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# Bible Encyclopedias

Weights and Measures

## 1911 Encyclopedia Britannica

## WEIGHTS AND MEASURES.

This subject may be most conveniently considered under three aspects - I. Scientific; II. Historical; and III. Commercial.## I. Scientific

## --1. * Units.*

In the United Kingdom two systems of weights and measures are now recognized -- the imperial and the metric. The fundamental units of these systems are -- of length, the yard and metre; and of mass, the pound and kilogram. The legal theory of the British system of weights and measures is:

(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 lb of water at 62Â° F., being in volume 277.274 cub. in., which contain each 252.724 grains of water in a vacuum at 62Â°, or 252.458 grains of water weighed with brass weights in air of 62Â° with the barometer at 30 in.

Of the metric units international definitions have been stated as follows:

(a ) The unit of volume for determinations of a high degree of accuracy is the volume occupied by the mass of 1 kilogram of pure water at its maximum density and under the normal atmospheric pressure; this volume is called litre.

(b ) In determinations of volume which do not admit of a high degree of accuracy the cubic decimetre can be taken as equivalent to the litre; and in these determinations expressions of volumes based on the cube of the unit of linear measure can be substituted for expressions based on the litre as defined above.

(c ) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. See:*Troisieme Conference Generale des Poids et Mesures* (Paris, 1901). * Metric Units Com. Roy. Soc.* (1898).

(d ) The term "weight" denotes a magnitude of the same nature as a force; the weight of a body is the product of the mass of the body by the acceleration of gravity; in particular, the normal weight of a body is the product of the mass of the body by the normal acceleration of gravity. The number adopted for the value of the normal acceleration of gravity is 980.965 cm/sec-squared.

## --2. * Standards.*

The metre (*metre-à-traits*) is represented by the distance marked by two fine lines on an iridio-platinum bar (t = 0Â° C.) deposited with the Standards Department. This metre (m.) is the only unit of metric extension by which all other metric measures of extension -- whether linear, superficial or solid -- are ascertained.

The kilogram (kg.) is represented by an iridio-platinum standard weight, of cylindrical form, by which all other metric weights, and all measures having reference to metric weight, are ascertained in the United Kingdom.

From the above four units are derived all other weights and measures (W. and M.) of the two systems.

The gallon is the standard measure of capacity in the imperial system for liquids and for dry goods.

In the United Kingdom the metric standard of capacity is the litre, represented (Order in Council, 19th May 1890) by the capacity of a hollow cylindrical brass measure whose internal diameter is equal to one-half its height, and which at 0Â° C., when filled to the brim, contains one kg. of distilled water of the temperature of 4Â° C., under an atmospheric pressure equal to 760 millimetres at 0Â° C. at sea-level and latitude 45Â°; the weighing being made in air, but reduced by calculation to a vacuum. In such definition an attempt has been made to avoid former confusion of expression as to capacity, cubic measure, and volume; the litre being recognized as a measure of capacity holding a given weight of water.

For the equivalent of the litre in terms of the gallon, see below III. *Commercial.*

In the measurement of the cubic inch it has been found that 2 the specific mass of the cubic inch of distilled water freed from air, and weighed in air against brass weights (= 8.13), at the temperature of 62Â° F., and under an atmospheric pressure equal to 30 in. (at 32Â° F.), is equal to 252.207 grains weight of water at its maximum density (4Â° C.). Hence a cubic foot of water would weigh 62.281 lb avoir., and not 62.321 lb as at present legally taken. See: *Phil. Trans.* (1892); and * Proc. Roy. Soc.* (1895), p. 143.

For the specific mass of the cubic decimetre of water at 4Â° C., under an atmospheric pressure equal to 760 mm., Guillaume and Chappuis of the Comite International des Poids et Mesures at Paris (C.I.P.M.) have obtained 0.9999707 kg., which has been accepted by the committee. See: *Proc. Verb. Com. Intern. des Poids et Mesures* (Iwo), p. 84. Congrês International de Physique reuni a Paris en 1900.

The two standards, the cubic inch and the cubic decimetre, may not be strictly comparable owing to a difference in the normal temperature (Centigrade and Fahrenheit scales) of the two units of extension, the metre and the yard.

Temperature on the Hydrogen Thermometer Scale Celsius........Faren. | Weight of Water | |||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Of a Cubic Decimetre in Grammes. | Of a Cubic Inch in Grains. | Of a Cubic Inch in Russian Dolis. | ||||||||||||||||||||||||||

0Â° | 32.0Â° | 999.716 | 252.821 | 368.686 | ||||||||||||||||||||||||

4 | 39.2 | 999.847 | 252.854 | 368.734 | ||||||||||||||||||||||||

15 | 59.0 | 998.979 | 252.635 | 368.414 | ||||||||||||||||||||||||

16 2/3 | 62.0 | 998.715 | 252.568 | 368.316 | ||||||||||||||||||||||||

20 | 68.0 | 998.082 | 252.407 | 368.083 For the weight of the cubic decimetre of water, as deduced from the experiments made in London in 1896 as to the weight of the cubic inch of water, D. Mendeleeff ( ## --3. National Standards
Rhineland foot, much used in Germany, = 12.357 in. = the foot of the Scotch or English cloth ell of 37.06 in., or 3 x 12.353. (Entry by: Henry James Chaney, I.S.O. 1842, 1906, formerly of the Standards Department of the Board of Trade and Secretary to the Royal Commission on Standards. Represented Great Britain at the International Conference on the Metric System, 1901. Author of ## II. Ancient HistoricalThough no line can be drawn between ancient and modern metrology, yet, owing to neglect, and partly to the scarcity of materials, there is a gap of more than a thousand years over which the connexion of units of measure is mostly guess-work. In the absence of the actual standards of ancient times the units of measure and of weight have to be inferred from the other remains; hence unit in this division is used for any more or less closely defined amount of length or weight in terms of which matter was measured. Except in a few cases, we shall not here consider any units of the middle ages. A constant difficulty in studying works on metrology is the need of distinguishing the absolute facts of the case from the web of theory into which each writer has woven them -- often the names used, and sometimes the very existence of the units in question, being entirely an assumption of the writer. Again, each writer has his own leaning: A. BÃ¶ckh, to the study of water-volumes and weights, even deriving linear measures therefrom; V. Queipo, to the connexion with Arabic and Spanish measures; J. Brandis, to the basis of Assyrian standards; Mommsen, to coin weights; and P. Bortolotti to Egyptian units; but F. Hultsch is more general, and appears to give a more equal representation of all sides than do other authors. In this article the tendency will be to trust far more to actual measures and weights than to the statements of ancient writers; and this position seems to be justified by the great increase in materials, and their more accurate means of study. The usual arrangement by countries has been mainly abandoned in favour of following out each unit as a whole, without recurring to it separately for every locality. The materials for study are of three kinds. 1: 2: 3: Principles Of Study. -- 1: 2: 3: 4: Having noticed variation in the gross, we must next observe its details. The only way of examining these is by drawing curves (28, 29 ), representing the frequency of occurrence of all the variations of a unit; for instance, in the Egyptian unit -- the kat -- counting in a large number how many occur between 140 and 141 grains, 141 and 142, and so on; such numbers represented by curves show at once where any particular varieties of the unit lie (see 5: 6: The idea of connecting volume and weight has received an immense impetus through the metric system, but it is not very prominent in ancient times. The Egyptians report the weight of a measure of various articles, amongst others water (6 ), but lay no special stress on it; and the fact that there is no measure of water equal to a direct decimal multiple of the weight-unit, except very high in the scale, does not seem as if the volume was directly based upon weight. Again, there are many theories of the equivalence of different cubic cubits of water with various multiples of talents (2, 3, 18, 24, 33 ); but connexion by lesser units would be far more probable, as the primary use of weights is not to weigh large cubical vessels of liquid, but rather small portions of precious metals. The Roman amphora being equal to the cubic foot, and containing 80 librae of water, is one of the strongest cases of such relations, being often mentioned by ancient writers. Yet it appears to be only an approximate relation, and therefore probably accidental, as the volume by the examples is too large to agree to the cube of the length or to the weight, differing 1/20, or sometimes even as 1/12. Relative to the uncertain connexion of length, capacity and weight in the ancient metrological systems of the East, Sir Charles Warren, R.E., has obtained by deductive analysis a new equivalent of the original cubit ( Sir C. Warren has derived a primitive unit from a proportion of the human body, by ascertaining the probable mean height of the ancient people in Egypt, and so thereby has derived a standard from the stature of man. The human body has furnished the earliest measure for many races (H. O. Arnold-Forster, So far this later research appears to confirm the opinion of BÃ¶ckh (2 ) that fundamental units of measure were at one time derived from weights and capacities. It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length. Another idea which has haunted the older metrologists, but is still less likely, is the connexion of various measures with degrees on the earth's surface. The lameness of the Greeks in angular measurement would alone show that they could not derive itinerary measures from long and accurately determined distances on the earth. 7: The relative value of gold and silver (17, 21 ) in Asia is agreed generally to have been 13+1/3 to 1 in the early ages of coinage; at Athens in 434 B.C. it was 14 to 1; in Macedon, 350 B.C., 12+1/2 to 1; in Sicily, 400 B.C., 15 to 1, and 300 B.C., 12 to 1; in Italy in 1st century, it was 12 to 1, in the later empire 13.9 to 1, and under Justinian. 14.4 to 1. Silver stood to copper in Egypt as 80 to 1 (Brugsch), or 120 to 1 (Revillout); in early Italy and Sicily as 250 to 1 (Mommsen), or 120 to 1 (Soutzo), under the empire 120 to 1, and under Justinian 100 to 1. The distinction of the use of standards for trade in general, or for silver or gold in particular, should be noted. The early observance of the relative values may be inferred from Num. vii. 13, 14, where silver offerings are 13 and 7 times the weight of the gold, or of equal value and one-half value. 8: The Hebrew "shekel of the sanctuary" is familiar; the standard volume of the apet was secured in the dromus of Anubis at Memphis (35 ); in Athens, besides the standard weight, twelve copies for public comparison were kept in the city; also standard volume measures in several places (2 ); at Pompeii the block with standard volumes cut in it was found in the portico of the forum (33 ); other such standards are known in Greek cities (Gythium, Panidum and Trajanopolis) (11, 33 ); at Rome the standards were kept in the Capitol, and weights also in the temple of Hercules (2 ); the standard cubit of the Nilometer was before Constantine in the Serapaeum, but was removed by him to the church (2 ). In England the Saxon standards were kept at Winchester before A.D. 950 and copies were legally compared and stamped; the Normans removed them to Westminster to the custody of the king's chamberlains at the exchequer; and they were preserved in the crypt of Edward the Confessor, while remaining royal property (9 ). The oldest English standards remaining are those of Henry VII. Many weights have been found in the temenos of Demeter at Cnidus, the temple of Artemis at Ephesus, and in a temple of Aphrodite at Byblus (44 ); and the making or sale of weights may have been a business of the custodians of the temple standards. 9: ## Standards of LengthMost ancient measures have been derived from one of two great systems, that of the cubit of 20.63 in., or the digit of 0.729 in.; and both these systems are found in the earliest remains. In. - First known in Dynasty IV. in Egypt, most accurately 20.620 in the Great Pyramid, varying 20.51 to 20.71 in Dyn. IV. to VI. (27 ). Divided decimally in 100ths; but usually marked in Egypt into 7 palms of 28 digits, approximately; a mere juxtaposition. (for convenience) of two incommensurate systems (25, 27 ). The average of several cubit rods remaining is 20.65, age in general about 2500 B.C. (33 ). At Philae, &c., in Roman times 20.76 on the Nilometers (44 ). This unit is also recorded by cubit lengths scratched on a tomb at Beni Hasan (44 ), and by dimensions of the tomb of Ramessu IV. and of Edfu temple (5 ) in papyri. From this cubit, Babylonia had this unit nearly as early as Egypt. The divided plotting scales lying on the drawing boards of the statues of Gudea ( 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. Asia Minor had this unit in early times-in the temples of Ephesus 20.55, Samos 20.62; Hultsch also claims Priene 20.90, and the stadia of Aphrodisias 20.67 and Laodicea 20.94. Ten buildings in all give 20.63 mean (18, 25 ); but in Armenia it arose to 20.76 in late Roman times, like the late rise in Egypt (25 ). It was specially divided into (1/5)th, the foot of (3/5)ths being as important as the cubit. In. =(3/5)x20.75. This was especially the Greek derivative of the 20.63 cubit. It originated in Babylonia as the foot of that system (24 ), in accordance with the sexary system applied to the early decimal division of the cubit. In Greece it is the most usual unit, occurring in the Propylaea at Athens 12.44, temple at Aegina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18 ); thirteen buildings giving an average of 12.45, mean variation .06 (25 ), = (3/5)ths of 20.75, m. var. .10. The digit= (1/4) palaeste, = (1/4) foot of 12.4; then the system is -- |1+(1/2)=cubit, 4=orguia ................................ 100= | In Etruria it probably appears in tombs as 12.45 (25 ); perhaps in Roman Britain; and in medieval England as 12.47 (25 ). In. This foot is scarcely known monumentally. On three Egyptian cubits there is a prominent mark at the 19th digit or 14 in., which shows the existence of such a measure (33 ). It became prominent when adopted by Philetaerus about 280 B.C. as the standard of Pergamum (42 ), and probably it had been shortly before adopted by the Ptolemies for Egypt. From that time it is one of the principal units in the literature (Didymus, &c.), and is said to occur in the temple of Augustus at Pergamum as 13.8 (18 ). Fixed by the Romans at 16 digits (13+1/3 = Roman foot), or its cubit at 1+4/5 Roman feet, it was legally = 13.94 at 123 B.C. (42 ); and 7+1/2 Philetaerean stadia were = Roman mile (18 ). The multiples of the 20.63 cubit are in late times generally reckoned in these feet of 2/3 cubit. The name "Babylonian foot" used by BÃ¶ckh (2 ) is only a theory of his, from which to derive volumes and weights; and no evidence for this name, or connexion with Babylon, is to be found. Much has been written (2, 3, 33 ) on supposed cubits of about 17 to 18 in. derived from 20.63--mainly in endeavouring to get a basis for the Greek and Roman feet; but these are really connected with the digit system, and the monumental or literary evidence for such a division of 20.63 will not bear examination. 17.30 = (5/6)x20.76. There is, however, fair evidence for units of 17.30 and 1.730 or (1/12) of 20.76 in Persian buildings ( 25 ) and the same is found in Asia Minor as 17.25 or (5/6)ths of 20.70. On the Egyptian cubits a small cubit is marked as about 17 in., which may well be this unit, as (5/6)ths of 20.6 is 17.2; and, as these marks are placed before the 23rd digit or 17.0, they cannot refer to 6 palms, or 17.7, which is the 24th digit, though they are usually attributed to that (33 ). We now turn to the second great family based on the digit. This has been so usually confounded with the 20.63 family, owing to the juxtaposition of 28 digits with that cubit in Egypt, that it should be observed how the difficulty of their incommensurability has been felt. For instance, Lepsius (3 ) supposed two primitive cubits of 13.2 and 20.63, to account for 28 digits being only 20.4 when free from the cubit of 20.63--the first 24 digits being in some cases made shorter on the cubits to agree with the true digit standard, while the remaining 4 are lengthened to fill up to 20.6. In the Dynasties IV. and V. in Egypt the digit is found in tomb sculptures as 0.727 (27 ); while from a dozen examples in the later remains we find the mean, 0.728 (25 ). A length of 10 digits is marked on all the inscribed Egyptian cubits as the "lesser span" (33 ). In Assyria the same digit appears as 0.730, particularly at Nimrud (25 ); and in Persia buildings show the 10-digit length of 7.34 (25 ). In Syria it was about 0.728, but variable; in eastern Asia Minor more like the Persian, being 0.732 (25 ). In these cases the digit itself, or decimal multiples, seem to have been used. 18.23 = 25x0.729. The pre-Greek examples of this cubit in Egypt, mentioned by BÃ¶ckh ( 2 ), give 18.23 as a mean, which is 25 digits of 0.7292 digits, close to 0.729, but has no relation to the 20.63 cubit. This cubit, or one nearly equal, was used in Judaea in the times of the kings, as the Siloam inscription names a distance of 1758 ft. as roundly 1200 cubits, showing a cubit of about 17.6 in. This is also evidently the Olympic cubit; and, in pursuance of the decimal multiple of the digit found in Egypt and Persia, the cubit of 25 digits was (1/4)th of the orguia of 100 digits, the series being -- | 25=cubit, 4= | Then, taking (2/3)rds of the cubit, or (1/6)th of the orguia, as a foot, the Greeks arrived at their foot of 12.14; this, though very well known in literature, is but rarely found, and then generally in the form of the cubit, in monumental measures. The Parthenon step, celebrated as 100 ft. wide, and apparently 225 ft. long, gives by Stuart 12.137, by Penrose 12.165, by Paccard 12.148, differences due to scale and not to slips in measuring. Probably 12.16 is the nearest value. There are but few buildings wrought on this foot in Asia Minor, Greece or Roman remains. The Greek system, however, adopted this foot as a basis for decimal multiplication, forming -- foot, 10=acaena, 10=plethron, which stand as (1/6)th of the other decimal series based on the digit. This is the agrarian system, in contrast to the orguia system, which was the itinerary series (33 ). Then a further modification took place, to avoid the inconvenience of dividing the foot in 16+(2/3) digits, and a new digit was formed -- longer than any value of the old digit -- of 1/16 of the foot, or 0.760, so that the series ran -- | 10=lichas This formation of the Greek system (25 ) is only an inference from the facts yet known, for we have not sufficient information to prove it, though it seems much the simplest and most likely history. 11.62 = 16x0.726. Seeing the good reasons for this digit having been exported to the West from Egypt--from the presence of the 18.23 cubit in Egypt, and from the 0.729 digit being the decimal base of the Greek long measures--it is not surprising to find it in use in Italy as a digit, and multiplied by 16 as a foot. The more so as the half of this foot, or 8 digits, is marked off as a measure on the Egyptian cubit rods ( 33 ). Though Queipo has opposed this connexion (not noticing the Greek link of the digit), he agrees that it is supported by the Egyptian square measure of the plethron, being equal to the Roman actus (33 ). The foot of 11.6 appears probably first in the prehistoric and early Greek remains, and is certainly found in Etrurian tomb dimensions as 11.59 (25 ). DÃ¶rpfeld considers this as the Attic foot, and states the foot of the Greek metrological relief at Oxford as 11.65 (or 11.61, Hultsch). Hence we see that it probably passed from the East through Greece to Etruria, and thence became the standard foot of Rome; there, though divided by the Italian duodecimal system into 12 unciae, it always maintained its original 16 digits, which are found marked on some of the foot-measures. The well-known ratio of 25:24 between the 12.16 foot and this we see to have arisen through one being (1/6)th of 100 and the other 16 digits--16+2/3: 16 being as 25: 24, the legal ratio. The mean of a dozen foot-measures (1 ) gives 11.616 Â± 0.008, and of long lengths and buildings 11.607 Â± 0.01. In Britain and Africa, however, the Romans used a rather longer form (25 ) of about 11.68, or a digit of 0.730. Their series of measures was -- digitus, 4=palmus, 4=pes, 5=passus, 125=stadium, 8=milliare; also uncia 0.968=(1/12)pes, palmipes 14.52=5 palmi, cubitus 17.43=6 palmi. Either from its Pelasgic or Etrurian use or from Romans, this foot appears to have come into prehistoric remains, as the circle of Stonehenge (26 ) is 100 ft. of 11.68 across, and the same is found in one or two other cases. 11.60 also appears as the foot of some medieval English buildings (25 ). We now pass to units between which we cannot state any connexion. 25.1 . -The earliest sign of this cubit is in a chamber at Abydos (44 ) about 1400 B.C.; there, below the sculptures, the plain wall is marked out by red designing lines in spaces of 25.13 Â± 0.03 in., which have no relation to the size of the chamber or to the sculpture. They must therefore have been marked by a workman using a cubit of 25.13. Apart from medieval and other very uncertain data, such as the Sabbath day's journey being 2000 middling paces for 2000 cubits, it appears that Josephus, using the Greek or Roman cubit, gives half as many more to each dimension of the temple than does the Talmud; this shows the cubit used in the Talmud for temple measures to be certainly not under 25 in. Evidence of the early period is given, moreover, by the statement in I Kings (vii. 26) that the brazen sea held 2000 baths; the bath being about 2300 cub. in., this would show a cubic of 25 in. The corrupt text in Chronicles of 3000 baths would need a still longer cubit; and, if a lesser cubit of 21.6 or 18 in, be taken, the result for the size of the bath would be impossibly small. For other Jewish cubits see 18.2 and 21.6. Oppert (24 ) concludes from inscriptions that there was in Assyria a royal cubit (7/6)ths of the U cubit, or 25.20; and four monuments show (25 ) a cubit averaging 25.28. For Persia Queipo (33 ) relies on, and develops, an Arab statement that the Arab cubit was the royal Persian, thus fixing it at about 25 in.; and the Persian guerze at present is 25, the royal guerze being 1+(1/2) times this, or 371 in. As a unit of 1.013, decimally multiplied, is most commonly to be deduced from the ancient Persian buildings, we may take 25.34 as the nearest approach to the ancient Persian unit. 21.6. -The circuit of the city wall of Khorsabad ( 24 ) is minutely stated on a tablet as 24,740 ft. (U), and from the actual size the U is therefore 10.806 in. Hence the recorded series of measures on the Senkereh tablet are valued (Oppert) as -- susi, |20=(palm), 3=U, 6=qanu, 2=sa, 5= (n), 12=us, 30=kasbu. Other units are the suklum or (1/2)U=5.4, and cubit of 2U=21.9, which are not named in this tablet. In Persia (24 ) the series on the same base was -- vitasti, 2=arasni, 360=asparasa, 30=parathaÃ±ha, 2=gÄv; probably yava, 6=angusta 10=vitasti; and gama = (3/5)arasni; also bÄzu = 2arasni. The values here given are from some Persian buildings (25 ), which indicate 21.4, or slightly less; Oppert's value, on less certain data, is 21.52. The Egyptian cubits have an arm at 15 digits or about 10.9 marked on them, which seems like this same unit (33 ). This cubit was also much used by the Jews (33 ), and is so often referred to that it has eclipsed the 25.1 cubit in most writers. The Gemara names 3 Jewish cubits (2 ) of 5, 6 and 7 palms; and, as Oppert (24 ) shows that 25.2 was reckoned 7 palms, 21.6 being 5 palms, we may reasonably apply this scale to the Gemara list, and read it as 18, 21.6 and 25.2 in. There is also a great amount of medieval and other data showing this cubit of 21.6 to have been familiar to the Jews after their captivity; but there is no evidence for its earlier date, as there is for the 25 in. cubit (from the brazen sea) and for the 18 in. cubit from the Siloam inscription. From Assyria also it passed into Asia Minor, being found on the city standard of Ushak in Phrygia (33 ), engraved as 21.8, divided into the Assyrian foot of 10.8, and half and quarter, 5 Copyright Statement These files are public domain. Bibliography Information
Chisholm, Hugh, General Editor. Entry for 'Weights and Measures'. 1911 Encyclopedia Britanica. https://www.studylight.org/encyclopedias/eng/bri/w/weights-and-measures.html. 1910. |