Metre

==== 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 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" />

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° 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: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]].|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:Struve Geodetic Arc-zoom-en.svg|thumb|Struve Geodetic Arc]]

It was well known that by measuring the latitude of two stations in [[Barcelona]], Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he didn't dare to admit this inaccuracy.<ref>{{Cite web |title=c à Paris; vitesse de la lumière ... |url=http://expositions.obspm.fr/lumiere2005/triangulation_plus.html |access-date=2021-10-12 |website=expositions.obspm.fr}}</ref><ref>{{Cite book |last=Jouffroy |first=Achille de (1785-1859) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k6338674m |title=Dictionnaire des inventions et découvertes anciennes et modernes, dans les sciences, les arts et l'industrie.... 2. H–Z / recueillis et mis en ordre par M. le marquis de Jouffroy; publié par l'abbé Migne,... |date=1852–1853 |pages=419 |language=EN}}</ref><ref name=":0" /> This was later explained by clearance in the central axis of the [[repeating circle]] causing wear and consequently the [[zenith]] measurements contained significant systematic errors.<ref name="Schiavon-2004">Martina Schiavon. La geodesia y la investigación científica en la Francia del siglo XIX : la medida del arco de meridiano franco-argelino (1870–1895). ''Revista Colombiana de Sociología'', 2004, Estudios sociales de la ciencia y la tecnologia, 23, pp. 11–30.</ref> [[Polar motion]] predicted by [[Leonhard Euler|Leonard Euler]] and later discovered by [[Seth Carlo Chandler]] also had an impact on accuracy of latitudes' determinations.<ref>{{Cite journal |last1=Yokoyama |first1=Koichi |last2=Manabe |first2=Seiji |last3=Sakai |first3=Satoshi |date=2000 |title=History of the International Polar Motion Service/International Latitude Service |journal=International Astronomical Union Colloquium |language=en |volume=178 |pages=147–162 |doi=10.1017/S0252921100061285 |issn=0252-9211|doi-access=free }}</ref><ref name="Perrier-1935" /><ref>{{Cite web |title=Polar motion {{!}} Earth's axis, wobble, precession {{!}} Britannica |url=https://www.britannica.com/science/polar-motion |access-date=2023-08-27 |website=www.britannica.com |language=en}}</ref><ref name="Torge-2016">{{Cite journal |last=Torge |first=Wolfgang |date=2016 |editor-last=Rizos |editor-first=Chris |editor2-last=Willis |editor2-first=Pascal |title=From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916 |url=https://link.springer.com/chapter/10.1007/1345_2015_42 |journal=IAG 150 Years |series=International Association of Geodesy Symposia |language=en |location=Cham |publisher=Springer International Publishing |volume=143 |pages=3–18 |doi=10.1007/1345_2015_42 |isbn=978-3-319-30895-1}}</ref> Among all these sources of error, it was mainly an unfavourable [[vertical deflection]] that gave an inaccurate determination of Barcelona's [[latitude]] and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.<ref name="Levallois-1991" />

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 |website=E-Periodica |date=1892 |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 neutre}} 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" />