Metre

2022-07-12T19:16:36Z

Stewikim:

{{Short description|SI unit of length}}
{{About|the unit of length|other uses of "metre" or "meter"|Meter (disambiguation)}}
{{Use British English|date=September 2012}}
{{Use dmy dates|date=April 2020}}
{{Infobox unit
| name = metre
| standard = [[SI base unit]]
| quantity = [[Length]]
| symbol = m<ref>
{{cite web
|url=http://physics.nist.gov/cuu/Units/meter.html
|title=Base unit definitions: Meter
|publisher=[[National Institute of Standards and Technology]]
|access-date=28 September 2010
}}</ref>
| dimension = L
| units1 = [[SI units]]
| inunits1 = {{unbulleted list
| {{val|1000|ul=mm}}
| {{val|0.001|ul=km}}
}}
| units2 = [[imperial units|Imperial]]/[[US customary units|US]] units
| inunits2 = {{unbulleted list
| ≈ {{val|1.0936|u=[[Yard|yd]]}}
| ≈ {{val|3.2808|u=[[Foot (unit)|ft]]}}
| ≈ {{val|39.37|u=[[Inch|in]]}}
}}
| units3 = Nautical units
| inunits3 = ≈ {{val|0.00053996|u=[[nautical mile|nmi]]}}
|image=Metric seal.svg
|caption=Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: {{lang|grc|ΜΕΤΡΩ ΧΡΩ}})}}

The '''metre''' ([[British English|Commonwealth spelling]]) or '''meter''' ([[American English|American spelling]]; [[American and British English spelling differences#-re, -er|see spelling differences]]) (from the French unit {{lang|fr|mètre}}, from the Greek noun {{lang|grc|μέτρον}}, "measure") is the [[SI base unit|base unit]] of [[length]] in the [[International System of Units]] (SI). The SI [[Units of measurement|unit]] symbol is '''m'''.

The metre is currently defined as the length of the path travelled by [[light]] in a vacuum in {{sfrac|1|299 792 458}} of a [[second]].

The metre was originally defined in 1793 as one ten-millionth of the distance from the [[equator]] to the [[North Pole]] along a [[great circle]], so the [[Earth's circumference]] is approximately {{val|40000}} km. In 1799, the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of [[krypton-86]]. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of [[proper length]].

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== Spelling ==
''Metre'' is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States<ref>
{{cite web
|url= http://www.nist.gov/document/special-publication-330
|title=The International System of Units (SI) – NIST
|publisher=[[National Institute of Standards and Technology]]
|location=US
|date=26 March 2008
|quote=The spelling of English words is in accordance with the United States Government Printing Office Style Manual, which follows Webster's Third New International Dictionary rather than the Oxford Dictionary. Thus the spellings "meter,"…rather than "metre,"...as in the original BIPM English text...
}}</ref><ref>The most recent official brochure about the International System of Units (SI), written in French by the ''{{lang|fr|Bureau international des poids et mesures}}'', [[International Bureau of Weights and Measures]] (BIPM) uses the spelling ''metre''; an English translation, included to make the SI standard more widely accessible also uses the spelling ''metre'' ([[#bipm2006|BIPM, 2006]], p. 130''ff''). However, in 2008 the U.S. English translation published by the U.S. [[National Institute of Standards and Technology]] (NIST) chose to use the spelling ''meter'' in accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of 1975 gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology ([[#turner|Turner]]). In 2008, NIST published the US version ([[#taylor2008a|Taylor and Thompson, 2008a]]) of the English text of the eighth edition of the BIPM publication ''{{lang|fr|Le Système international d'unités}} (SI)'' (BIPM, 2006). In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text ([[#taylor2008a|Taylor and Thompson (2008a), p. iii]]). The Director of the NIST officially recognised this publication, together with [[#taylor2008b|Taylor and Thompson (2008b)]], as the "legal interpretation" of the SI for the United States ([[#turner|Turner]]). Thus, the spelling ''metre'' is referred to as the "international spelling"; the spelling ''meter'', as the "American spelling".</ref><ref>{{cite web |url=http://www.metricationmatters.com/docs/Spelling_metre_or_meter.pdf |title=Spelling metre or meter |first=Pat |last=Naughtin |website=Metrication Matters |year=2008 |access-date=12 March 2017}}</ref><ref>{{cite web |url= http://grammarist.com/spelling/meter-metre/ |title=Meter vs. metre |website=[[Grammarist]] |access-date=12 March 2017}}</ref> and the Philippines,<ref>The Philippines uses [[Philippine English|English]] as an official language and this largely follows American English since the country became a colony of the United States. While the law that converted the country to use the metric system uses ''metre'' ([[#PH-BatasPambansa8|Batas Pambansa Blg. 8]]) following the SI spelling, in actual practice, ''meter'' is used in government and everyday commerce, as evidenced by laws (''kilometer'', [[#PH-RA7160|Republic Act No. 7160]]), Supreme Court decisions (''meter'', [[#PH-GR185240|G.R. No. 185240]]), and national standards (''centimeter'', [[#PH-PNSBAFS181-2016|PNS/BAFS 181:2016]]).</ref> which use ''meter.'' Other [[West Germanic languages]], such as German and Dutch, and [[North Germanic languages]], such as Danish, Norwegian, and Swedish,<ref>{{cite web |url=http://runeberg.org/nfbr/0164.html |title=295–296 (Nordisk familjebok / Uggleupplagan. 18. Mekaniker – Mykale) |trans-title=295–296 (Nordic Family Book / Owl Edition. 18. Mechanic – Mycular) |location=Stockholm |year=1913}}</ref> likewise spell the word ''Meter'' or ''meter''.

Measuring devices (such as [[ammeter]], [[speedometer]]) are spelled "-meter" in all variants of English.<ref>
{{cite dictionary
|url=http://dictionary.cambridge.org/results.asp?searchword=ammeter
|title=Cambridge Advanced Learner's Dictionary
|year=2008
|publisher=[[Cambridge University Press]]
|access-date=19 September 2012
}}, s.v. ammeter, meter, parking meter, speedometer.</ref> The suffix "-meter" has the same Greek origin as the unit of length.<ref>
{{cite dictionary
|title=American Heritage Dictionary of the English Language
|edition=3rd
|year=1992
|location=Boston
|publisher=[[Houghton Mifflin]]
}}, s.v. meter.</ref><ref>{{cite web
|title=-meter – definition of -meter in English
|url=https://en.oxforddictionaries.com/definition/-meter
|publisher=Oxford Dictionaries
}}
</ref>

== Etymology ==
The etymological roots of ''metre'' can be traced to the Greek verb {{lang|grc|μετρέω}} ({{transl|grc|metreo}}) (to measure, count or compare) and noun {{lang|grc|μέτρον}} ({{transl|grc|metron}}) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin ({{lang|la|metior, mensura}}), French ({{lang|fr|mètre, mesure}}), English and other languages. The Greek word is derived from the Proto-Indo-European root ''[[wikt:*meh₁-|*meh₁-]]'' 'to measure'. The motto {{lang|grc|ΜΕΤΡΩ ΧΡΩ}} ({{transl|grc|metro chro}}) in the seal of the [[International Bureau of Weights and Measures]] (BIPM), which was a saying of the Greek statesman and philosopher [[Pittacus of Mytilene]] and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word ''metre'' (for the French unit {{lang|fr|mètre}}) in English began at least as early as 1797.<ref name="Oxford">[[Oxford English Dictionary]], Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.</ref>
[https://abogadosdeaccidentesahora.com/locaciones/abogados-de-accidentes-en-huntington-park/abogado-de-accidente-de-carro-en-huntington-park/ Abogado de Accidente de Carro en Huntington Park]

== History of definition {{anchor|Definition}} ==
{{Main|History of the metre}}
[[File:Obs-Paris-meridienne.jpg|thumb|Meridian room of the [[Paris Observatory]] (or Cassini room): the [[Paris meridian]] is drawn on the ground.]]

===Pendulum or meridian===
In 1671 [[Jean Picard]] measured the length of a "[[seconds pendulum]]" and proposed a unit of measurement twice that length to be called the universal toise (French: ''Toise universelle'').<ref>{{Cite book|url=https://gallica.bnf.fr/ark:/12148/btv1b7300361b|title=Mesure de la terre [par l'abbé Picard]|last=texte|first=Picard, Jean (1620–1682). Auteur du|date=1671|website=Gallica|pages=3–4|language=EN|access-date=2018-09-13}} {{verify source |date=August 2019 |reason=This ref was deleted ([[Special:Diff/896869028]]) by a bug in VisualEditor and later restored by a bot from the original cite at [[Special:Permalink/893077111]] cite #18 – please verify the cite's accuracy and remove this {verify source} template. [[User:GreenC bot/Job 18]]}}</ref>{{sfn|Bigourdan|1901|pages=8, 158–159}} In 1675, [[Tito Livio Burattini]] suggested the term metre for a unit of length based on a [[pendulum]] length, but then it was discovered that the length of a seconds pendulum varies from place to place.<ref>{{cite book |last1=Lucendo |first1=Jorge |title=Centuries of Inventions: Encyclopedia and History of Inventions |date=23 April 2020 |publisher=Jorge Lucendo |page=246 |url=https://books.google.com/books?id=4l3eDwAAQBAJ&pg=PT246 |access-date=2 August 2021 |language=en}}</ref><ref>{{cite book |last1=Camerini |first1=Valentina |title=365 Real-Life Superheroes |date=1 December 2020 |publisher=Black Inc. |isbn=978-1-74382-138-1 |page=292 |url=https://books.google.com/books?id=f2HdDwAAQBAJ&pg=PA292 |language=en}}</ref><ref>{{cite web |title=Appendix B: Tito Livio Burattini's catholic meter |url=https://www.roma1.infn.it/~dagos/history/sm/node19.html |website=roma1.infn.it |access-date=3 August 2021}}</ref><ref>{{cite web |title=Science. 1791, l'adoption révolutionnaire du mètre |url=https://www.humanite.fr/science-1791-ladoption-revolutionnaire-du-metre-702009 |website=humanite.fr |access-date=3 August 2021 |language=fr |date=25 March 2021}}</ref><ref>{{cite web |title=The meter, an ingenious intuition from belluno {{!}} Italiani Come Noi |url=https://www.italianicomenoi.it/en/il-metro-geniale-intuizione-di-un-bellunese-2/ |website=italianicomenoi.it |access-date=3 August 2021}}</ref><ref>{{cite web |last1=Holtebekk |first1=Trygve |title=Meter |url=https://snl.no/meter |website=Store norske leksikon |access-date=3 August 2021 |language=nb |date=30 November 2020}}</ref><ref>{{Cite book|url=https://archive.org/details/bub_gb_TL4KAAAAIAAJ|title=A Textbook of Physics|last1=Poynting|first1=John Henry|last2=Thomson|first2=Joseph John|date=1907|publisher=C. Griffin|pages=[https://archive.org/details/bub_gb_TL4KAAAAIAAJ/page/n30 20]|language=en}} {{verify source |date=August 2019 |reason=This ref was deleted ([[Special:Diff/896869028]]) by a bug in VisualEditor and later restored by a bot from the original cite at [[Special:Permalink/893077111]] cite #20 – please verify the cite's accuracy and remove this {verify source} template. [[User:GreenC bot/Job 18]]}}</ref><ref>{{Cite book|url=https://gallica.bnf.fr/ark:/12148/btv1b7300361b|title=Mesure de la terre [par l'abbé Picard]|last=Picard|first=Jean (1620–1682) Auteur du texte|date=1671|pages=3–5|language=EN}}</ref><ref>{{Cite book|title=L'exploration du système solaire|last=Bond, Peter, (1948- ...).|date=2014|publisher=De Boeck|others=Dupont-Bloch, Nicolas.|isbn=9782804184964|edition=[Édition française revue et corrigée]|location=Louvain-la-Neuve|pages=5–6|oclc=894499177}}</ref>

Since [[Eratosthenes]], geographers had used [[meridian arc]]s to assess the size of the Earth, which in 1669, [[Jean Picard]] determined to have a radius of {{val|3269000}} [[toise]]s, treated as a simple sphere. In the 18th century, [[geodesy]] grew in importance as a means of empirically demonstrating the [[Gravity|theory of gravity]] and because the [[Earth radius|radius of the Earth]] was the unit to which all celestial distances were to be referred.<ref name="EB1911"/><ref>{{Cite book|last=Badinter|first=Élisabeth|url=https://www.worldcat.org/oclc/1061216207|title=Les passions intellectuelles|date=2018|publisher=Robert Laffont|others=Normandie roto impr.)|isbn=978-2-221-20345-3|location=Paris|oclc=1061216207}}</ref><ref>{{Cite web|last=von Struve|first=Friedrich Georg Wilhelm|date=July 1857|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|url=https://gallica.bnf.fr/ark:/12148/bpt6k30026|access-date=2021-08-30|website=Gallica|page=509|language=EN}}</ref>

=== Meridional definition ===
[[File:Panthéon de Paris, 16 January 2016.jpg|left|thumb|[[Paris]] [[Panthéon]]]]

As a result of the [[Lumières]] and during the [[French Revolution]], the [[French Academy of Sciences]] charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term ''mètre'' ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the [[quarter meridian]], the distance between the [[North Pole]] and the [[Equator]] along the [[Meridian (geography)|meridian]] through Paris.<ref>{{cite book |title=Physics for Scientists and Engineers |publisher=W.H. Freeman |isbn=0716783398 |edition=5th |last1=Tipler |first=Paul A. |last2=Mosca |first2=Gene |page=3|year=2004 }}</ref><ref>('decimalization is not of the essence of the metric system; the real significance of this is that it was the first great attempt to define terrestrial units of measure in terms of an unvarying astronomical or geodetic constant.) The metre was in fact defined as one ten-millionth of one-quarter of the [[earth's circumference]] at sea-level.' [[Joseph Needham]], ''[[Science and Civilisation in China]]'', Cambridge University Press, 1962 vol.4, pt.1, p.42.</ref><ref>{{cite book|url=https://books.google.com/books?id=Yr6lLFUC2ggC|title=Il senso della misura: la codifica della realtà tra filosofia, scienza ed esistenza umana|last=Agnoli|first=Paolo|date=2004|publisher=Armando Editore|isbn=9788883585326|pages=93–94,101|language=it|access-date=13 October 2015}}</ref><ref>{{cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k571270/f1.image|title=Rapport sur le choix d'une unité de mesure, lu à l'Académie des sciences, le 19 mars 1791|date=15 October 2007|publisher=Gallica.bnf.fr|language=fr|access-date=25 March 2013}}: "Nous proposerons donc de mesurer immédiatement un arc du méridien, depuis Dunkerque jusqu'a Bracelone: ce qui comprend un peu plus de neuf degrés & demi." [We propose then to measure directly an arc of the meridian between Dunkirk and Barcelona: this spans a little more than nine-and-a-half degrees."] p. 8</ref><ref>Paolo Agnoli and Giulio D’Agostini,[https://arxiv.org/abs/physics/0412078 'Why does the meter beat the second?,'] December, 2004 pp.1–29.</ref> On 26 March 1791, the French [[National Constituent Assembly (France)|National Constituant Assembly]] adopted the proposal.<ref name="Oxford" /><ref>{{Cite web|title=Archives Parlementaires|url=https://sul-philologic.stanford.edu/philologic/archparl/navigate/24/2/31/|url-status=live|access-date=2021-11-04|website=sul-philologic.stanford.edu|page=379}}</ref>

The [[French Academy of Sciences]] commissioned an expedition led by [[Jean Baptiste Joseph Delambre]] and [[Pierre Méchain]], lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in [[Dunkirk|Dunkerque]] and [[Montjuïc Castle (Barcelona)|Montjuïc castle]] in [[Barcelona]] at the [[longitude]] of the [[Panthéon|Paris Panthéon]] (see [[meridian arc of Delambre and Méchain]]).<ref>{{Cite web|url=http://www.bbc.com/travel/story/20180923-how-france-created-the-metric-system|title=How France created the metric system|last=Ramani|first=Madhvi|website=www.bbc.com|language=en|access-date=2019-05-21}}</ref> The expedition was fictionalised in Denis Guedj, ''Le Mètre du Monde''.{{sfn|Guedj|2001}} Ken Alder wrote factually about the expedition in ''The Measure of All Things: the seven year odyssey and hidden error that transformed the world''.{{sfn|Alder|2002}} This portion of the [[Paris meridian]] was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From 1801 to 1812 France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the [[French Geodesic Mission|Geodesic Mission to Peru]].<ref name="Larousse">{{Cite book|last=Larousse|first=Pierre (1817–1875)|url=https://gallica.bnf.fr/ark:/12148/bpt6k205363w|title=Grand dictionnaire universel du XIXe siècle : français, historique, géographique, mythologique, bibliographique.... T. 11 MEMO-O / par M. Pierre Larousse|date=1866–1877|pages=163|language=EN}}</ref><ref name="Levallois">{{Cite web|url=https://gallica.bnf.fr/ark:/12148/bpt6k5470853s|title=La Vie des sciences|last=Levallois|first=Jean-Jacques|date=1986|website=Gallica|pages=288–290, 269, 276–277, 283|language=FR|access-date=2019-05-13}}</ref> The latter was related by Larrie D. Ferreiro in ''Measure of the Earth: The Enlightenment Expedition that Reshaped Our World''.<ref>{{Cite journal|last=Robinson|first=Andrew|date=2011-08-10|title=History: How Earth shaped up|journal=Nature|language=en|volume=476|issue=7359|pages=149–150|doi=10.1038/476149a|bibcode=2011Natur.476..149R|issn=1476-4687|doi-access=free}}</ref><ref>{{Cite book|last=Ferreiro|first=Larrie D.|url=https://books.google.com/books?id=v6lItAEACAAJ&q=Measure+of+the+Earth:+The+Enlightenment+Expedition+that+Reshaped+Our+World|title=Measure of the Earth: The Enlightenment Expedition That Reshaped Our World|date=2013-06-25|publisher=Basic Books|isbn=978-0-465-06381-9|language=en}}</ref>

In the 19th century, geodesy underwent a revolution through advances in mathematics as well as improvements in the instruments and methods of observation, for instance accounting for individual bias in terms of the [[personal equation]]. The application of the [[least squares]] method to [[meridian arc]] measurements demonstrated the importance of the [[scientific method]] in geodesy. On the other hand, the invention of the [[Telegraphy|telegraph]] made it possible to measure [[Circle of latitude|parallel]] arcs, and the improvement of the [[Kater's pendulum|reversible pendulum]] gave rise to the study of the Earth's [[gravitational field]]. A more accurate determination of the [[Figure of the Earth]] would soon result from the measurement of the [[Struve Geodetic Arc]] (1816–1855) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progress in science would allow better measurement of Earth's size and shape.{{sfn|Clarke|Helmert|1911|pp=803–804}}<ref name=":4" /><ref name="unesco">{{Cite news|url=https://whc.unesco.org/uploads/nominations/1187.pdf|title=Nomination of the Struve geodetic arc for inscription on the World Heritage List|access-date=2019-05-13}}</ref><ref>{{Cite journal|last=Hirsch|first=Adolphe|title=Expériences chronoscopiques sur la vitesse des différentes sensations et de la transmission nerveuse|url=https://dx.doi.org/10.5169/seals-87978|access-date=2021-04-18|website=E-Periodica|year=1861|doi=10.5169/seals-87978|language=fr}}</ref>

In 1832, [[Carl Friedrich Gauss]] studied the [[Earth's magnetic field]] and proposed adding the [[second]] to the basic units of the metre and the [[kilogram]] in the form of the [[Centimetre–gram–second system of units|CGS system]] ([[centimetre]], [[gram]], second). In 1836, he founded the ''Magnetischer Verein'', the first international scientific association, in collaboration with [[Alexander von Humboldt]] and [[Wilhelm Eduard Weber|Wilhelm Edouard Weber]]. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, [[lightning]] and [[gravity]] in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the ''Magnetischer Verein'' would be followed by that of the Central European Arc Measurement (German: [[International Association of Geodesy|''Mitteleuropaïsche Gradmessung'']]) on the initiative of [[Johann Jacob Baeyer]] in 1863, and by that of the [[World Meteorological Organization|International Meteorological Organisation]] whose second president, the Swiss meteorologist and physicist, [[Heinrich von Wild]] would represent [[Russian Empire|Russia]] at the [[General Conference on Weights and Measures|International Committee for Weights and Measures]] (CIPM).<ref>{{Cite journal|date=2019-01-01|title=Les origines du système métrique en France et la Convention du mètre de 1875, qui a ouvert la voie au Système international d'unités et à sa révision de 2018|journal=Comptes Rendus Physique|language=en|volume=20|issue=1–2|pages=6–21|doi=10.1016/j.crhy.2018.12.002|issn=1631-0705|doi-access=free|last1=Débarbat|first1=Suzanne|last2=Quinn|first2=Terry|bibcode=2019CRPhy..20....6D}}</ref><ref>{{Cite book|title=Géophysique in Encyclopedia Universalis|publisher=Encyclopedia Universalis|year=1996|isbn=978-2-85229-290-1|pages=Vol 10, p. 370|oclc=36747385}}</ref><ref>{{Cite web|date=2015-12-08|title=History of IMO|url=https://public.wmo.int/en/about-us/who-we-are/history-IMO|access-date=2021-03-16|website=World Meteorological Organization|language=en}}</ref><ref>{{Cite web|title=Wild, Heinrich|url=https://hls-dhs-dss.ch/articles/028982/2014-11-11/|access-date=2021-03-16|website=hls-dhs-dss.ch|language=de}}</ref><ref>{{Cite web|date=1903|title=Heinrich VON WILD (1833-1902) in COMlTÉ INTERNATIONAL DES POIDS ET MESURES. PROCÈS-VERBAUX DES SÉANCES. DEUXIÈME SÉRIE. TOME II. SESSION DE 1903.|url=https://www.bipm.org/utils/common/pdf/obituaries/1903_CIPM_CH&RU_WILD-Heinrich.pdf|website=BIPM}}</ref><ref name=":1">{{Cite book|last=Quinn|first=T. J.|url=https://www.worldcat.org/oclc/861693071|title=From artefacts to atoms : the BIPM and the search for ultimate measurement standards|date=2012|isbn=978-0-19-990991-9|location=Oxford|pages=91–92, 70–72, 114–117, 144–147, 8|oclc=861693071}}</ref>

=== International prototype metre bar ===
{{quote|The influence of the intellect transcends mountains and leaps across oceans. At the time when [[George Washington]] warned his fellow countrymen against entangling political alliances with European countries, there was started a movement of far reaching importance in a small country in the heart of the Alps which (as we shall see) exerted a silent, yet potent scientific influence upon the young republic on the eastern shores of North America. |author=Florian Cajori<ref>{{cite periodical |last=Cajori |first=Florian |title=Swiss Geodesy and the United States Coast Survey.|url=http://www.jstor.org/stable/6721 |periodical=The Scientific Monthly |volume=13 |number=2 |publisher=American Association for the Advancement of Science |year=1921 |pages=117–129}}</ref>}}

[[File:HasslerCollection 001.jpg|thumb|Triangulation near [[New York City]], 1817.|left]]

In 1816, [[Ferdinand Rudolph Hassler]] was appointed first Superintendent of the [[U.S. National Geodetic Survey|Survey of the Coast]]. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for [[geodesy]] in the United States.<ref>{{Cite book |url=https://www.biodiversitylibrary.org/item/26092 |title=Transactions of the American Philosophical Society |last=Poupard |first=James |year=1825 |volume=2 |location=Philadelphia |publisher=Abraham Small |pages=234–240, 252–253, 274, 278}}</ref><ref>{{Cite journal|last=Cajori|first=Florian|date=1921|title=Swiss Geodesy and the United States Coast Survey|url=https://www.jstor.org/stable/6721|journal=The Scientific Monthly|volume=13|issue=2|pages=117–129|bibcode=1921SciMo..13..117C|issn=0096-3771}}</ref><ref name=":2">{{Citation|last=Clarke|first=Alexander Ross|title=XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James|year=1873|periodical=Philosophical Transactions|volume=163|page=463|place=London|doi=10.1098/rstl.1873.0014|doi-access=free}}</ref>{{sfn|Bigourdan|1901|pages=8, 158–159, 176-177}}

Since 1830, Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured [[Thermal expansion|coefficients of expansion]] to assess temperature effects on the measurements.<ref name=":8">{{Cite journal|last=Parr|first=Albert C.|date=2006-04-01|title=A Tale About the First Weights and Measures Intercomparison in the United States in 1832|url=https://www.nist.gov/publications/tale-about-first-weights-and-measures-intercomparison-united-states-1832|journal=Journal of Research of the National Institute of Standards and Technology|language=en|volume=111|issue=1|pages=31–32, 36|doi=10.6028/jres.111.003|pmid=27274915|pmc=4654608|via=NIST}}</ref>

[[File:Modell.Potsdamer.Kartoffel.jpg|thumb|Three-dimensional model of the so-called [[Geoid|"Potsdamer Kartoffel" (''Potato of Potsdam'')]] with a 15000 times magnification of the surface's level of the [[earth]], [[Potsdam]] (2017)]]

In 1841, [[Friedrich Bessel|Friedrich Wilhelm Bessel]], taking into account errors which had been recognized by [[Louis Puissant]] in the French meridian arc comprising the [[arc measurement of Delambre and Méchain]] which had been extended southward by [[François Arago]] and [[Jean-Baptiste Biot]], recalculated the [[flattening]] of the [[Earth ellipsoid]] making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of [[latitude]], and stated that the [[Earth quadrant]] used for determining the length of the metre was nothing more than a rather imprecise [[Conversion of units|conversion factor]] between the [[toise]] and the metre.<ref>{{Cite news|last=Viik|first=T|date=2006|title=F. W. BESSEL AND GEODESY|page=10|work=Struve Geodetic Arc, 2006 International Conference, The Struve Arc and Extensions in Space and Time, Haparanda and Pajala, Sweden, 13–15 August 2006|citeseerx=10.1.1.517.9501|url=https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.517.9501&rep=rep1&type=pdf|access-date=2021-09-23}}</ref><ref>{{Cite journal|last=Bessel|first=Friedrich Wilhelm|date=1841-12-01|title=Über einen Fehler in der Berechnung der französischen Gradmessung und seineh Einfluß auf die Bestimmung der Figur der Erde. Von Herrn Geh. Rath und Ritter Bessel|url=https://ui.adsabs.harvard.edu/abs/1841AN.....19...97B|journal=Astronomische Nachrichten|volume=19|issue=7|pages=97|doi=10.1002/asna.18420190702|bibcode=1841AN.....19...97B|issn=0004-6337}}</ref><ref name=":5" />

Regarding the precision of the conversion from the [[toise]] to the metre, both [[Unit of measurement|units of measurement]] were then defined by primary [[Standard (metrology)|standard]]s, and unique artifacts made of different [[alloy]]s with distinct coefficients of [[Thermal expansion|expansion]] were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called ''Toise de l'Académie'', was the French primary standard of the toise, and the metre was officially defined by the ''Mètre des Archives'' made of platinum. Besides the latter, another platinum and twelve iron standards of the metre were made in 1799. One of them became known as the ''Committee Meter'' in the United States and served as standard of length in the Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in [[Prussia]] and in [[France]]. A French scientific instrument maker, [[Jean Nicolas Fortin]], had made two direct copies of the Toise of Peru, the first for [[Friedrich Georg Wilhelm von Struve]] in 1821 and a second for [[Friedrich Bessel]] in 1823.<ref>{{Cite book|last=Wolf|first=M. C|url=https://www.worldcat.org/title/recherches-historiques-sur-les-etalons-de-poids-et-mesures-de-lobservatoire-et-les-appareils-qui-ont-servi-a-les-construire/oclc/16069502|title=Recherches historiques sur les étalons de poids et mesures de l'observatoire et les appareils qui ont servi a les construire.|date=1882|publisher=Gauthier-Villars|location=Paris|pages=20, 32|language=French|oclc=16069502}}</ref>{{sfn|Bigourdan|1901|pages=8, 158–159, 176-177}}<ref name=":1" /><ref name=":9" /><ref>{{Cite book|url=https://play.google.com/store/books/details?id=NiEEAQAAIAAJ|title=NIST Special Publication|date=1966|publisher=U.S. Government Printing Office|pages=529|language=en}}</ref>

On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the [[geoid]] is a ball, which on the whole can be assimilated to an oblate [[spheroid]], but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as 1861, after [[Friedrich von Schubert]] showed that the different meridians were not of equal length, Elie Ritter, a mathematician from [[Geneva]], deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse: the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations, in particular that of [[Montjuïc]] in the French meridian arc. By measuring the latitude of two stations in [[Barcelona]], Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. We know now that, in addition to other errors in the survey of Delambre and Méchain, an unfavourable [[vertical deflection]] gave an inaccurate determination of Barcelona's [[latitude]], a metre "too short" compared to a more general definition taken from the average of a large number of arcs.<ref name=":6">{{Cite book|last=Lebon|first=Ernest|url=https://gallica.bnf.fr/ark:/12148/bpt6k949666|title=Histoire abrégée de l'astronomie / par Ernest Lebon,...|year=1899|location=Paris|pages=168}}</ref><ref>{{Cite journal|last=Zuerich|first=ETH-Bibliothek|title=La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799)|url=https://dx.doi.org/10.5169/seals-234595|url-status=live|access-date=2021-10-12|website=E-Periodica|year=1991|pages=377–378|language=FR|doi=10.5169/seals-234595}}</ref><ref name=":5">{{Cite web|title=c à Paris ; vitesse de la lumière ...|url=http://expositions.obspm.fr/lumiere2005/triangulation_plus.html|access-date=2021-10-12|website=expositions.obspm.fr}}</ref><ref>{{Cite book|last1=Société de physique et d'histoire naturelle de Genève.|url=https://www.biodiversitylibrary.org/item/41152|title=Memoires de la Société de physique et d'histoire naturelle de Genève.|last2=Genève|first2=Société de physique et d'histoire naturelle de|date=1859|publisher=Georg [etc.]|volume=15|location=Geneve|pages=441–444}}</ref><ref>{{Cite book|last1=Société de physique et d'histoire naturelle de Genève.|url=https://www.biodiversitylibrary.org/item/50016|title=Memoires de la Société de physique et d'histoire naturelle de Genève.|last2=Genève|first2=Société de physique et d'histoire naturelle de|date=1861|publisher=Georg [etc.]|volume=16|location=Geneve|pages=196}}</ref>

Nevertheless [[Ferdinand Rudolph Hassler]]'s use of the metre in coastal survey contributed to the introduction of the [[Metric Act of 1866]] allowing the use of the metre in the United States, and also played an important role in the choice of the metre as international scientific unit of length and the proposal by the [[International Association of Geodesy|European Arc Measurement]] (German: ''Europäische Gradmessung'') to “establish a European [[International Bureau of Weights and Measures|international bureau for weights and measures]]”. However, in 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the [[French Geodesic Mission to the Equator]], might be so much damaged that comparison with it would be worthless, while Bessel had questionned the accuracy of copies of this standard belonging to [[Altona Observatory|Altona]] and [[Koenigsberg Observatory|Koenigsberg]] Observatories, which he had compared to each other about 1840. Indeed when the primary Imperial [[yard]] standard was partially destroyed in 1834, a new standard of reference had been constructed using copies of the "Standard Yard, 1760" instead of the pendulum's length as provided for in the Weights and Measures Act of 1824.<ref>{{Cite web|title=Metric Act of 1866 – US Metric Association|url=https://usma.org/laws-and-bills/metric-act-of-1866#locale-notification|access-date=2021-03-15|website=usma.org}}</ref><ref>{{Cite book|url=http://gfzpublic.gfz-potsdam.de/pubman/item/escidoc:108187:4/component/escidoc:272449/Generalbericht.mitteleurop%C3%A4ische.Gradmessung%201867.pdf|title=Bericht über die Verhandlungen der vom 30. September bis 7. October 1867 zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung|publisher=Central-Bureau der Europäischen Gradmessung|year=1868|location=Berlin|pages=123–134|language=german}}</ref><ref name=":11">{{Cite journal|last=Quinn|first=Terry|date=2019|title=Wilhelm Foerster's Role in the Metre Convention of 1875 and in the Early Years of the International Committee for Weights and Measures|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/andp.201800355|journal=Annalen der Physik|language=en|volume=531|issue=5|pages=2|doi=10.1002/andp.201800355|bibcode=2019AnP...53100355Q|s2cid=125240402|issn=1521-3889}}</ref><ref name=":9">{{Cite journal|last1=Clarke|first1=Alexander Ross|last2=James|first2=Henry|date=1867-01-01|title=X. Abstract of the results of the comparisons of the standards of length of England, France, Belgium, Prussia, Russia, India, Australia, made at the ordnance Survey Office, Southampton|url=https://royalsocietypublishing.org/doi/10.1098/rstl.1867.0010|journal=Philosophical Transactions of the Royal Society of London|volume=157|page=174|doi=10.1098/rstl.1867.0010|s2cid=109333769}}</ref><ref>{{Cite journal|last=Bessel|first=Friedrich Wilhelm|date=1840-04-01|title=Über das preufs. Längenmaaß und die zu seiner Verbreitung durch Copien ergriffenen Maaßregeln.|url=https://ui.adsabs.harvard.edu/abs/1840AN.....17..193B|journal=Astronomische Nachrichten|volume=17|issue=13|pages=193|doi=10.1002/asna.18400171302|bibcode=1840AN.....17..193B|issn=0004-6337}}</ref><ref>{{Cite book|last=Britain|first=Great|url=https://books.google.com/books?id=qKZFAAAAcAAJ&q=yard+pendulum&pg=PA759|title=The Statutes of the United Kingdom of Great Britain and Ireland|date=1824|language=en}}</ref><ref name=":3">{{Cite journal|last=Guillaume|first=Ed.|date=1916-01-01|title=Le Systeme Metrique est-il en Peril?|url=https://ui.adsabs.harvard.edu/abs/1916LAstr..30..242G|journal=L'Astronomie|volume=30|pages=244–245|bibcode=1916LAstr..30..242G|issn=0004-6302}}</ref>

In 1864, [[Urbain Le Verrier]] refused to join the first general conference of the [[International Association of Geodesy|Central European Arc Measurement]] because the French geodetic works had to be verified.<ref>{{Cite journal|last=Zuerich|first=ETH-Bibliothek|title=Rapport à la commission géodésique suisse sur la conférence géodésique internationale de Berlin|url=https://dx.doi.org/10.5169/seals-88011|access-date=2021-11-29|website=E-Periodica|year=1864|doi=10.5169/seals-88011|language=de}}</ref>

[[File:Appareil Ibáñez.jpg|thumb|Swiss baseline measurement with [[Carlos Ibáñez e Ibáñez de Ibero|Ibáñez]] apparatus in 1880.|356x356px]]

In 1866, at the meeting of the Permanent Commission of the association in [[Neuchâtel]], Antoine Yvon Villarceau announced that he had checked eight points of the [[Paris meridian|French arc]]. He confirmed that the metre was too short. It then became urgent to undertake a complete revision of the meridian arc. Moreover, while the extension of the French meridian arc to the [[Balearic Islands]] (1803–1807) had seemed to confirm the length of the metre, this survey had not been secured by any baseline in Spain. For that reason, [[Carlos Ibáñez e Ibáñez de Ibero]]'s announcement, at this conference, of his 1858 measurement of a baseline in [[Madridejos, Toledo|Madridejos]] was of particular importance. Indeed surveyors determined the size of [[Triangulation (surveying)|triangulation]] networks by measuring [[Baseline (surveying)|baselines]] which concordance granted the accuracy of the whole [[Surveying|survey]].<ref>{{Cite journal|last=Zuerich|first=ETH-Bibliothek|title=Sur les progrès des travaux géodésiques en Europe|url=https://dx.doi.org/10.5169/seals-88030|access-date=2021-11-29|website=E-Periodica|year=1865|doi=10.5169/seals-88030|language=de}}</ref><ref name=":5" /><ref>{{Cite EB1911|wstitle=Earth, Figure of the|volume=8|pages=801–813|first1=Alexander Ross|last1=Clarke|author1-link=Alexander Ross Clarke|first2=Friedrich Robert|last2=Helmert|author2-link=Friedrich Robert Helmert|ref=none}}</ref><ref>{{Cite web|last=texte|first=Académie des sciences (France) Auteur du|date=January 1836|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|url=https://gallica.bnf.fr/ark:/12148/bpt6k2961h|url-status=live|access-date=2021-11-29|website=Gallica|pages=428–433|language=EN}}</ref><ref name=":6" />

In 1867 at the second general conference of the [[International Association of Geodesy]] held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.<ref name=":0">{{Cite web|last=Hirsch|first=Adolphe|date=1891|title=Don Carlos IBANEZ (1825–1891)|url=http://www.bipm.org/utils/common/pdf/obituaries/1891_CIPM_ES_IBANEZ-Don-Carlos.pdf|access-date=22 May 2017|website=Bureau International des Poids et Mesures|pages=4, 8}}</ref><ref>{{Cite web |url=http://www.bipm.org/en/measurement-units/history-si/international-metre-commission.html |title=BIPM – International Metre Commission |website=www.bipm.org |access-date=26 May 2017}}</ref><ref name="IAG">{{Cite web|url=http://www.iag-aig.org/index.php?tpl=text&id_c=80&id_t=143 |title=A Note on the History of the IAG |website=IAG Homepage |access-date=26 May 2017}}</ref> The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of [[Johann Jacob Baeyer]], [[Adolphe Hirsch]] and [[Carlos Ibáñez e Ibáñez de Ibero]] who had devised two geodetic standards calibrated on the metre for the map of Spain.<ref name="Ross-James">{{Cite journal |first1=Clarke Alexander |last1=Ross |first2=Henry |last2=James |date=1873-01-01 |title=XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James |journal=Philosophical Transactions of the Royal Society of London |volume=163 |pages=445–469 |doi=10.1098/rstl.1873.0014|doi-access=free }}</ref><ref name=":0" /><ref name="IAG" /><ref name="Brunner">{{Cite web|url=https://gallica.bnf.fr/ark:/12148/bpt6k3001w|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|last=Brunner|first=Jean|date=1857|website=Gallica|pages=150–153|language=FR|access-date=2019-05-15}}</ref>

Ibáñez adopted the system which [[Ferdinand Rudolph Hassler]] used for the [[U.S. National Geodetic Survey|United States Survey of the Coast]], consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by [[Jean Brunner]], then his sons. [[Traceability|Measurement traceability]] between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by [[Jean-Charles de Borda|Borda]] and [[Antoine Lavoisier|Lavoisier]] for the survey of the [[meridian arc]] connecting [[Dunkirk]] with [[Barcelona]].<ref name="Soler">{{Cite journal|last=Soler|first=T.|date=1997-02-01|title=A profile of General Carlos Ibáñez e Ibáñez de Ibero: first president of the International Geodetic Association|journal=Journal of Geodesy|language=en|volume=71|issue=3|pages=176–188|doi=10.1007/s001900050086|bibcode=1997JGeod..71..176S|s2cid=119447198|issn=1432-1394}}</ref><ref name="Brunner" /><ref name="Wolf">{{Cite book|url=https://gallica.bnf.fr/ark:/12148/bpt6k9807509c|title=Recherches historiques sur les étalons de poids et mesures de l'Observatoire et les appareils qui ont servi à les construire / par M. C. Wolf...|last=Wolf|first=Charles (1827–1918) Auteur du texte|date=1882|pages=C.38–39, C.2–4|language=FR}}</ref><ref name=":0" /><ref>{{Cite web|last=Wolf|first=Rudolf|date=January 1891|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|url=https://gallica.bnf.fr/ark:/12148/bpt6k3068q|access-date=2021-08-30|website=Gallica|pages=370–371|language=EN}}</ref><ref>{{Cite journal|last=Brenni|first=Paolo|date=1996|title=19th Century French Scientific Instrument Makers - XI: The Brunners and Paul Gautier|url=https://www.unav.es/gep/TheBrunnersCartaParis.pdf|journal=Bulletin of the Scientific Instrument Society|volume=49|pages=3–5|via=Universidad de Navarra}}</ref><ref name="EB1911">{{Cite EB1911|wstitle= Geodesy |volume= 11 |last1= Clarke |first1= Alexander Ross |last2= Helmert |first2= Friedrich Robert | pages = 607–615 }}</ref><ref>{{Cite journal|last=Schiavon|first=Martina|date=2006-12-01|title=Les officiers géodésiens du Service géographique de l'armée et la mesure de l'arc de méridien de Quito (1901-1906)|url=http://journals.openedition.org/histoiremesure/1746|journal=Histoire & mesure|language=fr|volume=XXI|issue=XXI - 2|pages=55–94|doi=10.4000/histoiremesure.1746|issn=0982-1783}}</ref><ref name=":12">{{Cite book|url=https://play.google.com/store/books/details/Exp%C3%A9riences_faites_avec_l_appareil_%C3%A0_mesurer_les_b?id=uiwPAAAAQAAJ&hl=da|title=Expériences faites avec l'appareil à mesurer les bases appertant à la commission de la carte d'Espagne /: ouvrage publié par ordre de la reine|date=1860|publisher=J. Dumaine|language=fr}}</ref>

Hassler's metrological and geodetic work also had a favourable response in Russia.<ref name=":8" /> In 1869, the [[Russian Academy of Sciences|Saint Petersburg Academy of Sciences]] sent to the [[French Academy of Sciences]] a report drafted by [[Otto Wilhelm von Struve]], [[Heinrich von Wild]] and [[Moritz von Jacobi]] inviting his French counterpart to undertake joint action to ensure the universal use of the [[metric system]] in all scientific work.<ref name=":3" />

[[File:Metre alloy.jpg|thumb|Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray|alt=|left]]

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of 1874, a member of the Preparatory Committee since 1870 and Spanish representative at the Paris Conference in 1875, [[Carlos Ibáñez e Ibáñez de Ibero]] intervened with the [[French Academy of Sciences]] to rally France to the project to create an [[International Bureau of Weights and Measures]] equipped with the scientific means necessary to redefine the units of the [[metric system]] according to the progress of sciences.<ref name=":7" /><ref>{{Cite web|url=https://www.academie-sciences.fr/pdf/eloges/ibanez_notice.pdf|title=Carlos IBAÑEZ DE IBERO (14 avril 1825 – 29 janvier 1891), par Albert Pérard (inauguration d'un monument élevé à sa mémoire)|last=Pérard|first=Albert|date=1957|website=Institut de France – Académie des sciences|pages=26–28}}</ref><ref name=":1" /><ref>{{Citation|last=Dodis|first=Diplomatische Dokumente der Schweiz {{!}} Documents diplomatiques suisses {{!}} Documenti diplomatici svizzeri {{!}} Diplomatic Documents of Switzerland {{!}}|title=Bericht der schweizerischen Delegierten an der internationalen Meterkonferenz an den Bundespräsidenten und Vorsteher des Politischen Departements, J. J. Scherer|date=1875-03-30|url=https://dodis.ch/42045|publisher=Diplomatische Dokumente der Schweiz {{!}} Documents diplomatiques suisses {{!}} Documenti diplomatici svizzeri {{!}} Diplomatic Documents of Switzerland {{!}} Dodis|language=fr|access-date=2021-09-20}}</ref>

The [[Metre Convention]] (''Convention du Mètre'') of 1875 mandated the establishment of a permanent [[International Bureau of Weights and Measures]] (BIPM: ''{{lang|fr|Bureau International des Poids et Mesures}}'') to be located in [[Sèvres]], France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in 1889 at the first [[General Conference on Weights and Measures]] (CGPM: ''{{lang|fr|Conférence Générale des Poids et Mesures}}''), establishing the ''[[International Prototype Metre]]'' as the distance between two lines on a standard bar composed of an alloy of 90% [[platinum]] and 10% [[iridium]], measured at the melting point of ice.<ref name=":7">[[#nistmetre|National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)]]</ref>

[[File:US National Length Meter.JPG|thumb|Closeup of National Prototype Metre Bar No. 27, made in 1889 by the [[International Bureau of Weights and Measures]] (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960]]

The comparison of the new prototypes of the metre with each other and with the Committee metre (French: ''[[Mètre des Archives]]'') involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's [[Temperature measurement|thermometry]] work led to the discovery of special alloys of iron-nickel, in particular [[invar]], for which its director, the Swiss physicist [[Charles Édouard Guillaume|Charles-Edouard Guillaume]], was granted the [[Nobel Prize in Physics|Nobel Prize for physics]] in 1920.<ref>{{Cite web|url=https://www.bipm.org/fr/measurement-units/history-si/evolution_metre.html|title=BIPM – la définition du mètre|website=www.bipm.org|access-date=2019-05-15}}</ref>

[[File:Repsold.jpg|thumb|[[Gravimeter]] with variant of Repsold-Bessel pendulum|alt=|left]]

As [[Carlos Ibáñez e Ibáñez de Ibero]] stated, the progress of [[metrology]] combined with those of [[gravimetry]] through improvement of [[Kater's pendulum]] led to a new era of [[geodesy]]. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs and all determinations of the [[Gravity|force of gravity]] by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations.<ref name=":4" />

Moreover, at that time, [[statistician]]s knew that scientific observations are marred by two distinct types of errors, [[Observational error|constant errors]] on the one hand, and [[Randomness|fortuitous]] errors, on the other hand. The effects of the latters can be mitigated by the [[least squares|least-squares]] method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes that constantly act in the same way and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. However, the distinction between systematic and random errors is far from being as sharp as one might think at first assessment. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors in order to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections.<ref>{{Cite book|last=Ritter|first=Élie|url=https://play.google.com/books/reader?id=IVEDAAAAQAAJ&hl=fr&pg=GBS.PA7|title=Manuel théorique et pratique de l'application de la méthode des moindres carrés: au calcul des observations|date=1858|publisher=Mallet-Bachelier|language=fr}} {{PD-notice}}</ref><ref>{{Cite book|last=Perrier|first=Georges (1872-1946) Auteur du texte|url=https://gallica.bnf.fr/ark:/12148/bpt6k95002q|title=Cours de géodésie et d'astronomie / par G. Perrier|date=1933|pages=17–18|language=fr}} {{PD-notice}}</ref>

For metrology the matter of [[Thermal expansion|expansibility]] was fundamental; as a matter of fact the [[temperature]] measuring [[Observational error|error]] related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.<ref>{{Cite web|title=The Nobel Prize in Physics 1920|url=https://www.nobelprize.org/prizes/physics/1920/guillaume/lecture/|access-date=2021-03-13|website=NobelPrize.org|language=en-US}} {{PD-notice}}</ref><ref name=":4">{{Cite book|url=http://www.rac.es/ficheros/Discursos/DR_20080825_173.pdf|title=Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira|last=Ibáñez e Ibáñez de Ibero|first=Carlos|publisher=Imprenta de la Viuda e Hijo de D.E. Aguado|year=1881|location=Madrid|pages=70–78}} {{PD-notice}}</ref>

As the [[figure of the Earth]] could be inferred from variations of the [[seconds pendulum]] length with [[latitude]], the [[U.S. National Geodetic Survey|United States Coast Survey]] instructed [[Charles Sanders Peirce]] in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In 1886 the association of geodesy changed name for the [[International Association of Geodesy|International Geodetic Association]], which [[Carlos Ibáñez e Ibáñez de Ibero]] presided up to his death in 1891. During this period the [[International Association of Geodesy|International Geodetic Association]] (German: ''Internationale Erdmessung'') gained worldwide importance with the joining of [[United States]], [[Mexico]], [[Chile]], [[Argentina]] and [[Japan]].<ref name="Soler" /><ref>{{Cite web|url=http://www.unav.es/gep/Informe18.05.1877En.html|title=Report from Charles S. Peirce on his second European trip for the Anual Report of the Superintendent of the U. S. Coast Survey, New York, 18.05.1877|website=www.unav.es|access-date=2019-05-22}} {{PD-notice}}</ref><ref>{{Cite web|url=https://gallica.bnf.fr/ark:/12148/bpt6k3047v|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|last=Faye|first=Hervé|date=1880|website=Gallica|pages=1463–1466|language=FR|access-date=2019-05-22}}</ref><ref>{{Cite journal|last=Torge|first=Wolfgang|date=2016|editor-last=Rizos|editor-first=Chris|editor2-last=Willis|editor2-first=Pascal|title=From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916|journal=IAG 150 Years|volume=143|series=International Association of Geodesy Symposia|language=en|publisher=Springer International Publishing|pages=3–18|doi=10.1007/1345_2015_42|isbn=9783319308951}}</ref><ref>{{Cite journal|last=Torge|first=W.|date=2005-04-01|title=The International Association of Geodesy 1862 to 1922: from a regional project to an international organization|journal=Journal of Geodesy|language=en|volume=78|issue=9|pages=558–568|doi=10.1007/s00190-004-0423-0|bibcode=2005JGeod..78..558T|s2cid=120943411|issn=1432-1394}}</ref>

[[File:GPS-IIR.jpg|thumb|Artist's impression of a GPS-IIR satellite in orbit.|alt=]]

Efforts to supplement the various national [[surveying]] systems, which began in the 19th century with the foundation of the ''[[International Association of Geodesy|Mitteleuropäische Gradmessung]]'', resulted in a series of global [[ellipsoid]]s of the Earth (e.g., [[Friedrich Robert Helmert|Helmert]] 1906, [[John Fillmore Hayford|Hayford]] 1910 and 1924) which would later lead to develop the [[World Geodetic System]]. Nowadays the practical realisation of the metre is possible everywhere thanks to the [[atomic clock]]s embedded in [[GPS satellite blocks|GPS satellites]].<ref>Archived at [https://ghostarchive.org/varchive/youtube/20211211/INN9VYcVK90 Ghostarchive]{{cbignore}} and the [https://web.archive.org/web/20190606115645/https://www.youtube.com/watch?v=INN9VYcVK90&gl=US&hl=en Wayback Machine]{{cbignore}}: {{Citation|last=Laboratoire national de métrologie et d'essais|title=Le mètre, l'aventure continue...|date=2018-06-13|url=https://www.youtube.com/watch?v=INN9VYcVK90&t=1900s|access-date=2019-05-16}}{{cbignore}}</ref><ref name="entreprises">{{Cite web|url=https://www.entreprises.gouv.fr/metrologie/histoire-metre|title=Histoire du mètre|website=Direction Générale des Entreprises (DGE)|language=fr|access-date=2019-05-16}}</ref>

=== Wavelength definition ===
In 1873, [[James Clerk Maxwell]] suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.<ref>{{cite book |url=https://archive.org/details/electricandmagne01maxwrich |title=A Treatise On Electricity and Magnetism |first=James Clerk |last=Maxwell |author-link=James Clerk Maxwell |publisher=MacMillan and Co. |location=London |volume=1 |year=1873 |page=3}}</ref>

In 1893, the standard metre was first measured with an [[interferometer]] by [[Albert Abraham Michelson|Albert A. Michelson]], the inventor of the device and an advocate of using some particular [[wavelength]] of [[light]] as a standard of length. By 1925, [[interferometry]] was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new [[International System of Units]] (SI) as equal to {{val|1650763.73}} [[wavelength]]s of the [[orange (colour)|orange]]-[[red]] [[emission line]] in the [[electromagnetic spectrum]] of the [[krypton-86]] [[atom]] in a [[vacuum]].<ref name="Marion">{{cite book |last=Marion |first=Jerry B. |title=Physics For Science and Engineering |year=1982 |publisher=CBS College Publishing |isbn=978-4-8337-0098-6 |page=3}}</ref>

=== Speed of light definition ===
To further reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the [[second]] and the [[speed of light]]:<ref name="Res1" />

::The metre is the length of the path travelled by light in vacuum during a time interval of {{sfrac|1|299 792 458}} of a second.

This definition fixed the speed of light in [[vacuum]] at exactly {{val|299792458}} metres per second (≈{{val|300000|u=km/s}}).<ref name="Res1">{{cite web |url=http://www.bipm.org/en/CGPM/db/17/1/ |title=17th General Conference on Weights and Measures (1983), Resolution 1. |access-date=19 September 2012}}</ref> An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised [[helium–neon laser]] "a recommended radiation" for realising the metre.<ref name="recommendations-2" /> For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, {{nowrap|λ{{sub|HeNe}}}}, to be {{val|632.99121258|u=nm}} with an estimated relative standard uncertainty (''U'') of {{val|2.1|e=-11}}.<ref name="recommendations-2" /><ref name="uncertainty">The term "relative standard uncertainty" is explained by NIST on their web site: {{cite web |title=Standard Uncertainty and Relative Standard Uncertainty |work=The NIST Reference on constants, units, and uncertainties: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html |publisher=NIST |access-date=19 December 2011}}</ref><ref>[[#NRC2010|National Research Council 2010]].</ref> This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain [[atomic clock]] ({{nowrap|1=''U'' = {{val|5|e=-16}}}}).<ref>[[#NIST2011|National Institute of Standards and Technology 2011]].</ref> Consequently, a realisation of the metre is usually delineated (not defined) today in labs as {{val|1579800.762042|(33)}} wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.<ref name="recommendations-2">{{cite web |title=Iodine (λ ≈ 633 nm) |publisher=BIPM |url=http://www.bipm.org/utils/common/pdf/mep/M-e-P_I2_633.pdf |work=Mise en Pratique |year=2003 |access-date=16 December 2011}}</ref> This bracket notation expressing the error is explained in the article on [[Standard uncertainty#Measurements|measurement uncertainty]].

Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.<ref name="Beers2" /> A commonly used medium is air, and the [[National Institute of Standards and Technology]] (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.<ref name="NIST_calculator">The formulas used in the calculator and the documentation behind them are found at {{cite web |url=http://emtoolbox.nist.gov/Wavelength/Documentation.asp |title=Engineering metrology toolbox: Refractive index of air calculator |date=23 September 2010 |publisher=NIST |access-date=16 December 2011}} The choice is offered to use either the [http://emtoolbox.nist.gov/Wavelength/Edlen.asp modified Edlén equation] or the [http://emtoolbox.nist.gov/Wavelength/Ciddor.asp Ciddor equation]. The documentation provides [http://emtoolbox.nist.gov/Wavelength/Documentation.asp#EdlenorCiddor a discussion of how to choose] between the two possibilities.</ref> As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.<ref name="errors">{{cite web |url=http://emtoolbox.nist.gov/Wavelength/Documentation.asp#UncertaintyandRangeofValidity |title=§VI: Uncertainty and range of validity |work=Engineering metrology toolbox: Refractive index of air calculator |date=23 September 2010 |publisher=NIST |access-date=16 December 2011}}</ref> By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as {{val|1579800.762042|(33)}} wavelengths of helium–neon laser light in a vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any [[partial vacuum]] can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.<ref name="Dunning">{{cite book |title=Atomic, molecular, and optical physics: electromagnetic radiation, Volume 29, Part 3 |chapter=Physical limits on accuracy and resolution: setting the scale |chapter-url=https://books.google.com/books?id=FV4Y39AGYuYC&pg=PA316 |page=316 |first1=F. B. |last1=Dunning |first2=Randall G. |last2=Hulet |isbn=978-0-12-475977-0 |publisher=Academic Press |year=1997 |quote=The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air.}}</ref>

The metre is ''defined'' as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length,{{#tag:ref|The BIPM maintains a list of recommended radiations on their web site.<ref name="recommendations-1">{{cite web |title=Recommended values of standard frequencies |url=http://www.bipm.org/en/publications/mep.html |publisher=BIPM |date=9 September 2010 |access-date=22 January 2012}}</ref><ref>[[#NPL2010|National Physical Laboratory 2010]].</ref>}} and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser [[Interferometry|interferometers]] for a length measurement:<ref name="Beers2">
A more detailed listing of errors can be found in {{cite web |work=NIST length scale interferometer measurement assurance; NIST document NISTIR 4998 |title=§4 Re-evaluation of measurement errors |first1=John S |last1=Beers |first2=William B |last2=Penzes |url=https://www.nist.gov/calibrations/upload/4998.pdf |access-date=17 December 2011 |date=December 1992 |pages=9 ''ff'' }}
</ref><ref name="Webster2">[[#Zagar1999|Zagar, 1999, pp. 6–65''ff'']].</ref>
* uncertainty in vacuum wavelength of the source,
* uncertainty in the refractive index of the medium,
* [[least count]] resolution of the interferometer.
Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation

:<math> \lambda = \frac{c}{n f} </math>

which converts the unit of wavelength ''λ'' to metres using ''c'', the speed of light in vacuum in m/s. Here ''n'' is the [[refractive index]] of the medium in which the measurement is made, and ''f'' is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.<ref name="Webster2" />

=== Timeline ===
{|class="wikitable"
!width=130pt|Date!!Deciding body!!Decision
|-
| 8 May 1790||[[National Assembly (French Revolution)|French National Assembly]]||The length of the new metre to be equal to the length of a [[pendulum]] with a half-[[period (physics)|period]] of one [[second]].<ref name="Larousse" />
|-
|30 Mar 1791||French National Assembly||Accepts the proposal by the [[French Academy of Sciences]] that the new definition for the metre be equal to one ten-millionth of the length of a great circle [[Circular sector|quadrant]] along the Earth's [[meridian (geography)|meridian]] through Paris, that is the distance from the equator to the north pole along that quadrant.{{sfn|Bigourdan1901|pages=20–21}}
|-
|1795||colspan=2|Provisional metre bar made of brass and based on [[Paris meridian|Paris meridan]] arc (French: ''Méridienne de France'') measured by [[Nicolas-Louis de Lacaille|Nicolas-Louis de Lacaillle]] and [[César-François Cassini de Thury|Cesar-François Cassini de Thury]], legally equal to 443.44 [[Line (unit)|lines]] of the ''toise du Pérou'' (a standard [[Units of measurement in France before the French Revolution#Length|French unit of length]] from 1766).<ref name="Larousse" /><ref name="Levallois" /><ref name="Wolf" /><ref name="entreprises" /> [The line was 1/864 of a ''toise''.]
|-
|10 Dec 1799||French National Assembly||Specifies the platinum metre bar, presented on 22 June 1799 and deposited in the [[National Archives of France|National Archives]], as the final standard. Legally equal to 443.296 lines on the ''toise du Pérou''.<ref name="entreprises" />
|-
|24–28 Sept 1889||1st [[General Conference on Weights and Measures]] (CGPM)||Defines the metre as the distance between two lines on a standard bar of an alloy of [[platinum]] with 10% [[iridium]], measured at the melting point of ice.<ref name="entreprises" /><ref>{{Cite web|url=https://www.bipm.org/utils/common/pdf/CGPM/CGPM1.pdf|title=CGPM : Compte rendus de la 1ère réunion (1889).|website=BIPM}}</ref>
|-
|27 Sept – 6 Oct 1927||7th CGPM||Redefines the metre as the distance, at {{convert|0|C|K|abbr=on|lk=on}}, between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard [[atmospheric pressure|atmosphere of pressure]] and supported on two cylinders of at least 10 mm (1 cm) diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm (57.1 cm) from each other.<ref>{{Cite web|url=https://www.bipm.org/utils/common/pdf/CGPM/CGPM7.pdf|title=CGPM : Comptes rendus de le 7e réunion (1927)|page=49}}</ref>
|-
|14 Oct 1960||11th CGPM||Defines the metre as {{val|fmt=spaces| 1650763.73}} [[wavelength]]s in a [[vacuum]] of the [[electromagnetic radiation|radiation]] corresponding to the transition between the 2p{{sup|10}} and 5d{{sup|5}} quantum levels of the [[krypton]]-86 [[atom]].{{sfn|Judson|1976}}
|-
|21 Oct 1983||17th CGPM||Defines the metre as the length of the path travelled by [[light]] in a vacuum during a time interval of {{sfrac|299 792 458}} of a [[second]].<ref>[[#taylor2008a|Taylor and Thompson (2008a), Appendix 1, p. 70.]]</ref><ref>{{cite web |url=https://www.nationalgeographic.org/thisday/oct21/meter-redefined/ |title=Meter is Redefined |publisher=National Geographic Society |location=US |access-date=22 October 2019}}</ref>
|-
|2002||[[International Committee for Weights and Measures]] (CIPM)||Considers the metre to be a unit of [[proper length]] and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by [[general relativity]] to be negligible with respect to the uncertainties of realisation".<ref name="taylor2008a77">[[#taylor2008a|Taylor and Thompson (2008a), Appendix 1, p. 77.]]</ref>
|}

{| class="wikitable" style="margin:0 auto;"
|+Definitions of the metre since 1795{{sfn|Cardarelli|2003}}
! Basis of definition
! Date
! Absolute<br>uncertainty
! Relative<br>uncertainty
|-

| {{sfrac|10 000 000}} part of the [[Circular sector|quadrant]] along the [[meridian (geography)|meridian]], measurement by [[Jean Baptiste Joseph Delambre|Delambre]] and [[Pierre Méchain|Méchain]] (443.296 lines)
| 1795
| 500–100{{nbsp}}μm
| {{val|e=-4}}
|-
| First prototype ''{{lang|fr|[[History of the metre#Mètre des Archives|Mètre des Archives]]}}'' platinum bar standard
| 1799
| 50–10{{nbsp}}μm
| {{val|e=-5}}
|-
| Platinum-iridium bar at melting point of ice (1st [[CGPM]])
| 1889
| {{cvt|0.2–0.1|µm|nm}}
| {{val|e=-7}}
|-
| Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM)
| 1927
| n.a.
| n.a.
|-
| [[Hyperfine structure|Hyperfine]] atomic transition; {{val|fmt=spaces|1650763.73 }} wavelengths of light from a specified transition in [[krypton-86]] (11th CGPM)
| 1960
| 4{{nbsp}}nm
| {{val|4e-9}}<ref>[http://www.bipm.org/en/CGPM/db/17/1/ Definition of the metre] Resolution 1 of the 17th meeting of the CGPM (1983)</ref>
|-
| Length of the path travelled by light in a vacuum in {{sfrac|299 792 458}} second (17th CGPM)
| 1983
| 0.1{{nbsp}}nm
| {{val|e=-10}}
|}

==Early adoptions of the metre internationally==
{{Main|Metrication}}In France, the metre was adopted as an exclusive measure in 1801 under the [[French Consulate|Consulate]]. This continued under the [[First French Empire]] until 1812, when [[Napoleon]] decreed the introduction of the non-decimal ''[[mesures usuelles]]'', which remained in use in France up to 1840 in the reign of [[Louis Philippe I|Louis Philippe]].<ref name="Larousse" /> Meanwhile, the metre was adopted by the Republic of Geneva.<ref>{{Cite web|title=Metrisches System|url=https://hls-dhs-dss.ch/articles/013754/2014-05-22/|access-date=2021-12-15|website=hls-dhs-dss.ch|language=de}}</ref> After the joining of the [[canton of Geneva]] to [[Switzerland]] in 1815, [[Guillaume Henri Dufour]] published the first official Swiss map, for which the metre was adopted as the unit of length.<ref>{{Cite web|title=Kartografie|url=https://hls-dhs-dss.ch/articles/008258/2014-11-26/|access-date=2021-12-13|website=hls-dhs-dss.ch|language=de}}</ref><ref>{{Cite journal|last=Dufour|first=G.-H.|date=1861|title=Notice sur la carte de la Suisse dressée par l'État Major Fédéral|url=https://www.persee.fr/doc/globe_0398-3412_1861_num_2_1_7582|journal=Le Globe. Revue genevoise de géographie|volume=2|issue=1|pages=5–22|doi=10.3406/globe.1861.7582}}</ref> [[Napoleon III|Louis Napoléon Bonaparte]], a Swiss–French binational officer, was present when a baseline was measured near [[Zürich]] for the [[Topographic Map of Switzerland|Dufour map]], which would win the gold medal for a national map at the [[Exposition Universelle (1855)|Exposition Universelle of 1855]].<ref>{{Cite book|last=Durand|first=Roger|url=https://books.google.com/books?id=7-8LnQ9iF04C|title=Guillaume-Henri Dufour dans son Temps 1787-1875|date=1991|publisher=Librairie Droz|isbn=978-2-600-05069-2|pages=145|language=fr}}</ref><ref>{{Cite web|title=Napoleon III.|url=https://hls-dhs-dss.ch/articles/023316/2010-11-02/|access-date=2021-12-14|website=hls-dhs-dss.ch|language=de}}</ref><ref>{{Cite web|date=2019-07-14|title=Henri Dufour et la carte de la Suisse|url=https://blog.nationalmuseum.ch/fr/2019/07/dufour-le-cartographe/|access-date=2021-12-15|website=Musée national - Blog sur l'histoire suisse|language=fr-FR}}</ref> Among the scientific instruments calibrated on the metre that were displayed at the Exposition Universelle, was [[Jean Brunner|Brunner]]'s apparatus, a geodetic instrument devised for measuring the central baseline of Spain, whose designer, [[Carlos Ibáñez e Ibáñez de Ibero]] would represent Spain at the [[International Statistical Institute]]. In 1885, in addition to the Exposition Universelle and the second Statistical Congress held in Paris, an International Association for Obtaining a Uniform Decimal System of Measures, Weights, and Coins was created there.<ref name=":1" /><ref>{{Cite book|last=Yates|first=James|url=https://play.google.com/store/books/details?id=mAo_AAAAYAAJ|title=Narrative of the Origin and Formation of the International Association for Obtaining a Uniform Decimal System of Measures, Weights and Coins|date=1856|publisher=Bell and Daldy|pages=2-6|language=en}}</ref><ref>{{Cite journal|last=Brenni|first=Paolo|date=1996|title=19th Century French Scientific Instrument Makers - XI: The Brunners and Paul Gautier|url=https://www.unav.es/gep/TheBrunnersCartaParis.pdf|journal=Bulletin of the Scientific Instrument Society|volume=49|pages=3–5|via=UNAV}}</ref><ref>{{Cite journal|last=Appell|first=Paul|date=1925|title=Le centenaire du général Ibañez de Ibéro|url=https://education.persee.fr/doc/revin_1775-6014_1925_num_79_1_7841|journal=Revue internationale de l'enseignement|volume=79|issue=1|pages=208–211}}</ref> Copies of the Spanish standard were made for Egypt, France and Germany.<ref name=":13">{{Cite book|last=texte|first=Ismāʿīl-Afandī Muṣṭafá (1825-1901) Auteur du|url=https://gallica.bnf.fr/ark:/12148/bpt6k62478474|title=Recherche des coefficients de dilatation et étalonnage de l'appareil à mesurer les bases géodésiques appartenant au gouvernement égyptien / par Ismaïl-Effendi-Moustapha, ...|date=1864|language=EN}}</ref><ref>{{Cite book|last=Tardi|first=Pierre (1897-1972) Auteur du texte|url=https://gallica.bnf.fr/ark:/12148/bpt6k3355272d|title=Traité de géodésie / par le capitaine P. Tardi ; préface par le général G. Perrier|date=1934|pages=25|language=EN}}</ref><ref>{{Cite web|last=Zuerich|first=ETH-Bibliothek|title=Procès-verbaux des séances de la commission géodésique suisse|url=https://www.e-periodica.ch//digbib/view?pid=bsn-001%3A1877%3A11%3A%3A853|url-status=live|access-date=2021-12-18|website=E-Periodica|pages=14, 18|language=de}}</ref> These standards were compared to each other and with the Borda apparatus, which was the main reference for measuring all geodetic bases in France.<ref name=":13" /><ref name=":12" /><ref name="Soler" /> In 1869, Napoleon III convened the International Metre Commission, which was to meet in Paris in 1870. The [[Franco-Prussian War]] broke out, the [[Second French Empire]] collapsed, but the metre survived.<ref>{{Cite book|url=https://www.worldcat.org/oclc/1057452808|title=Histoire mondiale de la France|date=2018|others=Patrick Boucheron, Nicolas Delalande, Florian Mazel, Yann Potin, Pierre Singaravélou|isbn=978-2-7578-7442-4|edition=Édition augmentée de quinze notices inédites|location=Paris|pages=694|oclc=1057452808}}</ref><ref name=":11" />

=== Metre adoption dates by country ===
* [[France]]: 1801 - 1812, then 1840,<ref name="Larousse" />
* [[Canton of Geneva|Republic of Geneva]], Switzerland: 1813,<ref name=":10">{{Cite web|title=Metrisches System|url=https://hls-dhs-dss.ch/de/articles/013754/2014-05-22/|url-status=live|access-date=2021-12-09|website=hls-dhs-dss.ch|language=de}}</ref>
* [[Kingdom of the Netherlands]]: 1820,
* Kingdom of [[Belgium]]: 1830,
* [[Chile]]: 1848,
* [[Kingdom of Sardinia]], Italy: 1850,
* [[Spain]]: 1852,
* [[Portugal]]: 1852,
* [[Colombia]]: 1853,
* [[Ecuador]]: 1856,
* [[Mexico]]: 1857,
* [[Brazil]]: 1862,
* [[Argentina]]: 1863,
* [[Italy]]: 1863,
* [[German Empire]], [[Germany]]: 1872,
* [[Austria]], 1875,
* [[Switzerland]]: 1877.<ref name=":10" />

== SI prefixed forms of metre ==

[[SI prefix]]es can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km, [[astronomical unit]]s (149.6 Gm), [[light-year]]s (10 Pm), or [[parsec]]s (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

The terms ''micron'' and ''millimicron'' can be used instead of ''micrometre'' (μm) and ''nanometre'' (nm), but this practice may be discouraged.<ref>[[#taylor2008b|Taylor & Thompson 2003, p. 11.]]</ref>

{{SI multiples
| unit=metre
| symbol=m
| xd=[[decimetre]]
| xda=[[decametre]]
| xc=[[centimetre]]
| xh=[[hectometre]]
| xm=[[millimetre]]
| xk=[[kilometre]]
| xmc=[[micrometre]]
| xM=[[megametre]]
| xn=[[nanometre]]
| xG=[[gigametre]]
| xp=[[picometre]]
| xT=[[1 terametre|terametre]]
| xf=[[femtometre]]
| xP=[[1 petametre|petametre]]
| xy=[[yoctometre]]
}}

== Equivalents in other units ==
{| class=wikitable style="margin:0 auto;"
|-
! colspan="5" style="text-align:left;"|Metric unit<br/>expressed in non-SI units
! colspan="4" style="text-align:left;"|Non-SI unit<br/>expressed in metric units
|-
| 1 metre ||≈ ||style="text-align:right;"|1.0936 ||[[yard]]||
| 1 yard||≡ ||style="text-align:right;"|0.9144 ||metre
|-
| 1 metre ||≈ ||style="text-align:right;"|39.370 ||[[inch]]es||
| 1 inch||≡ ||style="text-align:right;"|0.0254 ||metre
|-
| 1 [[centimetre]] ||≈ ||style="text-align:right;"|{{val|0.39370}} ||inch||
| 1 inch||≡ ||style="text-align:right;"|2.54 ||centimetres
|-
| 1 [[millimetre]] ||≈ ||style="text-align:right;"|{{val|0.039370}} ||inch||
| 1 inch||≡ ||style="text-align:right;"|25.4 ||millimetres
|-
| 1 metre ||≡ ||style="text-align:right;"|[[Normalised notation|1 × 10{{sup|10}}]]||[[ångström]]||
| 1 ångström||≡ ||style="text-align:right;"|1 × 10{{sup|−10}} ||metre
|-
| 1 [[nanometre]] ||≡ ||style="text-align:right;"|10||ångström||
| 1 ångström||≡ ||style="text-align:right;"|100 ||[[picometre]]s
|}
Within this table, "inch" and "yard" mean "international inch" and "international yard"<ref>[[#AstinKaro1959|Astin & Karo 1959]].</ref> respectively, though approximate conversions in the left column hold for both international and survey units.
: "≈" means "is approximately equal to";
: "≡" means "equal by definition" or "is exactly equal to".

One metre is exactly equivalent to {{sfrac|5 000|127}}{{nbsp}}inches and to {{sfrac|1 250|1 143}}{{nbsp}}yards.


A simple [[mnemonic]] aid exists to assist with conversion, as three "3"s:
: 1 metre is nearly equivalent to 3{{nbsp}}[[Foot (unit)|feet]] {{frac|3|3|8}}{{nbsp}}inches. This gives an overestimate of 0.125{{nbsp}}mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

The ancient Egyptian [[cubit]] was about 0.5{{nbsp}}m (surviving rods are 523–529{{nbsp}}mm).<ref>Arnold Dieter (1991). [https://books.google.com/books?id=DU04vCP_TFAC ''Building in Egypt: pharaonic stone masonry'']. Oxford: Oxford University Press. {{ISBN|978-0-19-506350-9}}. p.251.</ref> Scottish and English definitions of the [[ell]] (two cubits) were 941{{nbsp}}mm (0.941{{nbsp}}m) and 1143{{nbsp}}mm (1.143{{nbsp}}m) respectively.<ref>{{Cite web |url=http://www.dsl.ac.uk/getent4.php?plen=7441&startset=10747969&query=ELL&fhit=ell&dregion=form&dtext=snd#fhit |title=Dictionary of the Scots Language |access-date=2011-08-06 |archive-url=https://web.archive.org/web/20120321184808/http://www.dsl.ac.uk/getent4.php?plen=7441&startset=10747969&query=ELL&fhit=ell&dregion=form&dtext=snd#fhit |archive-date=2012-03-21 |url-status=dead }}</ref><ref>{{Cite book |url=https://books.google.com/books?id=-BHnAAAAMAAJ&pg=PA221 |title=The Penny Magazine of the Society for the Diffusion of Useful Knowledge |publisher=Charles Knight |pages=221–22 |date=1840-06-06 |df=dmy-all}}</ref> The ancient Parisian ''toise'' (fathom) was slightly shorter than 2{{nbsp}}m and was standardised at exactly 2{{nbsp}}m in the [[mesures usuelles]] system, such that 1{{nbsp}}m was exactly {{frac|1|2}}{{nbsp}}toise.<ref name=H&H>{{cite web |url = https://archive.org/details/outlinesofevolut00halluoft/page/66 |title = Outlines of the evolution of weights and measures and the metric system |first1 = William |last1 = Hallock |first2 = Herbert T |last2 = Wade |publisher = The Macmillan Company |year = 1906 |pages = 66–69|location = London}}</ref> The Russian [[verst]] was 1.0668{{nbsp}}km.{{sfn|Cardarelli|2004}} The [[Scandinavian mile|Swedish mil]] was 10.688{{nbsp}}km, but was changed to 10{{nbsp}}km when Sweden converted to metric units.<ref>{{cite encyclopedia |url=https://snl.no/mil |title=Mil |encyclopedia=Store norske leksikon |first=Knut |last=Hofstad |access-date=2019-10-18 |df=dmy-all}}</ref>

== See also ==
{{Commons category}}
{{wiktionary|metre}}
* [[Conversion of units]] for comparisons with other units
* [[International System of Units]]
* [[Introduction to the metric system]]
* [[ISO 1]]{{spaced ndash}}standard reference temperature for length measurements
* [[Length measurement]]
* [[Metre Convention]]
* [[Metric system]]
* [[Metric prefix]]
* [[Metrication]]
* [[Orders of magnitude (length)]]
* [[SI prefix]]
* [[Speed of light]]
* [[Vertical metre]]

== Notes ==
{{Reflist|30em}}

== References ==
* {{Anchor|Alder2002}}{{cite book |title=The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed the World |first=Ken |last=Alder |year=2002 |publisher=Free Press |location=New York |isbn=978-0-7432-1675-3 |url-access=registration |url=https://archive.org/details/measureofallthin00alde }}
* {{Anchor|AstinKaro1959}}Astin, A. V. & Karo, H. Arnold, (1959), [http://www.ngs.noaa.gov/PUBS_LIB/FedRegister/FRdoc59-5442.pdf ''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, 30 June 1959)
* {{Anchor|BarbrowJudson1976}}{{cite book | title=Weights and Measures Standards of the United States, a brief history | first=Lewis V. | last=Judson | others=Derived from a prior work by Louis A. Fisher (1905) | editor-first=Louis E. | editor-last=Barbrow | publisher=[[US Department of Commerce]], [[National Bureau of Standards]] | location=USA | date=1976-10-01 | orig-year=1963 | id=NBS Special Publication 447; NIST SP 447; 003-003-01654-3 | lccn=76-600055 | url=https://www.nist.gov/pml/wmd/pubs/upload/sp-447-2.pdf | access-date=12 October 2015}}
* {{Cite book |last=Bigourdan |first=Guillaume |url=https://archive.org/details/lesystmemtri00bigo|title=Le système métrique des poids et mesures ; son établissement et sa propagation graduelle, avec l'histoire des opérations qui ont servi à déterminer le mètre et le kilogramme |trans-title=The metric system of weights and measures; its establishment and gradual propagation, with the history of the operations which served to determine the meter and the kilogram |date=1901 |publisher=Gauthier-Villars |location=Paris}}
* {{Anchor|Guedj2001}}{{cite book |title=La Mesure du Monde |trans-title=The Measure of the World |first=Denis |last=Guedj |translator-first=Art |translator-last=Goldhammer |publisher=University of Chicago Press |location=Chicago |year=2001}}
* {{Anchor|Cardarelli2003}}{{cite book |title=Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins |last=Cardarelli |first=François |year=2003 |publisher=Springer-Verlag London Limited |isbn=978-1-85233-682-0 |chapter=Chapter 2: The International system of Units |chapter-url=http://www.francoiscardarelli.ca/PDF_Files/ESU_Sample_Chapter_Section_1_2.pdf#page=6 |at=Table 2.1, p. 5 |quote=Data from Giacomo, P., Du platine à la lumière [From platinum to light], ''Bull. Bur. Nat. Metrologie'', '''102''' (1995) 5–14. |access-date=26 January 2017 |url=https://archive.org/details/encyclopaediaofs0000card }}
* {{cite book |last=Cardarelli |first=F. |year=2004 |title=Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins |publisher=Springer |edition=2nd |pages=[https://archive.org/details/encyclopaediaofs0000card/page/120 120]–124 |isbn=1-85233-682-X |url=https://archive.org/details/encyclopaediaofs0000card |url-access=registration}}
* {{EB1911|wstitle=Earth, Figure of the|volume=8|pages=801–813|first1=Alexander Ross|last1=Clarke|author1-link=Alexander Ross Clarke|first2=Friedrich Robert|last2=Helmert|author2-link=Friedrich Robert Helmert|ref=none}}
* {{anchor|nistmetre}}[http://physics.nist.gov/cuu/Units/meter.html ''Historical context of the SI: Meter'']. Retrieved 26 May 2010.
* {{Anchor|NIST2011}}National Institute of Standards and Technology. (27 June 2011). ''[https://www.nist.gov/pml/div688/grp50/primary-frequency-standards.cfm NIST-F1 Cesium Fountain Atomic Clock]''. Author.
* {{Anchor|NPL2010}}National Physical Laboratory. (25 March 2010). ''[http://www.npl.co.uk/science-technology/time-frequency/optical-frequency-standards-and-metrology/research/iodine-stabilised-lasers Iodine-Stabilised Lasers]''. Author.
* {{Anchor|NRC2010}}{{cite web|url=http://www.nrc-cnrc.gc.ca/eng/projects/inms/si-length.html |publisher=National Research Council Canada |title=Maintaining the SI unit of length |date=5 February 2010 |archive-url=https://web.archive.org/web/20111204014454/http://www.nrc-cnrc.gc.ca/eng/projects/inms/si-length.html |archive-date=4 December 2011 |url-status=dead }}
* {{Anchor|PH-BatasPambansa8}}Republic of the Philippines. (2 December 1978). ''[http://www.chanrobles.com/bataspambansabilang8.htm Batas Pambansa Blg. 8: An Act Defining the Metric System and its Units, Providing for its Implementation and for Other Purposes]''. Author.
* {{Anchor|PH-RA7160}}Republic of the Philippines. (10 October 1991). ''[https://www.officialgazette.gov.ph/downloads/1991/10oct/19911010-RA-7160-CCA.pdf Republic Act No. 7160: The Local Government Code of the Philippines]''. Author.
* {{Anchor|PH-GR185240}} Supreme Court of the Philippines (Second Division). (20 January 2010). ''[https://web.archive.org/web/20180427202441/http://sc.judiciary.gov.ph/jurisprudence/2010/january2010/185240.htm G.R. No. 185240]''. Author.
* {{Anchor|taylor2008a}}Taylor, B.N. and Thompson, A. (Eds.). (2008a). [https://web.archive.org/web/20171120061639/https://www.nist.gov/sites/default/files/documents/2016/12/07/sp330.pdf ''The International System of Units (SI)'']. United States version of the English text of the eighth edition (2006) of the International Bureau of Weights and Measures publication ''Le Système International d’ Unités (SI)'' (Special Publication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
* {{Anchor|taylor2008b}}Taylor, B.N. and Thompson, A. (2008b). [http://physics.nist.gov/cuu/pdf/sp811.pdf ''Guide for the Use of the International System of Units''] (Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008.
* {{Anchor|turner}}Turner, J. (Deputy Director of the National Institute of Standards and Technology). (16 May 2008).[https://www.nist.gov/pml/wmd/metric/upload/FRN_Vol_73_No_96_16May2008_SI_Interpretation.pdf "Interpretation of the International System of Units (the Metric System of Measurement) for the United States"]. ''Federal Register'' Vol. 73, No. 96, p.{{nbsp}}28432-3.
* {{Anchor|Zagar1999}}Zagar, B.G. (1999). [https://books.google.com/books?id=VXQdq0B3tnUC&pg=PT164#PPT160,M1 Laser interferometer displacement sensors] in J.G. Webster (ed.). ''The Measurement, Instrumentation, and Sensors Handbook.'' CRC Press. {{ISBN|0-8493-8347-1}}.

{{SI units}}
{{SI units of length}}
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[[Category:Metre| ]]
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