Editing Vertical deflection (section)

==Historical implications==
Vertical deflections were used to measure [[Earth's density]] in the [[Schiehallion experiment]].

Vertical deflection is the reason why modern [[prime meridian]] passes more than 100&nbsp;m to the east of the [[Prime meridian (Greenwich)|historical astronomic prime meridian]] in Greenwich.<ref>{{cite journal| title = Why the Greenwich meridian moved | first1 = Stephen | last1 = Malys | first2 = John H. | last2 = Seago | first3 = Nikolaos K. | last3 = Palvis | first4 = P. Kenneth | last4 = Seidelmann | first5 = George H. | last5 = Kaplan | journal = Journal of Geodesy | volume = 89 | issue = 12 | pages = 1263 | date = 1 August 2015 | doi = 10.1007/s00190-015-0844-y|bibcode = 2015JGeod..89.1263M | doi-access = free }}</ref>

The [[meridian arc measurement]] made by [[Nicolas-Louis de Lacaille]] north of [[Cape Town]] in 1752 ([[de Lacaille's arc measurement]]) was affected by vertical deflection.<ref>{{cite web
 |url=https://assa.saao.ac.za/sections/history/expeditions/arc_meridian
 |title=Arc of the Meridian
 |publisher=Astronomical Society of South Africa
 |access-date= 27 August 2020
 }}</ref> The resulting discrepancy with Northern Hemisphere measurements was not explained until a visit to the area by [[George Everest]] in 1820; [[Maclear's arc measurement]] resurvey ultimately confirmed Everest's conjecture.<ref>{{cite journal
 |title=Lacaille 250 years on
 |last=Warner
 |first=Brian
 |journal=Astronomy and Geophysics
 |date= 1 April 2002
 |volume=43
 |issue=2
 |pages=2.25–2.26
 |doi= 10.1046/j.1468-4004.2002.43225.x
 |doi-access=free
 }}</ref>

Errors in the [[meridian arc of Delambre and Méchain]] determination, which affected the original definition of the [[metre]],<ref name="Alder 2002 p. ">{{cite book | last=Alder | first=K. | title=The Measure of All Things: The Seven-year Odyssey and Hidden Error that Transformed the World | publisher=Free Press | year=2002 | isbn=978-0-7432-1675-3 | url=https://books.google.com/books?id=gQu6uMyYrB4C | access-date=2020-08-02 }}</ref> were long known to be mainly caused by an uncertain determination of [[Barcelona]]'s latitude later explained by vertical deflection.<ref>Jean-Étienne Duby, Rapport sur les travaux de la Société de Physique et d’Histoire naturelle de Genève de juillet 1860 à juin 1861 par M. le Pasteur Duby. Lu à la séance du 13 juin 1861, in Mémoires de la Société de physique et d’histoire naturelle de Genève, 16 (1861-1862), 196-197.</ref><ref name="VaníčekForoughi2019">{{cite journal|last1=Vaníček|first1=Petr|last2=Foroughi|first2=Ismael|title=How gravity field shortened our metre|journal=Journal of Geodesy|volume=93|issue=9|year=2019|pages=1821–1827|issn=0949-7714|doi=10.1007/s00190-019-01257-7|bibcode=2019JGeod..93.1821V|s2cid=146099564}}</ref><ref>{{Cite journal |last=Levallois |first=Jean-Jacques |title=La méridienne de Dunkerque à Barcelone et la déterminiation du mètre (1972-1799) |url=https://dx.doi.org/10.5169/seals-234595 |access-date=2022-12-23 |website=E-Periodica |year=1991 |language=fr |doi=10.5169/seals-234595}}</ref> When these errors where acknowledged in 1866,<ref>{{Cite journal |last=Hirsch |first=Adolphe |title=Sur les progrès des travaux géodésiques en Europe |url=https://dx.doi.org/10.5169/seals-88030 |access-date=2022-12-23 |website=E-Periodica |year=1865 |language=fr |doi=10.5169/seals-88030}}</ref> it became urgent to proceed to a new measurement of the French arc between Dunkirk and Perpignan. The operations concerning the revision of the French arc linked to Spanish triangulation were completed only in 1896. Meanwhile, the French geodesists had accomplished in 1879 the junction of Algeria to Spain, with the help of the geodesists of the Madrid Institute headed by the late [[Carlos Ibáñez e Ibáñez de Ibero|Carlos Ibañez Ibáñez de Ibero]] (1825–1891).{{efn|He had been president of the International Geodetic Association (now called [[International Association of Geodesy]]), first president of the [[General Conference on Weights and Measures|International Committee for Weights and Measures]], and one of the 81 initial members of the [[International Statistical Institute]].<ref>{{Cite EB1911|wstitle= Earth, Figure of the| volume= 8 |last1= Clarke |first1=  Alexander Ross |author1-link= Alexander Ross Clarke | |last2= Helmert |first2= Friedrich Robert |author2-link= Friedrich Robert Helmert| pages = 801&ndash;813|quote= see page 811 |short=1}}</ref>}}

Until [[Hayford ellipsoid]] was calculated in 1910, vertical deflections were considered as [[Observational error|random errors]].<ref name=":33">{{Cite book |title=Géodésie in Encyclopedia Universalis |publisher=Encyclopedia Universalis |year=1996 |isbn=978-2-85229-290-1 |pages=Vol 10, p. 302 |oclc=36747385}}</ref> Plumb line deviations were identified by [[Jean le Rond d'Alembert|Jean Le Rond d'Alembert]] as an important source of error in geodetic surveys as early as 1756. A few years later, in 1828, [[Carl Friedrich Gauss]] proposed the concept of [[geoid]].<ref>{{Cite web |last=d'Alembert |first=Jean Le Rond |date=1756 |title=Article Figure de la Terre, (Astron. Géog. Physiq. & Méch.), vol. VI (1756), p. 749b–761b |url=http://enccre.academie-sciences.fr/encyclopedie/article/v6-872-5/ |access-date=2022-12-23 |website=enccre.academie-sciences.fr}}</ref><ref>{{Cite web |last=US Department of Commerce |first=National Oceanic and Atmospheric Administration |title=What is the geoid? |url=https://geodesy.noaa.gov/GEOID/geoid_def.html |access-date=2022-12-23 |website=geodesy.noaa.gov |language=EN-US}}</ref>