Foot (unit)

Last updated

foot
Unit system imperial/US  units
Unit of length
Symbolft 
Conversions
1 ft in ...... is equal to ...
   imperial/US units   1/3  yd
 12  in
    metric (SI) units   0.3048  m

The foot (pl. feet; abbreviation: ft; symbol: ′, the prime symbol) is a unit of length in the imperial and US customary systems of measurement. Since the International Yard and Pound Agreement of 1959, one foot is defined as 0.3048  meter exactly. In customary and imperial units, the foot comprises 12  inches and three feet compose a yard.

The prime symbol, double prime symbol, triple prime symbol, quadruple prime symbol etc., are used to designate units and for other purposes in mathematics, the sciences, linguistics and music.

Length is a measure of distance. In the International System of Quantities, length is any quantity with dimension distance. In most systems of measurement, the unit of length is a base unit, from which other units are derived.

Imperial units system of units formerly used in the British Empire and still used in the United Kingdom

The system of imperial units or the imperial system is the system of units first defined in the British Weights and Measures Act of 1824, which was later refined and reduced. The imperial units replaced the Winchester Standards, which were in effect from 1588 to 1825. The system came into official use across the British Empire. By the late 20th century, most nations of the former empire had officially adopted the metric system as their main system of measurement, although some imperial units are still used in the United Kingdom, Canada and other countries formerly part of the British Empire. The imperial system developed from what were first known as English units, as did the related system of United States customary units.

Contents

Historically the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16  digits.

Ancient Greek units of measurement varied according to location and epoch. Systems of ancient weights and measures evolved as needs changed; Solon and other lawgivers also reformed them en bloc. Some units of measurement were found to be convenient for trade within the Mediterranean region and these units became increasingly common to different city states. The calibration and use of measuring devices became more sophisticated. By about 500 BC, Athens had a central depository of official weights and measures, the Tholos, where merchants were required to test their measuring devices against official standards.

Ancient Roman units of measurement

The ancient Roman units of measurement were largely built on the Hellenic system, which in turn was built upon Egyptian and Mesopotamian influences. The Roman units were comparatively consistent and well documented.

Chinese units of measurement

Chinese units of measurement, known in Chinese as the shìzhì, are the traditional units of measurement of the Han Chinese. Although Chinese numerals have been decimal (base-10) since the Shang, several Chinese measures use hexadecimal (base-16). Local applications have varied, but the Chinese dynasties usually proclaimed standard measurements and recorded their predecessor's systems in their histories.

The United States is the only industrialized nation that uses the international foot and the survey foot (a customary unit of length) in preference to the meter in its commercial, engineering, and standards activities. [1] The foot is legally recognized in the United Kingdom; road signs must use imperial units (however, distances on road signs are always marked in miles or yards, not feet), while its usage is widespread among the British public as a measurement of height. [2] [3] The foot is recognized as an alternative expression of length in Canada [4] officially defined as a unit derived from the meter [5] although both the U.K. and Canada have partially metricated their units of measurement. The measurement of altitude in international aviation is one of the few areas where the foot is used outside the English-speaking world.

United States customary units are a system of measurements commonly used in the United States. The United States customary system developed from English units which were in use in the British Empire before the U.S. became an independent country. However, the United Kingdom's system of measures was overhauled in 1824 to create the imperial system, changing the definitions of some units. Therefore, while many U.S. units are essentially similar to their Imperial counterparts, there are significant differences between the systems.

Metrication

Metrication or metrification is the act or process of converting the system of measurement traditionally used in a country, to the metric system. Worldwide, there has been a process of nations transitioning from their various local and traditional units of measurement, to the metric system. This process first began in France during the 1790s and has continued extensively world-wide over the following two centuries, but the metric system has not been fully adopted in all countries and sectors.

Aviation Design, development, production, operation and use of aircraft

Aviation, or air transport, refers to the activities surrounding mechanical flight and the aircraft industry. Aircraft includes fixed-wing and rotary-wing types, morphable wings, wing-less lifting bodies, as well as lighter-than-air craft such as balloons and airships.

The length of the international foot corresponds to a human foot with shoe size of 13 (UK), 14 (US male), 15.5 (US female) or 46 (EU sizing).

Shoe size Measurement scale indicating the fitting size of a shoe

A shoe size is an indication of the fitting size of a shoe for a person.

Historical origin

Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service. Woodcut published in the book Geometrei by Jakob Kobel (Frankfurt, c. 1535). Determination of the rute and the feet in Frankfurt.png
Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service. Woodcut published in the book Geometrei by Jakob Köbel (Frankfurt, c. 1535).

Historically the human body has been used to provide the basis for units of length. [6] The foot of a white male is typically about 15.3% of his height, [7] giving a person of 160 centimetres (5 ft 3 in) a foot of 245 millimetres (9.6 in) and one of 180 centimetres (5 ft 11 in) a foot of 275 millimetres (10.8 in).

Archaeologists believe that the Egyptians, Ancient Indians and Mesopotamians preferred the cubit while the Romans and the Greeks preferred the foot. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches (340 mm) and a cubit of 20.8 inches (530 mm). [8] The Egyptian equivalent of the foot—a measure of four palms or 16 digits—was known as the djeser and has been reconstructed as about 30 cm (12 in).

The ancient Egyptian units of measurement are those used by the dynasties of ancient Egypt prior to its incorporation in the Roman Empire and general adoption of Roman, Greek, and Byzantine units of measurement. The units of length seem to have originally been anthropic, based on various parts of the human body, although these were standardized using cubit rods, strands of rope, and official measures maintained at some temples.

Before the introduction of the Metric system, one may divide the history of Indian systems of measurement into three main periods: the pre-Akbar's period, the period of the Akbar system, and the British colonial period.

Ancient Mesopotamian units of measurement

Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer. Each city, kingdom and trade guild had its own standards until the formation of the Akkadian Empire when Sargon of Akkad issued a common standard. This standard was improved by Naram-Sin, but fell into disuse after the Akkadian Empire dissolved. The standard of Naram-Sin was readopted in the Ur III period by the Nanše Hymn which reduced a plethora of multiple standards to a few agreed upon common groupings. Successors to Sumerian civilization including the Babylonians, Assyrians, and Persians continued to use these groupings. Akkado-Sumerian metrology has been reconstructed by applying statistical methods to compare Sumerian architecture, architectural plans, and issued official standards such as Statue B of Gudea and the bronze cubit of Nippur.

The Greek foot (πούς, pous) had a length of ​1⁄600 of a stadion, [9] one stadion being about 181.2 m, [10] therefore a foot being at the time about 302 mm. Its exact size varied from city to city and could range between 270 mm and 350 mm, but lengths used for temple construction appear to have been about 295 mm to 325 mm, the former being close to the size of the Roman foot.

The standard Roman foot (pes) was normally about 295.7 mm (97% of today's measurement), but in the provinces, the pes Drusianus (foot of Nero Claudius Drusus) was used, with a length of about 334 mm. (In reality, this foot predated Drusus.) [11]

Originally both the Greeks and the Romans subdivided the foot into 16 digits, but in later years, the Romans also subdivided the foot into 12 unciae (from which both the English words "inch" and "ounce" are derived).

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD 790 Charlemagne attempted to reform the units of measure in his domains. His units of length were based on the toise and in particular the toise de l'Écritoire, the distance between the fingertips of the outstretched arms of a man. [12] The toise has 6 pieds (feet) each of 326.6 mm (12.86 in).

He was unsuccessful in introducing a standard unit of length throughout his realm: an analysis of the measurements of Charlieu Abbey shows that during the 9th century the Roman foot of 296.1 mm was used; when it was rebuilt in the 10th century, a foot of about 320 mm [Note 1] was used. At the same time, monastic buildings used the Carolingian foot of 340 mm. [Note 1] [13]

The procedure for verification of the foot as described in the 16th century posthumously published work by Jacob Koebel in his book Geometrei. Von künstlichem Feldmessen und absehen is: [14] [15]

Stand at the door of a church on a Sunday and bid 16 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 16th part of it shall be the right and lawful foot.

England

The unofficial public imperial measurement standards erected at the Royal Observatory in Greenwich in the 19th century Imperial measurement standards, Greenwich.JPG
The unofficial public imperial measurement standards erected at the Royal Observatory in Greenwich in the 19th century

The Neolithic long foot, first proposed by archeologists Mike Parker Pearson and Andrew Chamberlain, is based upon calculations from surveys of Phase 1 elements at Stonehenge. They found that the underlying diameters of the stone circles had been consistently laid out using multiples of a base unit amounting to 30 long feet, which they calculated to be 1.056 of a modern foot (0.3219m). Furthermore, this unit is identifiable in the dimensions of some stone lintels at the site and in the diameter of the "southern circle" at nearby Durrington Walls. Evidence that this unit was in widespread use across southern Britain is available from the Folkton Drums from Yorkshire (neolithic artifacts, made from chalk, with circumferences that exactly divide as integers into ten long feet) and a similar object excavated at Lavant, Sussex, again with a circumference divisible as a whole number into ten long feet. [16]

The measures of Iron Age Britain are uncertain and proposed reconstructions such as the Megalithic Yard are controversial. Later Welsh legend credited Dyfnwal Moelmud with the establishment of their units, including a foot of 9 inches. The Belgic or North German foot of 335 mm (13.2 inches) was introduced to England either by the Belgic Celts during their invasions prior to the Romans or by the Anglo-Saxons in the 5th and 6th century.

Roman units were introduced following their invasion in AD 43. The Roman foot had been previously standardized by Agrippa at around 296 mm or 11.65 inches. Following the Roman withdrawal and Saxon invasions, the Roman foot continued to be used in the construction crafts while the Belgic foot was used for land measurement. Both the Welsh and Belgic feet seem to have been based on multiples of the barleycorn, but by as early as 950 the English kings seem to have (ineffectually) ordered measures to be based upon an iron yardstick at Winchester and then London. Henry I was said to have ordered a new standard to be based upon his own arm and, by the c. 1300 Act concerning the Composition of Yards and Perches [17] traditionally credited to Edward I or II, the statute foot was a different measure exactly ​10⁄11 of the old foot. The barleycorn, inch, ell, and yard were likewise shrunk, while rods and furlongs remained the same. [18] The ambiguity over the state of the mile was resolved by the 1593 Act against Converting of Great Houses into Several Tenements and for Restraint of Inmates and Inclosures in and near about the City of London and Westminster, which codified the statute mile as comprising 5,280 feet. The differences among the various physical standard yards around the world, revealed by increasingly powerful microscopes, eventually led to the 1959 adoption of the international foot defined in terms of the meter.

Definition

International foot

The international yard and pound agreement of July 1959 defined the length of the international yard in the United States and countries of the Commonwealth of Nations as exactly 0.9144 meters. Consequently, the international foot is defined to be equal to exactly 0.3048 meters. This was 2  ppm shorter than the previous U.S. definition and 1.7 ppm longer than the previous British definition. [19]

The international standard symbol for a foot is "ft" (see ISO 31-1, Annex A). In some cases, the foot is denoted by a prime, which is often marked by an apostrophe, and the inch by a double prime; for example, 2 feet 4 inches is sometimes denoted as 2′−4″, 2′ 4″ or 2′4″. (See 'minute' for another case where prime and double prime symbols are used to denote first and second cuts in refining measurement.)

Pre-1959

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 by 39.37 inches = 1 m. In Imperial units, the foot was defined as ​1⁄3 yard, with the yard being realized as a physical standard (separate from the standard meter).

The yard standards of the different Commonwealth countries were periodically compared with one another. [20] The value of the United Kingdom primary standard of the yard was determined in terms of the meter by the National Physical Laboratory in 1964 as 0.9143969 m, [21] implying a pre-1959 foot in the UK of approximately 0.304798966667 m.

Survey foot

When the international foot was defined in 1959, a great deal of survey data was already available based on the former definitions, especially in the United States and in India. The small difference between the survey and the international foot would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when the state plane coordinate system (SPCS) is used in the US, because the origin of the system may be hundreds of thousands of feet (hundreds of miles) from the point of interest. Hence the previous definitions continued to be used for surveying in the United States and India for many years, and are denoted survey feet to distinguish them from the international foot. The United Kingdom was unaffected by this problem, as the retriangulation of Great Britain (1936–62) had been done in meters.

US survey foot

The United States survey foot is defined as exactly ​1200⁄3937 meters, approximately 0.304800609601 m. [22] Out of 50 states and six other jurisdictions, 40 have legislated that surveying measures should be based on the U.S. survey foot, six have legislated that they be made on the basis of the international foot, and ten have not specified the conversion factor from metric units. [23]

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2  ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile).

The National Bureau of Standards, National Geodetic Survey and the Department of Commerce's Office of the General Counsel are planning to phase out the US survey foot beginning in 2022. [24]

Indian survey foot

The Indian survey foot is defined as exactly 0.3047996 m, [25] presumably derived from a measurement of the previous Indian standard of the yard. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum, [26] which is also used by the Global Positioning System.

Historical use

Page from Austrian Lehrbuch des gesammten Rechnens fur die vierte Classe der Hauptschulen in den k.k. Staaten - 1848 Fussmasse1.jpg
Page from Austrian Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten – 1848

Metric foot

An ISO 2848 measure of 3 basic modules (30 cm) is called a "metric foot", but there were earlier distinct definitions of a metric foot during metrication in France and Germany.

France

In 1799 the meter became the official unit of length in France. This was not fully enforced, and in 1812 Napoleon introduced the system of mesures usuelles which restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, or pied métrique, was defined as one third of a meter. This unit continued in use until 1837. [28]

Germany

In southwestern Germany in 1806, the Confederation of the Rhine was founded and three different reformed feet were defined, all of which were based on the metric system: [29]

  • In Hesse, the Fuß (foot) was redefined as 25 cm.
  • In Baden, the Fuß was redefined as 30 cm.
  • In the Palatinate, the Fuß was redefined as being ​33 1⁄3 cm (as in France).

Other obsolete feet

Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably in length: the voet in Ieper, Belgium, was 273.8 millimetres (10.78 in) while the piede in Venice was 347.73 millimetres (13.690 in). Lists of conversion factors between the various units of measure were given in many European reference works including:

Many of these standards were peculiar to a particular city, especially in Germany (which, before German Unification in 1871, consisted of many kingdoms, principalities, free cities and so on). In many cases the length of the unit was not uniquely fixed: for example, the English foot was stated as 11 pouces 2.6 lignes (French inches and lines) by Picard, 11 pouces 3.11 lignes by Maskelyne and 11 pouces 3 lignes by D'Alembert. [37]

Most of the various feet in this list ceased to be used when the countries adopted the metric system. The Netherlands and modern Belgium adopted the metric system in 1817, having used the mesures usuelles under Napoleon [38] and the newly formed German Empire adopted the metric system in 1871. [39]

The palm (typically 200 mm to 280 mm) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was published[ clarification needed ] in Belgium which had the smallest foot measurements, grouped both units together, while J.F.G. Palaiseau devoted three chapters to units of length: one for linear measures (palms and feet), one for cloth measures (ells) and one for distances traveled (miles and leagues). In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.

LocationModern CountryLocal nameMetric
equivalent
(mm)		Comments
Vienna AustriaWiener Fuß316.102 [36] [40]
Tyrol AustriaFuß334.12 [29]
Ieper/Ypres Belgiumvoet273.8 [41]
Bruges/Brugge Belgiumvoet274.3 [41]
Brussels Belgiumvoet275.75 [41]
Hainaut Belgiumpied293.39 [33]
Liège Belgiumpied294.70 [33]
Kortrijk Belgiumvoet297.6 [41]
Aalst Belgiumvoet277.2 [41]
Mechelen Belgiumvoet278.0 [41]
Leuven Belgiumvoet285.5 [41]
Tournai Belgiumpied297.77 [33]
Antwerp Belgiumvoet286.8 [41]
China Chinatradesman's foot338.3 [42]
ChinaChinamathematician's foot333.2 [42]
ChinaChinabuilder's foot322.8 [42]
ChinaChinasurveyor's foot319.5 [42]
Moravia Czech Republicstopa295.95 [29]
Prague Czech Republicstopa296.4 [35] (1851) Bohemian foot or shoe
301.7 [30] (1759) Quoted as "11 pouces​1 3⁄4lignes" [Notes 1]
Denmark DenmarkFod313.85 [36] Until 1835, thereafter the Prussian foot
330.5 [30] (1759) Quoted as "​2 1⁄2lignes larger than the pied [of Paris]" [Notes 1]
France Francepied du roi324.84 [43] [Notes 2]
Angoulême Francepied d'Angoulême347.008 [44]
Bordeaux (urban)Francepied de ville de Bordeaux343.606 [44]
Bordeaux (rural)Francepied de terre de Bordeaux357.214 [44]
Strasbourg Francepied de Strasbourg294.95 [44]
Württemberg GermanyFuß286.49 [29]
Hanover GermanyFuß292.10 [29]
Augsburg GermanyRömischer Fuß296.17 [34]
Nuremberg GermanyFuß303.75 [34]
Meiningen-Hildburghausen GermanyFuß303.95 [29]
Oldenburg GermanyRömischer Fuß296.41 [29]
Weimar GermanyFuß281.98 [29]
Lübeck GermanyFuß287.62 [36]
Aschaffenburg GermanyFuß287.5 [33]
Darmstadt GermanyFuß287.6 [33] Until 1818, thereafter the Hessen "metric foot"
Bremen GermanyFuß289.35 [36]
Rhineland GermanyFuß313.7 [42]
Berlin GermanyFuß309.6 [42]
Hamburg GermanyFuß286.8 [42]
Bavaria GermanyFuß291.86 [29]
Aachen GermanyFuß282.1 [34]
Leipzig GermanyFuß282.67 [29]
Dresden GermanyFuß283.11 [29]
Saxony GermanyFuß283.19 [36]
Prussia Germany, Poland, Russia etc.Rheinfuß313.85 [36]
Frankfurt am Main GermanyFuß284.61 [29]
Venice & Lombardy Italy347.73 [29]
Turin Italy323.1 [42]
Rome Italypiede romano297.896 [44]
Malta Maltapied283.7 [42]
Utrecht Netherlandsvoet272.8 [42]
Amsterdam Netherlandsvoet283.133 [32] Divided into 11 duimen (inches)
Honsbossche en Rijpse Netherlandsvoet285.0 [32]
’s Hertogenbosch Netherlandsvoet287.0 [32]
Gelderland Netherlandsvoet292.0 [32]
Bloois (Zeeland) Netherlandsvoet301.0 [32]
Schouw Netherlandsvoet311.0 [32]
Rotterdam Netherlandsvoet312.43 [33]
Rijnland Netherlandsvoet314.858 [32]
Norway Norwayfot313.75 [45] (1824–1835) [Notes 3] Thereafter as for Sweden
Warsaw Polandstopa297.8 [46] until 1819
288.0 [33] (From 1819) Polish stopa
Lisbon PortugalPé330.0 [34] (From 1835) [Notes 4]
Riga Latviapēda274.1 [42]
South Africa South Africa Cape foot 314.858 [47] Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
Burgos and Castile SpainPie de Burgos/
Castellano		278.6 [30] (1759) Quoted as "122.43 lignes" [Notes 1]
Toledo SpainPie279.0 [30] (1759) Quoted as "10 pouces 3.7 lignes" [Notes 1]
Sweden Swedenfot296.9 [36] = 12 tum (inches). The Swedish fot was also used in Finland ("jalka").
Zürich Switzerland300.0 [42]
Galicia Ukraine, Polandstopa galicyjska296.96 [33] Part of Austria before World War I
Scotland United Kingdomfuit, fit, troigh305.287 [48] [Notes 5]

(In Belgium, the words pied (French) and voet (Dutch) would have been used interchangeably.)

Notes

  1. 1 2 3 4 The source document used pre-metric French units (pied, pouce and lignes)
  2. ↑ The original meter was computed using pre-metric French Units
  3. ↑ The Norwegian fot was defined in 1824 as the length of a (theoretical) pendulum that would have a period of ​12⁄38 seconds at 45° from the equator
  4. ↑ Prior to 1835, the pé or foot was not used in Portugal – instead a palm was used. In 1835 the size of the palm was increased from 217.37 mm (according to Palaiseau) to 220 mm
  5. ↑ The Scots foot ceased to be legal after the Act of Union in 1707

See also

Notes

  1. 1 2 The original reference was given in a round number of centimeters

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History of measurement

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Comparison of the imperial and US customary measurement systems

Both the imperial and United States customary systems of measurement derive from earlier English systems used in the Middle Ages, that were the result of a combination of the local Anglo-Saxon units inherited from German tribes and Roman units brought by William the Conqueror after the Norman Conquest of England in 1066.

Introduction to the metric system

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The international yard and pound are two units of measurement that were the subject of an agreement among representatives of six nations signed on 1 July 1959, namely the United States, United Kingdom, Canada, Australia, New Zealand and the Union of South Africa. The agreement defined the yard as exactly 0.9144 meters and the pound as exactly 0.45359237 kilograms.

Imperial and US customary measurement systems English (pre 1824), Imperial (post 1824) and US Customary (post 1776) units of measure

The imperial system of measurement and the US customary system of measurement are both derived from an earlier English system of measurement which in turn can be traced back to Ancient Roman units of measurement, and Carolingian and Saxon units of measure.

References

  1. ↑ "Appendix G – Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. Archived from the original on February 23, 2011. Retrieved February 4, 2007.
  2. ↑ Kelly, Jon (December 21, 2011). "Will British people ever think in metric?". BBC. Archived from the original on April 24, 2012.
  3. ↑ Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey that Transformed the World. London: Abacus.
  4. ↑ Weights and Measures Act Archived December 28, 2014, at the Wayback Machine , accessed January 2012, Act current to 2012-01-18. Basis for units of measurement 4.(1) All units of measurement used in Canada shall be determined on the basis of the International System of Units established by the General Conference of Weights and Measures. (...) Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefore are as added pursuant to subparagraph 6(1)(b)(ii).
  5. ↑ Weights and Measures Act Archived October 16, 2012, at the Wayback Machine
  6. ↑ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 23. ISBN   978-0-520-06072-2 . Retrieved February 2, 2012.
  7. ↑ Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January–February 2005). "Sexual dimorphism in foot length proportionate to stature" (PDF). Annals of Human Biology. 32 (1): 44–59. doi:10.1080/03014460400027581. Archived (PDF) from the original on June 8, 2011.
  8. ↑ Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117; "Archived copy" (PDF). Archived from the original (PDF) on June 26, 2015. Retrieved January 11, 2015.CS1 maint: archived copy as title (link)
  9. ↑ Herodotus; Rawlinson, George (May 14, 1861). "History of Herodotus : a new English version". New York D. Appleton – via Internet Archive.
  10. ↑ "Epidauros, Stadium (Building)". www.perseus.tufts.edu. Archived from the original on May 10, 2017.
  11. ↑ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 26. ISBN   978-0-520-06072-2 . Retrieved February 2, 2012.
  12. ↑ Russ Rowlett. "How Many? A Dictionary of Units of Measurement". Center for Mathematics and Science Education, University of North Carolina at Chapel Hill. Archived from the original on February 2, 2013. Retrieved February 28, 2011.
  13. ↑ Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu". Journal of the Society of Architectural Historians. 16 (2). JSTOR   987740.
  14. ↑ Jacob Koebel (1535). Geometrei. Von künstlichem Feldmessen und absehen (in German). Archived from the original on November 16, 2011.
  15. ↑ "Geometrey". digital.slub-dresden.de (in German). Saxon State Library. Retrieved February 22, 2019.
  16. ↑ Teather, Anne; et al. (February 8, 2019). "Getting the Measure of Stonehenge". British Archaeology (165): 48–51.
  17. ↑ Great Britain (1762). The statutes at large: from the Magna Charta, to the end of the eleventh Parliament of Great Britain, anno 1761 (continued to 1807). The statutes at large. 1. Printed by J. Bentham. p. 400. Retrieved November 30, 2011.
  18. ↑ Zupko, Ronald Edward (1977). British Weights and Measures: A History from Antiquity to the Seventeenth Century. University of Wisconsin Press. pp. 6, 10, 20. ISBN   978-0-299-07340-4.
  19. ↑ "On what basis is one inch exactly equal to 25.4 mm? Has the imperial inch been adjusted to give this exact fit and if so when?". National Physical Laboratory. Archived from the original on August 7, 2012. Retrieved July 24, 2012.
  20. ↑ See, for example, Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with the Imperial Standard Yard and the Imperial Standard Pound and with each other during the Years 1947 to 1948 (H.M.S.O., London, 1950). Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with each other during the Year 1957 (H.M.S.O., London, 1958).
  21. ↑ Bigg, P. H.; Anderton, Pamela (March 1964), "The United Kingdom standards of the yard in terms of the meter", British Journal of Applied Physics, 15 (3): 291–300, Bibcode:1964BJAP...15..291B, doi:10.1088/0508-3443/15/3/308 CS1 maint: uses authors parameter (link)
  22. ↑ A. V. Astin & H. Arnold Karo, (1959), Refinement of values for the yard and the pound Archived August 21, 2006, at the Wayback Machine , Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, June 30, 1959, 8:45 am)
  23. ↑ "State Plane Coordinate System", National Geodetic Survey, May 4, 2019.
  24. ↑ "Measuring Unit Change Coming in 2022", National Geodetic Survey, June 14, 2019.
  25. ↑ Schedule to the Standards of Weights and Measures Act, 1976.
  26. ↑ Survey of India, "National Map Policy – 2005" Archived March 31, 2010, at the Wayback Machine .
  27. ↑ Dr. Franz Mozhnik: Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten. Im Verlage der k.k. Schulbücher Verschleiß-Administration bey St. Anna in der Johannisgasse – Wien 1848
  28. ↑ Denis Février. "Un historique du mètre" (in French). Ministère de l'Économie, des Finances et de l'Industrie. Archived from the original on February 28, 2011. Retrieved March 10, 2011.
  29. 1 2 3 4 5 6 7 8 9 10 11 12 13 "Amtliche Maßeinheiten in Europa 1842" [Official measures in Europe 1842] (in German). Archived from the original on July 23, 2013. Retrieved September 22, 2012.
  30. 1 2 3 4 5 d'Anville, Jean Baptiste Bourguignon (1769). Traité des mesures itinéraires anciennes et modernes [Treatise of ancient and modern measures of distance] (in French). Paris: de l'Imprimerie Royale. Retrieved October 24, 2011.
  31. ↑ Palaiseau, JFG (October 1816). Métrologie universelle, ancienne et moderne: ou rapport des poids et mesures des empires, royaumes, duchés et principautés des quatre parties du monde. Bordeaux. Retrieved October 30, 2011.
  32. 1 2 3 4 5 6 7 8 Jacob de Gelder (1824). Allereerste Gronden der Cijferkunst [Introduction to Numeracy] (in Dutch). 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp. 163–176. Retrieved March 2, 2011.
  33. 1 2 3 4 5 6 7 8 9 Doursther, Horace (1840). Dictionnaire universel des poids et mesures anciens et modernes. Brussels: M. Hayez. pp. 402–418. Retrieved October 25, 2011.
  34. 1 2 3 4 5 Noback, Christian; Noback, Friedrich Eduard (1851). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze [Comprehensive pocketbook of money, weights and measures for all counties and trading centres] (in German). I. Leipzig: F. А. Brockhaus. Retrieved October 24, 2011.
  35. 1 2 Noback, Christian; Noback, Friedrich Eduard (1851). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze [Comprehensive pocketbook of money, weights and measures for all counties and trading centres] (in German). II. Leipzig: F. А. Brockhaus. Retrieved October 24, 2011.
  36. 1 2 3 4 5 6 7 8 Bruhns, Carl (1881). new manual of logarithms to seven places of decimals. Leipzig: Bernhard Tauchnitz. p. 610. Retrieved October 26, 2011.
  37. ↑ Thomas Jefferson (July 13, 1790). "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". United States House of Representatives. Archived from the original on June 6, 2011. Retrieved November 8, 2011.
  38. ↑ Jacob de Gelder (1824). Allereerste Gronden der Cijferkunst [Introduction to Numeracy] (in Dutch). The Hague and Amsterdam: de Gebroeders van Cleef. pp. 155–157. Retrieved March 2, 2011.
  39. ↑ Andreas Dreizler; et al. (April 20, 2009). "Metrologie" (PDF) (in German). Technische Universität Darmstadt. Retrieved March 28, 2011.[ dead link ]
  40. ↑ File
  41. 1 2 3 4 5 6 7 8 "Maten en gewichten" [Weights and measures] (in Dutch). Vlaamse Vereniging voor Familiekunde (Flemish Association for Family History). 2011. Archived from the original on April 25, 2012. Retrieved October 24, 2011.
  42. 1 2 3 4 5 6 7 8 9 10 11 12 Rose, Joshua (1900). Pattern Makers Assistant (9th ed.). New York: D. van Nostrand Co. p. 264.
  43. ↑ "Les anciennes unités et leurs équivalences" [Old units and their equivalences] (in French). Le Cybergroupe Généalogique de Charente Poitevine. 2011. Archived from the original on July 20, 2011. Retrieved February 25, 2011.
  44. 1 2 3 4 5 Guilhiermoz, P (1913). "De l'équivalence des anciennes mesures. A propos d'une publication récente" [Values of ancient measures quoted in recent publications]. Bibliothèque de l'École des chartes (in French). 74: 267–328. doi:10.3406/bec.1913.448498.
  45. ↑ halbo, leif (July 21, 2005). "Mål, vekt og norsk selvstendighet" [Dimensions, weight and Norwegian independence]. Aftenposten.
  46. ↑ [ citation needed ] – Information copied from pl:Stopa polska
  47. ↑ Tomasz Zakiewicz (April 2005). "The Cape Geodetic Standards and Their Impact on Africa" (PDF). FIG, Cairo. Archived (PDF) from the original on January 20, 2012. Retrieved January 4, 2012.
  48. ↑ "Scottish Weights and Measures: Distance and Area". Scottish Archive Network. Archived from the original on August 14, 2009. Retrieved January 28, 2010.
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