View source for Draft:History of the metre

{{Short description|Origins and values of the unit of length}}
{{broader|Metre}}
{{Multiple issues|
{{Synthesis|date=January 2025}}
{{Overly detailed|date=January 2025}}
}}
{{Use British English|date=November 2019}}
{{Use dmy dates|date=November 2022}}
[[File:Kilometre definition.svg|thumb|An early definition of the [[metre]] was one ten-millionth of the [[Earth quadrant]], the distance from the [[North Pole]] to the [[Equator]], measured along a [[meridian (geography)|meridian]] through [[Paris]].]]

The '''history of the metre''' starts with the [[Scientific Revolution]] that is considered to have begun with [[Nicolaus Copernicus]]'s publication of {{lang|la|[[De revolutionibus orbium coelestium]]}} in 1543. Increasingly accurate measurements were required, and scientists looked for measures that were universal and could be based on natural phenomena rather than royal decree or physical prototypes. Rather than the various complex systems of subdivision then in use, they also preferred a decimal system to ease their calculations.

With the [[French Revolution]] (1789) came a desire to replace many features of the [[Ancien Régime]], including [[Units of measurement in France before the French Revolution|the traditional units of measure]]. As a base unit of length, many scientists had favoured the [[seconds pendulum]] (a pendulum with a half-period of one second) one century earlier, but this was rejected as it had been discovered that this length varied from place to place with local gravity. A new unit of length, the ''metre'' was introduced – defined as one ten-millionth of the shortest distance from the North Pole to the equator [[Paris meridian|passing through Paris]], assuming an Earth [[flattening]] of {{Sfrac|1|334}}.

The historical French official standard of the metre was made available in the form of the {{lang|fr|[[Mètre des Archives]]}}, a platinum bar held in Paris. During the mid nineteenth century, following the [[American Revolution]] and [[Decolonization of the Americas|independence of Latin America]], the metre gained adoption in [[Americas]], particularly in scientific usage, and it was officially established as an international measurement unit by the [[Metre Convention]] of 1875 at the beginning of the [[Second Industrial Revolution]].

The {{lang|fr|[[Mètre des Archives]]}} and its copies such as the Committee Meter were replaced from 1889 at the initiative of the [[International Association of Geodesy|International Geodetic Association]] by thirty [[platinum-iridium]] bars kept across the globe.<ref>{{Cite web|url=https://www.bipm.org/fr/measurement-units/history-si/international-metre-commission.html|title=BIPM – Commission internationale du mètre|website=www.bipm.org|access-date=13 November 2019|archive-date=18 November 2018|archive-url=https://web.archive.org/web/20181118230835/https://www.bipm.org/fr/measurement-units/history-si/international-metre-commission.html|url-status=dead}}</ref> A better [[standardization]] of the new prototypes of the metre  and their comparison with each other and with the historical standard involved the development of specialized measuring equipment and the definition of a reproducible temperature scale.<ref name="la définition du mètre">{{Cite web |title=BIPM – la définition du mètre |url=https://www.bipm.org/fr/measurement-units/history-si/evolution_metre.html |access-date=17 June 2019 |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>

Progress in science finally allowed the definition of the metre to be dematerialized; thus in 1960 a new definition based on a specific number of wavelengths of light from a specific transition in [[krypton-86]] allowed the standard to be universally available by measurement. In 1983 this was updated to a length defined in terms of the [[speed of light]]; this definition was reworded in 2019:<ref name="2019metre">{{citation 
 |title = 9th edition of the SI Brochure
 |publisher = [[BIPM]]
 |url = https://www.bipm.org/en/publications/si-brochure/
 |date = 2019
 |page=131
 |df = dmy-all
 }}</ref>

{{blockquote|The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the [[speed of light in vacuum]] {{mvar|c}} to be {{val|299792458}} when expressed in the unit m⋅s{{sup|−1}}, where the second is defined in terms of the caesium frequency {{math|Δ''&nu;''<sub>Cs</sub>}}.}}

Where older traditional length measures are still used, they are now defined in terms of the metre – for example the [[yard]] has since 1959 officially been defined as exactly 0.9144 metre.<ref name="Nelson">{{cite journal |last=Nelson |first=Robert A. |date=December 1981 |title=Foundations of the international system of units (SI) |url=https://www.physics.umd.edu/deptinfo/facilities/lecdem/services/refs/refsa/Nelson-FoundationsSI.pdf |journal=[[The Physics Teacher]] |volume=19 |issue=9 |pages=596–613 |bibcode=1981PhTea..19..596N |doi=10.1119/1.2340901}}</ref>

== Universal measure: the metre linked to the figure of the Earth ==
[[File:Obs-Paris-meridienne.jpg|thumb|The Meridian room of the [[Paris Observatory]] (or Cassini room): the [[Paris meridian]] is drawn on the ground.|left]]

[[Galileo]] discovered [[gravitational acceleration]] to explain the fall of bodies at the surface of the Earth.<ref>{{Cite web |title=Museo Galileo - In depth - Gravitational acceleration |url=https://catalogue.museogalileo.it/indepth/GravitationalAcceleration.html |access-date=2023-12-29 |website=catalogue.museogalileo.it}}</ref> He also observed the regularity of the period of swing of the [[pendulum]] and that this period depended on the length of the pendulum.<ref>{{Cite web |title=Museo Galileo - In depth - Pendulum |url=https://catalogue.museogalileo.it/indepth/Pendulum.html |access-date=2023-12-29 |website=catalogue.museogalileo.it}}</ref>

[[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>
{{cite book
 |title=L'exploration du système solaire
 |last=Bond, Peter
 |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> They both also used a determination of the size of the Earth, then considered as a sphere, by [[Jean Picard]] through [[Triangulation (surveying)|triangulation]] of [[Paris meridian]].<ref name=":3" /><ref name="Levallois" /> In 1671, Jean Picard also measured the length of a [[seconds pendulum]] at [[Paris Observatory]] and proposed this unit of measurement to be called the astronomical radius (French: ''Rayon Astronomique'').<ref>{{Cite book |last=Picard |first=Jean (1620–1682) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/btv1b7300361b |title=Mesure de la terre [par l'abbé Picard] |date=1671 |pages=3–5 |language=EN}}</ref>{{sfn|Bigourdan|1901|pp=8,158–159}} In 1675, [[Tito Livio Burattini]] suggested the term ''{{Lang|it|metro cattolico}}'' meaning universal measure for this unit of length, but then it was discovered that the length of a seconds pendulum varies from place to place.<ref name="Earth-1911" /><ref>{{Cite book |last1=Poynting |first1=John Henry |url=https://archive.org/details/bub_gb_TL4KAAAAIAAJ |title=A Textbook of Physics |last2=Thomson |first2=Joseph John |date=1907 |publisher=C. Griffin |pages=[https://archive.org/details/bub_gb_TL4KAAAAIAAJ/page/n30 20] |language=en}}</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=2021-08-03 |language=fr |date=25 March 2021}}</ref><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=2021-08-02 |language=en}}</ref>

[[File:Repsold.jpg|thumb|[[Gravimeter]] with variant of [[Repsold–Bessel pendulum]]]]

[[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 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">
{{cite journal
 |last=Perrier |first=Général
 |date=1935
 |title=Historique Sommaire De La Geodesie
 |url=https://www.jstor.org/stable/43861533
 |journal=Thalès
 |volume=2 |pages=117–129, p. 128
 |issn=0398-7817
 |jstor=43861533
}}</ref><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 journal
 |last=Touzery |first=Mireille
 |date=2008-07-03
 |title=Émilie Du Châtelet, un passeur scientifique au XVIIIe siècle
 |url=https://journals.openedition.org/histoire-cnrs/7752
 |journal=La revue pour l'histoire du CNRS
 |language=fr
 |issue=21
 |doi=10.4000/histoire-cnrs.7752
 |issn=1298-9800
 |doi-access=free
}}</ref><ref name="Earth-1911">
{{cite EB1911
 |wstitle=Earth, Figure of the
 |volume= 8
 |pages=801–813
 |short=1
}}</ref><ref name="Levallois" />

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 |journal=Vermessung, 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&nbsp;– 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>

=== Meridional definition ===
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 {{val|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>

=== Early adoption of the metre as a scientific unit of length: the forerunners ===
[[File:HasslerCollection 001.jpg|left|thumb|Triangulation near [[New York City]], 1817]]

In 1816, [[Ferdinand Rudolph Hassler]] was appointed first Superintendent of the [[United States Coast and 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 October 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 |last1=American Philosophical Society. |url=https://www.biodiversitylibrary.org/item/26092 |title=Transactions of the American Philosophical Society |last2=Society |first2=American Philosophical |last3=Poupard |first3=James |date=1825 |volume=new ser.:v.2 (1825) |location=Philadelphia [etc.] |pages=234–278}}</ref><ref name="Cajori-1921" /><ref name="Clarke-1873" /><ref>{{cite web |url=https://celebrating200years.noaa.gov/historymakers/hassler/welcome.html |title=NOAA 200th Top Tens: History Makers: Ferdinand Rudolph Hassler |publisher=National Oceanic and Atmospheric Administration |location=US |date=2024-03-19 |access-date=2024-10-17}}</ref>

In 1830, Hassler became head of the Office of Weights and Measures, which became a part of the Survey of the Coast. 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="Parr-2006" />

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 [[International Meteorological Organisation]] whose president, the Swiss meteorologist and physicist, [[Heinrich von Wild]] would represent [[Russian Empire|Russia]] at the [[International Committee for Weights and Measures]] (CIPM).<ref name="Débarbat-2019">{{Cite journal |last1=Débarbat |first1=Suzanne |last2=Quinn |first2=Terry |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 |series=The new International System of Units / Le nouveau Système international d’unités |volume=20 |issue=1 |pages=6–21 |doi=10.1016/j.crhy.2018.12.002 |bibcode=2019CRPhy..20....6D |s2cid=126724939 |issn=1631-0705|doi-access=free }}</ref><ref name="Enc. Universalis-1996" /><ref>{{Cite web |date=2015-12-08 |title=History of IMO |url=https://public-old.wmo.int/en/about-us/who-we-are/history-IMO |archive-url=https://web.archive.org/web/20231218170901/https://public-old.wmo.int/en/about-us/who-we-are/history-IMO |url-status=dead |archive-date=18 December 2023 |access-date=2023-10-07 |website=public.wmo.int |language=en}}</ref><ref>{{Cite web |title=Wild, Heinrich |url=https://hls-dhs-dss.ch/articles/028982/2014-11-11/ |access-date=2023-10-07 |website=hls-dhs-dss.ch |language=de}}</ref><ref name="Von Wild-1903">''Heinrich VON WILD (1833–1902)'' in COMlTÉ INTERNATIONAL DES POIDS ET MESURES. PROCÈS-VERBAUX DES SÉANCES. DEUXIÈME SÉRIE. TOME II. SESSION DE 1903. pp. 5–7.</ref><ref name="Quinn-2012" />

In 1834, Hassler, measured at [[Fire Island]] the first [[Baseline (surveying)|baseline]] of the Survey of the Coast, shortly before [[Louis Puissant]] declared to the French Academy of Sciences in 1836 that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in the [[Arc measurement|meridian arc measurement]], which had been used to determine the length of the metre. Errors in the method of calculating the length of the [[Paris meridian]] were taken into account by Bessel when he proposed his [[Earth ellipsoid|reference ellipsoid]] in 1841.<ref>{{Cite book |last1=Hassler |first1=Harriet |url=http://archive.org/details/ferdinandrudolph1068hass |title=Ferdinand Rudolph Hassler (1770–1843) |last2=Burroughs |first2=Charles A. |date=2007 |others=NIST Research Library |pages=51–52}}</ref><ref name="Lebon-1899" /><ref>{{Cite book |last=Puissant |first=Louis (1769–1843) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k5323385b |title=Nouvelle détermination de la distance méridienne de Montjouy à Formentera, dévoilant l'inexactitude de celle dont il est fait mention dans la base du système métrique décimal, par M. Puissant,... lu à l'Académie des sciences, le 2 mai 1836 |language=EN}}</ref><ref name="Viik-2006" /><ref name=":1" />

[[File:Appareil Ibáñez.jpg|thumb|Ibáñez apparatus calibrated on the metric Spanish Standard and used at [[Aarberg]], in [[canton of Bern]], [[Switzerland]]]]

[[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" />

[[File:Struve Geodetic Arc-zoom-en.svg|thumb|Struve Geodetic Arc|left]]

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'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 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
more reliable measurements would have given a different value for the definition of this international standard. That does not invalidate the metre in any way but highlights the fact that continuing improvements in instrumentation made better measurements of the earth’s size possible.|title=Nomination of the STRUVE GEODETIC ARC for inscription on the WORLD HERITAGE LIST|source=p. 40}}

[[File:Britannica_Figure_of_the_Earth.jpg|thumb|'''West Europe–Africa Meridian-arc''': a meridian arc extending from the [[Shetland Islands]], through Great Britain, France and Spain to El Aghuat in Algeria, whose parameters were calculated from surveys carried out in the mid to late 19th century. It yielded a value for the equatorial radius of the earth ''a'' = 6 377 935 metres, the ellipticity being assumed as 1/299.15. The radius of curvature of this arc is not uniform, being, in the mean, about 600 metres greater in the northern than in the southern part. [[Prime meridian (Greenwich)|Greenwich meridian]] is depicted rather than [[Paris meridian]].]]

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 did 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]] 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" />

As early as 1861, [[Johann Jacob Baeyer]] sent a memorandum to the King of [[Prussia]] recommending international collaboration in [[Central Europe]] with the aim of determining the shape and dimensions of the Earth. At the time of its creation, the association had sixteen member countries: [[Austrian Empire]], [[Belgium|Kingdom of Belgium]], [[Denmark]], seven German states ([[Grand Duchy of Baden]], [[Kingdom of Bavaria]], [[Kingdom of Hanover]], [[Mecklenburg]], [[Kingdom of Prussia]], [[Kingdom of Saxony]], [[Saxe-Coburg and Gotha]]), [[Kingdom of Italy]], [[Netherlands]], [[Russian Empire]] (for [[Poland]]), [[Union between Sweden and Norway|United Kingdoms of Sweden and Norway]], as well as [[Switzerland]]. The [[International Association of Geodesy|Central European Arc Measurement]] created a Central Office, located at the Prussian Geodetic Institute, whose management was entrusted to Johann Jacob Baeyer.<ref>{{Cite journal |last=Levallois |first=J. J. |date=1980-09-01 |title=Notice historique |url=https://doi.org/10.1007/BF02521470 |journal=Bulletin géodésique |language=fr |volume=54 |issue=3 |pages=248–313 |doi=10.1007/BF02521470 |bibcode=1980BGeod..54..248L |s2cid=198204435 |issn=1432-1394 }}</ref><ref name="Torge-2016" />

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 |journal=Bulletin 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" />

[[Spain]] and [[Portugal]] joined the [[International Association of Geodesy|European Arc Measurement]] in 1866. [[Second French Empire|French Empire]] hesitated for a long time before giving in to the demands of the Association, which asked the French geodesists to take part in its work. It was only after the [[Franco-Prussian War]], that [[Charles-Eugène Delaunay]] represented [[France]] at the Congress of [[Vienna]] in 1871. In 1874, [[Hervé Faye]] was appointed member of the Permanent Commission which was presided by Carlos Ibáñez e Ibáñez de Ibero.<ref name="Lebon-1899">{{Cite book |last=Lebon |first=Ernest (1846–1922) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k949666 |title=Histoire abrégée de l'astronomie / par Ernest Lebon,... |date=1899 |pages=168–171 |language=EN}}</ref><ref>{{Cite journal |last1=Drewes |first1=Hermann |last2=Kuglitsch |first2=Franz |last3=Adám |first3=József |last4=Rózsa |first4=Szabolcs |date=2016 |title=The Geodesist's Handbook 2016 |url=http://link.springer.com/10.1007/s00190-016-0948-z |journal=Journal of Geodesy |language=en |volume=90 |issue=10 |pages=914 |doi=10.1007/s00190-016-0948-z |bibcode=2016JGeod..90..907D |s2cid=125925505 |issn=0949-7714}}</ref><ref name="CEM-2013" /><ref name="BEG-1868" />

The International Geodetic Association gained global importance with the accession of [[Chile]], [[Mexico]] and [[Japan]] in 1888; [[Argentina]] and [[United States|United-States]] in 1889; and [[British Empire]] in 1898. The convention of the International Geodetic Association expired at the end of 1916. It was not renewed due to the [[World War I|First World War]]. However, the activities of the [[International Latitude Service]] were continued through an {{Lang|fr|Association Géodesique réduite entre États neutres}} thanks to the efforts of [[H. G. van de Sande Bakhuyzen|H.G. van de Sande Bakhuyzen]] and Raoul Gautier (1854–1931), respectively directors of [[Leiden Observatory]] and [[Geneva Observatory]].<ref name="Soler-1997" /><ref name="Torge-2016" />

=== International prototype metre bar ===
[[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) in collaboration with [[Johnson Matthey|Johnson Mattey]] and given to the United States, which served as the standard for American cartography from 1890 replacing the Committee Meter, an authentic copy of the ''Mètre des Archives'' produced in 1799 in Paris, which [[Ferdinand Rudolph Hassler]] had brought to the United States in 1805|left]]

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, along 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=9, 11, 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" />

[[File:Metric standards Rijksmuseum.jpg|thumb|Historic Dutch replicas of metric standards in the collection of Rijksmuseum, Amsterdam: iron metre with case constructed by Étienne Lenoir in 1799, copper grave kilogram with case (1798), copper volume measures (1829)]]

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 |journal=Bulletin 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" />

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 questioned 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. This assertion was particularly worrying, because when the primary Imperial [[yard]] standard had partially been destroyed in 1834, a new standard of reference was constructed using copies of the "Standard Yard, 1760", instead of the pendulum's length as provided for in the [[Weights and Measures Act 1824]], because the pendulum method proved unreliable. Nevertheless [[Ferdinand Rudolph Hassler]]'s use of the metre and the creation of the Office of Standard Weights and Measures as an office within the Coast Survey contributed to the introduction of the [[Metric Act of 1866]] allowing the use of the metre in the United States, and preceded 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 for weights and measures".<ref name="Wolf 1882 20, 32" /><ref name=":5">{{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 name="BEG-1868" /><ref name="Quinn-2019">{{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 |journal=Annalen der Physik |language=en |volume=531 |issue=5 |pages=2 |bibcode=2019AnP...53100355Q |doi=10.1002/andp.201800355 |issn=1521-3889 |s2cid=125240402|doi-access=free }}</ref><ref name="Clarke-1867" /><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 |bibcode=1840AN.....17..193B |doi=10.1002/asna.18400171302 |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="Guillaume-1916">{{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><ref name=":4" />

[[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.|left]]

In 1855, the Dufour map (French: ''Carte Dufour''), the first [[Topographic Map of Switzerland|topographic map of Switzerland]] for which the metre was adopted as the unit of length, won the gold medal at the Exposition Universelle.<ref>{{Cite news |last=Abplanalp |first=Andrej |date=2019-07-14 |title=Henri Dufour et la carte de la Suisse |url=https://blog.nationalmuseum.ch/fr/2019/07/dufour-le-cartographe/ |archive-url=http://web.archive.org/web/20241225163218/https://blog.nationalmuseum.ch/fr/2019/07/dufour-le-cartographe/ |archive-date=2024-12-25 |access-date=2025-01-25 |work=Musée national - Blog sur l'histoire suisse |language=de-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> The Spanish standard a geodetic measuring device calibrated on the metre devised by Carlos Ibáñez e Ibáñez de Ibero and [[Frutos Saavedra Meneses]] was also displayed by [[Jean Brunner]] at the Exhibition.<ref>{{Cite web |title= |url=https://www.unav.es/gep/TheBrunnersCartaParis.pdf |archive-url=http://web.archive.org/web/20241203014633/https://www.unav.es/gep/TheBrunnersCartaParis.pdf |archive-date=2024-12-03 |access-date=2025-01-25 |website=www.unav.es}}</ref> On the sidelines of the [[Exposition Universelle (1855)]] and the second [[International Statistical Institute|Congress of Statistics]] held in Paris, an association with a view to obtaining a uniform decimal system of measures, weights and currencies was created in 1855.<ref name="Quinn-2012" /> Under the impetus of this association, a Committee for Weights and Measures and Monies (French: ''Comité des poids, mesures et monnaies'') was created during the [[Exposition Universelle (1867)]] in Paris and called for the international adoption of the metric system.<ref name=":6">{{Cite web |title=History – The BIPM 150 |url=https://thebipm150.org/history/ |access-date=2025-01-24 |language=}}</ref><ref name="Quinn-2012" />

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="Hirsch-1891">{{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=2017-05-22 |website=Bureau International des Poids et Mesures |pages=4, 8}}</ref><ref>{{Cite web |title=BIPM – International Metre Commission |url=http://www.bipm.org/en/measurement-units/history-si/international-metre-commission.html |access-date=2017-05-26 |website=www.bipm.org}}</ref><ref name="IAG">{{Cite web |title=A Note on the History of the IAG |url=http://www.iag-aig.org/index.php?tpl=text&id_c=80&id_t=143 |access-date=2017-05-26 |website=IAG Homepage}}</ref> According to a preliminary proposal made in [[Neuchâtel]] the precedent year, the General Conference recommended the adoption of the metre in replacement of the toise of Bessel, the creation of an International Metre Commission, and the foundation of a World institute for the comparison of geodetic standards, the first step towards the creation of the [[International Bureau of Weights and Measures]].<ref name="Ross-James">{{Cite journal |last1=Ross |first1=Clarke Alexander |last2=James |first2=Henry |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="Hirsch-1891" /><ref name="IAG" /><ref name="Brunner">{{Cite web |last=Brunner |first=Jean |date=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/bpt6k3001w |access-date=2019-05-15 |website=Gallica |pages=150–153 |language=FR}}</ref><ref>{{cite book |last=Guillaume |first=Charles-Édouard |title=La Création du Bureau International des Poids et Mesures et son Œuvre |publisher=Gauthier-Villars |year=1927 |location=Paris |page=321 |trans-title=The creation of the International Bureau of Weights and Measures and its work}}</ref>

Hassler's metrological and geodetic work also had a favourable response in Russia.<ref name="Parr-2006">{{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 |pmc=4654608 |pmid=27274915 |via=NIST}}</ref><ref name="Cajori-1921">{{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> 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]], whose theorem has long supported the assumption of an ellipsoid with three unequal axes for the figure of the Earth, inviting his French counterpart to undertake joint action to ensure the universal use of the [[metric system]] in all scientific work.<ref name="Guillaume-1916" /><ref name="Earth-1911" /> The [[French Academy of Sciences]] and the [[Bureau des Longitudes]] in Paris drew the attention of the French government to this issue. In November 1869, [[Napoleon III]] issued invitations to join the International Metre Commission.<ref name=":6" />

On 6 May 1873 during the 6th session of the French section of the Metre Commission, [[Henri Étienne Sainte-Claire Deville]] cast a 20-kilogram platinum-iridium ingot from Matthey in his laboratory at the [[École normale supérieure (Paris)]]. On 13 May 1874, 250 kilograms of platinum-iridium to be used for serveral national prototypes of the metre was cast at the [[Conservatoire national des arts et métiers]].<ref name=":6" /> 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 president of the Permanent Committee of the International Metre Commission, [[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="NIST-2003">[[#nistmetre|National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter)]]</ref><ref name="Pérard-1957" /><ref name="Quinn-2012" /><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 |access-date=2021-09-20 |publisher=Diplomatische Dokumente der Schweiz {{!}} Documents diplomatiques suisses {{!}} Documenti diplomatici svizzeri {{!}} Diplomatic Documents of Switzerland {{!}} Dodis |language=fr}}</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="NIST-2003" />

In 1883, at its seventh General Conference in Rome, the [[International Association of Geodesy|International Geodetic Association]] would also consider the choice of an [[Prime meridian|international prime meridian]] and would propose the [[Prime meridian (Greenwich)|Greenwich meridian]] hoping that Great Britain might respond in favour of the unification of weights and measures, by adhering to the [[Metre Convention]].

== Metrology and paradigm shift in physics ==
[[File:Komplet invarskih žica.png|thumb|Invar wire baseline apparatus]]

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>

In 1921, the Nobel Prize in Physics was awarded to another Swiss scientist, [[Albert Einstein]], who following [[Michelson–Morley experiment]] had questioned the [[luminiferous aether]] in 1905, just as [[Isaac Newton|Newton]] had questioned [[Mechanical explanations of gravitation|Descartes' Vortex theory]] in 1687 after [[Jean Richer]]'s pendulum experiment in [[Cayenne]], [[French Guiana]].<ref>{{Cite web |last=Huet |first=Sylvestre |title=Einstein, le révolutionnaire de la lumière |url=https://www.liberation.fr/week-end/2005/02/12/einstein-le-revolutionnaire-de-la-lumiere_509445/ |access-date=2023-10-07 |website=Libération |language=fr}}</ref><ref>{{Cite book |last=Ferreiro |first=Larrie D. |url=https://play.google.com/store/books/details?id=p-Y3DgAAQBAJ |title=Measure of the Earth: The Enlightenment Expedition That Reshaped Our World |date=2011-05-31 |publisher=Basic Books |isbn=978-0-465-02345-5 |pages=19–23 |language=en}}</ref><ref name=":3">{{Cite web |title=Lettres philosophiques/Lettre 15 - Wikisource |url=https://fr.wikisource.org/wiki/Lettres_philosophiques/Lettre_15 |access-date=2023-10-07 |website=fr.wikisource.org |language=fr}}</ref><ref name="Earth-1911" />

Furthermore, [[special relativity]] changed conceptions of [[time]] and [[mass]], while [[general relativity]] changed that of [[space]]. According to Newton, space was [[Euclidean geometry|Euclidean]], infinite and without boundaries and bodies gravitated around each other without changing the structure of space. [[Introduction to general relativity|Einstein's theory of gravity]] states, on the contrary, that the mass of a body has an effect on all other bodies while modifying the structure of space. A massive body induces a curvature of the space around it in which the path of light is inflected, as was demonstrated by the displacement of the position of a star observed near the Sun during an eclipse in 1919.<ref>Stephen Hawking, Paris, Dunod, 2003, 2014, 929 <abbr>p.</abbr>, p. 816–817</ref>

=== Wavelength definition ===
In 1873, [[James Clerk Maxwell]] suggested that light emitted by an element be used as the standard both for the unit of length 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> About the unit of length he wrote:

{{blockquote|text=In the present state of science the most universal standard of length which we could assume would be the wave length in vacuum of a particular kind of light, emitted by some widely diffused substance such as sodium, which has well-defined lines in its spectrum. Such a standard would be independent of any changes in the dimensions of the earth, and should be adopted by those who expect their writings to be more permanent than that body.|author=James Clerk Maxwell|title=''[[A Treatise on Electricity and Magnetism]]''|source=3rd edition, Vol. 1, p. 3}}

[[Charles Sanders Peirce]]'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>

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}}&nbsp;[[wavelength]]s of the [[orange (colour)|orange]]-[[red]] [[emission line]] in the [[electromagnetic spectrum]] of the [[krypton-86]] [[atom]] in [[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" /><ref>{{Cite web|last=BIPM|date=20 May 2019|title=Mise en pratique for the definition of the meter in the SI|url=https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf/0e011055-9736-d293-5e56-b8b1b267fd68?version=1.8&t=1637238031486&download=false|website=BIPM}}</ref>
:: The metre is the length of the path travelled by light in vacuum during a time interval of {{gaps|1|/|299|792|458}} of a second.

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]].

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=2011-12-16}} 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=2011-12-16}}</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 vacuum, and converting the wavelengths in 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=2012-01-22}}</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=2011-12-17 |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 ''&lambda;'' 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" />

The CIPM issued a clarification in 2002:
{{Blockquote|text=Its definition, therefore, applies only within a spatial extent sufficiently small that the effects of the non-uniformity of the gravitational field can be ignored (note that, at the surface of the Earth, this effect in the vertical direction is about 1 part in {{val|e=16}} per metre). In this case, the effects to be taken into account are those of special relativity only.}}

== 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 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>
|-
|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|pp=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&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 |archive-date=3 October 2015 |archive-url=https://web.archive.org/web/20151003055350/http://www.entreprises.gouv.fr/metrologie/histoire-metre |url-status=dead }}</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" />
|-
|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&nbsp;mm (1&nbsp;cm) diameter, symmetrically placed in the same horizontal plane at a distance of 571&nbsp;mm (57.1&nbsp;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 [[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 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>
|-
|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
|-
<!--
REMOVED THIS ENTRY AS THIS INFO IS SCREWED UP. BESSEL WOULD HAVE BEEN 8 YEARS OLD WHEN CARRYING OUT THIS. NEEDS TO BE LOOKED AT.
| {{sfrac|10 000 000}} part of the [[Circular sector|quadrant]] along the [[meridian (geography)|meridian]], astronomical measure by [[Friedrich Bessel|Bessel]] (443.44 lines)
| 1792
| {{val|0.5|–|0.1|u=mm}}
| {{val|e=-4}}
|-
-->
| {{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)
| 1795
| {{val|500|–|100|u=um}}
| {{val|e=-4}}
|-
| First prototype ''{{lang|fr|[[History of the metre#Mètre des Archives|Mètre des Archives]]}}'' platinum bar standard
| 1799
| {{val|50|–|10|u=um}}
| {{val|e=-5}}
|-
| Platinum–iridium bar at melting point of ice (1st [[CGPM]])
| 1889
| {{val|0.2|–|0.1|u=um}}
| {{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|1650763.73}} wavelengths of light from a specified transition in [[krypton-86]] (11th CGPM)
| 1960
| {{val|4|u=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 vacuum in {{sfrac|{{val|299792458}}}}&nbsp;second (17th CGPM)
| 1983
| {{val|0.1|u=nm}}
| {{val|e=-10}}
|}

==References==
{{Reflist}}