The New International Encyclopædia/Weights and Measures

by Samuel Wesley Stratton

WEIGHTS AND MEASURES. Standards of magnitude, of weight, and of value are essential for commercial and scientific purposes, and the facility with which national and international intercourse is carried on depends largely upon the uniformity of these standards. Naturally the units of measure adopted by primitive peoples were varied and imperfect, but as civilization advanced, trade increased, science developed, and more accurate standards became necessary. Their selection, whether by government action or by common consent, was left almost to chance, so that they have differed from nation to nation, from county to county, from town to town, and even from one trade or guild to another. The last two centuries, however, have witnessed a great advance in favor of uniformity. England, the United States, France, and several other nations have established uniformity in their respective territories, and the Latin nations have practically all adopted the metric system. The same advantage accruing from uniformity for one or several countries would evidently obtain if a universal system were adopted by the whole world.

The setting up of a system of measures is fraught with many difficulties. The selection, determination, construction, and copying of the standard furnish peculiar problems. The chief considerations affecting the selection of a standard are its relation to a recognized physical constant and the relative ease with which these standards may be determined. In the case of the unit of length, two constants have been favored, a fractional part of a terrestrial meridian, and the length of a seconds pendulum in a given locality. The nautical mile of 6080.20 feet or of 6080 feet is an example of the former and the seconds pendulum of 39.13+ inches an example of the latter. It is quite remarkable that the French meter, based upon the length of a meridian arc, should approximate so closely the length of the seconds pendulum. There need be no difficulty in establishing units of capacity, since these can be based upon the unit of length as exemplified in the metric system (q.v.).

In the case of the unit of weight it is necessary to select a quantity of some substance easily obtainable, and easily standardized as to quantity, purity, and density. Water is a substance which meets those requirements fairly well, and although the British system declares the weight of one cubic inch of distilled water at 62° F. to be 252.458 grains, and the metric system (q.v.) fixes the kilogram as the weight of one cubic decimeter of water at maximum density, the Anglo-Saxon still uses the troy pound and the avoirdupois pound (see below).

Although a fortunate selection be made, the determination and construction of a standard are difficult matters. The French engineers spent seven years in determining a kilometer, and even then failed to obtain 0.0001 of the earth's quadrant. The difficulties of establishing a standard pendulum and of computing the lengths of others vibrating in given times are many and great. In the first place, the experiments are made in air, and the buoyancy of the air lessens the actual weight of the pendulum. Then, since the earth has a diurnal motion on its axis, every object placed on it has a centrifugal tendency which modifies what otherwise would be its gravitation. This centrifugal tendency produces the earth's oblateness and causes a variation in the intensity of gravitation from one latitude to another. Thus a stone is actually heavier in Boston than in New York. This change in gravitation cannot be measured by a balance because the weights at each end of the balance are changed alike, but it is apparent in the motion of a clock; for a pendulum regulated to beat seconds in Washington is found to go too fast when taken to a higher latitude, and to lose time when carried nearer to the equator; and again the attraction which the earth exerts upon bodies placed near it diminishes with their distances from its centre, being inversely proportional to the squares of the distances, so that a clock carried from the bottom to the top of a hill loses time perceptibly. In addition to these niceties, there are others connected with the manipulation, such as the parallelism of the knife-edges, their bluntness, the amplitude of the oscillation, and the stability of the support, so that altogether the exact measurement of the length of the seconds pendulum is a matter of very great difficulty. (See Pendulum.) But granted that a length be chosen and be expressed as a distance between two lines on a metal bar, the tendency to oxidize in air, to change with temperature, and to wear with handling, all combat the preservation of the standard and interfere with the process of copying.

The principles of metrology summarized above, however, are modern compared to weights and measures themselves. Before man had developed beyond the savage state he felt the need of some methods of measurement. So old is the idea that there is found in Josephus the statement that Cain invented weights and measures. Upon the idea of numbers followed closely those of time, distance, and quantity. Measurement of time has been simplified by nature, which furnished the aboriginal, as well as the modern, standard, the diurnal rotation of the earth upon its axis. A measure of distance was easily furnished in the day's journey, as the Indian of the West indicates distance by the number of repetitions of the sign meaning from sunrise to sunset. As a smaller unit became necessary, the stride, or pace, came into use, and finally, as a still smaller unit, the dimensions of parts of the body appear. Although reference is made in Deuteronomy (ii. 3) to the ‘foot breadth’ and the foot came into very general use in Greek, Roman, and subsequent times, nevertheless the common unit in Asia Minor and Egypt was the cubit, derived from the length of the forearm, from the point of the elbow to the end of the middle finger. In the inscriptions and records of these countries continual reference is made to this unit and its subdivisions. Among the Greeks and Romans the pace and foot came into almost universal use, and by them were handed down to subsequent Western nations. The passus became the ‘pace,’ the mille (passuum) the ‘mile,’ and the pondus the ‘pound,’ which appear in most European nations until the present day. Under the Roman Empire the standards wore preserved in a Roman temple, and were the standards for the civilized world. With the fall of the Empire and the rise of small principalities, a chaotic condition as to standards developed which extended through the Middle Ages and thereafter, until in Italy alone, as late as the end of the eighteenth century, there were over two hundred lengths called the foot. Every little dukedom and principality had its own standards of weight and measure, and the insignificant intercourse between these small towns did not suffer from these conditions, but the maritime leagues felt the need of common standards.

An example of the method of deriving the standards in the sixteenth century in Germany is given by the following quotation from Koebel's work on surveying:

“To find the length of a rood in the right and lawful way, and according to scientific usage, you shall do as follows: Stand at the door of a church on a Sunday, and bid sixteen men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawful rood to measure and survey the land with, and the sixteenth part of it shall be a right and lawful foot.”

In England, we find Henry I. establishing the yard as the distance from the point of his nose to the end of his thumb, and Parliament seriously establishing standards of length and weight according to grains of wheat or barley. Doubtless, few people realize that shoes are still numbered according to the length of a grain of barley, in a system of numeration by thirteens. We have, as example of other units from the dimensions of the body, the ‘fathom’ (faethm, the embrace), the length of the two arms from tip to tip; the ‘hand,’ 4 inches; the ‘span,’ 9 inches; the ‘finger,’ ⅛ of a yard; the ‘nail,’ 2¼ inches, from the tip of the thumb nail to the base joint. Yard is derived from the word gyrdan, meaning the girth of the body.

It might appear surprising that the length of the cubit should have remained rather constant so long in Egypt, but where such important buildings were constructed and such continuity of dynasties was maintained, it should not be surprising that the unit or standard of length should have remained constant, inasmuch as the standards would naturally be handed down from dynasty to dynasty, and indeed, if destroyed, could easily be recovered from the dimensions of existing buildings, just as to-day it would be possible to restore the foot from the dimensions and descriptions of existing structures. Just as a carpenter to-day might lose a two-foot rule in the wall of a house, so 3000 years ago an Egyptian stone mason lost his two-cubit rule in the wall of a temple at Karnak. Subsequent ruin and excavation brought it to light, and allowed a direct comparison with the temple dimensions. At the present day, in some parts of China, the first step toward building a house is making a measuring stick, according to which all materials are purchased and the dimensions determined. This method suffices for simple exchange.

Standards of quantity or weight seem to have developed in a still more arbitrary manner. The cuneiform tablets of Babylon tell of ‘vessels’ of oil and ‘skins’ of wine, the volume being as arbitrary as the ‘jar’ or ‘amphora’ of the Romans. For dry produce the term often means simply a heap, large or small. With the introduction of the balance, weighing became possible, and pondus appears, designating essentially ‘a weight.’ Many ‘steel yards’ and balances (see Balance) were unearthed amid the ruins of Pompeii. As the pondus seems to be a haphazard unit, so also is the stone (14 pounds), still used in England, and the base of such units as the hundredweight (cwt.) or 112 pounds (8 stone), and the ton of 2240 pounds or 160 stone, also the bushel of 56 pounds (4 stone), etc.

The earliest systems of linear units seem to be based upon either the cubit (20.62 inches = 52.4 centimeters) or the digit (0.73 inch, or 1.85 cm.), probably derived from the breadth of the finger. The cubit appears first in Egypt in the Fourth Dynasty, and the great pyramid yields the value above given. Nevertheless, as might be expected, considerable variation occurs, even in Egypt (20.5 inches to 20.7 inches). The cubit was divided into hundredths, but as incommensurate, approximate subdivisions the one-seventh, ‘palm,’ and one-twenty-eighth, ‘digit,’ were used. Several extant cubit rods give an average of 20.65 inches. At the Nilometers it is 20.75. As multiples of the cubit (mahi) the xylon, 3 cubits, walking staff, the neut, 4 cubits, and the khet of 40 cubits, are found along with the schoenus of 12,000 cubits. About the same time a similar unit appears in Babylon, especially as the half of 20.89 inches or span of 10.44 inches, or 16 digits of 0.653 inches. A cubit of 20.5 inches is derivable from various buildings in Assyria and Babylonia, where a sexagesimal system existed. In Asia Minor the cubit derived from temples appears as 20.55 inches at Ephesus, 20.62 inches at Samos, while the stadium at Laodicea gives 20.94 inches. Three-fifths of the cubit of 20.75 inches, a combination of the Egyptian decimal and the Assyrian sexary system, is the commonest of Greek derivatives (12.44 inches) occurring in the Propylæa, the Temple of Ægina, the Olympian course, etc. Other and less important derivations from the cubit occur in restricted localities or periods. The digit appeared about simultaneously with the cubit, and some confusion arose from the belief that it was one twenty-eighth of a cubit; in reality they appear to be incommensurate, although 10 digits were often indicated on cubit sticks as the ‘lesser span.’ Practically the same unit appears in Assyria, Persia, and Asia Minor. The common Egyptian small unit of volume was the hon = about 29 cubic inches. The artaba was the practical equivalent of the Attic metretes. The Egyptian unit of weight was the kat = 146 grains; 100 kat = 10 uten = 1 tema. In Babylonia the talent = 360 stone = 3600 shekels = 66.4 pounds. The stadion appears very early as equal to one-thirtieth of a parasang, or about 148 meters, or 485 feet, the parasang being 14,550 feet, or 2.76 miles. This is the old itinerary stadion, used in measuring distances from place to place. As examples of Greek measures of length the following may be given:

1 stadion = 6 plethra or length of a furrow.

1 plethron = 16⅔ orgyia, similar to the fathom, the distance from tip to tip of the outstretched arms.

1 orgyion = 4 pecheis, or cubits.

1 pechus = 1½ pous (foot).

1 pous = 1⅓ spithame (span) from tip to tip of outstretched thumb and finger.

1 spithame = 3 palaisté or handbreadth.

1 palaisté = 4 dactyloi or finger-breadth.

2 stadia = a diaylos, 4 a hippikon, and 12 a dolichos. This Attic or Olympian stadion = 184.97 meters or 606 feet.

The common Greek measure of area was the plethron or square, on the unit of length = 0.095 hectare or 0.235 acre.

Greek units of volume, Attic, were as follows for liquids:

1 metretes = 12 chous = 72 xestes = 144 kotylé = 288 tetarton = 570 oxybaphon = 864 kyathos.

1 metretes = 39.39 liters or 43.33 quarts. For dry materials.

1 medimnos = 6 hecteus (modios) = 12 hemihectons = 48 choinix = 96 xestes = 192 kotylé = 1152 kyathos; 1 medimnos = 52.53 liters or 57.9 quarts.

The Greek units of mass or weight were 1 talent = 60 minæ = 6000 drachmai = 36,000 oboloi = 288,000 chalkia = 26.2 kilograms = 57.7 pounds.

In the Roman system we find the foot of 29.57 centimeters or 11.64 inches, duodecimally subdivided with special names as quincunx = 5/12 foot. etc., also 1 pes (foot) = 4 palmi = 16 digiti = ⁴⁄₅ palmines = ²⁄₃ cubitus, used in building; for geodetic work we have 1 actus = 12 decempeda (pertica, perch) = 24 passus = 48 gradus = 120 pedas. In traveling the following were used: A Roman mile (mille passuum) = 8 stadia = 1000 passus = 5000 pedes. The Romans used the jugerum (as) as the fundamental unit of area = 0.252 hectare or 0.623 acre. As nuiltiples we have 1 saltus = 4 centuriæ = 400 heredia = 800 jugera; 1 jugerum = 2 actus = 8 clìma = 288 scripula (decempeda quadrata) = 28,800 pedes quadrati.

Roman units of capacity were for liquids: 576 cyathus = 384 acetabulum = 192 quartarius = 90 hemina = 48 sextarius = 8 congius = 2 urna = 1 amphora = 26.26 liters = 28.9 quarts. For dry materials, 192 cyathus = 128 acetabulum = 64 quartarius = 32 hemina = 16 sextarius = 2 semodius = 1 modius = 8.754 liter = 9.62 quarts. The Roman unit of weight, the pound, was subdivided duodecimally with special names as semis ½, bes ⅔, etc., into 12 unciæ each equal to 4 sicilici = 24 scripula = 48 oboli = 144 siliquæ = 27.29 grams = 1.04 ounces.

Passing over the details of mediæval European units, it appears that in England, up to 1400, an old building foot existed, about 13.22 inches, and the mile = 79,200 inches, subdivided into 10 furlongs (100 chains) or 1000 fathoms. This fathom is half the Belgian pertica or perch, equals two yards or six feet. Unfortunately, this system was legally suppressed and gradually driven out in favor of the foot of 12 inches, which had been legally enforced as early as the tenth century. The league is a Gallic unit, and lasted in Wales ( = 1.56 miles) till the seventeenth century.

Prior to A.D. 950 the Saxon standards were kept at Winchester, where copies were compared and stamped. “The measure at Winchester shall be the standard,” was the decree of King Edgar. Under the Normans the standards were transferred to Westminster and placed in the care of the chamberlains of the exchequer, but their dimensions were not changed. These came later to be known as ‘The Standards of the Exchequer.’ In 1224 the rule is laid down that: 3 barleycorns = 1 inch; 12 inches = 1 foot; 3 feet = 1 ell (ulna); 5½ ulne = 1 perch; 40 perches long and 4 in breadth = 1 acre. The barleycorns are to be dry, laid end to end, and taken from the middle of the ear. Under Henry VI., Richard II., and Anne an extra inch or ‘thumb's breadth’ was added to the yard for stretching, of cloth. Richard II. decreed uniformity for the kingdom “except in Lancaster, which always had larger measures.”

A yard of Henry VII., dated 1490, and one of Elizabeth, 1588, are undoubtedly the oldest British standards of length, and they differ only about one hundredth of an inch from the present Imperial British yard. Still extant are also the Guildhall yard of 1660, ‘Rowley's Tower standard’ of 1720, etc. In 1742 the Royal Society had an accurate yard made, called ‘Graham's yard.’ A committee of Parliament in 1758 had two very accurate yards made by John Bird, who made another in 1760. These were 39.73 inches long and near each end was inserted a gold plug upon which the mark was made; they were of brass rods a trifle over an inch square in cross section.

In 1797 Sir George Shuckburgh Evelyn first used a comparator by Troughton for the accurate comparison of standards. The results obtained by him are as follows:

	Year	Inches
Henry VII. standard	1490	35.924
Elizabeth standard	1588	36.015
Guildhall standard	1660	36.032
Clockmaker's Co. standard	1671	35.972
Graham's scale, by Sisson	1742	36.0013
Graham's scale, by Sisson in the Exchequer	............	35.9933
General Roy's scale, by Bird	1745-60	30.00036
Mr. Aubert's scale, by Bird	1745-60	35.99880
Royal Society's scale, by Bird	1745-60	35.99955
Bird's Parliamentary standard	1758	36.00023
Bird's Parliamentary standard	1760	36.00002

The Clerk of the House of Commons took charge of the Bird standards until they were finally adopted by Parliament under George IV. on June 17, 1824, after another exhaustive investigation by Capt. Henry Kater. The legalization went into effect January 1, 1826. The act made elaborate provision for the restoration of this standard yard from its relation to the seconds pendulum, but when the Houses of Parliament burned down in 1834, destroying these standards, a royal commission decided against the recovery of the standard from the pendulum, and proceeded to derive a new standard from the extant standards. This new standard was adopted June 30, 1855. In 1870 it was recommended that mural fixed standards be established in populous towns for easy public comparison. Bronze blocks were inserted in the granite on the north side of Trafalgar Square, London, every ten feet to one hundred, and for the chain of 66 feet, and these standards were legalized in June, 1876, by act of the Council. Frequent committees have recommended to Parliament the adoption of the metric system, but with no success as yet. England and America will adopt the metric system at nearly the same time; neither alone can get along without it.

Early in the thirteenth century it was enacted under Henry III. that there should be uniformity in the weights and measures throughout the realm, and a little later it was determined that measures of capacity should be based upon weights. Soon afterwards weights were established upon the weight of grains of wheat, as follows: 32 wheat grains = 1 penny (pennyweight); 20 pence = 1 ounce; 12 ounces = 1 pound; 8 pounds = 1 gallon; 8 gallons = 1 London bushel; 8 bushels = 1 quarter. This was known as the ‘Tower pound’ and was in use until the middle of the fifteenth century.

As early as the thirteenth century, the gallon appears as eight pounds of wine, and the bushel as eight gallons; also in 1452 the gallon was defined as eight troy pounds of wheat, which in Elizabeth's time had become eight pounds avoirdupois. A statute of 1689 defines the wine gallon as 231 cubic inches, a unit still legal in the United States. The Imperial gallon of Great Britain contains 277.274 cubic inches and is used for the measurement of all liquid and dry substances. The Imperial British bushel contains 2218.192 cubic inches, and the Winchester bushel, the legal standard of the United States, contains 2150.42 cubic inches.

In England as well as elsewhere in Europe two pound-units have prevailed from mediæval times, a light pound for weighing articles of high value and a heavy pound for weighing articles of low value. Many of the lighter pounds used in the Latin States are variations of the old Roman standards, others are of Saxon origin, and still others of more recent date. The Italian pounds have varied from 300 to 350 grams, the average being about the weight of the old Roman pound of 325.8 grams. The Spanish, Portuguese, and Prussian light pounds have varied from 459 to 470 grams. The English light pound is the troy pound of 12 ounces, named from the city of Troyes, and declared a legal standard by Great Britain (1497) for weighing gold, silver, silk, and other valuable commodities. The troy pound of Elizabeth (1588) served as a standard for such articles until 1824 (still legal in the United States), and the Imperial standard troy pound (1758) was the only legal standard in Great Britain until 1856. The present standard troy pound is defined as 5760 grains, the troy pound used in the United States.

Of the heavy or so-called commercial pounds there have likewise been a great number. Their range is practically from 15 to 24 ounces, but heavy pounds of 28 and 36 ounces are said to have been used in Milan and Valencia. The standards of France, Germany, Denmark, and Holland range mostly from 488 to 500 grams. The avoirdupois pound was recognized as a standard in England during the reign of Edward III., and the Elizabethan standard (1588) of 7002 grains was derived from that of Edward. The Imperial pound avoirdupois of 7000 grains has been the English standard since 1856 and is generally copied by the United States. At the time it was legalized it was provided that in case the standards were destroyed they were to be recovered by the fact that 1 cubic inch of water at 62° F. and a barometric pressure of 30 inches of mercury, against brass weights in air, weighs 252.458 grains. When this standard perished in 1834 with the yard, it was not recovered by this method, but from other standards.

The development of the standards of France was essentially similar to that in other countries, except that the Revolution at the close of the eighteenth century precipitated the new conditions and resulted in the metric system (q.v.).

In the early colonial days in America the standards of the colonists were naturally those of the mother country, and in most cases copies of the home standards were brought over and intrusted to the care of special officers of the Commonwealth. In the English colonies it was usually the yard of 1588 that was employed. At the time of the Revolution the new country naturally continued with its existing English standards, and although the Constitution empowered Congress to “fix the standard of weights and measures,” nothing was done for a very long time. Thomas Jefferson in 1790, at the suggestion of Washington, brought in to Congress a proposition for a decimal system based upon a natural standard. He was not satisfied with proposed standards and urged the establishment of the ‘Leslie pendulum,’ a straight bar vibrating mean seconds when suspended at one end = 38.72368 inches.

In 1813 the Coast Survey imported a Troughton scale of 82 inches similar to the one used by Shuckburgh, and Superintendent Hassler made a very complete investigation of this as well as all the other standards which he could get, and finally recommended that the distance from the twenty-seventh to the sixty-third mark on the Troughton scale be adopted as the yard, at 62° F. This was adopted by the Treasury Department. In 1817 Hassler compared this American yard with the meter and toise, with the following result: 1 meter = 39.38024749 inches and 1 toise = 76.74+ inches.

On March 3, 1817, the Senate called upon the Secretary of State for an elaborate report relative to weights and measures of this and other countries. John Quincy Adams presented a very complete and exhaustive report, but practically advised that nothing be done at that time. The appendices of this report are very rich in early legal enactments. The matter was taken up again by the Senate in 1830, and again Mr. Hassler undertook a complete investigation of the standards. The Troughton scale of 1813 was taken as the standard, with the following results:

	Inches
The old Exchequer yard of 1820	35.987497
The old Exchequer ell of 1820	45.026101
Latter reduced to yard	36.020881
Copy of Exchequer yard, by Jones	35.9990285
Copy of Exchequer ell, by Jones	45.0389644
Reduced to yard	36.031171
Brass yard of Jones	35.993835
Brass ell of Jones	45.03343
Brass ell reduced to yard	36.026744
Troughton yard, mean of 52-inch scale	36.0002465
The scale of the University of Virginia	35.9952318
Iron yard of the Engineering Department	35.998776
The New York brass yard	36.01545

Gallatin in 1821 brought over to this country a standard platinum meter and kilogram. In 1827 he brought a troy pound of brass which was made the standard of mass in 1828 and has been the Mint standard ever since. The Treasury Department in 1830 adopted 231 cubic inches as the gallon and 2150.42 cubic inches as the bushel.

In 1856 the English Government sent to the United States two certified copies of the standard of length, and these are now known as ‘bronze standard No. 11’ and ‘Low Moor iron standard No. 57.’ In the same year, in order to encourage uniformity among the States, the Treasury Department sent to the Governor of each State a set of weights and measures complete. On July 28, 1866, the metric system of weights and measures was legalized by act of Congress. In 1875 the United States joined with a number of others in the establishment of the International Bureau of Weights and Measures at Paris, and as a result thereof received in 1889 Standard International Meters No. 21 and No. 27 and International Standard Kilograms No. 4 and No. 20. These are made of an alloy of platinum with 10 per cent. of iridium. April 5, 1893, the Treasury Department adopted meter No. 27 and kilogram No. 20 as the standards of the country, and since that time all measures are standardized against these, following the law of 1866 which defined the ratio of the yard to the meter as 3600 to 3937, and the ratio of the pound to the kilogram as 1 to 2.2046. For the history and derivation of the meter and kilogram, see Metric System.

The National Bureau of Standards of the United States was established July 1, 1901, and was made a bureau of the Department of Commerce and Labor by the act establishing that department. The bureau is the repository of the national standards of the Government already described. Its functions include the production of copies, multiples, and subdivisions of the fundamental standards; the construction of the derived standards used in measuring volume, capacity, velocity, pressure, energy, electricity, high and low temperature, and illumination; the comparison of the standards and measuring instruments used in scientific work, manufacturing, and commerce with those of the Government; the determination of physical constants; the development of methods of measurement; scientific research connected with metrology; and the dissemination of knowledge concerning these subjects as applied in the arts, sciences, and industries. Provision was made for scientific work and testing of the highest order of accuracy. Congress has provided for the work of the bureau new laboratories, a corps of specialists in the various lines of scientific work involved, and a full equipment of measuring apparatus and other accessory instruments.

False Weights and Measures. The necessity for prescribing and establishing a uniform system of weights and measures was early recognized by the English law. Before the Conquest, there were Anglo-Saxon laws regulating the sizes of measures used in market places, and since then Parliament has enacted many statutes upon the subject, the present English law being incorporated in the Weights and Measures Act. In the United States the power of regulating weights and measures was vested in Congress, but as that body has not attempted to exercise its authority, except in regard to standards for the collection of customs and internal revenue, the several States have been obliged to fix their own standards and prescribe penalties for the violation of their statutory provisions on this subject. Inspectors are usually appointed with power to visit places of business where either weights or measures are used, in order to detect and prosecute violations of the law. Besides forfeiture of the false instruments, a penalty of fine or imprisonment is usually imposed upon the offender. Such laws have been held to be a legitimate exercise of the police power.

Bibliography. Clark, “Standards of Linear Measures,” School of Mines Quarterly (New York, 1893); J. Q. Adams, Report on Weights and Measures (Philadelphia, 1821); Woolhouse, Measures, Weights, and Moneys of All Nations (London, 1881); Hultsch, Griechische und Römische Metrologie (Berlin, 1862); Giessler, Journal of the Franklin Institute, vol. 126, p. 122 (Philadelphia); Böckh, Metrologische Untersuchungen über Gewichte u. s. w. des Altertums (Berlin, 1838); Chisholm, On the Science of Weighing and Measuring (London, 1877); Clarke, Weights, Measures, and Money of All Nations (New York, 1875); Kelly, Universal Cambist (London, 1835), on English weights and measures; Alexander, Universal Dictionary of Weights and Measures, Ancient and Modern (Baltimore, 1850); Cavalli, Tableaux comparatifs des mesures, poids, etc., de tous les états du monde (Paris, 1874); Harkness, “The Progress of Science as Exemplified in the Art of Weighing and Measuring,” Bulletin of the Philosophical Society of Washington (Washington, 1888); Hilliger, “Studien zu mittelalterlichen Maszen und Gewichten,” Historische Vierteljahrsschrift (Leipzig, 1900); Hultsch, “Die Gewichte des Altertums,” in the Abhandlungen d. Kön. Sächs. Gesellsch. d. Wissenschaften, vol. 18 (Leipzig, 1898); Jackson, Modern Metrology (London, 1882); Lepsius, Die Längenmasze der Alten (Berlin, 1884); Mendenhall, “Fundamental Units of Measure,” Smithsonian Report (Washington, 1893); Noel, Science of Metrology (London, 1889). See also the Proceedings of the American Metrological Society (New York) and various bulletins and circulars of United States Bureau of Standards (Washington, 1901 et seq.). See Metric System; Mile; C. G. S. System.

The following table exhibits the chief units of extension, volume, and weight in use among the leading nations of the world. Their equivalents are expressed in the English system.

Foreign Weights and Measures.

Denomination	Where used	American equivalents
Almude	Portugal	4.422 gallons.
Arratel or libra	Portugal	1.011 pounds.
Arroba (dry)	Argentine Republic	25.3175 pounds.
Arroba (dry)	Brazil	32.38 pounds.
Arroba (dry)	Cuba	25.3664 pounds.
Arroba (dry)	Portugal	32.38 pounds.
Arroba (dry)	Spain	25.36 pounds.
Arroba (dry)	Venezuela	25.4024 pounds.
Arroba (liquid)	Cuba, Spain, Venezuela	4.263 gallons.
Arshine	Russia	28 inches.
Arshine (square)	Russia	5.44 square feet.
Baril	Argentine Republic and Mexico	20.0787 gallons.
Batman or tabriz	Persia	6.49 pounds.
Berkovets	Russia	361.12 pounds.
Bongkal	India	832 grains.
Bu	Japan	0.1193 inch.
Butt (wine)	Spain	140 gallons.
Candy	India (Bombay)	529 pounds.
Candy	India (Madras)	500 pounds.
Carga, or kin	Mexico and Salvador	300 pounds.
Catty	China	1.333⅓ (1⅓) pounds.
Catty	Japan	1.31 pounds.
Centaro	Central America	4.2631 gallons.
Centner	Bremen and Brunswick	117.5 pounds.
Centner	Denmark and Norway	110.11 pounds.
Centner	Prussia	113.44 pounds.
Centner	Sweden	99.7 pounds.
Centner	Vienna	123.5 pounds.
Chetvert	Russia	5.7748 bushels.
Chih	China	14 inches.
Cuadra	Argentine Republic	4.2 acres.
Cwt. (hundred-weight)
	British	112 pounds.
Dessiatine	Russia	2.6997 acres.
Dessiatine	Spain	1.599 bushels.
Fanega (dry)	Central America	1.5745 bushels.
Fanega (dry)	Chile	2.575 bushels.
Fanega (dry)	Cuba	1.599 bushels.
Fanega (dry)	Mexico	1.54728 bushels.
Fanega (liquid)	Spain	10 gallons.
Frail (raisins)	Spain	50 pounds.
Frasco	Argentine Republic	2.5096 quarts.
Frasco	Mexico	2.5 quarts.
Funt	Russia	0.9028 pound.
Garnice	Russian Poland	0.88 gallon.
Joch	Austria-Hungary	1.422 acres.
Ken	Japan	6 feet.
Klafter	Russia	216 cubic feet.
Koku	Japan	4.9629 bushels.
Korree	Russia	3.5 bushels.
Kwan	Japan	8.28 pounds.
Last	Belgium and Holland	85.134 bushels.
Last	England (dry malt)	82.52 bushels.
Last	Germany	2 metric tons (4,480 pounds).
Last	Prussia	112.29 bushels.
Last	Russian Poland	11⅜ bushels.
Last	Spain (salt)	4,760 pounds.
Li	China	2,115 feet.
Libra (pound)	Argentine Republic	1.0127 pounds.
Libra (pound)	Central America	1.043 pounds.
Libra (pound)	Chile	1.014 pounds.
Libra (pound)	Cuba	1.0161 pounds.
Libra (pound)	Mexico	1.01465 pounds.
Libra (pound)	Peru	1.0143 pounds.
Libra (pound)	Portugal	1.011 pounds.
Libra (pound)	Spain	1.0144 pounds.
Libra (pound)	Venezuela	1.0161 pounds.
Livre (pound)	Greece	1.1 pounds.
Load	England (timber)	Square, 50 cubic ft.; unhewn, 40 cubic ft.; inch planks, 600 superficial ft.
Marc	Bolivia	0.507 pounds.
Maund	India	822/7 pounds.
Mil	Denmark	4.68 miles.
Morgen	Prussia	0.63 acre.
Oke	Egypt	2.7225 pounds.
Oke	Greece	2.84 pounds.
Oke	Hungary	3.0817 pounds.
Oke	Turkey	2.82838 pounds.
Oke	Hungary and Wallachia	2.5 pints.
Oke	China, Japan, and Sumatra	133⅓ pounds.
Oke	Philippine Islands	137.9 pounds.
Pie	Argentine Republic	0.9478 foot.
Pie	Spain	0.91407 foot.
Pik	Turkey	27.9 inches.
Pood	Russia	36.112 pounds.
Pund (pound)	Denmark and Sweden	1.102 pounds.
Quarter	Great Britain	8.252 bushels.
Quarter	London (coal)	36 bushels.
Quintal	Argentine Republic	101.42 pounds.
Quintal	Brazil	130.06 pounds.
Quintal	Castile, Mexico, Chile, and Peru	101.41 pounds.
Quintal	Greece	123.3 pounds.
Sagene	Russia	7 feet.
Se	Japan	0.02451 acres.
Seer	India	1 pound 13 oz.
Shaku	Japan	11.9305 inches.
Sho	Japan	1.6 quarts.
Standard
(St. Petersburg)	Lumber measure	165 cubic feet.
Stone	British	14 pounds.
Sun	Japan	1.193 inches.
Tan	Japan	0.25 acre.
To	Japan	2 pecks.
Tondeland	Japan	1.36 acres.
Tsubo	Japan	6 feet square.
Tsun	China	1.41 inches.
Tunuland	Sweden	1.22 acres.
Vara	Argentine Republic	34.1208 inches.
Vara	Central America	34.87 indies.
Vara	Chili and Peru	33.367 inches.
Vara	Cuba	33.384 inches.
Vara	Mexico	33 Inches.
Vara	Spain	0.914 yard.
Vara	Venezuela	33.384 inches.
Vedro	Russia	2.707 gallons.
Verst	Russia	0.663 mile.
Vlocka	Russian Poland	41.98 acres.