This section is from "The American Cyclopaedia", by George Ripley And Charles A. Dana. Also available from Amazon: The New American Cyclopædia. 16 volumes complete..

**Weights And Measures**, means of determining by comparison, and expressing, in the former instance, the mass or quantity of matter of ponderable bodies, as shown by the effect of gravity upon them, and in the latter, the magnitudes of bodies, or of the various forms under which we regard and estimate space. The different species of quantity, of measure, and of unit may be classed as follows: 1, weights; 2, solidities or volumes (in body, or space); 3, surfaces; 4, angles; 5, lines; 6, times; 7, values (money, the artificial measure); 8, intensities or forces (expressed in weights or lengths). Quantity is always that which can be measured. But in order to find and express the measure of a quantity, we must first either find in nature or assume arbitrarily some fixed magnitude or value of the given kind, by comparison with which the relative amounts of the various examples of that kind of quantity are to be ascertained. This fixed magnitude or value is the unit of measure of the given kind of quantity, or in a given one among many systems of measuring it.

Whether found in nature or arbitrarily chosen, the unit itself is always incapable of measurement, and is, in se, an unknown magnitude; so that all measures are comparative or relative only. - Since four right angles just fill the entire space about any point in a plane, and so correspond to the entire circumference of a circle, the right angle becomes a natural measure, or invariable natural unit; and the value of any definite part of this or of the circle is equally fixed. The early geometers accordingly divided the circle or its circumference into 360 equal parts, one of these parts, 1°, becoming the unit of circular or of angular measure; and this measurement is still retained. In estimating time, two natural units present themselves, the day and the year. (See Calendae, and Year.) For the subject of measures of value, see Coin, Money, and the articles on the various denominations of money. For measures of intensity of various natural agencies, see Electeometee, Light, Theemometee, etc. See also the titles of the ordinary measures. The forms of measure to be considered in this article are: weight; measures of length, giving linear or long measures; of surface or area, giving square or superficial measures; and of solidity or volume.

Absolutely invariable standards of weight and measure have never yet been, and in the nature of the materials to be dealt with cannot be, attained; while to secure and reproduce measures of given sorts, the results of which shall be correct and uniform to within the least practicable degree of variability, is a problem upon which a vast amount of scientific research, ingenuity, and labor has been expended. - The balance, or scales, in a rude form, are known to have been in use from very early times. The Greeks, as appears from the Parian chronicle, believed weights, measures, and the stamping of gold and silver coins to have been alike the invention of Phidon, ruler of Argos, about the middle of the 8th century B. C. The units or counterpoises to be employed in weighing could easily be obtained by taking roughly equal bulks of some substance of nearly constant density, as iron or brass; but to render them more definite and accurate, it became necessary to call in the aid of more accurate measures of capacity; and a known volume of pure water and at known density is now the criterion universally resorted to for determining standards of weight.

This supposes that the volume or cubic contents are correctly known; and as we can practically only express content or capacity in terms of the cube of a length, and area in terms of the square of a length, it follows that, to obtain exact units of measure of all the kinds here to be considered, it is necessary first to fix, and to be able to reproduce with the utmost possible exactness, the unit of length. The weight of bodies in the air is slightly diminished by the buoyancy of the medium, and that of all bodies upon the earth by the centrifugal tendency due to its rotation, as well as by increase of elevation above the sea level, as in ascending mountains; but since of these three disturbances the last two affect the article weighed and the counterpoise in the same degree, and the first also if their form and volume be the same, while the difference it can occasion in the result is extremely slight in any case, it follows that in weighing ordinary articles with scales or steelyards, the true weight is still shown under all conditions of the kinds named, or at the least to within an extremely small fraction.

But weight determined by stretching or compressing a spring, as in the spring balance, will be strictly proportional to the force of gravity taking effect at the place, and hence will be lessened by the increased centrifugal force as we approach the equator, and by the diminishing attraction at heights. considerably above the sea level. - In the history of weights and measures, three periods distinctly present themselves: the ancient, or that in which the classical standards were employed, ending with the decline of the Roman empire; the middle, during which, while the names of the classical measures were in many instances preserved, the standards were lost, and the various national measures of Europe grew up; and the modern period, beginning near the close of the 16th century, and marked by the attempts made toward correcting the variableness found in the measures of most nations, and to attain to exact standards through a knowledge and application of physical principles. Among the earlier measures of length of various nations are found such as the finger's length, the digit (second joint of the forefinger), the finger's breadth, the palm, the span, the cubit (length of forearm), the nail, the orgyia (stretch of the arms), the foot, pace, etc.; and the names of these measures, their almost constant recurrence among different nations, and the close approximation in length of such as have, like the foot, more nearly acquired the character of arbitrary measures, alike establish the fact that, in its origin, measurement of lengths was by the application of parts of the human body.

In some parts of the East the Arabs, it is said, still measure the cubits of their cloth by the forearm, with the addition of the breadth of the other hand, which marks the end of the measure; and the width of the thumb was in like manner formerly added at the end of the yard by the English clothiers. Advantages of such measures for popular use are, that they are magnitudes known by observation and readily understood, and in an average way always capable of being recovered, when more arbitrary standards might be wholly lost. But their great disadvantage is extreme variableness, especially when directly applied; and in the gradual progress of men's minds toward exactness of conception and reasoning, though the precise period of the first of these may not now be known, three successive plans of insuring greater accuracy have presented themselves, and two at least have secured permanent adoption. The first is that of obtaining a uniform standard by exchanging the measures by parts of the body for conventional or arbitrary lengths which should represent their average, and which were to be established by law; and this point was doubtless reached at the same time among the Greeks and Romans. In England, arbitrary standards appear to have been known and in common use at an early date.

The names "grain" occurring in troy weight, and "barleycorn" in long measure, show what were in that country the originals or natural units resorted to in forming these measures; or at the least, what were the natural objects chosen as the means of fixing the value of such measures. A statute of Henry III. (1266) enacts " that an English penny, called the sterling, round, without clipping, shall weigh 32 grains of wheat, well dried and gathered out of the middle of the ear; and 20 pence [pennyweights] to make an ounce, 12 ounces a pound, 8 pounds a gallon of wine, and 8 gallons of wine a bushel of London, which is the 8th part of a quarter." Again, Edward II. (1324) provides that the length of 3 barleycorns, round and dry, shall make an inch, 12 inches a foot, etc. The difficulty of determining how much of the end of the grain should be removed to render it "round" makes this standard the less definite of the two. No record exists, however, of the actual construction of standard units based upon the above definitions in grains and barleycorns.

In comparisons of the recorded results of measurements in different countries of Europe, and at different periods, much confusion has existed and has been well nigh unavoidable, growing out of gradual or repeated changes in the standards in current use. As would be expected, the modern legal or conventional standards, as reproduced and in actual use, were found after a time to be subject to considerable variation. For example, from 1650 to 1688 there were in England three different measures- of the wine gallon: 1, the more general opinion and usage gave 231 cubic inches to the gallon; which, it should be noted, is the capacity of a cylinder of 6 in. height and 7 in. diameter, taking the circumference at 22 in.; 2, the customary standard at Guildhall, supposed to be of such capacity, was later found on measurement to contain only 224 cubic inches; 3, the real and' legal standard, preserved at the treasury, contained 282 cubic inches. The corn gallon differed from any of these, being 268*6 cubic inches.

Some suppose the gallons of 231 and 282 inches to have originated under separate enactments, the latter from one of Henry VII., directing that the gallon contain,8 lbs. of wheat; but Oughtred holds that the larger or beer gallon was allowed for liquids which yield froth, while the less gallon was that appropriated to the liquids, such as wine and oil, which, as not frothing, show at once their true volume. Variations of this sort in measures must have existed without intention, and increased; and hence the second step toward exactitude of measurements became necessary, namely, that of making accurate comparisons of the various standards of each given sort in a country. Attempts of this kind appear in England to have been commenced under the auspices of the royal society in 1736 and 1742; in the former year, by a comparison of the English, French, and old Roman standards; and in the latter, by the determination, by George Graham, of the length of a pendulum beating seconds at London (at 39.13 in.), and the construction of a standard yard. Of this, under direction of the house of commons, Mr. Bird prepared two accurate copies, respectively marked "Standard yard, 1758 " and "1760," and intended for adoption as the legal standards.

He determined and prepared also the pound troy, the original of that now in use. Of these two standards no intentional alteration has since been made; so that these and their derivatives are now in use in England and the United States. The third proposed step in the way of rendering measures exact, has reference rather to the means of making the standards recoverable in case they should be lost. In the definite pursuit of this purpose, the French philosophers of the time of the revolution took the lead, and devised the metric system, in which the unit of length is derived from the dimensions of the earth, and the units of capacity and weight are made dependent upon the former, while the whole has decimal multiples and subdivisions. As this system has since gone into very extended use, a full account of it will be given after completing the history of the English and American standards. The efforts of the French philosophers called attention in England to the desirableness of having the standards commensurable with a natural unit; and for this purpose the length of the seconds pendulum at London was selected.

Reports made in 1816, 1818, and 1820, to the house of commons, based on experiments and comparisons, in which Wollaston, Dr. Young, Capt. Kater, and Prof. Playfair took a prominent part, led to the adoption of the imperial measures and standards, under the act 5 George IV., which took effect Jan. 1, 1826, and which the law of 5 and 6 William IV., taking effect Jan. 1, 1836, did not modify in respect to the standards adopted. The weights and measures which had been in vogue in England previous to these acts, based on Bird's standards, 1758 and 1760, had meanwhile become established in the United States, so that here the standards of the old English system are still in force. In the imperial measures, the yard copied from the standard of 1760 was to be of brass, and measured at the temperature of 62° F., while its length was further defined by declaring that of the pendulum beating seconds of mean time in the latitude of London, at the above temperature, in a vacuum, and at the level of the sea, to be 39.1393 inches of the above standard.

The pound troy, from the standard of 1758, is also defined by determining that the cubic inch of distilled water weighed in air by brass weights, at 62°, the barometer being at 30 inches, is equal to 252.458 grains (the pound being 5,760 grains). The standard for measures of capacity, whether dry or liquid, was declared to be the gallon, to contain 10 lbs. avoirdupois weight (this pound being 7,000 grains troy) of distilled water, weighed in air, at 62° F,, the barometer showing 30 inches - this to be thenceforward the measure for all liquids; and the bushel was determined by the requirement that it should contain 8 such gallons. These standards only became compulsory as the sole legal measures after Jan. 1, 1836. The gallon in this system contains 277.274 cubic inches. The former wine gallon is hence 0.83311 of the imperial, or very nearly 6 of the former to 5 of the latter; while the old or Winchester bushel (so called because its standard was long preserved at Winchester) was 0.969447 of the imperial bushel, or about 33 of the former to 32 of the latter.

Soon after the standards were prepared they were destroyed by the burning of the houses of parliament (1834); but fortunately the astronomical society had procured a most carefully prepared copy of the imperial standard yard, and the mint was in possession of an exact copy of the pound, so that it was possible to reproduce the lost standards with great precision. The commission appointed in 1838 to restore them, of which Airy, Baily, Herschel, Lubbock, and Sheepshanks were members, after much investigation, reported in 1841 that, since the passage of the act 5 George IV., several elements of reduction of the pendulum experiments, on which some of its provisions were hased, had been found to be doubtful or erroneous, there having been defects in the agate planes of the pendulum used by Oapt. Kater, and errors in finding its specific gravity, and in reductions for buoyancy of the air and for elevation above the sea level. They concluded that the course prescribed in the act would not necessarily reproduce the original'yard; that the other definition in the act of the yard as a certain brass rod was the best that could be adopted; and that by aid of the astronomical society's scale, and a few other highly accurate copies known, the standard could be restored without sensible error.

Mr. Baily was selected to prepare the new standard,, having five copies of the preceding on which to base his comparison; and on his death in 1844 Mr. Sheepshanks continued the necessary observations, the latter alone executing in all, in the course of this labor, about 200,000 micrometric measurements. Of several standard copies finally prepared by him, each being a square inch bar, of a bronze consisting of copper with a small percentage of tin and zinc, 38 in. in length, with half-inch wells sunk to the middle of the bar, one inch from each end, in which the lines defining the yard are drawn on gold plugs, six were finally selected and reported by the commissioners in March, 1854; of these, the one marked "Bronze, 19" was selected as the parliamentary standard yard, the remaining five being deposited, along with copies of the standard of weight, with as many public institutions and scientific bodies. These standards were legalized in July, 1855; and in case of loss of the parliamentary copy, it was provided that the standards should be restored by comparison of the other selected copies, or such as might be available. Thus, the latest verdict of science may be regarded as adverse to the practicability of basing a system of weights and measures on any invariable natural unit of dimension.

Bronze bar No. 11, which has the standard length at a temperature of 61.79°, has been presented to the United States, and is the actual standard of comparison. - The weights and measures used by the various colonies planted in America were from the first the same with those of England at the corresponding period. Considerable variations naturally grew up in the different colonies, and the several weights and measures already in use being adopted with little or no change when these became states, the discrepancies continued to exist. By a resolution of the senate, March 3, 1817, John Qnincy Adams was commissioned to examine the subject of the weights and measures of the United States, including (it appears) the question of the desirableness of the adoption of the French system or some similar one. Mr. Adams had the standards employed in the various custom houses of the country examined and carefully measured during the years 1819- '20; and in a table accompanying his report, published in Washington in 1821, he shows that very considerable discrepancies then existed within the limits of the several states, and often within the same state, in all the measures of weight, dimension, and capacity.

He reviewed the French system at length, and reported unfavorably to its adoption, chiefly on the grounds of the popular repugnance to a new system, of the subversion of uniformity that for a time would result, and the inconvenience, in his view, of a decimal system. By an act of congress, May 19, 1828, the brass troy pound procured by the American minister at London in 1827, which was a copy prepared by Capt. Kater of the English standard, was declared the standard troy pound of the mint of the United States, conformably to which its coinage should be regulated. The senate, May 29, 1830, directed a new comparison of the weights and measures in use at the different custom houses. This was intrusted to Prof. Hassler; and though much discrepancy was found, the mean corresponded closely with the English standards verified in 1776. Under Mr. Hassler's supervision, accurate copies of the received standards of weights and measures were supplied to all the custom houses. Meanwhile, by a joint resolution of congress, June 14, 1836, the secretary of the treasury was directed to cause a complete set of all the weights and measures adopted as standards to be delivered to the governor of each state in the Union for the use of the states respectively.

These, as well as accurate balances for adjusting the weights, have been supplied, and the statutory standards of every state have been made conformable to the' standards so furnished. It is to be observed that congress has never made any enactment in reference to the old English standards which have come down to us, since the latter were necessarily in force as the national standards unless changed by legislative enactment. The only exception is the legalization of the troy pound, used in the mint, which is identical with the corresponding British troy pound. The other standards of the United States are the yard of 36 inches and the avoirdupois pound of 7,000 grains, both identical with the corresponding British imperial standards; the gallon, intended to represent the old wine gallon of 231 cubic inches, but defined as containing 58,372'2 grains of distilled water at its maximum density, weighed in air of the temperature of 62° F., and barometric pressure of 30 in.; and the bushel, containing 77.6274 pounds of water under the same conditions, equivalent to the old Winchester bushel of 2,150.42 cubic inches.

Before the completion of the new imperial standard, the American yard was taken from a scale made.for the United States by Troughton, which was supposed to be identical with the old standard and with the astronomical society's scale, but which had never been directly compared with either. On comparison with the bronze standard No. 11, the yard on the Troughton scale was found to be nearly 1/1000 of an inch too long, and hence all the copies furnished to the states are subject to that minute correction, since the British yard is unquestionably the only authentic representative of the old standard from which our measures are derived. The use of the metric standards has been legalized, but not made obligatory, in Great Britain since 1864, and in the United States since 1866. - Metric Standards. In France, as before mentioned, a radical change was made in the existing standards by the adoption in 1795 of a system according to which the 1/10000000 part of meridional quadrant of the earth should be the unit of length measure, called the metre; the unit of surface measure being the square of ten metres, called the are; the unit of capacity measure, the cube of a tenth part of the metre, called the litre; that of the measure of solidity, having the capacity of a cubic metre, called the stère; and the unit of weight being the weight of that quantity of distilled water at its maximum density which fills the cube of the 1/100 part of a metre, called the gramme.

Each unit has its decimal multiples and subdivisions, which are indicated by prefixes placed before the names of the several fundamental units. The prefixes denoting multiples, derived from the Greek, are déca, ten; hecto, hundred; Tcilo, thousand; and myria, ten thousand. Those denoting subdivisions are taken from the Latin, and are deci, tenth; centi, hundredth; and milli, thousandth. We thus have kilometre, metre, millimetre; kilogramme, gramme, milligramme. A complete list of the metric measures and their equivalents in American units will be found below in the general table of weights and measures of all countries, under the head of France. An arc of the meridian extending from Dunkirk to Barcelona, and comprising about 10° of latitude, was measured trigonometrically, in order to deduce from it, with the aid of other arcs previously measured in Peru and in Sweden, the length of the meridional quadrant passing through Paris. This length was found in terms of the toise or old fathom (six-foot) measure of France, which was used in the measurement of the base lines; and its ten-millionth part, or the length of the metre, was determined to be- 443.296 lines, the line being the 1/144 of a foot.

It appearing thus that four metres would exceed two toises by the 19th part of a toise, very nearly, the following process of constructing the metre was adopted: Nineteen pieces were made, as nearly as possible equal to each other, so that their aggregate would be a toise; upon careful comparison it was found that one had almost exactly the required length. This piece, together with the two toises that had served in the base measurements, was placed in the comparator and compared with four single metre bars abutted together, which were similarly compared with each other, and adjusted by grinding and polishing their ends until they had the desired length. These bars were, like the toises, of iron; one of them was chosen for the French standard, from which the platinum metre of the archives, which is the legal standard of France, was copied. Another of these original metres was brought to the United States, and has served as the standard for the geodesy of the coast survey, and for the construction of a metric standard for this country. The kilogramme was constructed by means of a cylinder of one fourth of a metre diameter and equal height, very carefully admeasured; it was hollow, and just heavy enough to sink freely in water.

The volume of water displaced by it being weighed by means of an approximate kilogramme and fractions, the correction required to reduce the experimental weight to the prescribed value of the weight of a cubic decimetre of water at its maximum density was deduced, making due allowances for the buoyancy of the air and all other requisite corrections. Finally a kilogramme of platinum was deposited in the archives of France as the prototype unit of weight. It has been found to be equal to 15,432.348 grains, or 2.2046212 pounds avoirdupois, by the most careful comparisons. The metre was found to be 39.37079 English inches, but the most recent and elaborate comparisons, made at the ordnance survey office in Southampton, indicate that it is only 39.37043 inches. The difficulty in making an exact comparison between the metre and the inch or the yard, arises from the fact that the metre is an end measure, of platinum, having its standard length at 32° F., while the yard is a line measure, of bronze, standard at 62° F. They eannot therefore be directly compared, and the dilatation by temperature comes into effect, and requires to be ascer-. tained with the utmost accuracy. The means of comparison for standards of length are different, according to their being line or end measures.

In the former case, when, as in the British yard, the standard length is contained between lines drawn upon the bar, the comparator is necessarily optical, which enables us to measure by means of micrometer microscopes the minute differences between different measures traced from the same standard by mechanical means. But when the standards are end measures or contained between the terminal planes of the bar, the comparison is necessarily made by actual contact, the rotation of a mirror or tilting of a delicate level being used as the means of indicating the minute differences. In standard measures of the latter kind, it is now customary to make the terminal surfaces very small and ground off parallel to each other by means of cylindrical bearings near each end of the bar. It is only by such means that parallelism approaching to geometrical accuracy can be obtained. In both kinds of comparison, a precision of the 1/100000 part of an inch may be reached. The greatest difficulty in obtaining extreme precision arises from the variability of temperature; and this is greatly enhanced when the measures compared are of different volume, and still more when of different metals.

In comparisons of precision, it is therefore necessary to insure a great uniformity of temperature, to prevent as much as possible the influence of the bodily heat of the observer upon the apparatus. In comparisons of weights, the accuracy attainable with the best balances at present in use is readily to the 1/1,000,000 part, and by repetition, under favorable conditions, may be pushed considerably further, to the 1/1000 of a grain in a pound, or at the utmost to 1/10 of a milligramme in a kilogramme. But for such precision it is necessary that the weighing be done in a vacuum, since minute errors will arise from movements of the air within the case of the balances, apart from the corrections due to the buoyancy of the air, which will affect differently weights of different volume. Even in France it was not found practicable at once to introduce the metric units into common use; and although they were at first made compulsory, it became necessary to relax the law so as to permit the use of halves and quarters of the several units. Since 1840, however, the metric measures have been the only ones in common use in France; and the system has found a very large acceptance among other nations.

This fact is chiefly due to the necessity existing in many countries of making some change for the unification of standards used in their various provinces, in order to remedy the evil of varying local standards, and to the additional advantage of international uniformity presented by the adoption of the metric system. For many years its use was limited to the nations of Latin origin cognate to the French, but the recent adoption of the metric system throughout the German empife has determined its prevalence on the European continent. - The only standard which may contend with the metre for universal adoption is the English inch, which is the common unit of length in the British empire, Russia, and the United States. Sir John Herschel has pointed out that the polar axis of the earth is almost exactly 500,500,000 inches, and that the inch may therefore be considered quite as properly a natural standard as the metre; and that the desirable correlation between volume and weight may be found in the fact that a cubic foot of distilled water weighs very nearly 1,000 ounces.

By slight changes of the units this relation might be made exact, and the inch become equal to the 1/500,000,000 part of the earth's polar axis, 25 of such inches making a cubit, equal to the 1/10,000,000 part of the polar radius. - With a view to the construction of more perfect and uniform copies of the metre and kilogrammes, and their distribution to different countries, an international standard commission, composed of scientific representatives from all civilized nations,was formed in 1869, mooting at Paris, and its work is now (1876) nearly completed. This movement has resulted in the establishment of a permanent international bureau of weights and measures, maintained at the common charge of the contracting powers, and having for its object the preservation of the international standards and their test copies; the maintenance of the apparatus for comparison; the periodic verification of the metres and other standards of different nations; the comparison of geodetic measuring bars, and scales used for scientific work; and in general the maintenance of extreme precision and permanence in the fundamental units of measure.

The new prototypes conform as exactly as possible to those heretofore recognized as standards, and no attempt has been made to make them conform more nearly to their theoretical definitions. In regard to the metre, it has been found as the result of more extended geodetic measurements, up to 1875, that the meridional quadrant exceeds 10,000,000 metres by about 1,850 metres, and that consequently the metre falls short of its definition by its 1/5400i part. The kilogramme is in like manner found to differ from its presumed value by some small fraction, in consequence of the great difficulty attending exact determinations of that kind. But it is now generally admitted that material standards, of which there are many exact copies, are all-sufficient for the preservation of the adopted units. The new standards are made of an alloy of platinum and iridium, which possesses the most desirable mechanical and chemical properties, insuring their remaining unchanged for all time. - See Panctou's Metrologie (Paris, 1780); Bessel on the Prussian unit of length (Berlin, 1839); the report of J. Q. Adams (Washington, 1821); Hassler's " Report on the Construction of Standards for the United States" (IT. R. Doc. 299,1832); the "Account of the Construction of the New National Standard of Length, and of its Principal Copies," in the " Philosophical Transactions " (vol. clxvii., London, 1857); account of the restoration of the standard of weight, in the "Philosophical Transactions " (1856); Bache's " Report on Standard Weights and Measures" (Sen. Ex. Doc. 27, 1857); J. IT. Alexander, "Universal Dictionary of Weights and Measures " (Baltimore, 1850); Woolhouse, " Measures, Weights, and Moneys of all Nations" (Weale's series, London, 1856); F. W. Clarke, " Weights, Measures, and Money of all Nations " (New York, 1875); Charles Davies, "The Metric System, etc." (New York, 1871); F. A. P. Barnard, "The Metric System" (New York, 1871); and reports of the warden of the standards (London), of which the 7th, 8th, and 9th (1872'5) are very interesting and valuable.

See also " Comparisons of Standards of Length made at the Ordnance Office, Southampton," by Capt. A. R. Clarke (1866), and " Report of the British Standards Commission on the Metric System " (1869). - The following is a summary of weights and measures in use among the principal nations of the globe, with their equivalents in the standards of the United States:

Length: the guz = 25 in., the covid = 19 in., the kassaba = 4-1 yards. Liquids: 128 vakias = 8 nusfias = 1 gudda = 2 gallons. Weights: 40 vakias = 1 maund = 3 lbs. avoirdupois; and 150 maunds = 15 frazils = 1 bahar = 450 lbs. The weights of Egypt are used in some parts.

(See Spain.) Metric system legal and used in customs.

Length: 1,728 punkte = 144 linien = 12 zoll = 1 fuss = 1.0371 ft.; 6 fuss = 1 klafter; and 4,000 klafter = 1 meile = 4.7142 m. Surface: 1,600 square klafter = 1 joch = 1*4288 acre. Liquid: 80 kannen = 40 raaasse = 4 viertel = 1 eimer = 14.95 galls.; and 32 eimer = 1 fuder. Dry: 16 muhlmaassel = 8 achtel = 4 viertel = 1 metze = 1745 bush.; and 30 metzen = 1 muth. Weight: 1 loth = 270.2 grs.; and 32 loth = 16 unzen = 4 vierding = 2 mark = 1 pfund = 1-2352 lb. The measures differ in some parts; the French measures, under different names, were made legal in 1876.

The fuss is 0-9842 ft.; the stiitze, 3 963 galls.; the malter, 4-257 bush. = 15 decalitres; the pfund, 1'1029 lb. avoirdupois. Metric system since 1872.

The fuss is 0-9517 ft.; the eimer, 16-944 galls.; the scheffel, 6.31 bush.; the pfund, 1-2346 lb. Metric system since 1872.

Since 1820, the French weights and measures, but retaining mainly the Dutch names; as, aune or elle for metre; litron or kan for litre; livre or pond for kilogramme. In weight, the denominations, ascending by tens, are the korrel, wigtje, lood, ons, and the pond = 2.20486 lbs. Surface: 100 sq. elles = 1 are = 119-6083 sq. yds. The cubic elle = 1 stère = 1-308 cub. yd.

The Prague foot = 11-88 in. The measures are generally those of Austria.

In general those of Portugal. But of Brazil pounds, 99 = 100 lbs. avoird.; 5 varas = 6 yds. The medida = | gall.; the alqueire = 1.135 bush.; the mark = 7.3781 oz. troy. Metric system now legal.

The fuss is 11.386 in.; the morgen, 0.6343 acre; the viertel, 1-915 gall.; the scheffel, 2.102 bush.; the pfund = 2 mark = 16 unzen = 32 loth = 1-0986 lb. avoird. (See Germany).

The weights and measures are those of Great Britain. Metric system legal, but not obligatory.

The Dutch standards were formerly in use, but are now mainly superseded by the English.

In general, those of Spain. Metric system legal.

Length: 100 fans = 10 tsuns = 1 chik or covid = 13.125 in.; and 100 chiks = 10 cheungs or fathoms = 1 yan = 109.4 ft. Liquid: 100 kops = 10 shings = 12 catties = 1 tau = 1.318 gall.; and 10 taus = 1 hwuh = 13.18 galls. Weight: 16 taels = 1 catty or pound = 11/3 lb. avoird.; 100 catties = 1 pecul or tam = 1381/3^ lbs.

Generally, those of Spain. In trade are also used 100 libras = 4 arrobas = 1 quintal = 101.75 lbs. avoird.; the vara = 33.333 in.; the fanega = 2.9 bush.; the arroba for wine, 3.42 galls.

Length: 144 linies = 12 tommes = 1 fod = 1-0298 ft.; and 24,000 fods = 12,000 alens = 1 miil = 4.68 m. Liquid: 8 potts = 4 kandes = 2-041 galls. Dry: 36 potts = 2 skjeppens = 1 fjerding = 0-990 bush.; and 88 fjerdings = 22 tondes = 1 last = 86-84 bush. Weight: 32 orts = 1 unze = 1.1029 oz. avoird.; and 16 unzes = 2 marks = 1 pund = 1-1029 lb.; 16 punds = l lispund; 20 lispunds = l skippund = 352-9 lbs.

Length: 36 jows = 12 ungleez = 3 moots or hands = 1 span = 9 in.; and 8 spans = 4 cubits = 2 guz or yards = 1 fathom; 1,00Q fathoms = 1 coss = 13/22 m. Weight (bazaar): 80 siccas = 16 chittacks = 1 seer = 2-0533 lbs.; and 40 seers = 1 maund. In Madras, the marcal is 3.25 galls.; the vis, 3.125 lbs. In Bombay, the hath is IS in.; the parah, 3.33 bush.; the seer, 0.7 lb. Many other variations, of course, exist in the different districts and islands. The metric system is now legalized, but the kilogramme is called ser. Special weights and measures may be authorized by the governor general, but must be a multiple or submultiple of the above.

The common cubit = 22-667 in.; that for Indian goods, 25 in.; for European cloths, 26-5 in. Dry: 24 rubahs = 6 weybehs = 1 ardeb = 5-00 bush. Weight: 144 dirrhems = 12 ukkiyehs = 1 lb. or rutl = 15-75 oz. avoird.; and 100 rutls = 1 cantar. The weights and measures vary, however, in different parts.

Length: 1,000 millimetres = 100 centimetres = 10 decimetres = 1 metre = 3937079 in.; and 10,000 metres = 1,000 decametres = 100 hectometres = 10 kilometres = 1 myriametre = 6.21382 m. Surface: 100 centiares = 1 are, i. e., 1 square décamètre = 0-0247 acre; and 100 ares = 10 decares = 1 hectare. Liquid: 1,000 millilitres = 100 centilitres = 10 decilitres = 1 litre, i. e., 1 cubic decimetre = 61-02705 cub. in. = 2.1134 pints; and 10,000 litres = 1,000 decalitres = 100 hectolitres = 10 kilolitres = 1 myrialitre = 2,641-8 galls. Solid: 10 decisteres = 1 stère, i. e., 1 cubic metre = 85-3166 cub. ft.; and 10 stères = 1 décastère. Weight: 1,000 milligrammes = 100 centigrammes = 10 decigrammes = 1 gramme = 15-43 grs. troy; and 10.000 grammes = 1,000 decagrammes = 100 hectogrammes = 10 kilogrammes = 1 myriagramme = 22-046 lbs. avoird. In the old system, of length: 144 lignes = 12 pouces =1" pied de roi "= 12-79 in.; and 12,000 pieds = 2,000 toises = 1 "lieue de poste." Weight: 72 grains = 1 gros; and 128 gros = 16 onces = 2 marcs = 1 poids de marc = 1-3116 lb. troy.

The fuss is 11-27in.; the viertel, 1-695 gall.; the malter or achtel = 4 simmer = 3-256 bush.; the pfund = 1.0314 lb. avoird. (See Germany).

The palmo is 0.8173 ft., the piede manuale 1-226 ft, the piede liprando 1.6857 ft., the braccio 1,907 ft.; the barile = 50 pinte = 19 605 galls.; the quarto = 12 gombette = 0-427 bush.; the rottolo = 18 once = 1.0483 lb. avoird. (See Italy).

The great diversity of weights and measures which has heretofore obtained in the different states has recently been done away with by the obligatory use of the metric standards throughout the empire. The old measures are noticed under the heads of the different states. In the use of the metric system there has been some adaptation of names to the language. Units of length: the meter or stab, zentimeter or new zoll, millimeter or strich. Surface: ar and hektar. Capacity: liter or kanne, hectoliter or fass; 50 liters make 1 scheffel; ½ liter is called- schoppen. Weight: kilogram = 2 pfund; 50 kilograms = 1 zentner; 1,000 kilograms = 1 tonne. The values of the metric unjts are precisely the same as in France.

For the value of the several units of weight and measure, see the preceding general statement. The denominations and values in the measures of length, surface, and solidity are the same as those of the United States. The same is true of the various systems of weight. The stone is 14 lbs. The units of liquid and of dry measure at present differ from those of the United States, as previously explained, being those known as the imperial: 1 imp. gallon = 1.2006 U. 8. gall.; 1 imp. bushel = 1-0315 U. S. bush. In customary use measures of the same name differ. Thus, in wine measure: 32 gills = 8 pints = 4 quarts = 1 gallon; 86 gallons = 1 tierce; 1½. tierce = 1 hogshead; 2 hogsheads = 1 pipe, butt, or puncheon. Beer measure: 32 gills = 8 pints = 4 quarts = 1 gallon; and 36 gallons = 4 firkins = 2 kilderkins = 1 barrel; 3 kilderkins (54 gallons) = 1 hogshead; 4 hogsheads = 2 butts = 1 tun. Dry (the gallon the same as for liquids): 32 gills = 8 pints = 4 quarts = 1 gallon; 8 gallons = 4 pecks = 1 bushel; and 80 bushels = 20 coombs = 10 quarters = 2 weys = 1 last. The pottle is ½ gallon; the strike, 2 bushels. The hogshead, pipe, and puncheon (liquid measure) differ also in the case of different wines or other spirituous liquors intended.

The old Scottish and Irish measures differed from the English, and were also variable with locality.

The French metrical system is in use. Of old measures of length, the short and long picha are 25 and 27 in., the cubit 18 in., the stadium 600 ft.; the kila is 0-9152 bush.; the pound, 0-8811 lb. avoird.

Length: 96 achtel = 12 zoll = 1 fuss = 0.9408 ft.; and 2 fuss = 1 elle; the meile = 46807 m. The morgen = 23852 acres. Liquid: 16 össel = 8 quartier = 4 kannen = 2 stubchen = 1 viertel = 1.9074 gall.; and 120 viertel = 24 anker = 6 ohm = 1 fuder; the eimer is 4 viertel. Dry: 8 spinte = 2 himt = 1 fass = 1-4941 bush.; and 60 fass = 30 scheffel = 3 wispel = 1 last. Weight: 82 pfennige = 8 quentchen = 2 loth = 1 unze = 1.068 oz. avoird.; and 16 unzen = 2 mark = 1 pfund = 1.068 lb. (See Germany).

Length: 144 linien or 96 achtel = 12 zoll = 1 fuss = 0.9542 ft.; and 16 fuss = 8 ellen = 1 ruthe; 25,400 fuss = 1 meile = 4-5901 m. Liquid: the denominations have the same scale and names as in Hamburg, except that the osse) is called nossel, the viertel being 2.072 galls.; the eimer is 16-576 galls. Dry: 24 vierfass or 18 drittel = 6 himt = 1 malter = 5.3056 bush.; and 16 malter = 2 wispel = 1 last. Weight: scale and names as in Hamburg, except the use of ortchen for spinte, the pfund being 1.0731 lb. avoird. (See Germany).

The metric system is now legal throughout the kingdom. For the former local weights and measures see names of states.

Length: the unit is the shaku = 11.948 in.; 1 shaku = 10 sun = 100 boo; 6 shaku = 1 ken; 60 ken = 1 cho; 39 cho = 1 ri = 2-444 m. Surface: 6 shaku square =.1 tsubo; 300 tsubo = 10 se = 1 tau; 10 tau = 1 cho = 2-458 acres. Capacity, dry and liquid: 100 sho = 10 to = 1 koku = 5.169 bush.; 10 go = 1 sho = 0.481 gall. Weight: 1 momme = 57.97 grains; 1,000 momme = 1 kuamme; 160 momme = 1 kin, also called catty, = 1.325 lb. avoird.

The fuss is 0.9542 ft.; the viertel, 1.979 gall.; the scheffel, 1.01 bush.; the pfund, 1.0686 lb. avoird. (See Germany).

The weights and measures are the same, throughout this state, as those of Hamburg, except that the measures of capacity are those of Lubeck. (See Germany).

The weights and measures are those of Spain, but with many local variations. The vara is 32.97 in.; the fanega, 1-55 bush.; the libra, 1.0142 lb. avoird.

The cubit or canna is 21 in.; the pic, 26 in.; the commercial pound is 1.19 lb., and the market pound 1.785 lb. avoird.

The palmo is 0.8652 ft., and the miglio 1.147 m.; the moggio, 0.87 acre; the barile (wine, &c), 11.57 galls., and the staio (oil), 2.616 galls.; the tomolo, 1.450 bush.; the libbra, 0.8594 lb. troy. (See Italy).

The French metrical system has been in use since 1317, but with the Dutch names. Length: the denominations from the millimetre to the kilometre inclusive take the names streep, duim, palm, elle, roede, mijle; the elle = 1 metre. Liquid: from the centilitre to the hectolitre inclusive, the names are vingerhoed, maatje, kan, vat; the kan = 1 litre. Dry: from the decilitre to the hectolitre the names are maatje, kop, schepel, mudde or zak; the kop = 1 litre; 30 mudde = 1 last. Weight: from the decigramme to the kilogramme the names are korrel, wigtje, lood, ons, pond; the wigtje = 1 gramme.

(See Sweden.) Metric standards now legal.

The royal guertze is 37½ in., the common, 25 in.; the artaba, 1.851 bush.; the rattel, 1.0568 lb. avoird.

The lokiec is 22.68 in.; the morg, 1.334 acre; the garniec, 1.057 gall.; the funt, 0.894 lb. avoird.

Length: 12 pontos = 1 linha; 96 linhas = 8 pollegadas = 1 palmo or span = 0.7214 ft.; and 10 palmos = 2 varas = 1 braca or fathom; the milha = 1.2786 m. The geira is 1.4453 acre. Liquid: 24 quartilhos = 6 canadas = 1 pote, cantaro, or alqueire = at Lisbon 2135 galls., at Oporto 3.313 galls.; and 2 potes = l almude. Dry: 32 outavas = 4 alquieres = 1 fanga=at Lisbon 1.535, and at Oporto 1937 bush.; and 15 fangas = 1 moio. Weight: 72 graos = 3 scropulos = 1 outava; 128 outavas =16 oncas = 1 arratel = 1.01186 b. avoird.; and 128 arrateles = 4 arrobas = 1 quintal = 129.518 lbs. avoird.

Length: 1.728 scrupel = 144 linien = 12 zoll = 1 fuss = 1.0298 ft.; and 12 fuss = 1 ruthe; 2,000 ruthen = 1 postmeile. The morgen is 0.631 acre. Liquid: 120 össel = 60 quartier = 2 anker = 1 eimer = 18.146 galls.; and 12 eimer = 6 ohm = 1 fuder. Dry: 64 mässchen = 16 metzen = 4 viertel = 1 scheffel = 1.560 bush.; and 72 scheffel = 6 malter = 1 last. Weight: 128 quentchen = 32 loth = 16 unzen = 2 mark (Cologne) = 1 pfund = 1.0311 lb. avoird. Metric system now legal and obligatory. (See Germany)

Length (commercial): the pie is 0.966 ft.; the palmo. 0.733 ft.; the braccio, 2.561 ft.; the palmo for cloth is 8.847 in. Length (in architecture, etc.): 120 decimi = 12 once = 1 palmo = 0.7325 ft.; and 10 palmi = 1 canna, the catena being 57½ palmi; and the pie= 16 once = 0.9767 ft. Liquid: 16 quartucci = 4 fogliette = 1 boccale = 0.4816 gall.; 32 boccali = 1 barile, and 16 barili = 1 botte. Dry: 4¾ quartucci = 13/8 scorzi = 1 starello = 0.5222 bush.; and 16 starelli = 4 quarte = 1 rubbio. Weight: 24 grani = 1 denaro; 24 denari = 1 oncia; 12 once = 1 libbra = 0.7477 lb. (See Italy).

Length: 16 vershoks = 1 arshin = 28 in.; and 1.500 arshin = 500 sazhens = 1 verst (properly versta) = 0.6629 m. Liquid: 100 tcharkas = 1 vedro = 3.249 galls.; 3 vedros = 1 anker (ankerok), and 40 vedros = 1 sorokovaya. Dry: 16 garnets = 8 tchetverkas = 2 tchetveriks = 1 payak = 1.489 bush.; and 4 payaks = 2 osmins = 1 tchetvert. Weight: 96 doli = 1 zolotnik = 0.1504 oz. avoird.; 12 lanas (each 8 zolotniks), or 32 loths (each 3 zolotniks) = 1 funt = 0.9026 lb. avoird.; and 1,200 funts = 30 poods = 10 berkovetz = 1 packen.

The fuss is 0.929 ft.; the kanne is 1.2723, and the eimer 20.039 galls.; the viertel is 0.737, and the scheffel 2.948 bush.; the pfund = 16 unzen = 1.0309 lb. avoird. (See Germany).

The ken is 3.153 ft.; the sesti, 1/3 bush.; the tael 0.129, and the catty 2.533 lbs. avoird.

The palmo is 9.53 in.; the salma (Messina), 2307 galls.; the grossa, 9.90 bush.; the libbra, 0.7 lb.; and the rottolo, heavy and light, 1.925 and 1.75 lb. avoird. (See Italy).

The metric system is now the legal one. The old weights and measures, as used in Madrid and Castile, are: Length: 144 puntos = 12 lineas = 1 pulgada = 0.927 in.; 12 pulgadas = 2 sesmas = 1 pie = 0.9273 ft.; and 12 pies = 4 varas = 1 estadal; the palmo is 8.346 in.; the legua = 8,000 varas = 4.2152 m. Liquid: 128 copas = 32 cuartillos = 8 azumbres = 1 arroba or cantaro = 4.263 galls, for wine; for oil, 1 arroba = 3.318 galls. Dry: 16 ochavillos = 4 raciones = 1 cuartillo; and 48 cuartillos = 24 medios = 12 almudes = 1 fanega = 160 bush.; and 12 fanegas = 1 cahiz = 19.20 bush. Weight: 12 granos = 1 tomin; 4S tomines = 16 adarmes = 8 ochavas = 1 onza = 0.0634 lb.; and 16 onzas = 2 marcos = 1 libra = 1.0144 lb. avoird.

Length: 144 linies = 12 turns = 1 fot = 0.9742 ft.; and 6 fots = 3 alns = 1 famn; 6,000 famns = 1 mil = 6.6423 m. Liquid: S2 jungfrus = 8 qvarters = 2 stops = 1 kanna = 0.691 gall.; and 48 kannas = 1 tunna = 83.17 galls. Dry: 224 orts = 56 qvarters = 14 stops = 7 kannas = 1 fjerding = 0.5196 bush.; and 8 fjerdings = 2 spanns = 1 tunna = 4.157 bush. Weight (commercial): 128 qvintins = 32 lods = 16 uns = 1 skalpund = 09376 lb. avoird.; and 400 skalpunds = 20 lispunds = 1 skeppund = 375.04 lbs. The above are the old measures. The system has since been decimalized, but based upon former units; 100 linies = 10 turns = 1 fot = 11.679 in.; 100 fots = 10 stangs = 1 ref. In both wet and dry capacity measure the cubic turn, cubic fot, etc, are U6ed. In weight 100 korrs = 1 ort; 100 orts = 1 skalpund = 0.93379 lb.; 100 skalpunds = 1 centner; 100 centners = 1 last. The metric system is to go into effect in 1878.

Prior to 1856 almost every canton had different measures; the present uniform system is semi-metric, and is in general use. Length: 100 lignes = 10 pouces = 1 pied = 30 centimetres or 11.8112 in.; 10 pieds = 1 perche; 16,000 pieds = 1 lieue = 2.983 m. Surface: the arpent, 400 pieds square = 3.558 acres. Liquid: the pot, 1.5 litre or 1.585 quart, is subdivided into ½, ¼, 1/8; 100 pots = 1 muld = 4 setier. Dry: 10 einines = 1 quateron = 15 litres or 0.4257 bush. Weight: the livre or pfund = 500 grammes or 1.1023 lb.; 100 livres = 1 quintal; 32 loth = 16 onces = 1 livre. In the German cantons the German names are used.

The Turkish dreah or pic = 3 palmi = 26.42 in.; the less dreah = 19.03 in. The barile = 24 bozze = 17.12 galls. The ueba = 4 temen = 16 orbahs = 3.05 bush. The Okie = 1 oz. troy; 1,600 okies = 100 rottols = 1 cantar = 109.7 lbs. avoird.

The pic or pike is 26.8 in.; the almud, 1.382 gall.; the killow, 0.940 bush. Weight: 400 drams = 4 chequees = 1 oke = 2.8286 lbs. avoird.; and 45 okes = 1 kintal or cantaro = 127.3 lbs. at Smyrna, but 140.3 lbs. at Constantinople.

The palmo is 0.9575 ft.; the braccio, 1.915 ft.; the barile (wine) = 20 flaschi = 40 boccali = 12.04 galls.; the sacco = 3 staja = 12 quarti = 2.075 bush.; the libbra = 12 once = 96 dramme = 0.7436 lb. avoird. (See Italy).

For the value of the several units of weight and measure, see the preceding general article. Length: 6 points = 1 line; 144 lines or 36 barleycorns = 12 inches = 1 foot; 16½ ft. = 5½ yards = 1 rod, pole, or perch; 320 rods = 80 chains = 8 furlongs = 1 mile (1,760 yds. or 5.230 ft.); 1 chain = 100 links, each of 7.92 in. The nail is 2¼ in.; the palm, 3 in.; the hand, 4 in.; the span, 9 in.; the quarter of cloth, 9 in.; the ell, Flemish, English, and French, respectively 3, 5, and 6 quarters; the cubit, 1½ ft.; the pace, 5 ft.; the fathom, 6 ft.; a cable's length, 120 fathoms; a league, 3 m.; a degree of the meridian, 69.046 m. Surface: 144 sq. in. = 1 sq. ft.; 272¼ sq. ft. = 30¼ sq. yds. = 1 sq. rod; 160 sq. rods = 4 roods = 1 sq. acre; 640 sq. acres = 1 sq. mile. Also, 160 sq rods = 10 chains = 1 sq. acre. Solid or cubic measure: 1,728 solid inches = 1 solid foot; 27 solid feet = 1 solid yard; 40 ft. of round timber, or 50 ft. of hewn = 1 ton or load; 128 solid feet = 1 cord (of wood). Liquid. - 1. Wine measure: 32 gills = 8 pints = 4 quarts = 1 gallon; 63 gallons = 2 barrels = 1 hogshead; and 4 hogsheads = 2 pipes = 1 tun. 2. Beer measure: 8 pints = 4 quarts = 1 gallon; 36 gallons = 1 barrel; 54 gallons = 1 hogshead.

Dry: 64 pints = 32 quarts = 4 pecks = 1 bushel; and 36 bushels = 1 chaldron. Weight. - 1. Avoirdupois: 7,00i> grains = 256 drams = 16 ounces = 1 pound; 112 lbs. = 4 quarters = 1 hundred weight; and 20 hundred weight = 1 ton. The hundred weight of 100 lbs. is coming into more general use. 2. Troy: 24 grains = 1 pennyweight; and 240 dwt. = 12 ounces = 1 pound troy, of 5,760 grains; this is the mint weight. 3. Apothecaries': 480 grains = 24 scruples = 8 drams = 1 ounce; and 12 ounces = 1 pound. The pound and ounce in this weight are the same as in troy weight.

In the decimal system, introduced in 1803, the metro or braccio = 10 palmi = 100 diti = the French mètre, and 1,000 metri = 1 miglio; the soma = 10 mine = 2.7512 bush.; the libbra metrica = 10 once = 100 grossi = 1,000 denari = 2.2046 lbs. avoird.

In those now or originally belonging to England, France, Holland, and Denmark, respectively, the British, French, Dutch, and Danish systems chiefly prevail. Spanish measures are partly in use in Trinidad, however; the Spanish vara in Curacoa; and in some of the Danish isles the British yard and the old French aune = 46.85 in.

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