Editing Metre Convention (section)

=== European geodesy ===
In Europe, except Spain,<ref name="Brunner-18572" /> surveyors continued to use measuring instruments calibrated on the Toise of Peru.<ref name="Quinn-2012">{{Cite book |last=Quinn |first=T. J. |title=From artefacts to atoms: the BIPM and the search for ultimate measurement standards |date=2012 |publisher=Oxford University Press |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> 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.<ref>{{Cite web |title=Borda et le système métrique |url=https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |archive-url=https://web.archive.org/web/20230829055653/https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |archive-date=29 August 2023 |access-date=2023-08-29 |website=Association Mesure Lab |language=fr-FR}}</ref><ref name="Viik-2006">{{Cite news |last=Viik |first=T |date=2006 |title=F. W. Bessel and geodesy |work=Struve Geodetic Arc, 2006 International Conference, The Struve Arc and Extensions in Space and Time, Haparanda and Pajala, Sweden, 13–15 August 2006 |pages=10, 6 |citeseerx=10.1.1.517.9501}}</ref> A French scientific instrument maker, [[Jean Nicolas Fortin]], 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 Wilhelm Bessel in 1823. In 1831, [[Henri-Prudence Gambey]] also realised a copy of the Toise of Peru which was kept at [[Altona Observatory]].<ref>{{Cite book |last=Wolf |first=M. C |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><ref>{{Cite book |last=Baeyer |first=Johann Jacob |title=Grösse und Figur der Erde |publisher=Georg Reimer |year=1861 |location=Berlin |publication-date=1861 |pages=87–94 |language=de}}</ref>

In the second half of the 19th century, the creation of the [[International Association of Geodesy|Central European Arc Measurement]] ({{Langx|de|Mitteleuropäische Gradmessung}}) would mark, following [[Carl Friedrich Gauss]],<ref>{{Cite book |last=Tardi |first=Pierre (1897-1972) Auteur du texte |url=https://gallica.bnf.fr/ark:/12148/bpt6k3355272d/f74.item |title=Traité de géodésie / par le capitaine P. Tardi ; préface par le général G. Perrier |date=1934 |pages=34 |language=EN}}</ref><ref name="Quinn-20122" /> Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve examples,<ref name=":9">{{Cite EB1911|wstitle=Earth, Figure of the|volume=8|last1=Clarke|first1=Alexander Ross|author-link1=Alexander Ross Clarke|last2=Helmert|first2=Friedrich Robert|author-link2=Friedrich Robert Helmert|pages=801-813|short=1}}</ref> the systematic adoption of more rigorous methods among them the application of the [[least squares]] in geodesy.<ref>{{Cite web |title=Mesure du 1er mètre: une erreur qui changea le monde |url=https://www.techniques-ingenieur.fr/actualite/articles/mesure-du-1er-metre-une-erreur-qui-changea-le-monde-2715/ |access-date=December 30, 2020 |website=Techniques de l'Ingénieur |language=fr-FR}}</ref><ref name="Lebon-1899" /> It 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]].<ref name="Clarke-1867" /> 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>

In 1866, an 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,<ref name="Clarke-1867" /> 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.<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 |page=193 |bibcode=1840AN.....17..193B |doi=10.1002/asna.18400171302 |issn=0004-6337}}</ref> In fact, the length of Bessel's Toise, which according to the then legal ratio between the metre and the Toise of Peru, should be equal to 1.9490348 m, would be found to be 26.2·10<sup>-6</sup> m greater during measurements carried out by [[Justin-Mirande René Benoit|Jean-René Benoît]] at the International Bureau of Weights and Measures. It was the consideration of the divergences between the different toises used by geodesists that led the [[International Association of Geodesy|European Arc Measurement]] ({{langx|de|links=no|Europäische Gradmessung}} ) to consider, at the meeting of its Permanent Commission in Neuchâtel in 1866, the founding 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>Guillaume, Charles-Édouard (1927). ''La Création du Bureau International des Poids et Mesures et son Œuvre'' [''The creation of the International Bureau of Weights and Measures and its work'']. Paris: Gauthier-Villars. p. 129-130.</ref><ref name="Pérard-1957" /> [[Spain]] joined the [[International Association of Geodesy|European Arc Measurement]] at this meeting.<ref>{{Cite web |date=2013-06-22 |title=El General Ibáñez e Ibáñez de Ibero, Marqués de Mulhacén {{!}} Revista e-medida |url=https://www.e-medida.es/numero-4/el-general-ibanez-e-ibanez-de-ibero-marques-de-mulhacen/ |access-date=2025-04-08 |language=es}}</ref> In 1867 at the second General Conference of the European Arc Measurement held in [[Berlin]], the question of international standard of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.<ref name=":0">{{Cite web |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 |url-status=live |archive-url=https://web.archive.org/web/20170722002232/http://www.iag-aig.org/index.php?tpl=text&id_c=80&id_t=143 |archive-date=22 July 2017 |access-date=16 May 2017 |website=IAG Homepage}}</ref> The conference recommended the adoption of the metric system (replacing [[Friedrich Bessel|Bessel]]'s toise) and the creation of an International Metre Commission.<ref name=":0" />