Metre

==== 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 lignes. This value was set by legislation on 7 April 1795.<ref name="Larousse" /><ref name="RNMF" /><ref name="Débarbat-1799" /><ref name=":0">{{Cite book |last=Delambre |first=Jean-Baptiste (1749–1822) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k110160s |title=Grandeur et figure de la terre / J.-B.-J. Delambre; ouvrage augmenté de notes, de cartes et publié par les soins de G. Bigourdan,... |date=1912 |pages=202–203, 2015, 141–142, 178 |language=EN}}</ref><ref>{{Cite web |title=Comprendre – Histoire de l'observatoire de Paris - Pierre-François-André Méchain |url=https://promenade.imcce.fr/fr/pages2/297.html |access-date=2023-10-15 |website=promenade.imcce.fr}}</ref>

In 1799, a commission including [[Johann Georg Tralles|Johan Georg Tralles]], [[Jean Henri van Swinden]], [[Adrien-Marie Legendre]] and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of the [[Triangulation (surveying)|triangulation]] between these two towns and determined the portion of the distance from the North Pole to the Equator it represented. Pierre Méchain's and Jean-Baptiste Delambre's measurements were combined  with the results of the [[French Geodesic Mission to the Equator|Spanish-French geodetic mission]] and a value of {{Sfrac|1|334}} was found for the Earth's flattening. However, French astronomers knew from earlier estimates of the Earth's flattening that different meridian arcs could have different lengths and that their curvature could be irregular. The distance from the North Pole to the Equator was then extrapolated from the measurement of the Paris meridian arc between Dunkirk and Barcelona and was determined as 5 130 740 toises. As the metre had to be equal to one ten-millionth of this distance, it was defined as 0.513074 toise or 3 feet and 11.296 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>