Foot (unit)

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Short description: Customary unit of length
foot
Unit systemImperial/US units
Unit ofLength
Symbolft or ′ 
Conversions
1 ft in ...... is equal to ...
   Imperial/US units   1/3 yd
   12 in
   Metric (SI) units   0.3048 m

30.48 cm

304.8 mm

The foot (pl. feet), standard symbol: ft,[1][2] is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, ′, is commonly used to represent the foot.[3] In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since an international agreement in 1959, the foot is defined as equal to exactly 0.3048 meters.

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.

The United States is the only industrialized country that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities.[4] The foot is legally recognized in the United Kingdom; road distance signs must use imperial units (however, distances on road signs are always marked in miles or yards, not feet; bridge clearances are given in meters as well as feet and inches), while its usage is widespread among the British public as a measurement of height.[5][6] The foot is recognized as an alternative expression of length in Canada.[7] Both the UK and Canada have partially metricated their units of measurement. The measurement of altitude in international aviation (the flight level unit) is one of the few areas where the foot is used outside the English-speaking world.

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 48 (EU sizing).[8][better source needed]

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 Geometrey by Jakob Köbel (Frankfurt, c. 1535).

Historically, the human body has been used to provide the basis for units of length.[9] The foot of an adult European-American male is typically about 15.3% of his height,[10] giving a person of 175 cm (5 ft 9 in) a foot-length of about 268 mm (10.6 in), on average.

Archaeologists believe that, in the past, the people of Egypt, India, and Mesopotamia preferred the cubit, while the people of Rome, Ancient Greece , and China preferred the foot. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches (335 mm) and a cubit of 20.8 inches (528 mm).[11] 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 (11.8 in).

The Greek foot (πούς, pous) had a length of 1/600 of a stadion,[12] one stadion being about 181.2 m (594 ft);[13] therefore a foot was, at the time, about 302 mm (11.9 in). Its exact size varied from city to city and could range between 270 mm (10.6 in) and 350 mm (13.8 in), but lengths used for temple construction appear to have been about 295 mm (11.6 in) to 325 mm (12.8 in); the former was close to the size of the Roman foot.

The standard Roman foot (pes) was normally about 295.7 mm (11.6 in) (97% of today's measurement),[14] but in some provinces, particularly Germania Inferior, the so-called pes Drusianus (foot of Nero Claudius Drusus) was sometimes used, with a length of about 334 mm (13.1 in). (In reality, this foot predated Drusus.)[15][16]

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.[17] The toise has 6 pieds (feet) each of 326.6 mm (12.9 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 (11.66 in) was used; when it was rebuilt in the 10th century, a foot of about 320 mm (12.6 in)[Note 1] was used. At the same time, monastic buildings used the Carolingian foot of 340 mm (13.4 in).[Note 1][18]

The procedure for verification of the foot as described in the 16th century posthumously published work by Jacob Köbel in his book Geometrei. Von künstlichem Feldmessen und absehen is:[19][20]

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

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 international foot (thus 12.672 inches or 0.3219 m). 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, the Lavant drum, excavated at Lavant, Sussex, again with a circumference divisible as a whole number into ten long feet.[21]

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 in) 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. 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 the length of his own arm and, by the c. 1300 Act concerning the Composition of Yards and Perches[22] traditionally credited to Edward I or II, the statute foot was a different measure, exactly 10/11 of the old (Belgic) foot. The barleycorn, inch, ell, and yard were likewise shrunk, while rods and furlongs remained the same.[23] 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, since a foot is one third of a yard, 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.[24]

The 1959 agreement concluded a series of step-by-step events, set off in particular by the British Standards Institution's adoption of a scientific standard inch of 25.4 millimetres in 1930.

Symbol

The IEEE standard symbol for a foot is "ft".[1] In some cases, the foot is denoted by a prime, often approximated by an apostrophe, and the inch by a double prime; for example, 2 feet 4 inches is sometimes denoted as 2′ 4″.[25]

Imperial units

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.[26] 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 to be 0.9143969 m,[27] implying a pre-1959 UK foot of 0.3047990 m.

The UK adopted the international yard for all purposes through the Weights and Measures Act 1963, effective January 1, 1964.[28]

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 foot 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.

U.S. survey foot

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 as 39.37 inches = 1 m (making a US foot exactly 1200/3937 meters, approximately 0.30480061 m).[29][30] 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.[31]

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

The National Institute of Standards and Technology, National Geodetic Survey, and the United States Department of Commerce are phasing out the US survey foot beginning in 2023.[32][33][29] However, its relevance may persist, as the Federal Register Notice says:[34]

The date of December 31, 2022, was selected to accompany the modernization of the National Spatial Reference System (NSRS) by NOAA's National Geodetic Survey (NGS). The reason for associating the deprecation of the U.S. survey foot with the modernization of the NSRS is that the biggest impact of the uniform adoption of the international foot will be for users of the NSRS, due to very large coordinate values currently given in U.S. survey feet in many areas of the U.S. Impacts related to the change to international feet will be minimized if a transition occurs concurrently with others [sic] changes in the NSRS. ...

The difference in timelines will have no effect on users of the existing NSRS (National Spatial Reference System), because NGS (NOAA's National Geodetic Survey) will continue to support the U.S. survey foot for components of the NSRS where it is used now and in the past [emphasis added]. In other words, to minimize disruption in the use of U.S. survey foot for existing NSRS coordinate systems, the change will apply only to the modernized NSRS.

Indian survey foot

The Indian survey foot is defined as exactly 0.3047996 m,[35] 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,[36] which is also used by the Global Positioning System.

Historical use

Page from Austrian Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten – 1848[37] (Combined mathematics textbook for the fourth form of senior schools in the Imperial–royal states.)

Metric foot

An ISO 2848 measure of 3 basic modules (30 cm) is called a "metric foot",[citation needed] 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.[38]

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:[39]

  • 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 Ypres, Belgium, was 273.8 millimeters (10.78 in) while the piede in Venice was 347.73 millimeters (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.[47]

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[48] and the newly formed German Empire adopted the metric system in 1871.[49]

The palm (typically 200–280 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).[citation needed]

Obsolete feet details

In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.[citation needed]

Location Modern country Local name Metric
equivalent
(mm) 		Comments
Vienna Austria Wiener Fuß 316.102[46][50]Template:Circular inline
Tyrol Austria Fuß 334.12[39]
Ypres (Ieper) Belgium voet 273.8[51]
Bruges/Brugge Belgium voet 274.3[51]
Brussels Belgium voet 275.75[51]
Hainaut Belgium pied 293.39[43]
Liège Belgium pied 294.70[43]
Kortrijk Belgium voet 297.6[51]
Aalst Belgium voet 277.2[51]
Mechelen Belgium voet 278.0[51]
Leuven Belgium voet 285.5[51]
Tournai Belgium pied 297.77[43]
Antwerp Belgium voet 286.8[51]
China China tradesman's foot 338.3[52]
China China mathematician's foot 333.2[52]
China China builder's foot 322.8[52]
China China surveyor's foot 319.5[52]
Moravia Czech Republic stopa 295.95[39]
Prague Czech Republic stopa 296.4[45] (1851) Bohemian foot or shoe
301.7[40] (1759) Quoted as "11 pouces 1+3/4 lignes"[Notes 1]
Denmark Denmark fod 313.85[46] Until 1835, thereafter the Prussian foot
330.5[40] (1759) Quoted as "2+1/2 lignes larger than the pied [of Paris]"[Notes 1]
France France pied du roi 324.84[53] [Notes 2]
Angoulême France pied d'Angoulême 347.008[54]
Bordeaux (urban) France pied de ville de Bordeaux 343.606[54]
Bordeaux (rural) France pied de terre de Bordeaux 357.214[54]
Strasbourg France pied de Strasbourg 294.95[54]
Württemberg Germany Fuß 286.49[39]
Hanover Germany Fuß 292.10[39]
Augsburg Germany römischer Fuß 296.17[44]
Nuremberg Germany Fuß 303.75[44]
Meiningen-Hildburghausen Germany Fuß 303.95[39]
Oldenburg Germany römischer Fuß 296.41[39]
Weimar Germany Fuß 281.98[39]
Lübeck Germany Fuß 287.62[46]
Aschaffenburg Germany Fuß 287.5[43]
Darmstadt Germany Fuß 287.6[43] Until 1818, thereafter the Hessen "metric foot"
Bremen Germany Fuß 289.35[46]
Rhineland Germany Fuß 313.7[52]
Berlin Germany Fuß 309.6[52]
Hamburg Germany Fuß 286.8[52]
Bavaria Germany Fuß 291.86[39]
Aachen Germany Fuß 282.1[44]
Leipzig Germany Fuß 282.67[39]
Dresden Germany Fuß 283.11[39]
Saxony Germany Fuß 283.19[46]
Prussia Germany, Poland, Russia etc. Rheinfuß 313.85[46]
Frankfurt am Main Germany Fuß 284.61[39]
Venice & Lombardy Italy 347.73[39]
Turin Italy 323.1[52]
Rome Italy piede romano 297.896[54]
Riga Latvia pēda 274.1[52]
Malta Malta pied 283.7[52]
Utrecht Netherlands voet 272.8[52]
Amsterdam Netherlands voet 283.133[42] Divided into 11 duimen (inches, lit. thumbs)
Honsbossche en Rijpse (nl) Netherlands voet 285.0[42]
's-Hertogenbosch Netherlands voet 287.0[42]
Gelderland Netherlands voet 292.0[42]
Bloois (Zeeland) Netherlands voet 301.0[42]
Schouw Netherlands voet 311.0[42]
Rotterdam Netherlands voet 312.43[43]
Rijnland Netherlands voet 314.858[42]
Norway Norway fot 313.75[55] (1824–1835)[Notes 3] Thereafter as for Sweden.
Warsaw Poland stopa 297.8[56] Until 1819
288.0[43] (From 1819) Polish stopa
Lisbon Portugal pé 330.0[44] (From 1835)[Notes 4]
South Africa South Africa Cape foot 314.858[57] Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
Burgos and Castile Spain pie de Burgos/
Castellano 		278.6[40] (1759) Quoted as "122.43 lignes"[Notes 1]
Toledo Spain pie 279.0[40] (1759) Quoted as "10 pouces 3.7 lignes"[Notes 1]
Sweden Sweden fot 296.9[46] = 12 tum (inches). The Swedish fot was also used in Finland (jalka).
Zürich Switzerland 300.0[52]
Galicia Ukraine, Poland stopa galicyjska 296.96[43] Part of Austria–Hungary before World War I
Scotland United Kingdom 305.287[58] [Notes 5]

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

Notes

  1. ↑ 1.0 1.1 1.2 1.3 The source document used pre-metric French units (pied, pouce and ligne).
  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.

Present day uses

International ISO-standard and other intermodal shipping containers

International Standards Organisation (ISO)-defined intermodal containers for efficient global freight/cargo shipping, were defined using feet rather than meters for their leading outside (corner) dimensions. All ISO-standard containers to this day are eight feet wide, and their outer heights and lengths are also primarily defined in, or derived from feet.
Quantities of global shipping containers are still primarily counted in Twenty-foot Equivalent Units, or TEUs.

Aviation

Everyday global (civilian) air traffic / aviation continues to be controlled in flight levels (flying altitudes) separated by thousands of feet (although typically read out in hundreds – e.g. flight level 330 actually means 33,000 feet, or about 10 kilometres in altitude).

Dimension

In measurement, the term "linear foot" (sometimes incorrectly referred to as "lineal foot") refers to the number of feet in a length of material (such as lumber or fabric) without regard to the width; it is used to distinguish from surface area in square foot.[59]

See also

Notes

  1. ↑ 1.0 1.1 The original reference was given in a round number of centimeters

References

  1. ↑ 1.0 1.1 "Recommended Unit Symbols, SI Prefixes, and Abbreviations". https://www.ewh.ieee.org/soc/ias/pub-dept/abbreviation.pdf. 
  2. ↑ BS350:Part 1:1974 Conversion factors and tables Part 1. Basis of tables. Conversion factors. British Standards Institution. 1974. pp. 5, 91. 
  3. ↑ Chicago Manual of Style (17th ed.). University of Chicago Press. 2017. ¶ 10.66. 
  4. ↑ "Appendix G – Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html. Retrieved February 4, 2007. 
  5. ↑ Kelly, Jon (December 21, 2011). "Will British people ever think in metric?". BBC. https://www.bbc.co.uk/news/magazine-16245391. 
  6. ↑ Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey that Transformed the World. London: Abacus.
  7. ↑ Weights and Measures Act , accessed January 2012, Act current to January 18, 2012. 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).
  8. ↑ Melissa (30 March 2016). "Why are shoe sizes as they are?". https://www.todayifoundout.com/index.php/2016/03/pedestrian-origins-modern-shoe-sizes/.  (12×3=36. US(m): 36−22=14, UK: 36−23=13, EU:30.5×1.5=45.75 then +2 "for comfort" plus rounding = 48)
  9. ↑ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 23. ISBN 978-0-520-06072-2. https://archive.org/details/bub_gb_AKJZvXOS7n4C. Retrieved February 2, 2012. 
  10. ↑ Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January–February 2005). "Sexual dimorphism in foot length proportionate to stature". Annals of Human Biology 32 (1): 44–59. doi:10.1080/03014460400027581. PMID 15788354. http://www.sscnet.ucla.edu/anthro/faculty/fessler/pubs/AHBFootSizeDimorphism.pdf. 
  11. ↑ Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117; "Archived copy". http://a.harappa.com/sites/g/files/g65461/f/Kenoyer%202010%20Measuring%20the%20Harappan%20World.pdf. 
  12. ↑ Herodotus; Rawlinson, George (May 14, 1861). "History of Herodotus : a new English version". New York D. Appleton. https://archive.org/details/historyofherod02hero. 
  13. ↑ "Epidauros, Stadium (Building)". https://www.perseus.tufts.edu/hopper/artifact?name=Epidauros,+Stadium&object=Building. 
  14. ↑ Hosch, William L. (ed.) (2010) The Britannica Guide to Numbers and Measurement New York, NY: Britannica Educational Publications, 1st edition. ISBN:978-1-61530-108-9, p.206
  15. ↑ Oswald Ashton Wentworth Dilke (May 22, 1987). Mathematics and measurement. University of California Press. p. 26. ISBN 978-0-520-06072-2. https://archive.org/details/bub_gb_AKJZvXOS7n4C. Retrieved February 2, 2012. 
  16. ↑ Duncan-Jones, R. P. (1980). "Length-Units in Roman Town Planning: The Pes Monetalis and the Pes Drusianus". Britannia 11: 127. doi:10.2307/525675. https://www.jstor.org/stable/525675?origin=crossref. 
  17. ↑ Russ Rowlett. "How Many? A Dictionary of Units of Measurement". Center for Mathematics and Science Education, University of North Carolina at Chapel Hill. http://www.unc.edu/~rowlett/units/dictT.html. 
  18. ↑ Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu". Journal of the Society of Architectural Historians 16 (2): 2–5. doi:10.2307/987740. 
  19. ↑ Jacob Koebel (1535) (in de). Geometrei. Von künstlichem Feldmessen und absehen. http://www.robweir.com/blog/2007/12/right-and-lawful-rood.html. 
  20. ↑ "Geometrey" (in de-DE). Saxon State Library. https://digital.slub-dresden.de/werkansicht/dlf/8082/1/cache.off. 
  21. ↑ Teather, Anne (February 8, 2019). "Getting the Measure of Stonehenge". British Archaeology (165): 48–51. 
  22. ↑ 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. https://books.google.com/books?id=iPQuAAAAIAAJ&q=Compositio+ulnarum+et+perticarum&pg=PA400. Retrieved November 30, 2011. 
  23. ↑ 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. https://books.google.com/books?id=pWUgAQAAIAAJ. 
  24. ↑ "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. http://www.npl.co.uk/reference/faqs/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-(faq-length). 
  25. ↑ Chicago Manual of Style (17th ed.). University of Chicago Press. 2017. ¶ 10.66. 
  26. ↑ 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).
  27. ↑ 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. doi:10.1088/0508-3443/15/3/308. Bibcode: 1964BJAP...15..291B. http://www.iop.org/EJ/abstract/0508-3443/15/3/308/. Retrieved May 16, 2009. 
  28. ↑ Thoburn v Sunderland City Council [2002] EWHC 195 (Admin) (18 February 2002)
  29. ↑ 29.0 29.1 Mitchell, Alanna (August 18, 2020). "America Has Two Feet. It's About to Lose One of Them" (in en-US). The New York Times. ISSN 0362-4331. https://www.nytimes.com/2020/08/18/science/foot-surveying-metrology-dennis.html. 
  30. ↑ A. V. Astin & H. Arnold Karo (1959). "Refinement of values for the yard and the pound". . Washington DC: National Bureau of Standards. Republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, filed June 30, 1959)
  31. ↑ "State Plane Coordinate System", National Geodetic Survey, May 4, 2019.
  32. ↑ "U.S. Survey Foot | NIST - Putting the Best 'Foot' Forward: Ending the Era of the U.S. Survey Foot (1959 to 2022)"[full citation needed]
  33. ↑ "Measuring Unit Change Coming in 2022", National Geodetic Survey, June 14, 2019.
  34. ↑ "Deprecation of the United States (U.S.) Survey Foot". October 5, 2020. https://www.federalregister.gov/documents/2020/10/05/2020-21902/deprecation-of-the-united-states-us-survey-foot. 
  35. ↑ Schedule to the Standards of Weights and Measures Act, 1976.
  36. ↑ Survey of India, "National Map Policy – 2005" .
  37. ↑ 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
  38. ↑ Denis Février. "Un historique du mètre" (in fr). Ministère de l'Économie, des Finances et de l'Industrie. http://www.industrie.gouv.fr/metro/aquoisert/metre.htm. 
  39. ↑ 39.00 39.01 39.02 39.03 39.04 39.05 39.06 39.07 39.08 39.09 39.10 39.11 39.12 "Amtliche Maßeinheiten in Europa 1842" (in de). http://www.spasslernen.de/geschichte/groessen/mas4.htm. 
  40. ↑ 40.0 40.1 40.2 40.3 40.4 d'Anville, Jean Baptiste Bourguignon (1769) (in fr). Traité des mesures itinéraires anciennes et modernes. Paris: de l'Imprimerie Royale. https://books.google.com/books?id=eAkOAAAAQAAJ. Retrieved October 24, 2011. 
  41. ↑ 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. https://books.google.com/books?id=ahjPAAAAMAAJ. Retrieved October 30, 2011. 
  42. ↑ 42.0 42.1 42.2 42.3 42.4 42.5 42.6 42.7 Jacob de Gelder (1824) (in nl). Allereerste Gronden der Cijferkunst. 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp. 163–176. https://archive.org/details/allereerstegron00ramagoog. Retrieved March 2, 2011. 
  43. ↑ 43.0 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 Doursther, Horace (1840). Dictionnaire universel des poids et mesures anciens et modernes. Brussels: M. Hayez. pp. 402–418. https://archive.org/details/dictionnaireuni00dourgoog. Retrieved October 25, 2011. "liege." 
  44. ↑ 44.0 44.1 44.2 44.3 44.4 Noback, Christian; Noback, Friedrich Eduard (1851) (in de). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze. I. Leipzig: F. А. Brockhaus. https://books.google.com/books?id=AkhTAAAAMAAJ. Retrieved October 24, 2011. 
  45. ↑ 45.0 45.1 Noback, Christian; Noback, Friedrich Eduard (1851) (in de). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze. II. Leipzig: F. А. Brockhaus. https://books.google.com/books?id=KEpTAAAAMAAJ. Retrieved October 24, 2011. 
  46. ↑ 46.0 46.1 46.2 46.3 46.4 46.5 46.6 46.7 Bruhns, Carl (1881). new manual of logarithms to seven places of decimals. Leipzig: Bernhard Tauchnitz. p. 610. https://books.google.com/books?id=GoMNAQAAIAAJ. Retrieved October 26, 2011. 
  47. ↑ Thomas Jefferson (July 13, 1790). "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". United States House of Representatives. http://avalon.law.yale.edu/18th_century/jeffplan.asp. 
  48. ↑ de Gelder, Jacob (1824) (in nl). Allereerste Gronden der Cijferkunst. The Hague and Amsterdam: De Gebroeders van Cleef. pp. 155–157. https://archive.org/details/allereerstegron00ramagoog. Retrieved March 2, 2011. 
  49. ↑ Dreizler, Andreas (April 20, 2009). "Metrologie" (in de). Technical University of Darmstadt. http://www.csi.tu-darmstadt.de/media/csi/institutes/nearwallreactiveflows/bilderdateien_1/messtechnik/mtmnormen.pdf. 
  50. ↑ File
  51. ↑ 51.0 51.1 51.2 51.3 51.4 51.5 51.6 51.7 "Maten en gewichten" (in nl). Vlaamse Vereniging voor Familiekunde (Flemish Association for Family History). 2011. http://www.familiekunde-vlaanderen.be/maten-en-gewichten. 
  52. ↑ 52.00 52.01 52.02 52.03 52.04 52.05 52.06 52.07 52.08 52.09 52.10 52.11 Rose, Joshua (1900). Pattern Makers Assistant (9th ed.). New York: D. van Nostrand Co.. pp. 264. 
  53. ↑ "Les anciennes unités et leurs équivalences" (in fr). Le Cybergroupe Généalogique de Charente Poitevine. 2011. http://www.cgcp.asso.fr/FAQ/divers/anciennes_unites.php. 
  54. ↑ 54.0 54.1 54.2 54.3 54.4 Guilhiermoz, P (1913). "De l'équivalence des anciennes mesures. A propos d'une publication récente" (in fr). Bibliothèque de l'École des chartes 74: 267–328. doi:10.3406/bec.1913.448498. 
  55. ↑ halbo, leif (July 21, 2005). "Mål, vekt og norsk selvstendighet" (in no). Aftenposten. 
  56. ↑ [citation needed] – Information copied from :pl:Stopa polska
  57. ↑ Tomasz Zakiewicz (April 2005). "The Cape Geodetic Standards and Their Impact on Africa". Cairo: FIG. http://www.fig.net/pub/cairo/papers/wshs_03/wshs03_02_zakiewich.pdf. 
  58. ↑ "Scottish Weights and Measures: Distance and Area". Scottish Archive Network. http://www.scan.org.uk/measures/distance.asp. 
  59. ↑ "Units: L". http://www.unc.edu/~rowlett/units/dictL.html. 



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