Metre: Difference between revisions

| caption = TheHistorical historical standardpublic metre standard in Paris

The '''metre''' (or '''meter''' in [[American and British English spelling differences#-re, -er|US spelling]]; symbol: '''m''') is the [[SI base unit|base unit]] of [[length]] in the [[International System of Units]] (SI). Since 2019, the metre has been defined as the length of onethe path travelled by light in vacuum during a time interval of {{sfrac|{{val|299792458}}}} of a [[second]], where the second is defined by a [[Caesium standard|hyperfine cobratransition penilefrequency of limbcaesium]].<ref name="SIBrochure9thEd">

Measuring devices (such as [[ammeter]], [[speedometer]]) are spelled "-meter" in all variants of English.<ref>{{cite encyclopedia

}}{{Dead link|date=August 2024 |bot=InternetArchiveBot |fix-attempted=yes }}, s.v. ammeter, meter, parking meter, speedometer.</ref> The suffix "-meter" has the same Greek origin as the unit of length.<ref>

The etymological roots of ''metre'' can be traced to the Greek verb {{lang|grc|μετρέω}} ({{transliteration|grc|metreo}}) ((I) measure, count or compare)<ref>{{LSJ|metre/w|μετρέω|ref}}.</ref> and noun {{lang|grc|μέτρον}} ({{transliteration|grc|metron}}) (a measure),<ref>{{LSJ|me/tron|μέτρον|shortref}}.</ref> 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'. {{cn-citation needed span|The motto {{lang|grc|ΜΕΤΡΩ ΧΡΩ}} ({{transliteration|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||date=March 2024}}. 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>

== History of definition <span class="anchor" id="History"></span><span class="anchor" id="Definition"></span> ==

[[Kepler's laws of planetary motion]] served both to the discovery of [[Newton's law of universal gravitation]] and to the determination of the distance from Earth to the Sun by [[Giovanni Domenico Cassini]].<ref>{{Cite web |title=M13. From Kepler's Laws To Universal Gravitation – Basic Physics |url=https://www.basic-physics.com/m13-from-keplers-laws-to-universal-gravitation/ |access-date=2023-12-30 |language=en-US |archive-date=30 December 2023 |archive-url=https://web.archive.org/web/20231230092030/https://www.basic-physics.com/m13-from-keplers-laws-to-universal-gravitation/ |url-status=dead }}</ref><ref>

[[Christiaan Huygens]] found out the [[centrifugal force]] which explained variations of gravitational acceleration depending on latitude.<ref>{{Cite web |last=Silas |first=Walter |date=2022-10-30 |title=Centrifugal force Vs centripetal force |url=https://probingphysics.com/centrifugal-force-vs-centripetal-force/ |access-date=2023-12-30 |website=Probing the Universe |language=en-US }}{{Dead link|date=August 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{Cite web |title=Gravity: Notes: Latitude Dependent Changes in Gravitational Acceleration |url=https://pburnley.faculty.unlv.edu/GEOL452_652/gravity/notes/GravityNotes18LatitudeVariations.htm |access-date=2023-12-30 |website=pburnley.faculty.unlv.edu}}</ref> He also mathematically formulated the link between &nbsp;the length of the [[Pendulum|simple pendulum]] and gravitational acceleration.<ref name="Perrier-1935" /> According to [[Alexis Clairaut]], the study of variations in gravitational acceleration was a way to determine the [[figure of the Earth]], whose crucial parameter was the [[flattening]] of the [[Earth ellipsoid]]. In the 18th century, in addition of its significance for [[cartography]], [[geodesy]] grew in importance as a means of empirically demonstrating the [[Gravity|theory of gravity]], which [[Émilie du Châtelet]] promoted in France in combination with [[Gottfried Wilhelm Leibniz|Leibniz's]] mathematical work and because the [[Earth radius|radius of the Earth]] was the unit to which all celestial distances were to be referred. Indeed, Earth proved to be an [[Spheroid|oblate spheroid]] through geodetic surveys in [[French Geodesic Mission to the Equator|Ecuador]] and [[French Geodesic Mission to Lapland|Lapland]] and this new data called into question the value of [[Earth radius]] as Picard had calculated it.<ref name="Perrier-1935">

After the [[Anglo-French Survey (1784–1790)|Anglo-French Survey]], the [[French Academy of Sciences]] commissioned an expedition led by [[Jean Baptiste Joseph Delambre]] and [[Pierre Méchain]], lasting from 1792 to 1798, which measured the distance between a belfry in [[Dunkirk]] and [[Montjuïc Castle (Barcelona)|Montjuïc castle]] in [[Barcelona]] at the [[longitude]] of the [[Panthéon|Paris Panthéon]]. When the length of the metre was defined as one ten-millionth of the distance from the [[North Pole]] to the [[Equator]], the flattening of the Earth ellipsoid was assumed to be {{Sfrac|1|334}}.<ref>{{Cite book |last=Capderou |first=Michel |url=https://books.google.com/books?id=jRQXQhRSrz4C |title=Satellites : de Kepler au GPS |date=2011-10-31 |publisher=Springer Science & Business Media |isbn=978-2-287-99049-6 |pages=46 |language=fr}}</ref><ref>{{Cite web |last=Ramani |first=Madhvi |title=How France created the metric system |url=http://www.bbc.com/travel/story/20180923-how-france-created-the-metric-system |access-date=2019-05-21 |website=www.bbc.com |language=en}}</ref><ref name="Levallois">{{Cite web |last=Levallois |first=Jean-Jacques |date=1986 |title=La Vie des sciences |url=https://gallica.bnf.fr/ark:/12148/bpt6k5470853s |access-date=2019-05-13 |website=Gallica |pages=262, 285, 288–290, 269, 276–277, 283 |language=FR}}</ref><ref>Jean-Jacques Levallois, La méridienne de Dunkerque à Barcelone et la détermination du mètre (1792 – 1799), Vermessung, Photogrammetrie, Kulturtechnik, 89 (1991), 375-380.</ref><ref name="Levallois-1991">{{Cite journal |last=Zuerich |first=ETH-Bibliothek |year=1991 |title=La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799) |url=https://dx.doi.org/10.5169/seals-234595 |language=FR |pages=377–378 |doi=10.5169/seals-234595 |access-date=2021-10-12 |websitejournal=E-PeriodicaVermessung, Photogrammetrie, Kulturtechnik: VPK = Mensuration, Photogrammétrie, Génie Rural|volume=89 |issue=7 }}</ref><ref name="Martin-2008">{{Cite journal |last1=Martin |first1=Jean-Pierre |last2=McConnell |first2=Anita |date=2008-12-20 |title=Joining the observatories of Paris and Greenwich |url=https://royalsocietypublishing.org/doi/10.1098/rsnr.2008.0029 |journal=Notes and Records of the Royal Society |language=en |volume=62 |issue=4 |pages=355–372 |doi=10.1098/rsnr.2008.0029 |s2cid=143514819 |issn=0035-9149}}</ref>

In 1841, [[Friedrich Bessel|Friedrich Wilhelm Bessel]] using the [[Least squares|method of least squares]] calculated from several [[arc measurement]]s a new value for the flattening of the Earth, which he determinated as {{Sfrac|1|299.15}}.<ref name=":2">{{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 |pages=509, 510 |language=EN}}</ref><ref name="Viik-2006">{{Cite news |last=Viik |first=T |date=2006 |title=F. W. Bessel and geodesy |pages=10, 6 |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}}</ref><ref name=":1">{{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 |bibcode=1841AN.....19...97B |doi=10.1002/asna.18420190702 |issn=0004-6337}}</ref> He also devised a new instrument for measuring gravitational acceleration which was first used in [[Switzerland]] by [[Emile Plantamour]], [[Charles Sanders Peirce]], and Isaac-Charles Élisée Cellérier (8.01.1818 – 2.10.1889), a [[Geneva]]n mathematician soon independently discovered a mathematical formula to correct [[Observational error|systematic errors]] of this device which had been noticed by Plantamour and [[Adolphe Hirsch]].<ref>{{citation-attribution|{{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}}}}</ref><ref>{{Cite journal |date=1880 |title=Rapport de M. Faye sur un Mémoire de M. Peirce concernant la constance de la pesanteur à Paris et les corrections exigées par les anciennes déterminations de Borda et de Biot |url=https://gallica.bnf.fr/ark:/12148/bpt6k3047v/f1457.image.r=1880%201880 |journal=[[Comptes rendus hebdomadaires des séances de l'Académie des sciences]] |volume=90 |pages=1463–1466 |access-date=2018-10-10 |via=[[Gallica]]}}</ref> This allowed [[Friedrich Robert Helmert]] to determine a remarkably accurate value of {{Sfrac|1|298.3}} for the flattening of the Earth when he proposed his [[Earth ellipsoid|ellipsoid of reference]] in 1901.<ref name="Enc. Universalis-1996">{{Cite book |title=Encyclopedia Universalis |publisher=Encyclopedia Universalis |year=1996 |isbn=978-2-85229-290-1 |pages=320, 370. Vol 10 |oclc=36747385}}</ref> This was also the result of the [[Metre Convention]] of 1875, when the metre was adopted as an international scientific unit of length for the convenience of continental European geodesists following the example of [[Ferdinand Rudolph Hassler]].<ref name="Brunner-1857">{{Cite web |last=Brunner |first=Jean |date=1857-01-01 |title=Appareil construit pour les opérations au moyen desquelles on prolongera dans toute l'étendue de l'Espagne le réseau trigonométrique qui couvre la France in Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels |url=https://gallica.bnf.fr/ark:/12148/bpt6k3001w |access-date=2023-08-31 |website=Gallica |pages=150–153 |language=FR}}</ref><ref name="Pérard-1957">{{Cite web |last=Pérard |first=Albert |date=1957 |title=Carlos Ibáñez e Ibáñez de Ibero (14 avril 1825 – 29 janvier 1891), par Albert Pérard (inauguration d'un monument élevé à sa mémoire) |url=https://www.academie-sciences.fr/pdf/eloges/ibanez_notice.pdf |website=Institut de France – Académie des sciences |pages=26–28}}</ref><ref>Adolphe Hirsch, ''Le général Ibáñez notice nécrologique lue au comité international des poids et mesures, le 12 septembre et dans la conférence géodésique de Florence, le 8 octobre 1891'', Neuchâtel, imprimerie Attinger frères.</ref><ref>{{Cite web |last=Wolf |first=Rudolf |date=1891-01-01 |title=Histoire de l'appareil Ibañez-Brunner in 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=2023-08-31 |website=Gallica |pages=370–371 |language=FR}}</ref><ref name="Clarke-1873">{{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 |periodical=Philosophical Transactions |volume=163 |page=463 |year=1873 |place=London |doi=10.1098/rstl.1873.0014 |doi-access=free}}</ref><ref name="BEG-1868">{{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>

In 1790, one year before it was ultimately decided that the metre would be based on the [[Meridian arc#Quarter meridian|Earth quadrant]] (a quarter of the [[Earth's circumference]] through its poles), [[Talleyrand]] proposed that the metre be the length of the seconds pendulum at a [[latitude]] of 45°. This option, with one-third of this length defining the [[Foot (unit)|foot]], was also considered by [[Thomas Jefferson]] and others for [[Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States|redefining the yard in the United States]] shortly after gaining independence from the [[The Crown|British Crown]].<ref>{{Cite web |title=The seconds pendulum |url=https://www.roma1.infn.it/~dagos/history/sm/node3.html |access-date=2023-10-06 |website=www.roma1.infn.it}}</ref><ref>{{cite book|last=Cochrane|first=Rexmond|title=Measures for progress: a history of the National Bureau of Standards|chapter-url=http://nvl.nist.gov/nvl2.cfm?doc_id=505 |year=1966 |publisher=[[United States Department of Commerce|U.S. Department of Commerce]] |page=532 |chapter=Appendix B: The metric system in the United States |access-date=2011-03-05 |archive-url=https://web.archive.org/web/20110427023306/http://nvl.nist.gov/nvl2.cfm?doc_id=505|archive-date=2011-04-27|url-status=dead}}</ref>

Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included [[Jean-Charles de Borda|Borda]], [[Joseph-Louis Lagrange|Lagrange]], [[Pierre-Simon Laplace|Laplace]], [[Gaspard Monge|Monge]], and [[Marquis de Condorcet|Condorcet]] – decided that the new measure should be equal to one ten-millionth of the distance from the [[North Pole]] to the [[Equator]], determined through measurements along the meridian passing through Paris. Apart from the obvious consideration of safe access for French surveyors, the Paris meridian was also a sound choice for scientific reasons: a portion of the quadrant from Dunkirk to Barcelona (about 1000&nbsp;km, or one-tenth of the total) could be surveyed with start- and end-points at sea level, and that portion was roughly in the middle of the quadrant, where the effects of the Earth's oblateness were expected not to have to be accounted for. Improvements in the measuring devices designed by Borda and used for this survey also raised hopes for a more accurate determination of the length of this meridian arc.<ref name="Larousse" /><ref name="RNMF">{{Cite web |title=L'histoire des unités {{!}} Réseau National de la Métrologie Française |url=https://metrologie-francaise.lne.fr/fr/metrologie/histoire-des-unites |access-date=2023-10-06 |website=metrologie-francaise.lne.fr}}</ref><ref>{{Cite book |last1=Biot |first1=Jean-Baptiste (1774–1862) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k1510037p |title=Recueil d'observations géodésiques, astronomiques et physiques, exécutées par ordre du Bureau des longitudes de France en Espagne, en France, en Angleterre et en Écosse, pour déterminer la variation de la pesanteur et des degrés terrestres sur le prolongement du méridien de Paris... rédigé par MM. Biot et Arago,... |last2=Arago |first2=François (1786-1853) Auteur du texte |date=1821 |pages=viii–ix |language=EN}}</ref><ref name="Débarbat-1799" /><ref name="Martin-2008" />

The task of surveying the Paris meridian arc took more than six years (1792–1798). The technical difficulties were not the only problems the surveyors had to face in the convulsed period of the aftermath of the French Revolution: Méchain and Delambre, and later [[François Arago|Arago]], were imprisoned several times during their surveys, and Méchain died in 1804 of yellow fever, which he contracted while trying to improve his original results in northern Spain. In the meantime, the commission of the French Academy of Sciences calculated a provisional value from older surveys of 443.44 &nbsp;lignes. This value was set by legislation on 7 April 1795.<ref name="Larousse" /><ref name="RNMF" /><ref name="Débarbat-1799" /><ref name=":0">{{Cite book |last=Delambre |first=Jean-Baptiste (1749–1822) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k110160s |title=Grandeur et figure de la terre / J.-B.-J. Delambre ; ouvrage augmenté de notes, de cartes et publié par les soins de G. Bigourdan,... |date=1912 |pages=202–203, 2015, 141–142, 178 |language=EN}}</ref><ref>{{Cite web |title=Comprendre – Histoire de l'observatoire de Paris - Pierre-François-André Méchain |url=https://promenade.imcce.fr/fr/pages2/297.html |access-date=2023-10-15 |website=promenade.imcce.fr}}</ref>

In 1799, a commission including [[Johann Georg Tralles|Johan Georg Tralles]], [[Jean Henri van Swinden]], [[Adrien-Marie Legendre]] and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of the [[Triangulation (surveying)|triangulation]] between these two towns and determined the portion of the distance from the North Pole to the Equator it represented. Pierre Méchain's and Jean-Baptiste Delambre's measurements were combined with the results of the [[French Geodesic Mission to the Equator|Spanish-French geodetic mission]] and a value of {{Sfrac|1|334}} was found for the Earth's flattening. However, French astronomers knew from earlier estimates of the Earth's flattening that different meridian arcs could have different lengths and that their curvature could be irregular. The distance from the North Pole to the Equator was then extrapolated from the measurement of the Paris meridian arc between Dunkirk and Barcelona and was determined as 5 130 740 &nbsp;toises. As the metre had to be equal to one ten-millionth of this distance, it was defined as 0.513074 &nbsp;toise or 3 &nbsp;feet and 11.296 &nbsp;lines of the Toise of Peru, which had been constructed in 1735 for the [[French Geodesic Mission to the Equator]]. When the final result was known, a bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22 June 1799 (4 messidor An VII in the Republican calendar) as a permanent record of the result.<ref name="Clarke-1867" /><ref name="Levallois" /><ref name="Larousse" /><ref name="Débarbat-1799">{{Cite web |last=Suzanne |first=Débarbat |title=Fixation de la longueur définitive du mètre |url=https://francearchives.gouv.fr/fr/pages_histoire/39436 |access-date=2023-10-06 |website=FranceArchives |language=fr}}</ref><ref>{{Cite web |title=Histoire du mètre {{!}} Métrologie |url=https://metrologie.entreprises.gouv.fr/fr/point-d-histoire/histoire-du-metre |access-date=2023-10-06 |website=metrologie.entreprises.gouv.fr}}</ref><ref name="Débarbat-2019" /><ref>{{Cite book |last1=Delambre |first1=Jean-Baptiste (1749–1822) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k110604s |title=Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone. T. 1 / , exécutée en 1792 et années suivantes, par MM. Méchain et Delambre, rédigée par M. Delambre,... |last2=Méchain |first2=Pierre (1744–1804) Auteur du texte |date=1806–1810 |pages=93–94, 10 |language=EN}}</ref>

[[Egyptian astronomy]] has ancient roots which were revived in the 19th century by the modernist impetus of [[Muhammad Ali of Egypt|Muhammad Ali]] who founded in Sabtieh, [[Boulaq]] district, in [[Cairo]] an Observatory which he was keen to keep in harmony with the progress of this science still in progress. In 1858, a Technical Commission was set up to continue, by adopting the procedures instituted in Europe, the cadastre work inaugurated under Muhammad Ali. This Commission suggested to Viceroy [[Sa'id of Egypt|Mohammed Sa'id Pasha]] the idea of buying geodetic devices which were ordered in France. While [[Mahmud Ahmad Hamdi al-Falaki]] was in charge, in Egypt, of the direction of the work of the general map, the viceroy entrusted to [[Ismail Mustafa al-Falaki]] the study, in Europe, of the precision apparatus calibrated against the metre intended to measure the geodesic bases and already built by [[Jean Brunner]] in Paris. Ismail Mustafa had the task to carry out the experiments necessary for determining the expansion coefficients of the two platinum and brass bars, and to compare the Egyptian standard with a known standard. The Spanish standard designed by [[Carlos Ibáñez e Ibáñez de Ibero]] and [[Frutos Saavedra Meneses]] was chosen for this purpose, as it had served as a model for the construction of the Egyptian standard. In addition, the Spanish standard had been compared with [[Jean-Charles de Borda|Borda]]'s double-toise N° &nbsp;1, which served as a comparison module for the measurement of all geodesic bases in France, and was also to be compared to the Ibáñez apparatus. In 1954, the connection of the southerly extension of the [[Struve Geodetic Arc]] with an arc running northwards from [[South Africa]] through [[Egypt]] would bring the course of a major [[meridian arc]] back to land where [[Eratosthenes]] had founded [[geodesy]].<ref>{{Cite book |last=Jamʻīyah al-Jughrāfīyah al-Miṣrīyah |url=http://archive.org/details/bulletindelasoc00almgoog |title=Bulletin de la Société de géographie d'Égypte |date=1876 |publisher=[Le Caire] |others=University of Michigan |pages=6–16}}</ref><ref>{{Cite book |last=texte |first=Ismāʿīl-Afandī Muṣṭafá (1825–1901) Auteur du |url=https://gallica.bnf.fr/ark:/12148/bpt6k840511v |title=Notes biographiques de S. E. Mahmoud Pacha el Falaki (l'astronome), par Ismail-Bey Moustapha et le colonel Moktar-Bey |date=1886 |pages=10–11 |language=EN}}</ref><ref>{{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 news |title=Nomination of the STRUVE GEODETIC ARC for inscription on the WORLD HERITAGE LIST |pages=40, 143–144 |url=https://whc.unesco.org/uploads/nominations/1187.pdf}}</ref><ref name="Soler-1997" />

Seventeen years after Bessel calculated his [[Earth ellipsoid|ellipsoid of reference]], some of the meridian arcs the German astronomer had used for his calculation had been enlarged. This was a very important circumstance because the influence of errors due to [[vertical deflection]]s was minimized in proportion to the length of the meridian arcs: the longer the meridian arcs, the more precise the image of the [[Earth ellipsoid]] would be.<ref name=":2" /> After [[Struve Geodetic Arc]] measurement, it was resolved in the 1860s, at the initiative of [[Carlos Ibáñez e Ibáñez de Ibero]] who would become the first president of both the [[International Association of Geodesy|International Geodetic Association]] and the [[General Conference on Weights and Measures|International Committee for Weights and Measure]], to remeasure the arc of meridian from [[Dunkirk]] to [[Formentera]] and to extend it from [[Shetland]] to the [[Sahara]].<ref>J. M. López de Azcona, "Ibáñez e Ibáñez de Ibero, Carlos", ''Dictionary of Scientific Biography'', vol. VII, 1–2, Scribner's, New York, 1981.</ref><ref>{{Cite book |last=commission |first=Internationale Erdmessung Permanente |url=https://play.google.com/store/books/details?id=M1PnAAAAMAAJ |title=Comptes-rendus des séances de la Commission permanente de l'Association géodésique internationale réunie à Florence du 8 au 17 octobre 1891 |date=1892 |publisher=De Gruyter, Incorporated |isbn=978-3-11-128691-4 |pages=23–25, 100–109 |language=fr}}</ref><ref name="CEM-2013">{{Cite web |title=El General Ibáñez e Ibáñez de Ibero, Marqués de Mulhacén |url=https://www.e-medida.es/numero-4/el-general-ibanez-e-ibanez-de-ibero-marques-de-mulhacen/}}</ref><ref name="Soler-1997">{{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 |url=https://doi.org/10.1007/s001900050086 |journal=Journal of Geodesy |language=en |volume=71 |issue=3 |pages=176–188 |citeseerx=10.1.1.492.3967 |doi=10.1007/s001900050086 |bibcode=1997JGeod..71..176S |s2cid=119447198 |issn=1432-1394}}</ref> This did not pave the way to a new definition of the metre because it was known that the theoretical definition of the metre 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 from the measurement of a single meridian arc.<ref name="Levallois-1991" /> In 1859, [[Friedrich von Schubert]] demonstrated that several meridians had not the same length, confirming an hypothesis of [[Jean le Rond d'Alembert|Jean Le Rond d’Alembertd'Alembert]]. He also proposed an ellipsoid with three unequal axes.<ref>{{Citation |last=Historische Commission bei der königl. Akademie der Wissenschaften |title=Schubert, Theodor von |date=1908 |url=https://de.wikisource.org/wiki/ADB:Schubert,_Theodor_Friedrich_von |work=Allgemeine Deutsche Biographie, Bd. 54 |pages=231 |access-date=2023-10-01 |series=Allgemeine Deutsche Biographie |edition=1. |place=München/Leipzig |publisher=Duncker & Humblot}}</ref><ref>{{Cite web |last=D'Alembert |first=Jean Le Rond |title=Figure de la Terre, in Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, par une Société de Gens de lettres |url=https://artflsrv04.uchicago.edu/philologic4.7/encyclopedie0922/navigate/6/2075 |access-date=2023-10-01 |website=artflsrv04.uchicago.edu}}</ref> In 1860, Elie Ritter, a mathematician from [[Geneva]], using Schubert's data computed that the Earth ellipsoid could rather be a spheroid of revolution accordingly to [[Adrien-Marie Legendre]]’s's model.<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, 484–485}}</ref> However, the following year, resuming his calculation on the basis of all the data available at the time, Ritter came to the conclusion that the problem was only resolved in an approximate manner, the data appearing too scant, and for some affected by [[vertical deflection]]s, in particular the latitude of [[Montjuïc]] in the French meridian arc which determination had also been affected in a lesser proportion by systematic errors of the [[repeating circle]].<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=165–196}}</ref><ref name="Schiavon-2004" /><ref name="Levallois-1991" />{{Blockquote|text=The definition of the length of a metre in the 1790s was founded upon Arc measurements in France and Peru with a definition that it was to be 1/40 millionth of the circumference of the earth measured through the poles. Such were the inaccuracies of that period that within a matter of just a few years

It was well known that 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 and that he didn'tdid not dare to admit this inaccuracy.<ref>{{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 |last=Jouffroy |first=Achille de (1785-1859) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k6338674m |title=Dictionnaire des inventions et découvertes anciennes et modernes, dans les sciences, les arts et l'industrie.... 2. H–Z / recueillis et mis en ordre par M. le marquis de Jouffroy ; publié par l'abbé Migne,... |date=1852–1853 |pages=419 |language=EN}}</ref><ref name=":0" /> This was later explained by clearance in the central axis of the [[repeating circle]] causing wear and consequently the [[zenith]] measurements contained significant systematic errors.<ref name="Schiavon-2004">Martina Schiavon. La geodesia y la investigación científica en la Francia del siglo XIX : la medida del arco de meridiano franco-argelino (1870–1895). ''Revista Colombiana de Sociología'', 2004, Estudios sociales de la ciencia y la tecnologia, 23, pp. 11–30.</ref> [[Polar motion]] predicted by [[Leonhard Euler|Leonard Euler]] and later discovered by [[Seth Carlo Chandler]] also had an impact on accuracy of latitudes' determinations.<ref>{{Cite journal |last1=Yokoyama |first1=Koichi |last2=Manabe |first2=Seiji |last3=Sakai |first3=Satoshi |date=2000 |title=History of the International Polar Motion Service/International Latitude Service |journal=International Astronomical Union Colloquium |language=en |volume=178 |pages=147–162 |doi=10.1017/S0252921100061285 |issn=0252-9211|doi-access=free }}</ref><ref name="Perrier-1935" /><ref>{{Cite web |title=Polar motion {{!}} Earth's axis, wobble, precession {{!}} Britannica |url=https://www.britannica.com/science/polar-motion |access-date=2023-08-27 |website=www.britannica.com |language=en}}</ref><ref name="Torge-2016">{{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 |url=https://link.springer.com/chapter/10.1007/1345_2015_42 |journal=IAG 150 Years |series=International Association of Geodesy Symposia |language=en |location=Cham |publisher=Springer International Publishing |volume=143 |pages=3–18 |doi=10.1007/1345_2015_42 |isbn=978-3-319-30895-1}}</ref> Among all these sources of error, it was mainly an unfavourable [[vertical deflection]] that gave an inaccurate determination of Barcelona's [[latitude]] and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.<ref name="Levallois-1991" />

Baeyer's goal was a new determination of anomalies in the shape of the Earth using precise triangulations, combined with gravity measurements. This involved determining the [[geoid]] by means of gravimetric and leveling measurements, in order to deduce the exact knowledge of the terrestrial spheroid while taking into account local variations. To resolve this problem, it was necessary to carefully study considerable areas of land in all directions. Baeyer developed a plan to coordinate geodetic surveys in the space between the parallels of [[Palermo]] and [[Freetown Christiania|Freetown Christiana]] ([[Denmark]]) and the meridians of [[Bonn]] and Trunz (German name for [[Milejewo]] in [[Poland]]). This territory was covered by a triangle network and included more than thirty observatories or stations whose position was determined astronomically. Bayer proposed to remeasure ten arcs of meridians and a larger number of arcs of parallels, to compare the curvature of the meridian arcs on the two slopes of the [[Alps]], in order to determine the influence of this mountain range on [[vertical deflection]]. Baeyer also planned to determine the curvature of the seas, the [[Mediterranean Sea]] and [[Adriatic Sea]] in the south, the [[North Sea]] and the [[Baltic Sea]] in the north. In his mind, the cooperation of all the States of [[Central Europe]] could open the field to scientific research of the highest interest, research that each State, taken in isolation, was not able to undertake.<ref>{{Cite journal |last=Zuerich |first=ETH-Bibliothek |title=Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892 |url=https://doi.org/10.5169/seals-88335 |access-date=2023-10-11 |websitejournal=E-PeriodicaBulletin de la Société des Sciences Naturelles de Neuchâtel |date=1892 |volume=21 |page=33 |language=fr |doi=10.5169/seals-88335}}</ref><ref name="Quinn-2019" />

After the [[French Revolution]], [[Napoleonic Wars]] led to the adoption of the metre in [[Latin America]] following [[decolonization|independence]] of [[Empire of Brazil|Brazil]] and [[Hispanic America]], while the [[American Revolution]] prompted the foundation of the [[United States Coast and Geodetic Survey|Survey of the Coast]] in 1807 and the creation of the [[National Institute of Standards and Technology|Office of Standard Weights and Measures]] in 1830. In [[continental Europe]], Napoleonic Wars fostered German nationalism which later led to [[unification of Germany]] in 1871. Meanwhile, most European countries had adopted the metre. In the 1870s, [[German Empire]] played a pivotal role in the unification of the metric system through the [[International Association of Geodesy|European Arc Measurement]] but its overwhelming influence was mitigated by that of neutral states. While the German astronomer [[Wilhelm Julius Foerster]], director of the [[Berlin Observatory]] and director of the German Weights and Measures Service boycotted the Permanent Committee of the International Metre Commission, alongsidealong with the Russian and Austrian representatives, in order to promote the foundation of a permanent [[International Bureau of Weights and Measures]], the German born, Swiss astronomer, [[Adolphe Hirsch]] conformed to the opinion of Italy and Spain to create, in spite of French reluctance, the International Bureau of Weights and Measures in France as a permanent institution at the disadventage of the [[Conservatoire national des arts et métiers|''Conservatoire national des Arts et Métiers'']].<ref name="Quinn-2019" /><ref name="Von Wild-1903" /><ref>{{Cite web |date=30 March 1875 |title=Bericht der schweizerischen Delegierten an der internationalen Meterkonferenz an den Bundespräsidenten und Vorsteher des Politischen Departements, J. J. Scherer in Erwin Bucher, Peter Stalder (ed.), Diplomatic Documents of Switzerland, vol. 3, doc. 66, dodis.ch/42045, Bern 1986. |url=https://dodis.ch/42045 |website=Dodis}}</ref>

At that time, [[Unit of measurement|units of measurement]] were 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 an artifact made of platinum kept in the National Archives. Besides the latter, another platinum and twelve iron standards of the metre were made by [[Étienne Lenoir (instrument maker)|Étienne Lenoir]] in 1799. One of them became known as the ''Committee Meter'' in the United States and served as standard of length in the [[United States Coast and Geodetic Survey|United States Coast Survey]] until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, except Spain, 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]]. These measuring devices consisted of bimetallic rulers in platinum and brass or iron and zinc fixed together at one extremity to assess the variations in length produced by any change in temperature. The combination of two bars made of two different metals allowed to take [[thermal expansion]] into account without measuring the temperature. A French scientific instrument maker, [[Jean Nicolas Fortin]], had made three direct copies of the Toise of Peru, one for [[Friedrich Georg Wilhelm von Struve]], a second for [[Heinrich Christian Schumacher]] in 1821 and a third for Friedrich Bessel in 1823. In 1831, [[Henri-Prudence Gambey]] also realized a copy of the Toise of Peru which was kept at [[Altona Observatory]].<ref name="Wolf 1882 20, 32">{{Cite book |last=Wolf |first=M. C |url=https://www.worldcat.org/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=7–8, 20, 32 |language=French |oclc=16069502}}</ref>{{sfn|Bigourdan|1901|pp=8,158–159,176–177}}<ref name="Quinn-2012">{{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=20, 37–38, 91–92, 70–72, 114–117, 144–147, 8 |oclc=861693071}}</ref><ref name="Clarke-1867">{{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 name="NIST Special Publication">{{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><ref>{{Cite web |title=Borda et le système métrique |url=https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |access-date=2023-08-29 |website=Association Mesure Lab |language=fr-FR |archive-date=29 August 2023 |archive-url=https://web.archive.org/web/20230829055653/https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |url-status=dead }}</ref><ref name="Viik-2006" /><ref name="Clarke-1873" /><ref name="Brunner-1857" />

In the second half of the 19th century, the creation of the [[International Association of Geodesy|International Geodetic Association]] would mark the adoption of new scientific methods.<ref>{{Cite journal |last=Zuerich |first=ETH-Bibliothek |date=1892 |title=Exposé historique des travaux de la commission géodésique suisse de 1862 à 1892 |url=https://doi.org/10.5169/seals-88335 |language=de |doi=10.5169/seals-88335 |access-date=2023-08-29 |websitejournal=E-PeriodicaBulletin de la Société des Sciences Naturelles de Neuchâtel|volume=21 |page=33 }}</ref> It then became possible to accurately measure parallel arcs, since the difference in longitude between their ends could be determined thanks to the invention of the [[electrical telegraph]]. Furthermore, advances in [[metrology]] combined with those of [[gravimetry]] have 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 [[gravitational acceleration]] by means of pendulum.<ref>Carlos Ibáñez e Ibáñez de Ibero, ''Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira'', Madrid, Imprenta de la Viuda e Hijo de D.E. Aguado, 1881, p. 78</ref><ref name="Clarke-1867" />

The comparison of the new prototypes of the metre with each other 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]], whose practically negligible coefficient of expansion made it possible to develop simpler baseline measurement methods, and for which its director, the Swiss physicist [[Charles Édouard Guillaume|Charles-Edouard Guillaume]], was granted the [[Nobel Prize in Physics]] in 1920. Guillaume's Nobel Prize marked the end of an era in which [[metrology]] was leaving the field of [[geodesy]] to become a [[Technology|technological]] application of [[physics]].<ref>{{Cite web |title=BIPM – la définition du mètre |url=https://www.bipm.org/fr/measurement-units/history-si/evolution_metre.html |access-date=2019-05-15 |website=www.bipm.org |archive-date=30 April 2017 |archive-url=https://web.archive.org/web/20170430075245/http://www.bipm.org/fr/measurement-units/history-si/evolution_metre.html |url-status=dead }}</ref><ref>{{Cite journal |date=1934-12-01 |title=Dr. C. E. Guillaume |journal=Nature |language=en |volume=134 |issue=3397 |pages=874 |doi=10.1038/134874b0 |bibcode=1934Natur.134R.874. |s2cid=4140694 |issn=1476-4687|doi-access=free }}</ref><ref>{{Cite journal |last=Guillaume |first=C.-H.-Ed |date=1906-01-01 |title=La mesure rapide des bases géodésiques |journal=Journal de Physique Théorique et Appliquée |volume=5 |pages=242–263 |url=https://zenodo.org/record/2007289 |doi=10.1051/jphystap:019060050024200}}</ref>

[[Charles Sanders Peirce]]’s's work promoted the advent of American science at the forefront of global metrology. Alongside his intercomparisons of artifacts of the metre and contributions to gravimetry through improvement of reversible pendulum, Peirce was the first to tie experimentally the metre to the wave length of a spectral line. According to him the standard length might be compared with that of a wave of light identified by a line in the [[Sunlight|solar spectrum]]. Albert Michelson soon took up the idea and improved it.<ref name=":4">{{Cite journal |last=Crease |first=Robert P. |date=2009-12-01 |title=Charles Sanders Peirce and the first absolute measurement standard |url=https://doi.org/10.1063/1.3273015 |journal=Physics Today |volume=62 |issue=12 |pages=39–44 |doi=10.1063/1.3273015 |bibcode=2009PhT....62l..39C |s2cid=121338356 |issn=0031-9228}}</ref><ref>{{Cite journal |last=Lenzen |first=Victor F. |date=1965 |title=The Contributions of Charles S. Peirce to Metrology |url=https://www.jstor.org/stable/985776 |journal=Proceedings of the American Philosophical Society |volume=109 |issue=1 |pages=29–46 |jstor=985776 |issn=0003-049X}}</ref>

This definition fixed the speed of light in [[vacuum]] at exactly {{val|299792458}} &nbsp;metres per second<ref name="Res1">{{cite web |url=https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1 |title=17th General Conference on Weights and Measures (1983), Resolution 1. |access-date=2022-12-07}}</ref> (≈{{val|300000|u=km/s}} or ≈1.079 &nbsp;billion &nbsp;km/hour<ref>The exact value is {{val|299792458|u=m/s}} = {{val|1079252848.8|u=km/h}}.</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=2011-12-19}}</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 vacuum, the error stated being only that of frequency determination.<ref name="recommendations-2">{{cite web |title=Iodine (&lambda; ≈ 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=2011-12-16}}</ref> This bracket notation expressing the error is explained in the article on [[Standard uncertainty#Measurements|measurement uncertainty]].

| 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 1&nbsp;[[second]].<ref name="Larousse">{{Cite book |last=Larousse |first=Pierre |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>

|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 &nbsp;[[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">{{Cite book |last=Wolf |first=Charles (1827–1918) Auteur du texte |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... |date=1882 |pages=C.38–39, C.2–4 |language=FR}}</ref><ref name="entreprises">{{Cite web |title=Histoire du mètre |url=https://www.entreprises.gouv.fr/metrologie/histoire-metre |access-date=2019-05-16 |website=Direction Générale des Entreprises (DGE) |language=fr}}</ref> [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 &nbsp;lines on the ''toise du Pérou''.<ref name="entreprises" />

|21 Oct 1983||17th CGPM||Defines the metre as the length of the path travelled by [[light]] in 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=2019-10-22 }}{{Dead link|date=August 2024 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>

| {{sfrac|{{val|10000000}}}} part of the [[Circular sector|quadrant]] along the [[meridian (geography)|meridian]], measurement by [[Jean Baptiste Joseph Delambre|Delambre]] and [[Pierre Méchain|Méchain]] (443.296 &nbsp;lines)

| Length of the path travelled by light in vacuum in {{sfrac|{{val|299792458}}}} &nbsp;second (17th CGPM)

[[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&nbsp;Gm), [[light-year]]s (10&nbsp;Pm), or [[parsec]]s (31&nbsp;Pm), rather than in Mm, Gm,or Tm, Pm, Em, Zm orlarger Ymmultiples; "30&nbsp;cm", "30&nbsp;m", and "300&nbsp;m" are more common than "3&nbsp;dm", "3&nbsp;dam", and "3&nbsp;hm", respectively.

| 1 &nbsp;metre ||≈ ||style="text-align:right;"|1.0936 ||[[yard]]||

| 1 &nbsp;metre ||≈ ||style="text-align:right;"|39.370 ||[[inch]]es||

| 1 &nbsp;[[centimetre]] ||≈ ||style="text-align:right;"|{{val|0.39370}} ||inch||

| 1 &nbsp;[[millimetre]] ||≈ ||style="text-align:right;"|{{val|0.039370}} ||inch||

| 1 &nbsp;metre ||= ||style="text-align:right;"|10{{sup|10}}||[[ångström]]||

| 1 &nbsp;[[nanometre]] ||= ||style="text-align:right;"|10||ångström||

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

A simple [[mnemonic]] to assist with conversion is "three 3s": 1 &nbsp;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.

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 2&nbsp;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>

* {{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}}