# Repeating circle > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Repeating_circle > Markdown URL: https://mediated.wiki/source/Repeating_circle.md > Source: https://en.wikipedia.org/wiki/Repeating_circle > Source revision: 1292723815 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Type of angular measurement instrument}} thumb|12-inch repeating circle.{{clarify|reason=Where is the second telescope as described in the article?|date=April 2022}} [[File:Reflecting circle-CnAM 1842-IMG 4998-gradient.jpg|thumb|Borda reflecting circle, on display at [Conservatoire national des arts et métiers](/source/Conservatoire_national_des_arts_et_m%C3%A9tiers).]] The '''repeating circle''' is an instrument for [geodetic surveying](/source/geodetic_surveying), developed from the [reflecting circle](/source/Reflecting_instrument) by [Étienne Lenoir](/source/%C3%89tienne_Lenoir_(instrument_maker)) in 1784.{{cite book |last = Daumas |first = Maurice |title = Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers |publisher = Portman Books |location = London |date = 1989 |isbn = 978-0-7134-0727-3 }} He invented it while an assistant of [Jean-Charles de Borda](/source/Jean-Charles_de_Borda), who later improved the instrument. It was notable as being the equal of the [great theodolite](/source/Ramsden_surveying_instruments) created by the renowned instrument maker, [Jesse Ramsden](/source/Jesse_Ramsden). It was used to [measure](/source/arc_measurement) the [meridian arc](/source/meridian_arc) from [Dunkirk](/source/Dunkirk) to [Barcelona](/source/Barcelona) by [Jean Baptiste Delambre](/source/Jean_Baptiste_Joseph_Delambre) and [Pierre Méchain](/source/Pierre_M%C3%A9chain) (see: [meridian arc of Delambre and Méchain](/source/meridian_arc_of_Delambre_and_M%C3%A9chain)). == Construction and operation == The repeating circle is made of two [telescope](/source/telescope)s mounted on a shared axis with scales to measure the angle between the two. The instrument combines multiple measurements to increase accuracy with the following procedure: thumb|400px|center|Mode of operation:
(1) The instrument is aligned so its plane includes the two points to be measured, and each telescope is aimed at a point;
(2) Keeping the angle between the telescopes locked, the left (black) telescope is rotated clockwise to aim at the right point;
(3) the right (gray) telescope's position is noted, and it is rotated back to the left point. At this stage, the angle on the instrument is double the angle of interest between the points. Repeating the procedure causes the instrument to show 4× the angle of interest, with further iterations increasing it to 6×, 8×, and so on. In this way, many measurements can be added together, allowing some of the random measurement errors to cancel out.{{cite book |first = Ken |last = Alder |title = The Measure Of All Things |date = 2002 |publisher = Simon and Schuster |isbn = 0-7432-1675-X |url-access = registration |url = https://archive.org/details/measureofallthin00alde }} == Use in geodetic surveys == The repeating circle was used by [César-François Cassini de Thury](/source/C%C3%A9sar-Fran%C3%A7ois_Cassini_de_Thury), assisted by [Pierre Méchain](/source/Pierre_M%C3%A9chain), for the [triangulation](/source/Triangulation_(surveying)) of the [Anglo-French Survey](/source/Anglo-French_Survey_(1784%E2%80%931790)). It would later be used for the [Arc measurement of Delambre and Méchain](/source/Arc_measurement_of_Delambre_and_M%C3%A9chain) 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](/source/Paris_meridian).{{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|url-access=subscription }} When the [metre](/source/metre) was chosen as an international unit of length, it was well known that by measuring the latitude of two stations in [Barcelona](/source/Barcelona), Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation and that he did not dare to admit this inaccuracy.{{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=2025-03-28 |website=Techniques de l'Ingénieur |language=fr-FR}}{{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}} This was later explained by clearance in the central axis of the repeating circle causing wear and consequently the [zenith](/source/zenith) measurements contained significant [systematic errors](/source/Observational_error).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. == See also == * [Reflecting circles](/source/Reflecting_circles) * [Meridional definition](/source/Meridional_definition) * [Grade (angle)](/source/Grade_(angle)) == References == Category:Surveying instruments {{Sci-hist-stub}} {{Civil-engineering-stub}} {{Measurement-stub}} --- Adapted from the Wikipedia article [Repeating circle](https://en.wikipedia.org/wiki/Repeating_circle) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Repeating_circle?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.