacuum. No standard litre exists, all liquid measures being legally fixed by weight. The metre was supposed, when established in 1799, to be a ten-millionth of the quadrant of the earth through Paris; it differs from this theoretical amount by about 1 in 4000.

The legal equivalents between the British and French systems are—metre = 39.37079 inches; kilogramme = 15432.34874 grains. By the more exact comparisons of Captain Clarke (1866) the metre (at 0° C., 32° F.) is equal to 39.37043196 inches of the yard at 62° F.; but Rogers in 1882 compared the metre as 39.37027. It must always be remembered that a French metre of perfect legal exactitude will, by expanding from 32° to 62° F., become equal to a greater number of inches when the two measures are placed together; thus a brass metre is equal to 39.382 inches when compared with British measures at the same temperature, and this is its true commercial equivalent. The kilogramme determination above is that of Professor Miller (1844), against the kilogramme des Archives, but in 1884 the international kilogramme yielded 15432.35639.

For further details, see H. W. Chisholm, Weighing and Measuring (Nature series), 1877, and Reports of the Warden of the Standards, subsequently of the Standards Department (all in British Museum Newspaper Room), for all practical details,—especially reports on metre (1868–9), errors of grain weights (1872), principles of measuring (long paper of German Standards Commission, translated 1872), Trafalgar Square standards (1876), density of water (1883), toleration of error, British and international (1883), standard wire and plate gauges in inches (1883), besides numerous practical tables, mainly in the earlier numbers before the wardenship was merged in the Board of Trade.

II. 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[10] of measure is mostly guess-work. Hence, 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. Therefore we shall here take the more pains to show what the actual authority is for each conclusion. Again, each writer has his own leaning: Böckh, to the study of water-volumes and weights, even deriving linear measures therefrom; Queipo, to the connexion with Arabic and Spanish measures; Brandis, to the basis of Assyrian standards; Mommsen, to coin weights; and Bortolotti to Egyptian units; but 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 the more accurate means of study of late. 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 (kátib'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 per cent.; 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 a short time ago; but the collections in the last three years from Naucratis (28),[11] 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; hence there is need for a general revision of the whole subject. 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 1400 from the mean. Covering a longer time, we find an average variation of 1200 in the Attic foot (25), 1150 in the English foot (25), 1170 in the English itinerary foot (25). So we may say that an average variation of 1400 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 136, 160, and 167, 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 160 in place of 136 (29). Taking a wider range of place and time, the Roman libra has an average variation of 150 in the examples of better period (43), and in those of Byzantine age 135 (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 140 to 170 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 1170 in some thousands of years (25, 44). The Italian mile has lengthened 1100 since Roman times (2) ; the English mile lengthened about 1300 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 150 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 140 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 1300 larger than the earlier form of it, and the later form in Britain and Africa perhaps another 1300 larger (25). Probably measures tend to increase and weights to decrease in transmission from time to time or place to place; but far more data are needed to study this.

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 katcounting 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. p. 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 Phœnician 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 Phœnician 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 Phœnician 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 Phœnician 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 minæ, would be transmitted by commerce, while after the introduction of coinage the lesser values of shekels and drachmæ 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 ounces of water; also the cubic inch is very nearly 250 grains, while the gallon has actually been fixed at 10  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 libræ 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 ${\displaystyle \scriptstyle {\frac {1}{20}}}$, or sometimes even ${\displaystyle \scriptstyle {\frac {1}{12}}}$. All that can be said therefore to the many theories connecting weight and measure is that they are possible, but our knowledge at present does not admit of proving or disproving their exactitude. Certainly vastly more evidence is needed before we would, with Böckh (2), derive fundamental measures through the intermediary of the cube roots of volumes. Soutzo wisely remarks on the intrinsic improbability of refined relations of this kind (Étalons Ponderaux Primitifs, note, p. 4).

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${\displaystyle \scriptstyle {\frac {1}{3}}}$ to 1 in the early ages of coinage; at Athens in 434 B.C. it was 14 : 1; in Macedon, 350 B.C., 12${\displaystyle \scriptstyle {\frac {1}{2}}}$ : 1; in Sicily, 400 B.C., 15 : 1, and 300 B.C., 12 : 1; in Italy, in 1st century, it was 12 : 1, in the later empire 13·9 : 1, under Justinian 14·4 : 1, and in modern times 15·5 : 1, but at present 23 : 1,—the fluctuations depending mainly on the opening of large mines. Silver stood to copper in Egypt as 80 : 1 (Brugsch), or 120 : 1 (Revillout); in early Italy and Sicily as 250 : 1 (Mommsen), or 120 : 1 (Soutzo), under the empire 120 : 1, under Justinian 100 : 1; at present it is 150 : 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 Regulation 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 Serapæum, but was removed by him to the church (2). In England the Saxon standards were kept at Winchester before 950 A.D., 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, medimnus, 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 inches, or the digit of .729 inch; and both these systems are found in the earliest remains.

20.63 ins.—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 or 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 1000 B.C. (33). At Philæ, &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 schœnus 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 12 of 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. .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 rose to 20.76 in late Roman times, like the late rise in Egypt (25). It was specially divided into 15th, the foot of 35ths being as important as the cubit.   12.45 ins.
35 of 20.75.
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 Propykea at Athens 12.44, temple at Ægina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18); thirteen buildings giving an average of 12.45, mean variation .06 (25), = 35 of 20.75, m. var. .10. The digit = 14 palæste, = 14 foot of 12.4; then the system is

 foot, ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 112=cubit, 4=orguia. ........................................ 100= ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ stadion. 10............. ............... =acæna, 10=plethron, 6= 12.4 inch 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 mediæval England as 12.47 (25).   13.8 ins.
23 of 20.7.
This foot is scarcely known monumentally. On three Egyptian cubits there is a prominent mark at the 19th digit or 14 inches, which shows the existence of such a measure (33). It became prominent when adopted by Philetærus 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 (1313=Roman foot), or its cubit at 145 Roman feet, it was legally =13.94 at 123 B.C. (42); and 712 Philetærean stadia were = Roman mile (18). The multiples of the 20.63 cubit are in late times generally reckoned in these feet of 23 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 17–18 inches 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
56 of 20.76.
There is, however, fair evidence for units of 17.30 and 1.730 or 112 of 20.76 in Persian buildings (25); and the same is found in Asia Minor as 17.25 or 56 of 20.70. On the Egyptian cubits a small cubit is marked as about 17 inches, which may well be this unit, as 56 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.   .727 ins. In the Dynasties IV. and V. in Egypt the digit is found in tomb sculptures as .727 (27); while from a dozen examples in the later remains we find the mean .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 .730, particularly at Nimrud (25); and in Persia buildings show the 10-digit length of 7.34 (25). In Syria it was about .728, but variable; in eastern Asia Minor more like the Persian, being .732 (25). In these cases the digit itself, or decimal multiples, seem to have been used.     18.23
25 × .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 .729, and has no relation to the 20.63 cubit. This cubit, or one nearly equal, was used in Judæa in the times of the kings, as the Siloam inscription names a distance of 1758 feet as roundly 1200 cubits, showing a cubit of about 17.6 inches. 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 14 of the orguia of 100 digits, the series being

 old digit, ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 25=cubit, 4= ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ orguia, 10=amma, 10=stadion. 100................= .729 inch 18.2 72.9 729 7296

Then, taking 23 of the cubit, or 16 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 feet wide, and apparently 225 feet 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=acæna 10=plethron, 12.16 inches 121.6 1216

which stand as 16th 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 1623 digits, and a new digit was formed—longer than any value of the old digitof 116 of the foot, or .760, so that the series ran

 digit ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 10=lichas 96............. =orguia 10=amma, 10=stadion. ·76 inch 7·6 72·9 729 7290

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
16 × ·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 ·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 unciæ, 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 ${\displaystyle \scriptstyle {\frac {1}{6}}}$ of 100 and the other 16 digits,—16${\displaystyle \scriptstyle {\frac {2}{3}}}$ : 16 being as 25 : 24, the legal ratio. The mean of a dozen foot-measures (1) gives 11·616±·008, and of long lengths and buildings 11·607±·01. In Britain and Africa, however, the Romans used a rather longer form (25) of about 11·68, or a digit of ·730. Their series of measures was }}

 digitus, 4=palmus, 4=pes, 5=passus, 125=stadium, 8=milliare; ·726 inch 2·90 11·62 58·1 7262 58,100

also

 uncia ·968=${\displaystyle \scriptstyle {\frac {1}{12}}}$ 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 feet of 11·68 across, and the same is found in one or two other cases. 11·60 also appears as the foot of some mediæval 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±·03 inches, 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 mediæval 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 inches. Evidence of the early period is given, moreover, by the statement in 1 Kings (vii. 26) that the brazen sea held 2000 baths; the bath being about 2300 cubic inches, this would show a cubit of 25 inches. The corrupt text in Chronicles of 3000 baths would need a still longer cubit; and, if a lesser cubit of 21·6 or 18 inches 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 of ${\displaystyle \scriptstyle {\frac {7}{6}}}$ 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 hashama cubit was the royal Persian, thus fixing it at about 25 inches; and the Persian guerze at present is 25, the royal guerze being 1${\displaystyle \scriptstyle {\frac {1}{2}}}$ times this, or 37${\displaystyle \scriptstyle {\frac {1}{2}}}$ inches. 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 feet (U), and from the actual size the U is therefore 10·806 inches. Hence the recorded series of measures on the Senkereh tablet are valued (Oppert) as

 susi, ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 20=(palm), 3=U, 6=qanu, 2=sa, 5=(n), 12=us, 30=kasbu. 60.................... =U, 60......................... =(n). ·18 inch 3·6 .mw-parser-output .wst-running-header{display:flex;width:100%;text-align:center;justify-content:space-between}.mw-parser-output .wst-running-header-4 .wst-running-header-cell:nth-child(2){text-align:left}.mw-parser-output .wst-running-header-4 .wst-running-header-cell:nth-child(3){text-align:right}.mw-parser-output .wst-running-header-cell:first-child{text-align:left}.mw-parser-output .wst-running-header-cell:last-child{text-align:right}.mw-parser-output .wst-running-header-cell>p{margin:0}   10·80 64·8 129·6 648 7,776 223,280

Other units are the suklum or ${\displaystyle \scriptstyle {\frac {1}{2}}}$U=5·4, and cubit of 2U=21·6, 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=gãv; 10·7 inches 21·4 7704 231,120 462,240

probably

 yava, 6=angusta, 10=vitasti; and gama =${\displaystyle \scriptstyle {\frac {3}{5}}}$ arasnl; also bazu = 2 arasni. ·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 6 palms, we may reasonably apply this scale to the Gemara list, and read it as 18, 21·6, and 25·2 inches. There is also a great amount of mediæval 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-inch cubit (from the brazen sea) and for the 18-inch 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, 5·4 and 2·7. Apparently the same unit is found (18) at Heraclea in Lucania, 21·86; and, as the general foot of the South Italians, or Oscan foot (18), best defined by the 100 feet square being ${\displaystyle \scriptstyle {\frac {3}{10}}}$ of the jugerum, and therefore = 10·80 or half of 21·60. A cubit of 21·5 seems certainly to be indicated in prehistoric remains in Britain, and also in early Christian buildings in Ireland (25).

22·2.—Another unit not far different, but yet distinct, is found apparently in Punic remains at Carthage (25), about 11·16 (22·32), and probably also in Sardinia as 11·07 (22·14), where it would naturally be of Punic origin. In the Hauran 22·16 is shown by a basalt door (British Museum), and perhaps elsewhere in Syria (25). It is of some value to trace this measure, since it is indicated by some prehistoric English remains as 22·4.

20·0.—This unit may be that of the pre-Semitic Mesopotamians, as it is found at the early temple of Muḳayyir (Ur); and, with a few other cases (25), it averages 19·97. It is described by Oppert (24), from literary sources, as the great U of 222 susi or 39·96, double of 19·98; from which was formed a reed of 4 great U or 159·8. The same measure decimally divided is also indicated by buildings in Asia Minor and Syria (25).

19·2.—In Persia some buildings at Persepolis and other places (25) are constructed on a foot of 9·6, or cubit of 19·2; while the modern Persian arish is 38·27 or 2×19·13. The same is found very clearly in Asia Minor (25), averaging 19·3; and it is known in literature as the Pythic foot (18, 33) of 9·75, or ${\displaystyle \scriptstyle {\frac {1}{2}}}$ of 19·5, if Censorinus is rightly understood. It may be shown by a mark (33) on the 26th digit of Sharpe's Egyptian cubit = 19·2 inches.

13·3.—This measure does not seem to belong to very early times, and it may probably have originated in Asia Minor. It is found there as 13·35 in buildings. Hultsch gives it rather less, at 13·1, as the "small Asiatic foot." Thence it passed to Greece, where it is found (25) as 13·36. In Romano-African remains it is often found, rather higher, or 13·45 average (25). It lasted in Asia apparently till the building of the palace at Mashita (620 A.D.), where it is 13·22, according to the rough measures we have (25). And it may well be the origin of the dirá‘ Stambuli of 26·6, twice 13·3. Found in Asia Minor and northern Greece, it does not appear unreasonable to connect it, as Hultsch does, with the Belgic foot of the Tungri, which was legalized (or perhaps introduced) by Drusus when governor, as ${\displaystyle \scriptstyle {\frac {1}{8}}}$ longer than the Roman foot, or 13·07; this statement was evidently an approximation by an increase of 2 digits, so that the small difference from 13·3 is not worth notice. Further the pertica was 12 feet of 18 digits, i.e., Drusian feet.

Turning now to England, we find (25) the commonest building foot up to the 15th century averaged 13·22. Here we see the Belgic foot passed over to England, and we can fill the gap to a considerable extent from the itinerary measures. It has been shown (31) that the old English mile, at least as far back as the 13th century, was of 10 and not 8 furlongs. It was therefore equal to 79,200 inches, and divided decimally into 10 furlongs, 100 chains, or 1000 fathoms. For the existence of this fathom (half the Belgic pertica) we have the proof of its half, or yard, needing to be suppressed by statute (9) in 1439, as "the yard and full hand," or about 40 inches, evidently the yard of the most visual old English foot of 13·22, which would be 39·66. We can restore then the old English system of long measure from the buildings, the statute-prohibition, the surviving chain and furlong, and the old English mile shown by maps and itineraries, thus:—

 foot, 3=yard, 2=fathom, 10=chain, 10=furlong, 10=mile. 13·22 39·66 79·32 793 7932 79,320

Such a regular and extensive system could not have been put into use throughout the whole country suddenly in 1250, especially as it must have had to resist the legal foot now in use, which was enforced (9) as early as 950. We cannot suppose that such a system would be invented and become general in face of the laws enforcing the 12-inch foot. Therefore it must be dated some time before the 10th century, and this brings it as near as we can now hope to the Belgic foot, which lasted certainly to the 3d or 4th century, and is exactly in the line of migration of the Belgic tribes into Britain. It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12-inch foot, and repressed by statutes both against its yard and mile, we should need but a small change to place our measures in accord with the metre.

The Gallic leuga, or league, is a different unit, being 1.59 British miles by the very concordant itinerary of the Bordeaux pilgrim. This appears to be the great Celtic measure, as opposed to the old English, or Germanic, mile. In the north-west of England and in Wales this mile lasted as 1.56 British miles till 1500; and the perch of those parts was correspondingly longer till this century (31). The "old London mile" was 5000 feet, and probably this was the mile which was modified to 5280 feet, or 8 furlongs, and so became the British statute mile.

Standards of Area.—We cannot here describe these in detail. Usually they were formed in each country on the squares of the long measures. The Greek system was—

 foot, 36= hexapodes 100= ................ acæna 25=aroura, 4=plethron. 1.027 sq. ft. 36.96 102.68 2567 10,268

The Roman system was—

 pes, 100=decempeda, 36=clima, 4=actus, 2=jugerum, 94 sq. ft. 94 3384 13,536 27,672
 jugerum, 2=heredium, 100=centuria, 4=saltus. .6205 acre 1.241 124.1 496.4

Standards of Volume.—There is great uncertainty as to the exact values of all ancient standards of volume, the only precise data being those resulting from the theories of volumes derived from the cubes of feet and cubits. Such theories, as we have noticed, are extremely likely to be only approximations in ancient times, even if recognized then; and our data are quite inadequate for clearing the subject. If certain equivalences between volumes in different countries are stated here, it must be plainly understood that they are only known to be approximate results, and not to give a certain basis for any theories of derivation. All the actual monumental data that we have are alluded to here, with their amounts. The impossibility of safe correlation of units necessitates a division by countries.

Egypt.—The hon was the usual small standard; by 8 vases which have contents stated in hons (8, 12, 20, 22, 33, 40) the mean is 29.2 cubic inches ± .6; by 9 unmarked pottery measures (30) 29.1±.16, and divided by 20; by 18 vases, supposed multiples of hon (1), 32.1±2. These last are probably only rough, and we may take 29.2 cubic inches ± .5. This was reckoned (6) to hold 5 utens of water (uten 1470 grains), which agrees well to the weight; but this was probably an approximation, and not derivative, as there is (14) a weight called shet of 4.70 or 4.95 uten, and this was perhaps the actual weight of a hon. The variations of hon and uten, however, cover one another completely. From ratios stated before Greek times (35) the series of multiples was

 ro, 8=hon, 4=honnu, 10=apet ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ ............ 10=(Theban), 10=sa. or besha 4=tama 3.65 cub. in. 29.2 116.8 1168 4672 11,680 116,800

(Theban) is the "great Theban measure."

In Ptolemaic times the artaba (2336.), modified from the Persian, was general in Egypt, a working equivalent to the Attic metretes,—value 2 apet or 12 tama; medinmus = tama or 2 artabas, and fractions down to 1400 artaba (35). In Roman times the artaba remained (Didymus), but 16 was the usual unit (name unknown), and this was divided down to 124 or 1144 artaba (35),—thus producing, by 172 artaba a working equivalent to the xestes and sextarius (35). Also a new Roman artaba (Didymus) of 1540. was brought in. Beside the equivalence of the hon to 5 utens weight of water, the mathematical papyrus (35) gives 5 besha=23 cubic cubit (Revillout's interpretation of this as 1 cubit³ is impossible geometrically, see Rev. Eg., 1881, for data); this is very concordant, but it is very unlikely for 3 to be introduced in an Egyptian derivation, and probably therefore only a working equivalent. The other ratio of Revillout and Hultsch, 320 hons = cubit³ is certainly approximate.

Syria, Palestine, and Babylonia.—Here there are no monumental data known; and the literary information does not distinguish the closely connected, perhaps identical, units of these lands. Moreover, none of the writers are before the Roman period, and many relied on are mediæval rabbis. A large number of their statements are rough (2, 18, 33), being based on the working equivalence of the bath or epha with the Attic metretes, from which are sometimes drawn fractional statements which seem more accurate than they are. This, however, shows the bath to be about 2500 cubic inches. There are two better data (2) of Epiphanius and Attic medinmus=112 baths, and saton (13 bath) =138 modii; these give about 2240 and 2260 cubic inches. The best datum is in Josephus (Ant., iii. 15, 3), where 10 baths =41 Attic or 31 Sicilian medimni, for which it is agreed we must read modii (33); hence the bath =2300 cubic inches. Thus these three different reckonings agree closely, but all equally depend on the Greek and Roman standards, which are not well fixed. The Sicilian modius here is 1031, or slightly under 13, of the bath, and so probably a Punic variant of the 13 bath or saton of Phœnicia. One close datum, if trustworthy, would be log of water = Assyrian mina bath about 2200 cubic inches. The rabbinical statement of cubic cubit of 21.5 holding 320 logs puts the bath at about 2250 cubic inches; their log-measure, holding six hen's eggs, shows it to be over rather than under this amount; but their reckoning of bath = 12 cubit cubed is but approximate; by 21.5 it is 1240, by 25.1 it is 1990 cubic inches. The earliest Hebrew system was—

 (log, 4=kab) .............. 3=hin, 6 ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ = ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ bath, or ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$, 10= ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ homer—wet. ‘issarón .......... 10 epha or kor—dry. 32 cub. in. 128 230 283 2300 23,000

‘Issarón ("tenth-deal") is also called gomer. The log and kab are not found till the later writings; but the ratio of hin to issaron is practically fixed in early times by the proportions in Num. xv. 4–9. Epiphanius stating great hin=18 xestes, and holy hin=9, must refer to Syrian xestes, equal to 24 and 12 Roman; this makes holy hin as above, and great hin a double hin, i.e., seah or saton. His other statements of saton=56 or 50 sextaria remain unexplained, unless this be an error for bath =56 or 50 Syr. sext. and =2290 or 2560 cubic inches. The wholesale theory of Revillout (35) that all Hebrew and Syrian measures were doubled by the Ptolemaic revision, while retaining the same names, rests entirely on the resemblance of the names apet and epha, and of log to the Coptic and late measure lok. But there are other reasons against accepting this, besides the improbability of such a change.

The Phœnician and old Carthaginian system was (18)—

 log, 4=kab, 6=saton, 30=corus, 31 cub. in. 123 740 22,200

valuing them by 31 Sicilian = 41 Attic modii (Josephus, above).

The old Syrian system was (18)—

 cotyle, 2=Syr. xestes, 18=sabitha or saton, 112=collathon, 2=bath-artaba; 21 cub. in. 41 740 1110 2220

also

 Syr. xestes, 45=maris, 2=metretes or artaba. 41 1850 3700

The later or Seleucidan system was (18)

 cotyle, 2=Syr. xestes, 90=Syr. metretes, 22 44 4000

the Syrian being 113 Roman sextarii.

The Babylonian system was very similar (18)—

 (14), 4=capitha, ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 15=maris 18=.........epha, 10=homer, 6=achane 33 cub. in. 132 1980 2380 23,800 142,800

The approximate value from capitha=2 Attic chœnices (Xenophon) warrants us in taking the achane as fixed in the following system, which places it closely in accord with the preceding.

In Persia Hultsch states—

 capetis........... 48=artaba, 40 ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ =achane. maris.................. 72 74.4 cub. in. 1983 3570 142,800

the absolute values being fixed by artaba = 51 Attic chœnices (Herod., i. 192). The maris of the Pontic system is 12 of the above, and the Macedonian and Naxian maris 110 of the Pontic (18). By the theory of maris = 15 of 20.6³ it is ???.; by maris = Assyrian talent, 1850, in place of 1850 or 1980 stated above; hence the more likely theory of weight, rather than cubit, connexion is nearer to the facts.

Æginetan System.—This is so called from according with the Æginetan weight. The absolute data are all dependent on the Attic and Roman systems, as there are no monumental data. The series of names is the same as in the Attic system (18). The values are 113 × the Attic (Athenæus, Theophrastus, &c.) (2, 18), or more closely 11 to 12 times 18 of Attic. Hence, the Attic cotyle being 17.5 cubic inches, the Æginetun is about 25.7. The Bœotian system (18) included the achane; if this = Persian, then cotyle = 24.7. Or, separately through the Roman system, the mnasis of Cyprus (18)=170 sextarii; then the cotyle=24.8. By the theory of the metretes being 112 talents Æginetan, the cotyle would be 23.3 to 24.7 cubic inches by the actual weights, which have tended to decrease. Probably then 25.0 is the best approximation. By the theory (18) of 2 metretes = cube of the 18.67 cubit from the 12.45 foot, the cotyle would be about 25.4, within .4; but then such a cubit is unknown among measures, and not likely to be formed, as 12.4 is 35 of 20.6. The Æginetan system then was—

 cotyle, 4 =chœnix ${\displaystyle \scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}}$ 3=chous......................................... 16 ${\displaystyle \scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}}$ =medimnus. 8=.......... hecteus, 4=metretes, 1 12 25 cub. in. 100 300 800 3200 4800

This was the system of Sparta, of Bœotia (where the aporryma=4 chœnices, the cophinus=6 chœnices, and saites or saton or hecteus=2 aporryma, while 30 medimni=achane, evidently Asiatic connexions throughout), and of Cyprus (where 2 choes=Cyprian medimnus, of which 5=medimnus of Salamis, of which 2=mnasis) (18).

Attic or Usual Greek System.—The absolute value of this system is far from certain. The best data are three stone slabs, each with several standard volumes cut in them (11, 18), and two named vases. The value of the cotyle from the Naxian slab is 15.4 (best, others 14.6–19.6); from a vase about 16.6; from the Panidum slab 17.1 (var. 16.2-18.2) ; from a Capuan vase 17.8 ; from the Ganus slab 17.8 (var. 17-18). From these we may take 17.5 as a fair approximation. It is supposed that the Panathenaic vases were intended as metretes; this would show a cotyle of 14.4-17.1. The theories of connexion give, for the value of the cotyle, metretes = Æginetan talent, 15.4-16.6 ; metretes 43 of 12.16 cubed, 16.6; metretes=${\displaystyle \scriptstyle {\frac {27}{20}}}$ of 12·16 cubed, 16·8; medimnus=2 Attic talents, hecteus=20 minæ, chœnix=2${\displaystyle \scriptstyle {\frac {1}{2}}}$ minæ, 16·75; metretes=3 cubic spithami (${\displaystyle \scriptstyle {\frac {1}{2}}}$ cubit=9·12), 17·5; 6 metretes=2 feet of 12·45 cubed, 17·8 cubic inches for cotyle. But probably as good theories could be found for any other amount; and certainly the facts should not be set aside, as almost every author has done, in favour of some one of half a dozen theories. The system of multiples was for liquids—

 cyathus 1${\displaystyle \scriptstyle {\frac {1}{2}}}$=oxybaphon, 4=cotyle, 12=chous, 12=metretes 2·9 cub. in. 4·4 17·5 210 2520

with the tetarton (8·8), 2=cotyle, 2=xestes (35·), introduced from the Roman system. For dry-measure—

 cyathus, 6=cotyle, 4=chœnix, 8=hecteus, 6=medimnus, 2·9 cub. in. 17·5 70 500 3360

with the xestes, and amphoreus (1680)=${\displaystyle \scriptstyle {\frac {1}{2}}}$ medimnus, from the Roman system. The various late provincial systems of division are beyond our present scope (18). System of Gythium.—A system differing widely both in units and names from the preceding is found on the standard slab of Gythium in the southern Peloponnesus (Rev. Arch., 1872). Writers have unified it with the Attic, but it is decidedly larger in its unit, giving 19·4 (var. 19·1–19·8) for the supposed cotyle. Its system is—

 cotyle, 4=hemihecton, 4=chous, 3 = (n). 58 cub. in. 232 932 2796

And with this agrees a pottery cylindrical vessel, with official stamp on it (ΔΗΜΟΣΙΟΝ, &c.), and having a fine black line traced round the inside, near the top, to show its limit; this seems to be probably very accurate, and contains 58 5 cubic inches, closely agreeing with the cotyle of Gythium. It has been described (Rev. Arch., 1872) as an Attic chœnix. Gythium being the southern port of Greece, it seems not too far to connect this 58 cubic inches with the double of the Egyptian hon = 58 - 4, as it is different from every other Greek system. Roman System.—The celebrated Farnesian standard congius of bronze of Vespasian, “mensuræ exactæ in Capitolio P. X.,” contains 206 7 cubic inches (2), and hence the amphora 1654. By the sextarius of Dresden (2) the amphora is 1695; by the congius of Ste Genevieve (2) 1700 cubic inches ; and by the ponderarium measures at Pompeii (33) 1540 to 1840, or about 1620 for a mean. So the Farnesian congius, or about 1650, may best be adopted. The system for liquid was—

 quartarius, 4=sextarius, 4=congius, 4=urna, 2=amphora; 8·6 cub. ins. 34·4 206 825 1650

for dry measure 16 sextarii = modius, 550 cubic inches; and to both systems were added from the Attic the cyathus (2 87), acetabulum (4 "3), and hemina (17 "2 cubic inches). The Roman theory of the amphora being the cubic foot makes it 1569 cubic inches, or decidedly less than the actual measures; the other theory of its containing 80 libræ of water would make it 1575 by the commercial or 1605 by the monetary libra, again too low for the measures. Both of these theories therefore are rather working equivalents than original derivations; or at least the interrelation was allowed to become far from exact. Indian and Chinese Systems.—On the ancient Indian system see Numismata Orientalia, new ed., i. 24; on the ancient Chinese, Nature, xxx. 565, and xxxv. 318.

Standards of Weight.—For these we have far more complete data than for volumes or even lengths, and can ascertain in many cases the nature of the variations, and their type in each place. The main series on which we shall rely here are those (1) from Assyria (38) about 800 B.C. ; (2) from the eastern Delta of Egypt (29) (Defenneh) ; (3) from western Delta (28) (Nancratis) ; (4) from Memphis (44), all these about the 6th century B.C., and therefore before much interference from the decreasing coin standards ; (5) from Cnidus ; (6) from Athens ; (7) from Corfu ; and (8) from Italy (British Museum) (44). As other collections are but a fraction of the whole of these, and are much less completely examined, little if any good would be done by including them in the combined results, though for special types or inscriptions they will be mentioned.

146 grains. The Egyptian unit was the kat, which varied between 138 and 155 grains (28, 29). There were several families or varieties within this range, at least in the Delta, probably five or six in all (29). The original places and dates of these cannot yet be fixed, except for the lowest type of 138-140 grains; this belonged to Heliopolis (7), as two weights (35) inscribed of "the treasury of An" show 139 9 and 140 - 4, while a plain one from there gives 138 8; the variety 147-149 may belong to Hermopolis (35), accord ing to an inscribed weight. The names of the kat and tcina are fixed by being found on weights, the uteu by inscriptions ; the series was

00, 10 = kat, 10 = uten, 10 = tcma. 14 -G gi-s. 140 1460 14,000

The tema is the same name as the large wheat measure (35), which was worth 30,000 to 19,000 grains of copper, according to Ptolemaic receipts and accounts (Rev. Eg., 1881, 150), and therefore very likely worth 10 utens of copper in earlier times when metals were scarcer. The kat was regularly divided into 10; but another divi sion, for the sake of interrelation with another system, was in ^ and , scarcely found except in the eastern Delta, where it is common (29) ; and it is known from a papyrus (38) to bo a Syrian weight. The uten is found-f-6 = 245, in Upper Egypt (rare) (44). Another division (in a papyrus) (38) is a silver weight of j-%- kat = about 88, perhaps the Babylonian siglus of 86. The uten was also binarily divided into 128 peks of gold in Ethiopia; this may refer to another standard (see 129) (33). The Ptolemaic copper coinage is on two bases, the uten, binarily divided, and the Ptolemaic five shekels (1050), also binarily divided. (This result is from a larger number than other students have used, and study by diagrams.) The theory (3) of the derivation of the uten from TsVff cubic cubit of water would fix it at 1472, which is accordant; but there seems no authority either in volumes or weights for taking 1500 utens. .Another theory (3) derives the uten from T^-J- of the cubic cubit of 24 digits, or better f of 20 63; that, however, will only fit the very lowest variety of the uten, while there is no evidence of the existence of such a cubit. The kat is not unusual in Syria (44), and among the haematite weights of Troy (44) are nine examples, average 144, but not of extreme varieties. 12Q cr- 258 f ^ no S rea t standard of Babylonia became the y^Vk . -i r r nk. parent of several other systems; and itself AC F i n and its derivatives became more widely 46o,000. n ,1 ,T i i TX spread than any other standard. It was known in two forms, one system (24) of

urn, C0=sikhir, 6 = shekel, 10 = stone, G=maneh, 60=talent,; 30 grs. 21-5 129 1290 7750 465,000

and the other system double of this in each stage except the talent. These two systems are distinctly named on the weights, and are known now as the light and,heavy Assyrian systems (19, 24). (It is better to avoid the name Babylonian, as it has other meanings also.) There are no weights dated before the Assyrian bronze lion weights (9, 17, 19, 38) of the llth to 8th centuries B.C. Thirteen of this class average 127 2 for the shekel ; 9 haematite barrel-shaped weights (38) give 128 2 ; 16 stone duck-weights (38), 126 5. A heavier value is shown by the precious metals, the gold plates from Khorsabad (18) giving 129, and the gold daric coinage (21, 35) of Persia 129 2. Nine weights from Syria (44) average 128 8. This is the system of the " Babylonian " talent, by Herodotus = 70 minse Euboic, by Pollux =70 mina; Attic, by .(Elian = 72 miiife Attic, and therefore about 470,000 grains. In Egypt this is found largely at Naucratis (28, 29), and less commonly at Defenneh (29). In both places the distribution, a high type of 129 and a lower of 127, is like the monetary and trade varieties above noticed ; while a smaller number of examples are found, fewer and fewer, down to 118 grains. At Memphis (44) the shekel is scarcely known, and a J mina weight was there converted into another standard (of 200). A few barrel weights are found at Karnak, and several egg-shaped shekel weights at Gebelen (44) ; also two cuboid weights from there (44) of 1 and 10 utens are marked as 6 and 60, which can hardly refer to any unit but the heavy shekel, giving 245. Hultsch refers to Egyptian gold rings of Dynasty XVIII. of 125 grains. That this unit penetrated far to the south in early times is shown by the tribute of Kush (34) in Dynasty XVIII.; this is of 801, 1443, and 23,741 kats, or 15 and 27 manehs and 7J talents when reduced to this system. And the later Ethiopia gold unit of the pek (7), or y-^- of the uten, was 10 - 8 or more, and may therefore be the sikhir or obolos of 21 "5. But the fraction T ^, or a continued binary division repeated seven times, is such a likely mode of rude subdivision that little stress can be laid on this. In later times in Egypt a class of large glass scarabs for funerary purposes seem to be adjusted to the shekel (30). Whether this system or the Phoenician on 224 grains was that of the Hebrews is uncertain. There is no doubt but that in the Maccabcan times and onward 218 was the shekel ; but the use of the word darkemon by Ezra and Nehemiah, and the probabilities of their case, point to the darag-maneh, ^ manch, or shekel of Assyria ; and the mention of 3 shekel by Nehemiah as poll tax nearly proves that the 129 and not 218 grains is intended, as 218 was never--- 3. But the Maccabean use of 218 may have been a reversion to the older shekel ; and this is strongly shown by the fraction shekel (1 Sam. ix. 8), the continual mention of large decimal numbers of shekels in the earlier books, and the certain fact of 100 shekels being = mina. This would all be against the 129 or 258 shekel, and for the 218 or 224. There is, however, one good datum if it can be trusted : 300 talents of silver (2 Kings xviii. 14) are 800 talents on Sennacherib s cylinder (34), while the 30 talents of gold is the same in both accounts. Eight hundred talents on the Assyrian silver standard would be 267 or roundly 300 talents on the heavy trade or gold system, which is therefore probably the Hebrew. Probably the 129 and 224 systems coexisted in the country ; but on the whole it seems more likely that 129 or rather 258 grains was the Hebrew shekel before the Ptolemaic times, especially as the 100 shekels to the mina is parallelled by the following Persian system (Hultsch)—

120 gls. Cl.X) 7750

the Hebrew system being

cerah 20 = shekel, 100 = maneh, 30 = talent, l-."9 Krs. 25S? 25,800 774,000

and, considering that the two Hebrew cubits are the Babylonian and Persian units, and the volumes are also Babylonian, it is the more likely that the weights should have come with these. From the cast this unit passed to Asia Minor ; and six multiples of 2 to 20 shekels (av. 127) are found among the haematite weights of Troy (44), including the oldest of them. On the ^Egean coast it often occurs in early coinage (17), at Lampsacus 131-129, Phocrea 256-4, Cyzicus 252-247, Methymna 124 "6, &c. In later times it was a main unit of North Syria, and also on the Euxine, leaden weights of Antioch (3), Callatia, and Tomis being known (38). The mean of these eastern weights is 7700 for the mina, or 128. But the leaden weights of the west (44) from Corfu, &c., average 7580, or 126 3 ; this standard was kept up at Cyzicus in trade long after it was lost in coinage. At Corinth the unit was evidently the Assyrian and not the Attic, being 129 6 at the earliest (17) (though modified to double Attic, or 133, later) and being-f 3, and not into 2 drachms. And this agrees with the mina being repeatedly found at Corcyra, and with the same standard passing to the Italian coinage (17) similar in weight, and in division into ^, the heaviest coinages (17) down to 400 B.C. (Terina, Velia, Sybaris, Posidonia, Metapontum, Tarentum, &c. ) being none over 126, while later on many were adjusted to the Attic, and rose to 134. Six disk weights from Carthage (44) show 126. It is usually the case that a unit lasts later in trade than in coinage; and the prominence of this standard in Italy may show how it is that this mina (18 uncife = 7400) was known as the "Italic" in the days of Galen and Dioscorides (2). -i no A variation on the main system was made by forming a r^nrf 8 m i na f 50 shekels. This is one of the Persian series (gold), and the of the Hebrew series noted above. But it is most striking when it is found in the mina form which distinguishes it. Eleven weights from Syria and Cnidus (44) (of the curious type with two breasts on a rectangular block) show a mina of 6250 (125 "0); audit is singular that this class is exactly like weights of the 224 system found with it, but yet quite distinct in standard. The same passed into Italy and Corfu (44), averaging 6000, divided in Italy into uncife (^), and scripulfe (^-j), and called litra (in Corfu ?). It is known in the coinage of Hatria (18) as 6320. And a strange division of the shekel in 10 (probably therefore connected with this decimal mina) is shown by a series of bronze weights (44) with four curved sides and marked with circles (British Museum, place unknown), which may be Romano-Gallic, averaging 125-4-10. This whole class seems to cling to sites of Phoenician trade, and to keep clear of Greece and the north, perhaps a Phoenician form of the 129 system, avoiding the sexagesimal multiples.

If this unit have any connexion with the kat, it is that a kat of gold is worth 15 shekels or mina of silver ; this agrees well with the range of both units, only it must be remembered that 129 was used as gold unit, and another silver unit deduced from it. More likely then the 147 and 129 units originated independently in Egypt and Babylonia.

o fi From 129 grains of gold was adopted an equal value ^ s ^ vcr= 1720, on the proportion of 1 : 13j, and this was Divided n 10 = 172, which was used either in Such a proportion is indicated in Num. vii., where the gold spoon of 10 shekels is equal in value to the bowl of 130 shekels, or double that of 70, i.e., the silver vessels were 200 and 100 sigli. The silver plates at Khorsabad (18) we find to be 80 sigli of 84 6. The Persian silver coinage shows about 86 ; the danak was g of this, or 287. Xcnophon and others state it at about 84. As a monetary weight it seems to have spread, perhaps entirely, in consequence of the Persian dominion; it varies from 174 downwards, usually 167, in Aradus, Cilicia, and on to the ^Egean coast, in Lydia and in Macedonia (17). The silver bars found at Troy averaging 2744, 01 , j mina of 8232, have been attributed to this unit (17) ; but no division of the mina in ^ is to be expected, and the average i rather low. Two hfematite weights from Troy (44) show 86 and 87 2. The mean from leaden weights of Chios, Tenedos (44), &c., is 8430. A duck-weight of Camirus, probably early, gives 8480 the same passed on to Greece and Italy (17), averaging 8610 ; bui in Italy it was divided, like all other units, into uncife and scripuLc (44). It is perhaps found in Etrurian coinage as 175-172 (17). By the Romans it was used on the Danube (18), two weights of the first legion there showing 8610 ; and this is the mina of 20 uncia? (8400) named by Roman writers. The system was

obol, 6 = siglus, 100 = mina, C0 = talent. 14-3 grs. 80 8COO 516,000

A derivation from this was the ,^ of 172, or 57 3, the so-callei Phocfean drachma, equal in silver value to the fa of the gold 258 grains. It was used at Phocaea as 58 5, and passed to the colonie of Posidonia and Velia as 59 or 118. The colony of Massilia Drouht it into Gaul as 58 2-54 9.|1}} That tnis unit (commonly called Phoenician) is derived S24- doubted, both being 11 I ono^ from tllc 129 s y steni can nart lly Vo nnii so intimately associated in Syria and Asia Minor. /-,uuu. The re i at i on j 3 258 : 229 : : 9 : 8 ; but the exact form in which the descent took place is not settled : ^V of 129 of gold is worth 57 of silver or a drachm, of 230 (or by trade weights 127 and 226) ; otherwise, deriving it from the silver weight of 86 already formed, the drachm is of the stater, 172, or double of the Persian danak of 287, and the sacred unit of Didyma in Ionia was this half drachm, 27 ; or thirdly, what is indicated by the Lydian coinage (17), 86 of gold was equal to 1150 of silver, 5 shekels, or y 1 ^ mina. Other proposed derivations from the kat or pek are not satisfactory. In actual use this unit varied greatly: at Naucratis (29) there are groups of it at 231, 223, and others down to 208 ; this is the earliest form in which we can study it, and the corre sponding values to these are 130 and 126, or the gold and trade varieties of the Babylonian, while the lower tail down to 208 cor responds to the shekel down to 118, which is just what is found. Hence the 224 unit seems to have been formed from the 129, after the main families or types of that had arisen. It is scarcer at Defenneh (29) and rare at Memphis (44). Under the Ptolemies, however, it became the great unit of Egypt, and is very prominent in the later literature in consequence (18, 35). The average of coins (21) of Ptolemy; I. gives 219 6, and thence they gradually diminish to 210, the average (33) of the whole series of Ptolemies being 218. The "argenteus" (as Revillout transcribes a sign in the papyri) (35) was of 5 shekels, or 1090 ; it arose about 440 B.C., and became after 160 B.C. a weight unit for copper. In Syria, as early as the 15th century B.C., the tribute of the Rutennu, of Naliaraina, Megiddo, Anaukasa, &c. (34), is on a basis of 454-484 kats, or 300 shekels ( T V talent) of 226 grains. The commonest weight at Troy (44) is the shekel, averaging 224. In coinage it is one of the commonest units in early times ; from Phoenicia, round the coast to Macedonia, it is predominant (17) ; at a maximum of 230 (lalysus), it is in Macedonia 224, but seldom exceeds 220 else where, the earliest Lydian of the 7th century being 219, and the general average of coins 218. The system was

(1) 8= drachm, 4= shekel, 25=mina, 120=talent. 7 gvs. 56 224 5COO 672,000

From the Phoenician coinage it was adopted for the Maccabean. It is needless to give the continual evidences of this being the later Jewish shekel, both from coins (max. 223) and writers (2, 18, 33) ; the question of the early shekel we have noticed already under 129. In Phoenicia and Asia Minor the mina was specially made in the form with two breasts (44), 19 such weights averaging 5600 (= 224) ; and thence it passed into Greece, more in a double value of 11,200 (= 224). From Phoenicia this naturally became the main Punic unit ; a bronze weight from lol (18), marked 100, gives a drachma of 56 or 57 (224-228) ; and a Punic inscription (18) names 28 drachma; = 25 Attic, and . . 57 to 59 grains (228-236); while a prob ably later series of 8 marble disks from Carthage (44) show 208, but vary from 197 to 234. In Spain it was 236 to 216 in different series (17), and it is a question whether the Massiliote drachmae of 58-55 are not Phoenician rather than Phocaic. In Italy this mina became naturalized, and formed the "Italic mina" of Hero, Priscian, &c. ; also its double, the mina of 26 uncife or 10,800, =50 shekels of 216; the average of 42 weights gives 5390 (= 215 6), and it was divided both into 100 drachma;, and also in the Italic mode of 12 uncife and 288 scripulse (44). The talent was of 120 minre of 5400, or 3000 shekels, shown by the talent from Hercu- laneum, TA, 660,000 and by the weight inscribed PONDO cxxv. (i.e., 125 librne) TALKNTUM SICLOUVM. iii., i.e., talent of 3000 shekels (2) (the M being omitted ; just as Epiphanius describes this talent as 125 libra;, or 6 ( = 9) nomismata, for 9000). This gives the same approximate ratio 96 : 100 to the libra as the usual drachma reckon ing. The Alexandrian talent of Festus, 12,000 denarii, is the same talent again. It is. believed that this mina-f-12 uncife by the Romans is the origin of the Arabic ratl of 12 iikiyas, or 5500 grains (33), which is said to have been sent by Harun al-Rashid to Charlemagne, and so to have originated the French monetary pound of 5666 grains. But, as this is probably the same as the English monetary pound, or tower pound of 5400, which was in use earlier (see Saxon coins), it seems more likely that this pqund (which is common in Roman weights) was directly inherited from the Roman civilization.

f.f) Another unit, which has scarcely been recognized in aTon"- 8 metrology hitherto, is prominent in the weights from 400 000 ^" v r )t &gt; some ^ we S nts f rom Naucratis and 15 from Defenneh plainly agreeing on this and on no other basis. Its value varies between 76 5 and 81 5, mean 79 at Naucratis (29) or 81 at Defenneh (29). It has been connected theoretically with a binary division of the 10 shekels or "stone " of the Assyrian systems (28), 1290 -f 16 being 80 6 ; this is suggested by the most usual mul tiples being 40 and 80 = 25 and 50 shekels of 129; it is thus akin to the mina of 50 shekels previously noticed. The tribute of the Asi, Rutennu, Khita, Assam, &e., to Thothmes III. (34), though in uneven numbers of kats, comes out in round thousands of units when reduced to this standard. That this unit is quite distinct from the Persian 86 grains is clear in the Egyptian weights, which maintain a wide gap between the two systems. Next, in Syria three inscribed weights of Antioch and Berytus (18) show a mina of about 16,400, or 200 x 82. Then at Abydus, or more probably from Babylonia, there is the large bronze lion-weight, stated to have been origin ally 400,500 grains; this has been continually 60 by different writers, regardless of the fact (Rev. Arch., 1862, 30) that it bears the numeral 100 ; this therefore is certainly a talent of 100 minse of 4005 ; and as the mina is generally 50 shekels in Greek systems it points to a weight of 80 - 1. Farther west the same unit occurs in several Greek weights (44) which show a mina of 7800 to 8310, mean 8050-rlOO = 80 5. Turning to coinage, we find this often, but usually overlooked as a degraded form of the Persian 86 grains siglos. But the earliest coinage in Cilicia, before the general Persian coinage (17) about380 B.C., is Tarsus, 164 grains ; Soli, 169, 163,158; Nagidus, 158, 161-153 later; Issus,166; Mallus, 163-154, all of which can only by straining be classed as Persian ; but they agree to this standard, which, as we have seen, was used in Syria, in earlier times by the Khita, &c. The Milesian or "native" system of Asia Minor (18) is fixed by Hultsch at 163 and 81 "6 grains, the coins of Miletus (17) showing 160, 80, and 39. Coming down to literary evidence, this is abundant. Bb ckh decides that the "Alexandrian drachma" was of the Solonic 67, or = 80 5, and shows that it was not Ptolemaic, or Rhodian, or JEginetan, being distinguished from these in inscriptions (2). Then the "Alexandrian mina" of Dioscorides and Galen (2) is 20 uncia; = 8250 ; in the "Analecta" (2) it is 150 or 158 drachms -81 00. Then Attic : Euboic or jEginetan : : 18 : 25 in the metrologists (2), and the Euboic talent = 7000 "Alexandrian" drachma;; the drachma therefore is 80 0. The "Alexandrian" wood talent : Attic talent:: 6 : 5 (Hero, Didymus), and . . 480,000, which is 60 minre of 8000. Pliny states the Egyptian talent at 80 libra = 396, 000 ; evidently = the Abydus lion talent, which is-=-100, and the mina is . . 3960, or 50x79 "2. The largest weight is the "wood" talent of Syria (i8) = 6 Roman talents, or 1,860,000, evidently 120 Antioch minse of 15,500 or 2 x 7750. This evidence is too distinct to be set aside; and, exactly confirming as it does the Egyptian weights and coin weights, and agreeing with the early Asiatic tribute, it cannot be overlooked in future. The system was

drachm, 2 = stater, 50 = mina, 1GO = talcnt. 80 grs. 1GO 8000 400,000 480,000 on 1 ? t ion

This system, the AEginetan, one of the most important to the Greek world, has been thought to Jjn ftnft be a degradation of the Phoenician (17, 21), supposing 220 grains to have been reduced in primitive Greek usage to 194. But we are now able to prove that it was an independent system (1) by its not ranging usually over 200 grains in Egypt before it passed to Greece; (2) by its earliest example, perhaps before the 224 unit existed, not being over 208; and (3) by there being no intermediate linking on of this to the Phoenician unit in the large number of Egyptian weights, nor in the Ptolemaic coinage, in which both standards are used. The first example (30) is one with the name of Amenhotep I. (17th century B.C.) marked as " gold 5," which is 5 x 207 6. Two other marked weights are from Memphis (44), showing 201 8 and 196 - 4, and another Egyptian 191 4. The range of the (34) Naucratis weights is 186 to 199, divided in two groups averaging 190 and 196, equal to the Greek monetary and trade varieties. Ptolemy I. and II. also struck a series of coins (32) averaging 199. In Syria hrematite weights are found (30) averaging 198 5, divided into 99 2, 49 6, and 24 8 ; and the same division is shown by gold rings from Egypt (38) of 24 9. In the medical papyrus (38) a weight of kat is used, which is thought to be Syrian; now f kat = 92 to 101 grains, or just this weight which we have found in Syria ; and the weights of f and |- kat are very rare in Egypt except at Defenneh (29), on the Syrian road, where they abound. So we have thus a weight of 207-191 in Egypt on marked weights, joining therefore completely with the .ffiginetan unit in Egypt of 199 to 186, and coinage of 199, and strongly connected with Syria, where a double mina of Sidon (18) is 10,460 or 50 x 209 2. Probably before any Greek coinage we find this among the haematite weights of Troy (44), ranging from 208 to 193 2 (or 104- 96 6), i.e., just covering the range from the earliest Egyptian down to the early AEginetan coinage. Turning now to the early coinage, we see the fuller weight kept up (17) at Samos (202), Miletus (201), Calymna (100, 50), Methymna and Scepsis (99, 49),[12] Ionia (197); while the coinage of AEgina (17, 12), which by its wide diffusion made this unit best known, though a few of its earliest staters go up even to 207, yet is characteristically on the lower of the two groups which we recognize in Egypt, and thus started

what has been considered the standard value of 194, or usually 190, decreasing afterwards to 184. In later times, in Asia, however, the fuller weight, or higher Egyptian group, which we have just noticed in the coinage, was kept up (17) into the scries of cistophori (196-191), as in the Ptolemaic series of 199. At Athens the old mina was fixed by Solon at 150 of his drachmae (18) or 9800 grains, according to the earliest drachma?, showing a stater of 196 ; and this continued to be the trade mina in Athens, at least until 160 B.C., but in a reduced form, in which it equalled only 138 Attic drachmae, or 9200. The Greek mina weights show (44), on an average of 37, 9650 ( = stater of 193), varying from 186 to 199. In the Hellenic coinage it varies (18) from a maximum of 200 at Pharae to 192, usual full weight; this unit occupied (17) all central Greece, Peloponnesus, and most of the islands. The system was—

obol, C = drachm, 2 = stater, 50 = mina, C0=talent. 16 grs. 96 192 9600 576,000

It also passed into Italy, but in a smaller multiple of 25 drachmae, or | of the Greek mina; 12 Italian weights (44) bearing value marks (which cannot therefore be differently attributed) show a libra of 2400 or 4 of 9600, which was divided in uncire and sextulae, and the full-sized mina is known as the 24 uncia mina, or talent of 120 libra; of Vitruvius and Isidore (i8) = 9900. Hultsch states this to be the old Etruscan pound.

412 4950 grs.

With the trade mina of 9650 in Greece, and recognized AQKO in Italy, we can hardly doubt that the Roman libra is OU grs. the ]m]f of thig mina At Athens it was 2 x 4900; an( | on the average of all the Greek weights it is 2 x 4825, so that 4950 the libra is as close as we need expect. The division by 12 does not affect the question, as every standard that came into Italy was similarly divided. In the libra, as in most other standards, the value which happened to be first at hand for the coinage was not the mean of the whole of the weights in the country ; the Phoenician coin weight is below the trade average, the Assyrian is above, the .ZEginetan is below, but the Roman coinage is above the average of trade weights, or the mean standard. Rejecting all weights of the lower empire, the average (44) of about 100 is 4956; while 42 later- Greek weights (nomisma, &c. ) average 4857, and 16 later Latin ones (solidus, &c. ) show 4819. The coinage standard, however, was always higher ( 1 8) ; the oldest gold shows 5056, the Campanian Roman 5054, the consular gold 5037, the aurei 5037, the Constantine solidi 5053, and the Justinian gold 4996. Thus, though it fell in the later empire, like the trade weight, yet it was always above that. Though it has no exact relation to the congius or amphora, yet it is closely = 4977 grains, the ^ of the cubic foot of water. If, however, the weight in a degraded form, and the foot in an unde- graded form, come from the East, it is needless to look for an exact relation between them, but rather for a mere working equivalent, like the 1000 ounces to the cubic foot in England. Bb ckh has re marked the great diversity between weights of the same age, those marked "Ad August! Temp" ranging 4971 to 5535, those tested by the fussy prefect Q. Junius Rusticus vary 4362 to 5625, and a set in the British Museum (44) belonging together vary 4700 to 5168. The series was—

siliqua, 6= scripulum, 4 = suxtula, C = uncia, 12 = libra, 2·87 grs. 17·2 68·7 412 4950

the greater weight being the centumpondium of 495,000. Other weights were added to these from the Greek system—

obolus, 6 = dniehnia, 2 = sicilicus, 4 = uncia; 8 6 grs. 51-5 103 412

and the sextula after Constantine had the name of solidus as a coin weight, or nomisma in Greek, marked N on the weights. A beautiful set of multiples of the scripulum was found near Lyons (38). from 1 to 10 × 17·28 grains, showing a libra of 4976. In Byzantine times in Egypt glass was used for coin-weights (30), averaging 68 for the solidus = 4896 for the libra. The Saxon and Norman ounce is said to average 416·5 (Num. Chron., 1871, 42), apparently the Roman uncia inherited.

67 grs. 6700; 402,000

 chalcous, 8=obolus, 6=drachma, 100=mina, 60=talanton. 1·4 grs. 11·17 67 6700 402,000

Turning now to its usual trade values in Greece (44), the mean of 113 gives 67·15; but they vary more than the Egyptian examples, having a sub-variety both above and below the main body, which itself exactly coincides with the Egyptian weights. The greater part of those weights which bear names indicate a mina of double the usual reckoning, so that there was a light and a heavy system, a mina of the drachma and a mina of the stater, as in the Phœnician and Assyrian weights. In trade both the minæ were divided in ${\displaystyle \scriptstyle {\frac {1}{2}}}$, ${\displaystyle \scriptstyle {\frac {1}{4}}}$, ${\displaystyle \scriptstyle {\frac {1}{8}}}$, ${\displaystyle \scriptstyle {\frac {1}{3}}}$, and ${\displaystyle \scriptstyle {\frac {1}{6}}}$, regardless of the drachmæ. This unit passed also into Italy, the libra of Picenum and the double of the Etrurian and Sicilian libra (17); it was there divided in unciæ and scripulæ (44), the mean of 6 from Italy and Sicily being 6600; one weight (bought in Smyrna) has the name “Leitra” on it. In literature it is constantly referred to; but we may notice the “general mina” (Cleopatra), in Egypt, 16 unciæ=6600; the Ptolemaic talent, equal to the Attic in weight and divisions (Hero, Didymus); the Antiochian talent, equal to the Attic (Hero); the treaty of the Romans with Antiochus, naming talents of 80 libræ, i.e., mina of 16 unciæ; the Roman mina in Egypt, of 15 unciæ, probably the same diminished; and the Italic mina of 16 unciæ. It seems even to have lasted in Egypt till the Middle Ages, as Jabarti and the “kátib's guide” both name the raṭl misri (of Cairo) as 144 dirhems=6760.

We have now ended our outline of ancient metrology, omitting all details that were not really necessary to a fair judgment on the subject, but trying to make as plain as possible the actual bases of information, to trust to no opinions apart from facts, and to leave what is stated as free as possible from the influence of theories. Theoretical values have nowhere been adopted here as the standards, contrary to the general practice of metrologists; but in each case the standard value is stated solely from the evidence in hand, quite regardless of how it will agree with the theoretical deduction from other weights or measures. Great refinement in statements of values is needless, looking to the uncertainties which beset us. There are innumerable theories unnoticed here; only those are explained which seem to have a reasonable likelihood, and others are only mentioned where it is needful to show that they have not been overlooked. In many cases fuller detail is given of less important points, when they have not been published before, and no other information can be referred to elsewhere; when any point is abundantly proved and known, it has been passed with a mere mention. Finally, to indicate where further information on different matters may be found reference is frequently made by a number to the list of works given below, some early and other works being omitted, of which all the data will be found in later books.

For historical reference we may state the following units legally abolished.

English Weights and Measures Abolished.—The yard and handful, or 40 inch ell, abolished in 1439. The yard and inch, or 37 inch ell (cloth measure), abolished after 1553; known later as the Scotch ell=37·06. Cloth ell of 45 inches, used till 1600. The yard of Henry VII.=35·963 inches. Saxon moneyers pound, or Tower pound, 5400 grains, abolished in 1527. Mark, ${\displaystyle \scriptstyle {\frac {2}{3}}}$ pound=3600 grains. Troy pound in use in 1415, established as monetary pound 1527, now restricted to gold, silver, and jewels, excepting diamonds and pearls. 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 cubic inches, and wine gallon of 1707=231 cubic inches, both abolished in 1824. Winchester corn bushel of 8×268·8 cubic inches and gallon of 274${\displaystyle \scriptstyle {\frac {1}{4}}}$ 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.

 ligne, 12=pouce, 12=pied, 6=toise, 2000=lieue de poste. ·08883 in. 1·0658 12·7892 76·735 2·42219 miles.
 grain, 72=gros, 8=ouce???, 8=marc, 2=poids de marc. ·8197 gr. 59·021 472·17 3777·33 1·0792 ℔.

Rhineland foot, much used in Germany, = 12·357 inches = the foot of the Scotch or English cloth ell of 37·06 inches, or 3×12·353.

(1) A. Aurès, Métrologie Égyptienne, 1880; (2) A. Böckh, Metrologische Untersuchungen, 1838 (general); (3) P. Bortolotti, Del Primitivo Cubito Egizio, 1883; (4) J. Brandis, Münz-, Mass-, und Gewicht-Wesen, 1866 (specially Assyrian); (5) H. Brugsch, in Zeits. Aeg. Sp., 1870 (Edfu); (6) M. F. Chabas, Détermination Métrique, 1867 (Egyptian volumes); (7) Id., Recherches sur les Poids, Mesures, et Monnaies des anciens Égyptiens; (8) Id., Ztschr. f. Aegypt. Sprache, 1867, p. 57, 1870, p. 122 (Egyptian volumes); (9) H. W. Chisholm, Weighing and Measuring, 1877 (history of English measures); (10) Id., Ninth Rep. of Warden of Standards, 1875 (Assyrian); (11) A. Dumont, Mission en Thrace (Greek volumes); (12) Eisenlohr, Ztschr. Aeg. Sp., 1875 (Egyptian hon); (13) W. Golénischeff, in Rev. Eg., 1881, 177 (Egyptian weights); (14) C. W. Goodwin, in Ztschr. Aeg. Sp., 1873, p. 16 (shet); (15) B. V. Head, in Num. Chron., 1875; (16) Id., Jour. Inst. of Bankers, 1879 (systems of weight) ; (17) Id., Historia Numorum, 1887 (essential for coin weights and history of systems); (18) F. Hultsch, Griechische und Romische Metrologie, 1882 (essential for literary and monumental facts); (19) Ledrain, in Rev. Eg., 1881, p. 173 (Assyrian); (20) Leemans, Monumens Égyptiens, 1838 (Egyptian hon); (21) T. Mommsen, Histoire de la Moinaie Romaine; (22) Id., Monuments Divers (Egyptian weights); (23) Sir Isaac Newton, Dissertation upon the Sacred Cubit, 1737; (24) J. Oppert, Étalon des Mesures Assyriennes, 1875; (25) W. M. F. Petrie, Inductive Metrology, 1877 (principles and tentative results); (26) Id., Stonehenge, 1880 ; (27) Id., Pyramids and Temples of Gizeh, 1883; (28) Id., Naukratis, i., 1886 (principles, lists, and curves of weights); (29) Id., Tanis, ii., 1887 (lists and curves); (30) Id., , 1883, 419 (weights, Egyptian, &c.); (31) Id., Proc. Roy. Soc. Edin., 1883–84, 254 (mile); (32) R. S. Poole, Brit. Mus. Cat. of Coins, Egypt; (33) Vazquez Queipo, [{lang|fr|Essai sur les Systèmes Metriques}}, 1859 (general, and specially Arab and coins); (34) Records of the Past, vols. i., ii., vi. (Egyptian tributes, &c.); (35) E. Revillout, in Rev. Eg., 1881 (many papers on Egyptian weights, measures, and coins); (36) E. T. Rogers, Num. Chron., 1873 (Arab glass weights); (37) M. H. Sauvaire, in Jour. As. Soc., 1877, translation of Elias of Nisibis, with notes (remarkable for history of balance); Schillbach (lists of weights, all in next): (38) M. C. Soutzo, Étalons Pondéraux Primitifs, 1884 (lists of all weights published to date); (39) Id., Systèmes Monétaires Primitifs, 1884 (derivation of units); (40) G. Smith, in Zeits. Aeg. Sp., 1875; (41) L. Stern, in Rev. Eg., 1881, 171 (Egyptian weights); (42) P. Tannery, Rev. Arch., xli., 152; (43) E. Thomas, Numismata Orientalia, pt. i. (Indian weights). Many isolated papers in Revue Archéologique, Hellenic Journal, &c., are not specified above; and (44) a great amount of material is yet unpublished of weighings of weights of Troy (supplied through Dr Schliemann's kindness), Memphis, at the British Museum, Turin, &c., which may probably appear before long, and which has been utilized in this article.

III. Commercial.

In this section we shall only refer to such measures as are in actual use at the present time; the various systems of the Continental towns have been superseded by the metric system now in force, and are therefore not needed now except for historical purposes.

Length:—

 inch, 12=foot, 3=yard, 5${\displaystyle \scriptstyle {\frac {1}{2}}}$=pole, 4=chain 10=furlong 8=mile. 1 in. 12 36 198 792 7920 63360

Hand, 4 inches; fathom, 2 yards; knot or geographical mile = 1′ = 1·1507 miles. The chain is divided in 100 links for land measure; link = 7·92 inches.

Terms of square measure are squares of the long measures.

Volume: dry:—

 pint, 2=quart, 4=gallon, 2=peck, 4=bushel, 8=quarter. cub. in. 34·659 69·318 277·274 554·548 2218·19 17745·6

Gill=${\displaystyle \scriptstyle {\frac {1}{4}}}$ pint; pottle=2 quarts; 5 quarters=wey or load; 2 weys=last.

Volume: wet:—

 Pint and quart } gallon, 9=firkin, { 4=barrel or } 2=pipe, butt, or as above. hogshead, puncheon. cub. ins. 277·274 2495·5 9981·9 19963·8

Avoirdupois weight, for everything not excepted below:—

 drachm, 16=ounce, 16=pound, 14=stone, 2=quarter, 4=hundred, 20=ton. 27·3 grains. 437·5 7000 98,000 196,000 grs. 112 ℔ 2240 ℔ .

Troy weight (gold, silver, platinum, and jewels, except diamonds and pearls):—

 grain, 24=pennyweight, 20=ounce, 12=pound. 1 grain 24 480 5760

Diamond and pearl weight:—

 grain, 4=carat, 150=ounce Troy. ·8 grain 3·2 480

Apothecaries' dispensing weight, for prescriptions only:—

 grain, 20=scruple, 3=drachm, 8=ounce, 12=pound. 1 grain 20 60 480 5760

Apothecaries' fluid measure:—

 minim, 60=drachm, 8=ounce, 20=pint, 8=gallon. 91 gr., water 54·7 437·5 8,750 70,000 ·036 cub. in. ·216 1·733 34·659 277·274

Metric System.—The report to the French National Assembly proposing this system was presented 17th March 1791, the meridian measurements finished and adopted 22d June 1799, an intermediate system of division and names tolerated 28th May 1812, abolished and pure decimal system enforced 1st January 1840. Since then Netherlands, Spain (1850), Italy, Greece, Austria (legalized 1876), Germany, Norway and Sweden (1878), Switzerland, Portugal, Mexico, Venezuela, Argentine Republic, Hayti, New Grenada, Mauritius, Congo Free State, and other states have adopted this system. The use of it is permissive in Great Britain, India, Canada, Chili, &c. The theory of the system is that the metre is a 10,000,000th of a quadrant of the earth through Paris; the litre is a cube of 116 metre; the gramme is 11000 of the litre filled with water at 4° C.; the franc weighs 5 grammes. The multiples are as follows:—

 British. France. Netherlands. Other Names. ·039 inch millimetre streep strich ·394 ,, centimetre duim zentimeter 3·937 ,, decimetre palm ... 39·370 ,, metre elle or aune metre, stab ·62138 mile kilometre mijle kilometer, stadion ·176 pint decilitre maatje ... 1·761 ,, litre kop liter or kanne 17·608 ,, decalitre schepel ... 88·038 ,, (50 litres) ... scheffel 176·077 ,, hectolitre mudde { hektoliter, fasse, ⁠kilot ·015 grain milligramme ... ... 15·43 ,, gramme wigtije dr??? 154·32 ,, decagramme lood loi??? 1543·23 ,, hectogramme ons ... 7716·17 ,, (500 grammes) ... pfund, livre 15432·35 ,, kilogramme pond ... 110·23 ℔ (50 kilogr.) ... { zentner, zollcent- ⁠ner 220·46 ,, 100 kilogr. ... { centner métri- ⁠que, quintal 2204·62 ,, 1000 kilogr. ... tonne, tonneau

In land measure the unit is the are (10 metres square)=119·60 square yards; and the hectare=2·4736 acres. Other multiples of the units are merely nominal and not practically used.

Table for Conversion of British and Metric Units.

 Inches. Milli-metres. Metres. Feet. CubicInches. CubicCentimetres. CubicMetres. CubicFeet. 1 25·399 1 3·2809 1 16·386 1 35·316 2 50·799 2 6·5618 2 32·772 2 70·633 3 76·199 3 9·8427 3 49·168 3 105·950 4 101·598 4 13·1230 4 85·545 4 141·266 5 126·998 5 16·4045 5 81·931 5 176·583 6 152·397 6 19·6854 6 98·317 6 211·S99 7 177·797 7 22·9663 7 114·703 7 247·216 8 203·196 8 26·2472 8 131·089 8 282·533 9 228·596 9 29·5281 9 147·476 9 317·849 Pints. Litres. Litres. Gallons. Grains. Grammes. Kilos. Pounds. 1 ·56755 1 ·22024 1 ·064799 1 2·6792 2 1·13310 2 ·44049 2 ·129598 2 5·3584 3 1·70265 3 ·66073 3 ·194397 3 8·0377 4 2·27020 4 ·88098 4 ·259196 4 10·7169 5 2·83775 5 1·10122 5 ·323994 5 13·3961 6 3·40530 6 1·32146 6 ·388794 6 16·0754 7 3·97286 7 1·34171 7 ·453593 7 18·7546 8 4·54041 8 1·76195 8 ·518392 8 21·4338 9 5·10796 9 1·98220 9 ·583190 9 24·1130

For approximate conversion either way use the following ratios:—8 metres = 315 inches (to 110000); 8 kilometres = 5 miles (to 1170); 4 litres = 7 pints (to 1100); 7 grammes = 108 grains (to 14000).

Burmah.—Paulgaut 1 inch, taim 18 inches, saundaung 22 inches, dha 154 inches, dain 2·43 miles. Kait 251 grains, vis 3·59 , sait 14·36, ten 57·36, candy 533 .

Candia.Pic 25·11 inches, carga (corn) 4·19 bushels, rottolo 1·165 , cantaro 116·5 , okka 2 65 .}}

Ceylon.Seer 1·86 pints; 10 parrahs, 1 amomam, 5·6 bushels.

China.Fau ·141 inches, tsun 1·41, chik 14·1, cheung 141, yan 1410 = 117·5 feet. Other chiks—itinerary 12·17, imperial 12·61, surveyor's 12·70, Peking 13·12, Canton 14·70 inches. Li = 1800 chiks of 12·17, 13·12, or 14·1. Kop 3·3 cubic inches; 10 = shing tsong ·96 pint, tau 9·6 (12 catties of water), hwuh 96 pints. Tael 580·3 grains; 16 = catty, 9328 grains or 1·333 ; picul 133·3 .

Denmark.Tomme 1·03 inches, fod 12·357, aln 24·714; mül 4·6807 miles. Pott ·2126 gallons; 2 = kande, 2 = stübchen, 2 = viertel 1·7008 gallons; anker 8·2914 gallons. Pot ·02657 bushel, skieppe ·47835, fjerding ·9567, tonne 3·8268, last 84·188 bushels. Ort 15·1 grains, quintin 60·3, lod 241·2, unze 482·5, mark 3860, pund 7720 = 1·103  = 12 kilogramme. Lispund 17·646 , skippund 3·151 cwt. Tönde (land) 1·25 acres, (coal) 4·6775 bushels.

Egypt.Dirá' of Nilometer 21·3 inches, dirá' beledi 22·7, dirá' handasi 25·13, pic or dirá Stambuli 26·65 inches; pic of land, 29·53, ḳaṣab 139·8 inches. Feddán 1120 acre. Rub'a 6·6 pints or quarts, wébe 6·6 gallons, ardeb 39·6 or 46·4 gallons. Dirhem 60·65 grains, raṭl 1·0131 , oḳḳa 2·7274 , ḳanṭár 101·31 .

India.gaz = yard. gaz 27 inches, háth 18 inches. covid 18·6 inches. cottah (ḳaṭṭhá) 80 square yards; 20 = biggah, 1600 square yards. 24 mauris = cawri, 6400 square yards. Seer, 40 = maund, 20 = candy. Equivalents of Indian and other weights are as follows:—

 Commercial Weights, &c. Avoirdupois. BengalFactory. Madras. Bombay. ℔ oz. dr. mds. s. ch. mds. vls. pol. mds. s. plce. Acheen bahar of 200 } 423 6 13 5 26 13 16 7 10 15 4 27 ⁠catties of 2·117 ℔. Acheen guncha of 10 } 220 0 0 2 37 13 ·7 8 6 16 7 34 8 ·6 ⁠nelly. Anjengo candy of 20 } 560 0 0 7 20 0 22 3 8 20 0 0 ⁠maunds. Bencoolen bahar. 560 0 0 7 20 0 22 3 8 20 0 0 Bengal factory maund. 74 10 10 ·7 1 0 0 2 7 35 ·7 2 26 20 Bengal bazaar maund 82 2 2 ·1 1 4 0 3 2 11 ·3 2 37 10 Bombay candy of 20 } 560 0 0 7 20 0 22 3 8 20 0 0 ⁠maunds. Bussorah maund of 76 } 90 4 0 1 8 5 ·6 3 4 35 ·2 3 8 27 ·9 ⁠vakias. Bussorah maund of 24 } 28 8 0 0 15 4 ·3 1 1 4 ·8 1 0 21 ·4 ⁠vakias. Calicut maund of 100 } 30 0 0 0 16 1 ·1 1 1 24 1 2 25 ·7 ⁠pools. Cochin candy of 20 } 543 8 0 7 11 2 ·6 21 5 36 ·8 19 16 12 ·9 ⁠maunds. Gombroon bazaar candy. 7 8 0 0 4 0 0 2 16 0 10 21 ·4 Goa candy of 20 maunds. 495 0 0 6 25 2 ·9 19 6 16 17 27 4 ·3 Jonkceylon bahar of 8 } 485 5 5 ·3 6 20 0 19 3 12 17 13 10 ⁠capins. Madras candy of 20 } 500 0 0 6 28 0 20 0 0 17 34 8 ·6 ⁠maunds. Mocha bahar of 15 frazils 450 0 0 6 0 1 18 0 0 16 2 25 ·7 } 8 12 0 0 4 11 0 2 32 0 12 15 ⁠maund. Mysore candy of 7 morahs. 560 0 0 7 20 0 22 3 8 20 0 0 Pegu candy of 150 vis. 500 0 0 6 28 0 20 0 0 17 34 8 ·6 Penang pecul of 100 } 133 5 5 ·3 1 31 6 5 2 26 4 30 14 ·3 ⁠catties. Surat maund of 40 seers. 37 5 5 ·3 0 20 0 1 3 37 ·9 1 13 10 Surat pucca maund. 74 10 10 ·7 1 0 0 2 7 35 ·7 2 26 20 Tillycherry candy of } 600 0 0 8 0 2 24 0 0 21 17 4 ·3 ⁠20 maunds.

Bengal bazaar weights are 110 greater than factory weights. Grain and native liquids are usually weighed.

Japan.Boo, 10 = sun, 10 = shaku (11·948 inches = 1033 metre), 6 = ken, 60 = cho, 39 = ri (2·647 miles). Go (11·1 cubic inches), 10 = sho, 10 = to, 10 = koku (5·011 bushels). Momme 57·97 grains, 160 = kin or catty (1·325 ), 1000 momme = kuamme (8·281 ).

Java.Ell 2734 inches. Kanne ·3282 gallon; rand, 396 = leaguer of arrack, 13313 gallons; 360 rands = leaguer of wine. Rice-sack, 2 = picul 13558 , 5 = timbang; coyang 3581 .

Malacca.Covid 1818 inches; buncal 832 grains (gold and silver); kip 41  (tin); 100 catties = picul, 135 ; 3 piculs = bahar; 40 piculs = coyau of salt or rice; 500 gantons = 50 measures = 1 last, nearly 29 cwts.; chupah = 214 ; gautang (=ganton?), 9  of water at 62°.

Malta.Palmo 10·3 inches, foot 7·2 and 11·17 inches, canna 82·4 inches; 16 tumoli = salma, 4·44 acres. Caffiso (oil) 4·58 gallons; barile (wine) 9·16 gallons; salma (corn) 7·9 bushels. Ounce 407·2 grains; rottolo 1·745 ; cantaro 174·5 .

Mexico.—Vara 32·97 inches. Fanega 1·50 bushels. Libra 1·0142 .

Morocco.—Canna 21 inches, commercial rottolo 119 , 100 = quintal; market rottolo 1·785 .

Persia.—Gaz (gueze), 6 handbreadths or 25 inches. Royal gaz 3712 inches. Arash 38·27 inches. Parasang or farsakh 3 geographical miles (an hour's walk for a horse). Sextario (21 cubic inches), 4 = chenica, 2 = capicha (2·4 quarts), 25 = artaba (1·9 bushels). (These, as the native names show, are not native measures. As Chardin remarks, there are no true measures of capacity; even liquids are sold by weight.) Dirhem, 143 (Bussora), 147·8 (Tabriz), or 150 grs. Mescal, 2 = dirhem, 50 = ratl (7300 grains), 6 = man or batman.

Russia.—Vershok (1·75 inches), 16 = archine, 3 = sagene (7 feet British, legally), 500 = verst (·663 mile); 2400 square sagenes = deciatine (2·7 acres). Tcharkey (·216 pint), 100 = vedro, 3 = anker, 40 vedros = sarakovaia (324·6 gallons). Garnietz 2 = tchetverka, 4 = tchetverik, 2 = paiak, 2 = osmin, 2 = tchetvert (5·77 bushels). Dola (·68578 grains); 96 = zolotnic; 8 = laua; 12 = funt (6319·7279 grains); 40 = pud (36·112 ); 10 = berkovitz; 3 = packen. Also 3 zolotnices = 1 loth.

Siam.—Nin, 12 = küb (10 inches), 2 = sok, 4 = wa (79·999 inches on silver bar at 85° Fahr.). Thangsat, 10×10×20 nin, actual standard 1159·8477 cubic inches at 85° = 2·08 pecks. Thanan, 5×5×4 nin, standard 57·8800 at 85° = 1·67 pints. Tical or bat (234·04 grains), 4 = tael, 4 = catty or chang, 50 = picul or hap (133·738 ).

Turkey.—Pic 26·8 or 27·06 inches; larger pic 27·9. Almud 1·15 gallons (of oil = 8 okas); 4 killows = fortin of 3·7 bushels (killow of rice=10 okas). Dram (49·5 grains), 100=chequi, 4=oka (2·8286 ); dram (49·5 grains), 180=rotl, 100=kintal or kantar (127·29 ).

United States.—Inch=1·000049 British inch, and other measures in proportion. Gallon=·83292 British gallon. Bushel=;·96946 British bushel. Weight, as Great Britain.

As weights of grain are often needed we add pounds weight in cubic feet.

 Wheat,Usual. Pease,American. IndianCorn. Oats,Russian. Beans,Egyptian. Barley,English. Rice. Loose....... 49 50 44 28 46 39 } 56 Close........ 53 12 54 47 33 50 44

See Report of Standards Department, 1884.

WEIMAR, the capital of the grand-duchy of SaxeWeimar-Eisenach, the largest of the Thuringian states, is situated in a pleasant valley on the lira, 50 miles south west of Leipsic and 136 miles south-west of Berlin. Containing no very imposing edifices, and plainly and irregularly built, the town presents at first a somewhat unpretending and even dull appearance; but there is an air of elegance in its quiet and clean streets, which recalls the fact that it is the residence of a grand-duke and his court, and it still retains an indescribable atmosphere of refinement, dating from its golden age, when it won the titles of "poets city" and "the German Athens."

Weimar has now no actual importance, though it will always remain a literary Mecca. It is a peaceful little German town, abounding in excellent educational, literary, artistic, and benevolent institutions; its society is cultured, though perhaps a little narrow; while the even tenour of its existence is undisturbed by any great commercial or manufacturing activity. The population in 1885 was 21,565; in 1782, six years after Goethe's arrival, it was about 7000; and in 1834, two years after his death, it was 10,638.

Plan of Weimar.

The reign of Goethe's friend and patron, the grand-duke Charles Augustus (1775-1828), represents accurately enough the golden age of Weimar; though even during the duke's minority, his mother, the duchess Amalia, had begun to make the little court a focus of light and leading in Germany. The most striking building in Weimar is the extensive palace, erected for Charles Augustus under the superintendence of Goethe 1789-1803, in place of one burned down in 1770. This building, with the associations of its erection, and its "poets' rooms," dedicated to Goethe, Schiller, Herder, and Wieland, epitomizes the characteristics of the town. The main interest of Weimar centres in these men and their more or less illustrious contemporaries; and, above all, Goethe, whose altar to the "genius hujus loci" still stands in the ducal park, is himself the genius of the place, just as Shakespeare is of Stratford-on-Avon, or Luther of Wittenberg. Goethe's residence from 1782 to 1832 (now opened as a "Goethe museum," with his collections and other reminiscences), the simple "garden-house" in the park, where he spent many summers, Schiller's humble abode, where he lived from 1802 till his death in 1805, and the grand-ducal burial vault, where the two poets rest side by side, are among the most frequented pilgrim resorts in Germany. Rietschel's bronze group of Goethe and Schiller (unveiled in 1857) stands appropriately in front of the theatre (much altered in 1868) which attained such distinction under their combined auspices. Not far off is the largo and clumsy parish church, built about 1400, of which Herder became pastor in 1776; close to the church is his statue, and his house is still the parsonage. Within the church are the tombs of Herder and of Duke Bernhard of Weimar, the hero of the Thirty Years War. The altar-piece—a Crucifixion—is said to be the masterpiece of Lucas Cranach, whose house is pointed out in the market-place. Wieland, who came to Weimar in 1772 as the duke's tutor, is also commemorated by a statue, and his house is indicated by a tablet. Among the other prominent buildings in Weimar are the library, containing 200,000 volumes and a valuable collection of portraits, busts, and literary and other curiosities; the museum, built in 1863-68 in the Renaissance style; the ancient church of St James, with the tombs of Lucas Cranach and Musæus; and the townhouse, built in 1841. Various points in the environs of Weimar are also interesting from their associations. Separated from the town by the park, laid out in the so-called English style by Goethe, is the chateau of Belvedere, built in 1724. To the north-east is Tiefurt, often the scene of al-fresco plays, in which the courtiers were the actors and the rocks and trees the scenery; and to the north-west is the chateau of Ettersburg, another favourite resort of Charles Augustus and his court.

The history of Weimar, apart from its brilliant record at the end of the 18th and the beginning of the 19th century, is of comparatively little interest. The town is said to have existed in the 9th century, and in the 10th to have belonged to a collateral branch of the family of the counts of Orlamunde. About 1376 it fell to the landgraves of Thuringia, and in 1440 it passed to the electors of Saxony. In 1806 it was visited by Napoleon, whose half-formed intention of abolishing the duchy was only averted by the tact and address of the duchess Luise. The Muses have never left Weimar. Since 1860 it has been the seat of a good school of painting, repre sented by the landscape painters Preller, Kalckreuth, and Max Schmidt, and the historical painters Pauwels, Heumann, and Verlat. The frequent residence here also of the Abbe Liszt, from 1848 till his death in 1886, has preserved for Weimar quite an important place in the musical world.

WEISSENFELS, an industrial town in the province of Saxony, Prussia, is situated on the Saale, 1812 miles south west of Leipsic and 19 miles south of Halle. It contains three churches, a spacious market-place, and various educational and benevolent institutions. The former palace, called the Augustusburg, built in 1664-90, occupies a site on a sandstone eminence near the town; this spacious edifice is now used as a military school. Weissenfels manufactures machinery, sugar, pasteboard, paper, leather goods, pottery, and gold and silver wares. It contains also an iron-foundry, and carries on trade in timber and grain. In the neighbourhood are large deposits of sandstone and lignite. Weissenfels is a place of considerable antiquity, and from 1657 till 1746 it was the capital of the dukes of Saxe-Weissenfels, a branch of the electoral house of Saxony. The body of Gustavus Adolphus was embalmed at Weissenfels after the battle of Liitzen. The population of the town in 1885 was 21,766.

WEKA, or Weeka. See Ocydrome.

WELLESLEY, Richard Wesley (or Wellesley), Marquis of (1760-1842), eldest son of the first earl of Mornington, an Irish peer, and eldest brother of the duke of Wellington, was born June 20, 1760. He was sent to Eton, where he was distinguished as an excellent classical scholar, and to Christ Church, Oxford. By his father's death in 1781 he became earl of Mornington, taking his seat in the Irish House of Peers. In 1784 he entered the English House of Commons as member for Beeralston. Soon afterwards he was appointed a lord of the treasury by Pitt, with whom he rapidly grew in favour. In 1793 he became a member of the board of control over Indian affairs; and, although he was best known to the public by his speeches

1. The word weight has in common use two meanings,—(1) the force exerted between the earth and a body, and (2) a mass which is weighed against other bodies. In scientific use, however, weight means only a property of matter by which it is most convenient to compare the relative amounts of masses.
2. See Nature, xxx. 205.
3. Computed from Fizeau, Ann. Bur. Long., 1878.
4. Computed from Chisholm, Weighing and Measuring, 1877, p. 162; also see p. 158.
5. Computed from Report of Standards Department, 1883.
6. Computed from Chisholm, op. cit., p. 112.
7. See Chisholm, op. cit., pp. 188, 189. For less refined purposes measuring bars should be supported on two points, 21 per cent, of the whole length from the ends. This equalizes the strains in the curves, and makes a minimum distortion.