Arc measurement of Delambre and Méchain

The French Academy of Sciences, responsible for the concept and definition of the metre, was established in 1666. In the 18th century it had determined the first reasonably accurate distance to the Sun and organised important work in geodesy and cartography. In the 18th century, in addition to its significance for cartography, geodesy grew in importance as a means of empirically demonstrating Newton's law of universal gravitation, which Émilie du Châtelet promoted in France in combination with Leibniz's mathematical work and because the radius of the Earth was the unit to which all celestial distances were to be referred.{{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}}{{Cite book |last=Badinter |first=Élisabeth |url= |title=Les passions intellectuelles |date=2018 |publisher=Robert Laffont |isbn=978-2-221-20345-3 |series=Bouquins |location=Paris}}{{Cite EB1911|wstitle=Earth, Figure of the|volume=8|pages=801–813|short=1}} Among the results that would impact the definition of the metre: Earth proved to be an oblate spheroid through geodetic surveys in Ecuador and Lapland.{{Cite journal |last1=Débarbat |first1=Suzanne |last2=Quinn |first2=Terry |date=2019 |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 |url=https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2018.12.002/ |journal=Comptes Rendus. Physique |language=fr |volume=20 |issue=1–2 |pages=6–21 |doi=10.1016/j.crhy.2018.12.002 |issn=1878-1535}}{{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 |volume=143 |language=en |location=Cham |publisher=Springer International Publishing |pages=3–18 |doi=10.1007/1345_2015_42 |isbn=978-3-319-30895-1}}

The first reasonably accurate distance to the Sun was determined in 1684 by Giovanni Domenico Cassini. Knowing that directly measurements of the solar parallax were difficult he chose to measure the Martian parallax. Having sent Jean Richer to Cayenne, part of French Guiana, for simultaneous measurements, Cassini in Paris determined the parallax of Mars when Mars was at its closest to Earth in 1672. Using the circumference distance between the two observations, Cassini calculated the Earth-Mars distance, then used Kepler's laws to determine the Earth-Sun distance. His value, about 10% smaller than modern values, was much larger than all previous estimates.{{Cite book |last=Rossi |first=Elisabetta |url=http://www.fedoabooks.unina.it/public/presses/1/17_Rossi_1.pdf |title=Unveiling the Size of the Universe: The first Accurate Measurement of the Earth-Sun Distance by Giovanni Domenico Cassini |date=2024 |publisher=FedOA - Federico II University Press |doi=10.6093/978-88-6887-277-9}}

Although it had been known since classical antiquity that the Earth was spherical, by the 17th century, evidence was accumulating that it was not a perfect sphere. In 1672, Jean Richer found the first evidence that gravity was not constant over the Earth (as it would be if the Earth were a sphere); he took a pendulum clock to Cayenne, French Guiana and found that it lost {{frac|2|1|2}} minutes per day compared to its rate at Paris.{{cite book

| last = Poynting

| first = John Henry

|author2=Joseph John Thompson

| title = A Textbook of Physics, 4th Ed.

| publisher = Charles Griffin & Co.

| year = 1907

| location = London

| page = [https://archive.org/details/bub_gb_TL4KAAAAIAAJ/page/n30 20]

| url = https://archive.org/details/bub_gb_TL4KAAAAIAAJ

}}{{cite conference

| first = Lenzen

| last = Victor F.

|author2=Robert P. Multauf

| title = Paper 44: Development of gravity pendulums in the 19th century

| book-title = United States National Museum Bulletin 240: Contributions from the Museum of History and Technology reprinted in Bulletin of the Smithsonian Institution

| pages = 307

| publisher = Smithsonian Institution Press

| year = 1964

| location = Washington

| url = https://books.google.com/books?id=A1IqAAAAMAAJ&pg=RA2-PA307

| access-date = 2009-01-28}} This indicated the acceleration of gravity was less at Cayenne than at Paris. Pendulum gravimeters began to be taken on voyages to remote parts of the world, and it was slowly discovered that gravity increases smoothly with increasing latitude, gravitational acceleration being about 0.5% greater at the geographical poles than at the Equator.

In 1687, Isaac Newton had published in the Principia as a proof that the Earth was an oblate spheroid of flattening equal to {{sfrac|1|230}}.Isaac Newton: [https://archive.org/details/bub_gb_KaAIAAAAIAAJ/page/n408 Principia, Book III, Proposition XIX, Problem III], translated into English by Andrew Motte. A searchable modern translation is available at [http://17centurymaths.com 17centurymaths]. Search the following [http://17centurymaths.com/contents/newton/book3s1.pdf pdf file] for 'spheroid'. This was disputed by some, but not all, French scientists. A meridian arc of Jean Picard was extended to a longer arc by Giovanni Domenico Cassini and his son Jacques Cassini over the period 1684–1718.{{cite book

|year=1880

|last=Clarke

|first=Alexander Ross

|author-link=Alexander Ross Clarke

|title=Geodesy

|url= https://archive.org/details/in.ernet.dli.2015.42772 |publisher=Clarendon Press

|location=Oxford

|oclc=2484948}}. Freely available online at [https://archive.org/details/cu31924004129650 Archive.org] and [https://www.forgottenbooks.com/en/books/Geodesy_10059832 Forgotten Books] ({{ISBN|9781440088650}}). In addition the book has been reprinted by [https://www.bookdepository.com/Geodesy-Alexander-Ross-Clarke/9781293262535 Nabu Press] ({{ISBN|978-1286804131}}), the first chapter covers the history of early surveys. The arc was measured with at least three latitude determinations, so they were able to deduce mean curvatures for the northern and southern halves of the arc, allowing a determination of the overall shape. The results indicated that the Earth was a prolate spheroid (with an equatorial radius less than the polar radius). To resolve the issue, the French Academy of Sciences (1735) undertook expeditions to Peru (Bouguer, Louis Godin, de La Condamine, Antonio de Ulloa, Jorge Juan) and to Lapland (Maupertuis, Clairaut, Camus, Le Monnier, Abbe Outhier, Anders Celsius). The resulting measurements at equatorial and polar latitudes confirmed that the Earth was best modelled by an oblate spheroid, supporting Newton. However, by 1743, Clairaut's theorem had completely supplanted Newton's approach.

Clairaut confirmed that Newton's theory that the Earth was ellipsoidal was correct, but that his calculations were in error, and he wrote a letter to the Royal Society of London with his findings.{{Cite book|title = The Problem of the Earth's Shape from Newton to Clairaut|last = Greenburg|first = John|publisher = Cambridge University Press|year = 1995|isbn = 0-521-38541-5|location = New York|pages = [https://archive.org/details/problemofearthss1995gree/page/132 132]|url = https://archive.org/details/problemofearthss1995gree/page/132}} The society published an article in Philosophical Transactions the following year, 1737.{{Cite journal|last1 = Clairaut|first1 = Alexis|last2 = Colson|first2 = John|date = 1737|title = An Inquiry concerning the Figure of Such Planets as Revolve about an Axis, Supposing the Density Continually to Vary, from the Centre towards the Surface|jstor = 103921|journal = Philosophical Transactions}} In it Clairaut pointed out (Section XVIII) that Newton's Proposition XX of Book 3 does not apply to the real earth. It stated that the weight of an object at some point in the earth depended only on the proportion of its distance from the centre of the earth to the distance from the centre to the surface at or above the object, so that the total weight of a column of water at the centre of the earth would be the same no matter in which direction the column went up to the surface. Newton had in fact said that this was on the assumption that the matter inside the earth was of a uniform density (in Proposition XIX). Newton realized that the density was probably not uniform, and proposed this as an explanation for why gravity measurements found a greater difference between polar regions and equatorial regions than what his theory predicted. However, he also thought this would mean the equator was further from the centre than what his theory predicted, and Clairaut points out that the opposite is true. Clairaut points out at the beginning of his article that Newton did not explain why he thought the earth was ellipsoid rather than like some other oval, but that Clairaut, and James Stirling almost simultaneously, had shown why the earth should be an ellipsoid in 1736.

Clairaut's article did not provide a valid equation to back up his argument as well. This created much controversy in the scientific community.

It was not until Clairaut wrote Théorie de la figure de la terre in 1743 that a proper answer was provided. In it, he promulgated what is more formally known today as Clairaut's theorem.

File:Anglo-French survey of 1784-1790.jpg.|left|296x296px]]

File:Reflecting circle-CnAM 1842-IMG 4998-gradient.jpg devised by Jean-Charles de Borda and constructed by Étienne Lenoir]]

Geodetic surveys found practical applications in French cartography and in the Anglo-French Survey, which aimed to connect Paris and Greenwich Observatories and led to the Principal Triangulation of Great Britain.{{Cite book|url=http://public.eblib.com/choice/publicfullrecord.aspx?p=418081|title=Full meridian of glory: perilous adventures in the competition to measure the Earth|last=Murdin|first=Paul|date=2009|publisher=Copernicus Books/Springer|isbn=978-0-387-75534-2|location=New York; London|language=en}}{{Cite journal|last1=Martin|first1=Jean-Pierre|last2=McConnell|first2=Anita|date=20 December 2008|title=Joining the observatories of Paris and Greenwich|journal=Notes and Records of the Royal Society|language=en|volume=62|issue=4|pages=355–372|doi=10.1098/rsnr.2008.0029|issn=0035-9149|doi-access=free}} The unit of length used by the French was the {{lang|fr|Toise de Paris}}, while the English one was the yard, which became the geodetic unit used in the British Empire.{{Cite journal |last=Portet |first=Pierre |date=2011 |title=La mesure de Paris |trans-title=The measure of Paris |url=https://halshs.archives-ouvertes.fr/halshs-01672844 |journal=HAL Open Science |language=fr |publisher=Laboratoire de Médiévistique Occidentale de Paris |via=Sciences de l'Homme et de la Société}}{{Cite journal |last1=Clarke |first1=Alexander Ross |last2=James |first2=Henry |date=1 January 1873 |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 |language=en |volume=163 |pages=445–469 |doi=10.1098/rstl.1873.0014 |issn=0261-0523 |doi-access=free}}{{Cite journal |last=Clarke |first=Alexander Ross |date=1 January 1867 |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 |journal=Philosophical Transactions of the Royal Society of London |language=en |volume=157 |pages=161–180 |doi=10.1098/rstl.1867.0010 |issn=0261-0523 |s2cid=109333769}}

In 1783 the director of the Paris Observatory, César-François Cassini de Thury, addressed a memoir to the Royal Society in London, in which he expressed grave reservations about the latitude and longitude measurements undertaken at the Royal Greenwich Observatory. He suggested that the correct values might be found by combining the Paris Observatory figures with a precise trigonometric survey between the two observatories. This criticism was roundly rejected by Nevil Maskelyne who was convinced of the accuracy of the Greenwich measurements but, at the same time, he realised that Cassini's memoir provided a means of promoting government funding for a survey which would be valuable in its own right.{{Cite journal |last1=Martin |first1=Jean-Pierre |last2=McConnell |first2=Anita |date=2008-10-21 |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 |volume=62 |issue=4 |pages=355–372 |doi=10.1098/rsnr.2008.0029}}

For the triangulation of the Anglo-French Survey, César-François Cassini de Thury was assisted by Pierre Méchain. They used the repeating circle, an instrument for geodetic surveying, developed from the reflecting circle by Étienne Lenoir in 1784. He invented it while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the equal of the great theodolite created by the renowned instrument maker, Jesse Ramsden. It would later be used to measure the meridian arc from Dunkirk to Barcelona by Jean Baptiste Delambre and Pierre Méchain as improvements in the measuring device designed by Borda and used for this survey also raised hopes for a more accurate determination of the length of the French meridian arc.

File:Dunkerque Belfort.JPG

From the French revolution of 1789 came an effort to reform measurement standards, leading ultimately to remeasure the meridian passing through Paris in order to define the metre.{{Cite book |last=Alder |first=Ken |title=The Values of Precision |chapter-url=https://www.degruyter.com/document/doi/10.1515/9780691218120-004/html |chapter=TWO A Revolution to Measure: The Political Economy of the Metric System in France |date=1995-12-31 |publisher=Princeton University Press |isbn=978-0-691-21812-0 |editor-last=Wise |editor-first=M. Norton |pages=39–71 |doi=10.1515/9780691218120-004}}{{rp|52}}

The question of measurement reform was placed in the hands of the French Academy of Sciences, who appointed a commission chaired by Jean-Charles de Borda. Instead of the seconds pendulum method, the commission of the French Academy of Sciences – whose members included Borda, Lagrange, Laplace, Monge and Condorcet – decided that the new measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris at the longitude of Paris pantheon, which became the central geodetic station in Paris.{{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}}{{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 |date=24 September 2018 |language=en}} Jean Baptiste Joseph Delambre otained the fundamental co-ordinates of the Pantheon by triangulating all the geodetic stations around Paris from the Pantheon's dome.{{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}}

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 km, or one-tenth of the total) could be surveyed with start- and end-points at sea level,{{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}} 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.{{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}}

The expedition would take place after the Anglo-French Survey, thus the French meridian arc, which would extend northwards across the United Kingdom, would also extend southwards to Barcelona, later to Balearic Islands. Jean-Baptiste Biot and François Arago would publish in 1821 their observations completing those of Delambre and Mechain. It was an account of the length's variations of portions of one degree of amplitude of the meridian arc along the Paris meridian as well as the account of the variation of the seconds pendulum's length along the same meridian between Shetland and the Balearc Islands.{{Cite book |last1=Biot |first1=Jean-Baptiste |url=https://gallica.bnf.fr/ark:/12148/bpt6k1510037p/f567.item |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, faisant suite au troisième volume de la Base du Système métrique |last2=Arago |first2=François |date=1821 |pages=523, 529 |language=fr |author-link1=Jean-Baptiste Biot |author-link2=François Arago |access-date=14 September 2018 |via=Gallica}}{{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 |page=46 |language=fr}}

The task of surveying the meridian arc fell to Pierre Méchain and Jean-Baptiste Delambre, and 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 Revolution: Méchain and Delambre, and later François 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.

File:Rodez-coquelicots480.JPG, seen here dominating the Rodez skyline at left.|186x186px|left]]

The project was split into two parts – the northern section of 742.7 km from the belfry of the Church of Saint-Éloi, Dunkirk to Rodez Cathedral which was surveyed by Delambre and the southern section of 333.0 km from Rodez to the Montjuïc Fortress, Barcelona which was surveyed by Méchain. Although Méchain's sector was half the length of Delambre, it included the Pyrenees and hitherto unsurveyed parts of Spain.{{cite book

|title = The Measure of all Things – The Seven-Year-Odyssey that Transformed the World |last= Alder |first= Ken |year= 2002 |publisher= Abacus |location= London |isbn= 0-349-11507-9 |pages= 227–230}}

Delambre measured a baseline of about 10 km (6,075.90 {{lang|fr|toises}}) in length along a straight road between Melun and Lieusaint. In an operation taking six weeks, the baseline was accurately measured using four platinum rods, each of length two {{lang|fr|toises}} (a {{lang|fr|toise}} being about 1.949 m). These measuring devices consisted of bimetallic rulers in platinum and brass fixed together at one extremity to assess the variations in length produced by any change in temperature.{{Cite news |last=Viik |first=T |date=2006 |title=F.W. Bessel and Geodesy |url=https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.517.9501 |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=6, 10 |citeseerx=10.1.1.517.9501}}{{Cite web |date=2023-08-29 |title=Borda et le système métrique - Association Mesure Lab |url=https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |access-date=2025-02-21 |archive-url=https://web.archive.org/web/20230829055653/https://mesurelab.fr/wp/metrologie/histoire-de-la-metrologie/borda-et-le-systeme-metrique/ |archive-date=2023-08-29}} Borda's double-toise N°1 became the main reference for measuring all geodetic bases in France. Intercomparisons of baseline measuring devices were essential, because of thermal expansion. Indeed, geodesists tried to accurately assess temperature of standards in the field in order to avoid temperature systematic errors.{{Cite journal |last=Guillaume |first=Ch-Ed |date=1906 |title=La mesure rapide des bases géodésiques |url=https://jphystap.journaldephysique.org/articles/jphystap/abs/1906/01/jphystap_1906__5__242_0/jphystap_1906__5__242_0.html |journal=Journal de Physique Théorique et Appliquée |language=fr |volume=5 |issue=1 |pages=242–263 |doi=10.1051/jphystap:019060050024200 |issn=0368-3893}} Thereafter he used, where possible, the triangulation points used by Nicolas Louis de Lacaille in his 1739-1740 survey of French meridian arc from Dunkirk to Collioure.{{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}} Méchain's baseline was of a similar length (6,006.25 {{lang|fr|toises}}), and also on a straight section of road between Vernet (in the Perpignan area) and Salces (now Salses-le-Chateau).{{cite book

|title = The Measure of all Things – The Seven-Year-Odyssey that Transformed the World

|last= Alder

|first= Ken

|year= 2002

|publisher= Abacus

|location= London

|isbn= 978-0349115078

|pages = 240–241}}

File:First Metre, Paris.jpg

To put into practice the decision taken by the National Convention, on 1 August 1793, to disseminate the new units of the decimal metric system,{{Cite web |last=Maury |first=Jean-Pierre |date=2007 |title=Grandes lois de la République : les mesures républicaines |url=https://mjp.univ-perp.fr/france/1793mesures.htm |website=Digithèque de matériaux juridiques et politiques}} it was decided to establish the length of the metre based on a fraction of the meridian in the process of being measured. The decision was taken to fix the length of a provisional metre (French: mètre provisoire) determined by the measurement of the Meridian of France from Dunkirk to Collioure, which, in 1740, had been carried out by Nicolas Louis de Lacaille and Cesar-François Cassini de Thury. The length of the metre was established, in relation to the toise of the Academy also called toise of Peru, at 3 feet 11.44 lines, taken at 13 degrees of the temperature scale of René-Antoine Ferchault de Réaumur in use at the time. This value was set by legislation on 7 April 1795. It was therefore metal bars of 443.44 {{lang|fr|lignes}} that were distributed in France in 1795-1796.{{cite book |author=National Industrial Conference Board |url=https://books.google.com/books?id=tSUoAAAAYAAJ&pg=PA10 |title=The metric versus the English system of weights and measures ... |publisher=The Century Co. |year=1921 |pages=10–11 |access-date=5 April 2011}} This was the metre installed under the arcades of the rue de Vaugirard, almost opposite the entrance to the Senate.

File:Castell de Montjuic - Fossat entrada - Barcelona (Catalonia).jpg in Barcelona, Spain – the southern end of the meridian arc|185x185px|left]]

End of November 1798, Delambre and Méchain returned to Paris with their data, having completed the survey to meet a foreign commission composed of representatives of Batavian Republic: Henricus Aeneae and Jean Henri van Swinden, Cisalpine Republic: Lorenzo Mascheroni, Kingdom of Denmark: Thomas Bugge, Kingdom of Spain: Gabriel Císcar and Agustín de Pedrayes, Helvetic Republic: Johann Georg Tralles, Ligurian Republic: Ambrogio Multedo, Kingdom of Sardinia: Prospero Balbo, Antonio Vassali Eandi, Roman Republic: Pietro Franchini, Tuscan Republic: Giovanni Fabbroni who had been invited by Talleyrand. The French commission comprised Jean-Charles de Borda, Barnabé Brisson, Charles-Augustin de Coulomb, Jean Darcet, René Just Haüy, Joseph-Louis Lagrange, Pierre- Simon Laplace, Louis Lefèvre-Ginneau, Pierre Méchain and Gaspar de Prony.{{Cite LarousseXIXe|title=Métrique|volume=11|pages=163–164}}{{Cite book |last=Bigourdan |first=Guillaume |url=https://archive.org/details/lesystmemtri00bigo |title=Le système métrique des poids et mesures; son établissement et sa propagation graduelle, avec l'histoire des opérations qui ont servi à déterminer le mètre et le kilogramme |date=1901 |publisher=Paris : Gauthier-Villars |others=University of Ottawa |pages=[https://archive.org/details/lesystmemtri00bigo/page/7 7], 148-154}}{{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 |language=EN}}

In 1799, a commission including Johann Georg Tralles, Jean Henri van Swinden, Adrien-Marie Legendre, Pierre-Simon Laplace, Gabriel Císcar, Pierre Méchain and Jean-Baptiste Delambre calculated the distance from Dunkirk to Barcelona using the data of the 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 Geodetic Mission to the Equator and a value of {{Sfrac|1|334}} was found for the Earth's flattening. Pierre-Simon Laplace originally hoped to figure out the Earth ellipsoid problem from the sole measurement of the arc from Dunkirk to Barcelona, but this portion of the meridian arc led for the flattening to the value of {{Sfrac|1|150}} considered as unacceptable.{{Cite journal |last=Levallois |first=Jean-Jacques |date=May–June 1986 |title=L'Académie Royale des Sciences et la Figure de la Terre |trans-title=The Royal Academy of Sciences and the Shape of the Earth |url=https://gallica.bnf.fr/ark:/12148/bpt6k5470853s |journal=La Vie des Sciences |language=FR |volume=3 |page=290 |bibcode=1986CRASG...3..261L |access-date=4 September 2018 |via=Gallica}} This value was the result of a conjecture based on too limited data. Another flattening of the Earth was calculated by Delambre, who also excluded the results of the French Geodetic Mission to Lapland and found a value close to {{Sfrac|1|300}} combining the results of Delambre and Méchain arc measurement with those of the Spanish-French Geodetic Mission taking in account a correction of the astronomic arc.{{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=261-262, 288–290 [269, 276–277, 283] |language=FR}}{{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}} 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}} 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 Peru. 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.

However, Louis Puissant declared in 1836 to the French Academy of Sciences that Jean Baptiste Joseph Delambre and Pierre Méchain had made errors in the triangulation of the meridian arc, which had been used for determining the length of the metre.{{Cite web |last=Puissant |first=Louis |year=1836 |title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels |url=https://gallica.bnf.fr/ark:/12148/bpt6k2961h |url-status=live |archive-url=https://web.archive.org/web/20060914191223/http://gallica.bnf.fr:80/ark:/12148/bpt6k2961h |archive-date=September 14, 2006 |access-date=January 11, 2020 |website=Gallica |pages=428–433}} This is why Antoine Yvon Villarceau verified the geodetic operations at eight points of the Paris meridian arc from 1861 to 1866. Some of the errors in the operations of Delambre and Méchain were then corrected.

Moreover it was later asserted that the {{Lang|fr|Mètre des Archives}} was short by about 200 micrometres because of miscalculation of the flattening of the Earth ellipsoid, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe.{{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, 13-14, 20, 37–38, 91–92, 70–72, 114–117, 144–147, 8 |oclc=861693071}} Most of the difference was due to the failure to take vertical deflections into account; which was beyond the reach of Delambre and Méchain because the Earth's gravitational field had not yet been studied.{{Cite journal |last=Vaníček |first=Petr |last2=Foroughi |first2=Ismael |date=2019-09-01 |title=How gravity field shortened our metre |url=https://link.springer.com/article/10.1007/s00190-019-01257-7?fromPaywallRec=false |journal=Journal of Geodesy |language=en |volume=93 |issue=9 |pages=1821–1827 |doi=10.1007/s00190-019-01257-7 |issn=1432-1394}}

File:Britannica Figure of the Earth.jpg at the top of the map, 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. The Greenwich meridian is depicted rather than the Paris meridian.{{cite EB1911|wstitle=Earth, Figure of the |volume= 08 |last1 = Clarke|first1= Alexander Ross |last2= Helmert|first2= Friedrich Robert |pages= 801–813}}|alt=]]

In 1870 Ibáñez founded the Spanish National Geographic Institute which he then directed until 1889.{{Cite web|url=https://www.ign.es/web/ign/portal/qsm-nuestra-historia|title=Instituto Geográfico Nacional|last=Nacional|first=Instituto Geográfico|website=Geoportal oficial del Instituto Geográfico Nacional de España|language=es-ES|access-date=December 11, 2019}}{{Cite web |title=150 aniversario del Instituto Geográfico Nacional (1870-2020) |url=https://www.ign.es/web/resources/publicaciones/150aniversario/index.html |access-date=2023-01-06 |website=150 aniversario del Instituto Geográfico Nacional (1870-2020)}} At the time it was the world's biggest geographic institute.{{Cite book |last=Hirsch |first=Adolphe |url=https://play.google.com/books/reader?id=M1PnAAAAMAAJ&pg=GBS.PA101&hl=fr |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=101-109 |language=fr |trans-title=General Ibáñez}} It encompassed geodesy, general topography, leveling, cartography, statistics and the general service of weights and measures. Spain had adopted the metric system in 1849. The Government was urged by the Spanish Royal Academy of Sciences to approve the creation of a large-scale map of Spain in 1852.{{Cite web|url=http://www.unav.es/gep/MilitaresYMarinosRealSociedadGeografica.pdf|title=Militares y marinos en la Real Sociedad Geográfica|last=Núñez de las Cuevas|first=Rodolfo|year=2005|website=Universidad de Navarra|access-date=May 22, 2017}}

The following year Carlos Ibáñez e Ibáñez de Ibero was appointed to undertake this task. As all the scientific and technical equipment for a vast undertaking of this kind had to be created, Ibáñez, in collaboration with Frutos Saavedra Meneses drew up the project of a new apparatus for measuring bases. He recognized that the end standards with which the most perfect devices of the eighteenth century and those of the first half of the nineteenth century were still equipped, that Jean-Charles de Borda or Friedrich Wilhelm Bessel simply joined measuring the intervals by means of screw tabs or glass wedges, would be replaced advantageously for accuracy by the system, designed by Ferdinand Rudolph Hassler for the United States Coast Survey, and which consisted of using a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central base of Spain, and the simple iron ruler with inlaid mercury thermometers which was used in Switzerland.{{Cite journal|last=Cajori|first=Florian|year=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}}

File:Appareil Ibáñez.jpg

Ibáñez and Saavedra went to Paris to supervise the production by Jean Brunner of a measuring instrument calibrated against the metre which they had devised and which they later compared with Borda's double-toise N°1 which was the main reference for measuring all geodetic bases in France and whose length was by definition 3.8980732 metres at a specified temperature.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3001w|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels. Géodésie. – Appareil construit pour les opérations au moyen desquelles on prolongera dans toute l'étendue de l'Espagne le réseau trigonométrique qui couvre la France.|last=Brunner|first=Jean|date=January 26, 1857|publisher=Gauthier-Villars|location=Paris|pages=150–152}}{{Cite news |last=Viik |first=T |date=2006 |title=F.W. Bessel and Geodesy |url=https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.517.9501 |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=6, 10 |citeseerx=10.1.1.517.9501}}{{Cite journal|last1=Clarke|first1=A. R.|last2=James|first2=Henry|date=January 1, 1873|title=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|journal=Philosophical Transactions of the Royal Society of London|volume=163|pages=445–469, p. 16|doi=10.1098/rstl.1873.0014|issn=0261-0523|doi-access=free}}{{Cite book|url=https://play.google.com/store/books/details/Exp%C3%A9riences_faites_avec_l_appareil_%C3%A0_mesurer_les_b?id=uiwPAAAAQAAJ&hl=da|title=Expériences faites avec l'appareil à mesurer les bases appartenant à la commission de la carte d'Espagne /: ouvrage publié par ordre de la reine|last1=Ibáñez e Ibáñe de Ibero|first1=Carlos|last2=Saavedra Menesès|first2=Carlos|publisher=J. Dumaine|year=1860|language=fr|translator-last=Laussedat|translator-first=Aimé}}{{Cite book|last1=Delambre|first1=Jean-Baptiste (1749–1822) Auteur du texte|url=https://gallica.bnf.fr/ark:/12148/bpt6k1106055|title=Base du système métrique décimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone. T. 3 /, 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=139, 228}} The four-metre-long Spanish measuring instrument, which became known as the Spanish Standard (French: Règle espagnole), was replicated in order to be used in Egypt.{{Cite journal|last=Guillaume|first=Ch-Ed|year=1906|title=La mesure rapide des bases géodésiques|journal=Journal de Physique Théorique et Appliquée|language=fr|volume=5|issue=1|pages=242–263|doi=10.1051/jphystap:019060050024200|issn=0368-3893|url=https://zenodo.org/record/2007289}}{{Cite web|url=https://www.bipm.org/utils/common/pdf/obituaries/1920_CIPM_ES_ARRILLAGA-Francesco-da-Paula.pdf|title=Notice nécrologique de F. DA PAULA ARRILLAGA Y GARRO|last=Guillaume|first=Charles-Édouard|year=1920|website=BIPM|access-date=2019-06-10|archive-date=2017-04-22|archive-url=https://web.archive.org/web/20170422033808/http://www.bipm.org/utils/common/pdf/obituaries/1920_CIPM_ES_ARRILLAGA-Francesco-da-Paula.pdf|url-status=dead}} In 1863, Ibáñez and Ismail Effendi Mustafa compared the Spanish Standard with the Egyptian Standard in Madrid.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3016q|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|last=texte|first=Académie des sciences (France) Auteur du|date=July 1, 1864|publisher=Gauthier-Villars|location=Paris|page=623}}{{Cite book|url=http://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|last=Ismaïl-Effendi-Moustapha|date=1864|publisher=V. Goupy|location=Paris}}{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k777528|title=Base centrale de la triangulation géodésique d'Espagne|last=Ibáñez e Ibáñez de Íbero|first=Carlos|publisher=impr. de M. Rivadeneyra|year=1865|location=Madrid|pages=Appendice N.° 9 p. CXCIII, Appendice N.° 11 p. CCLI|translator-last=Laussedat|translator-first=Aimé}} These comparisons were essential, because of thermal expansion. Indeed, geodesists tried to accurately assess temperature of standards in the field in order to avoid temperature systematic errors.

Jean Brunner displayed the Ibáñez-Brunner apparatus at the Exposition Universelle of 1855.{{Cite journal|last=Brenni|first=Paolo|year=1996|title=19th Century French Scientific Instrument Makers – XI: The Brunners and Paul Gautier|url=https://www.unav.es/gep/TheBrunnersCartaParis.pdf|journal=Bulletin of the Scientific Instrument Society|volume=49|pages=3–5|via=Universidad de Navarra}} Copies of the Spanish standard{{Cite web|last=Wolf|first=Rudolf|year=1891|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels|url=https://gallica.bnf.fr/ark:/12148/bpt6k3068q|url-status=live|access-date=July 29, 2021|website=Gallica|pages=370–371|archive-url=https://web.archive.org/web/20070222173955/http://gallica.bnf.fr:80/ark:/12148/bpt6k3068q |archive-date=February 22, 2007 }} were also made for France{{Cite book |last=Tardi |first=Pierre |url=https://gallica.bnf.fr/ark:/12148/bpt6k3355272d |title=Traité de géodésie |date=1934 |pages=25, 26–32|author-link=Pierre Tardi}}{{Cite journal|last=Schiavon|first=Martina|date=December 1, 2006|title=Les officiers géodésiens du Service géographique de l'armée et la mesure de l'arc de méridien de Quito (1901–1906)|url=http://journals.openedition.org/histoiremesure/1746|journal=Histoire & mesure|language=fr|volume=XXI|issue=XXI – 2|pages=55–94|doi=10.4000/histoiremesure.1746|issn=0982-1783|doi-access=free}} and Germany.{{Cite web|last=Zuerich|first=ETH-Bibliothek|year=1879|title=Procès-verbaux des séances de la commission géodésique suisse|url=https://www.e-periodica.ch//digbib/view?pid=bsn-001%3A1877%3A11%3A%3A853|url-status=live|access-date=July 29, 2021|website=E-Periodica|page=14|language=fr|archive-url=https://web.archive.org/web/20210729085259/https://www.e-periodica.ch//digbib/view?pid=bsn-001:1877:11::853 |archive-date=July 29, 2021 }} These standards would be used for the most important operations of European geodesy. Indeed, the southward extension of Paris meridian's triangulation by Pierre Méchain (1803–1804), then François Arago and Jean-Baptiste Biot (1806–1809) had not been secured by any baseline measurement in Spain.{{Cite web|title=c à Paris; vitesse de la lumière ...|url=http://expositions.obspm.fr/lumiere2005/triangulation_plus.html|access-date=August 5, 2021|website=expositions.obspm.fr}}

In 1858 Spain's central geodetic base of triangulation was measured in Madridejos (Toledo) with exceptional precision for the time thanks to the Spanish Standard.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3068q|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels. Notice sur le général Ibañez, correspondant de l'Académie.|last=J. Bertrand|first=Académie des sciences (France) Auteur du|date=January 1, 1891|publisher=Gauthier-Villars|location=Paris|pages=266–269}} Ibáñez and his colleagues wrote a monograph which was translated into French by Aimé Laussedat.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3019n|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels. Géodésie. – Sur les travaux géodésiques exécutés en Espagne, à propos de la publication d'une traduction de l'ouvrage intitulé: Base centrale de la triangulation géodésique de l'Espagne.|last=Laussedat|first=Académie des sciences (France) Auteur du|date=January 1, 1866|publisher=Gauthier-Villars|location=Paris|pages=1007–1010}} The experiment, in which the results of two methods were compared, was a landmark in the controversy between French and German geodesists about the length of geodesic triangulation bases, and empirically validated the method of General Johann Jacob Bayer, founder of the International Association of Geodesy.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3015d|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels. Géodésie. – Sur les opérations en cours d'exécution pour la carte d'Espagne, d'après les renseignements donnés à l'académie de Madrid par M. le colonel Ibañez.|last=Laussedat|first=Académie des sciences (France) Auteur du|date=January 1, 1864|publisher=Gauthier-Villars|location=Paris|pages=70–72}}

From 1865 to 1868 Ibáñez added the survey of the Balearic Islands with that of the Iberian Peninsula.{{Cite book|last=Ibañez é Ibañez de Ibero|first=Carlos|url=https://archive.org/details/descripciongeod00ibergoog|title=Descripcion geodesica de las islas Baleares|date=1871|publisher=Madrid, Impr. de M. Rivadeneyra|others=Harvard University}} For this work, he devised a new instrument, which allowed much faster measurements. In 1869, Ibáñez brought it along to Southampton where Alexander Ross Clarke was making the necessary measurements to compare the Standards of length used in the World.{{Cite journal|last1=Clarke Alexander Ross|last2=James Henry|date=January 1, 1867|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|journal=Philosophical Transactions of the Royal Society of London|volume=157|pages=161–180|doi=10.1098/rstl.1867.0010|s2cid=109333769}} Finally, this second version of the appliance, called the Ibáñez apparatus, was used in Switzerland to measure the geodetic bases of Aarberg, Weinfelden and Bellinzona.A. Hirsch et J. Dumur, Lausanne, Commission Géodésique Suisse, 1888, 116 p.

In 1865 the triangulation of Spain was connected with that of Portugal and France. In 1866 at the conference of the Association of Geodesy in Neuchâtel, Ibáñez announced that Spain would collaborate in remeasuring and extending the French meridian arc.{{Cite web|last=Ibáñez e Ibáñez de Ibero|first=Carlos|year=1866|title=Exposé de l'état des Travaux géodésiques poursuivis en Espagne, communiqué a la Commission permanente de la Conférence internationale, par le Colonel Ibañez, membre de l'Académie Royale des sciences et délégué du Gouvernement espagnol. in General-Bericht über die mitteleuropäische Gradmessung für das Jahr 1865. :: Publications IASS|url=https://gfzpublic.gfz-potsdam.de/rest/items/item_108064_3/component/file_108063/content|access-date=December 10, 2019|website=publications.iass-potsdam.de|pages=56–58}} From 1870 to 1894, François Perrier, then Jean-Antonin-Léon Bassot proceeded to a new survey. In 1879 Ibáñez and François Perrier completed the junction between the geodetic networks of Spain and Algeria and thus completed the measurement of a meridian arc which extended from Shetland to the Sahara.{{Cite book|url=http://gallica.bnf.fr/ark:/12148/bpt6k3046j|title=Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés... par MM. les secrétaires perpétuels. Géodésie. – Jonction géodésique de l'Algérie avec l'Espagne, opération internationale exécutée sous la direction de MM. le général Ibañez et F. Perrier.|last=Perrier|first=Académie des sciences (France) Auteur du|date=July 1, 1879|publisher=Gauthier-Villars|location=Paris|pages=885–889}} This connection was a remarkable enterprise where triangles with a maximum length of 270 km were observed from mountain stations (Mulhacén, Tetica, Filahoussen, M'Sabiha) over the Mediterranean Sea.{{Cite book|title=IAG 150 Years|volume = 143|last=Torge|first=Wolfgang|date=2015|publisher=Springer, Cham|pages=3–18|doi=10.1007/1345_2015_42|chapter = From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy 1862–1916|series = International Association of Geodesy Symposia|isbn = 978-3-319-24603-1}}{{Cite book|url=https://catalogue.bnf.fr/ark:/12148/cb30632199p|title=Jonction géodésique et astronomique de l'Algérie avec l'Espagne, exécutée en commun en 1879, par ordre des gouvernements d'Espagne et de France, sous la direction de M. le général Ibañez,... pour l'Espagne, M. le colonel Perrier,... pour la France|last1=Ibáñez e Ibáñez de Íbero|first1=Carlos|last2=Perrier|first2=François|date=1886|publisher=Impr. nationale|location=Paris}}

This meridian arc was named West Europe-Africa Meridian-arc by Alexander Ross Clarke and Friedrich Robert Helmert. It yielded a value for the equatorial radius of the earth a = 6 377 935 metres, the ellipticity being assumed as 1/299.15 according to Bessel ellipsoid.{{Cite journal|last=Bessel|first=Friedrich Wilhelm|date=December 1, 1841|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=http://adsabs.harvard.edu/abs/1841AN.....19...97B|journal=Astronomische Nachrichten|volume=19|issue=7 |page=97|doi=10.1002/asna.18420190702|bibcode=1841AN.....19...97B |issn=0004-6337}}{{Cite news|last=Viik|first=T|year=2006|title=F. W. BESSEL AND GEODESY|page=10|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}} 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.

According to the calculations made at the central bureau of the International Geodetic Association, the net does not follow the meridian exactly, but deviates both to the west and to the east; actually, the meridian of Greenwich is nearer the mean than that of Paris.

In the 19th century, astronomers and geodesists were concerned with questions of longitude and time, because they were responsible for determining them scientifically and used them continually in their studies. The International Geodetic Association, which had covered Europe with a network of fundamental longitudes, took an interest in the question of an internationally-accepted prime meridian at its seventh general conference in Rome in 1883.{{sfnp|Hirsch|von Oppolzer|1884|p=[https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=178 178]}} Indeed, the Association was already providing administrations with the bases for topographical surveys, and engineers with the fundamental benchmarks for their levelling. It seemed natural that it should contribute to the achievement of significant progress in navigation, cartography and geography, as well as in the service of major communications institutions, railways and telegraphs.{{Sfnp|Hirsch|von Oppolzer|1884|p=[https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=138 138{{ndash}}139], [https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=145 145]}} From a scientific point of view, to be a candidate for the status of international prime meridian, the proponent needed to satisfy three important criteria. According to the report by Carlos Ibáñez e Ibáñez de Ibero, it must have a first-rate astronomical observatory, be directly linked by astronomical observations to other nearby observatories, and be attached to a network of first-rate triangles in the surrounding country.{{Sfnp|Hirsch|von Oppolzer|1884|p=[https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=138 138{{ndash}}139], [https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=145 145]}} Four major observatories could satisfy these requirements: Greenwich, Paris, Berlin and Washington. The conference concluded that Greenwich Observatory best corresponded to the geographical, nautical, astronomical and cartographic conditions that guided the choice of an international prime meridian, and recommended the governments should adopt it as the world standard.{{sfnp|Hirsch|von Oppolzer|1884|p=[https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=201 201]|loc=Resolution III}} The Conference further hoped that, if the whole world agreed on the unification of longitudes and times by the Association's choosing the Greenwich meridian, Great Britain might respond in favour of the unification of weights and measures, by adhering to the Metre Convention.{{Sfnp|Hirsch|von Oppolzer|1884|p=[https://books.google.co.uk/books?id=2AVKAQAAMAAJ&pg=PA202 202]|loc=Resolution VIII}}

• Cartography of France
• Earth's circumference#Historical use in the definition of units of measurement
• {{section link|Earth radius|History}}
• International Bureau of Weights and Measures
• {{section link|History of geodesy|Prime meridian and standard of length}}
• {{section link|History of the metre|Meridional definition}}
• {{section link|Meridian arc|17th and 18th centuries}}
• {{section link|Metre|Early adoption of the metre as a scientific unit of length: the forerunners}}
• Metre Convention
• Paris meridian#The West Europe-Africa Meridian-arc

{{reflist}}

• {{Cite book |title=Comptes-rendus des seances de la Septiéme Conférence Géodésique Internationale pour la mesure des degrés en Europe. Reunie a Rome du 15 au 24 Octobre 1863 |editor-first1=A. |editor-last1=Hirsch |editor-first2=Th. |editor-last2=von Oppolzer |date=1884 |publisher=G. Reimer |trans-title=Proceedings of the Seventh International Geodesic Conference for the measurement of degrees in Europe. Held in Rome from 15 to 24 October 1863 |chapter=Rapport de la Commission chargée d'examiner les propositions du bureau de l'Association sur l'unification des longitudes et des heures |trans-chapter=Report of the Commission charged with examining the proposals of the Bureau of the Association on the unification of longitudes and times. |language=fr |location=Berlin |chapter-url=https://books.google.com/books?id=2AVKAQAAMAAJ}}

Category:Geodetic surveys