Editing Pendulum (section)

== History ==
[[File:EastHanSeismograph.JPG|thumb|Replica of [[Zhang Heng]]'s [[seismometer]]. The pendulum is contained inside.]]

One of the earliest known uses of a pendulum was a 1st-century [[seismometer]] device of [[Han dynasty]] Chinese scientist [[Zhang Heng]].<ref name="morton 70">Morton, W. Scott and Charlton M. Lewis (2005). China: Its History and Culture. New York: McGraw-Hill, Inc., p. 70</ref> Its function was to sway and activate one of a series of levers after being disturbed by the tremor of an [[earthquake]] far away.<ref name="needham volume 3 627 629">Needham, Volume 3, 627-629</ref>  Released by a lever, a small ball would fall out of the urn-shaped device into one of eight metal toads' mouths below, at the eight points of the compass, signifying the direction the earthquake was located.<ref name="needham volume 3 627 629" />

Many sources<ref>{{cite book
 | last = Good | first = Gregory
 | title = Sciences of the Earth: An Encyclopedia of Events, People, and Phenomena
 | publisher = Routledge
 | year = 1998
 | page = 394
 | url = https://books.google.com/books?id=vdqXVddh0hUC
 | isbn = 978-0-8153-0062-5}}</ref><ref>{{cite encyclopedia
 | title = Pendulum
 | encyclopedia = Encyclopedia Americana
 | volume = 21
 | pages = 502
 | publisher = The Americana Corp.
 | url = https://books.google.com/books?id=39JMAgAAQBAJ&dq="ibn+yunus"+pendulum&pg=RA2-PA126
 | year = 1967
 | isbn = 978-0-19-538207-5
 | access-date = 2009-02-20
}}</ref><ref>{{cite book
 | last = Baker
 | first = Cyril Clarence Thomas
 | title = Dictionary of Mathematics
 | publisher = G. Newnes
 | year = 1961
 | page = 176
 | url = https://books.google.com/books?id=RlkYAAAAMAAJ&q=Ibn+Yunis+pendulum
}}</ref><ref>{{cite book
 | author-link = Roger G. Newton
 | last = Newton | first = Roger G.
 | title = Galileo's Pendulum: From the Rhythm of Time to the Making of Matter
 | publisher = Harvard University Press
 | year = 2004
 | location = US
 | page = [https://archive.org/details/galileospendulum0000newt/page/52 52]
 | url = https://archive.org/details/galileospendulum0000newt
 | url-access=registration
 | isbn = 978-0-674-01331-5
}}</ref> claim that the 10th-century Egyptian astronomer [[Ibn Yunus]] used a pendulum for time measurement, but this was an error that originated in 1684 with the British historian [[Edward Bernard]].<ref>{{cite journal
 | last=King | first=D. A.
 | title=Ibn Yunus and the pendulum: a history of errors
 | journal=Archives Internationales d'Histoire des Sciences
 | year=1979 | volume=29 | issue=104
 | pages=35–52
}}, reprinted on the [https://muslimheritage.com/ibn-yunus-and-the-pendulum-a-history-of-errors/ Muslim Heritage] website.
</ref><ref>{{cite journal
 | last = Hall | first = Bert S.
 | title = The scholastic pendulum
 | journal = Annals of Science
 | volume = 35 | issue = 5
 | pages = 441–462
 | date = September 1978
 | issn =  0003-3790
 | doi =10.1080/00033797800200371
}}</ref><ref>{{cite web
 | author1 = O'Connor, J. J.
 | author2 = Robertson, E. F.
 | date = November 1999
 | url = http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Yunus.html
 | title = Abu'l-Hasan Ali ibn Abd al-Rahman ibn Yunus
 | publisher = University of St Andrews
 | access-date = 2007-05-29
}}</ref><ref name="Akyeampong">{{cite encyclopedia
 | editor-last1  = Akyeampong | editor-first1 = Emmanuel K.
 | editor-last2  = Gates | editor-first2 = Henry Louis Jr.
 | title = Ibn Yunus
 | encyclopedia  = Dictionary of African Biography
 | volume = 3
 | publisher = Oxford Univ. Press
 | date   = 2012
 | pages  = 126–127
 | language = 
 | url    = https://archive.org/details/isbn_9780195382075_3/page/126/
 | url-access = registration
 | isbn   = 978-0-19-538207-5
}}</ref>

During the [[Renaissance]], large hand-pumped pendulums were used as sources of power for manual reciprocating machines such as saws, bellows, and pumps.<ref>{{cite book
 | last = Matthews | first = Michael R.
 | title = Time for science education
 | publisher = Springer
 | year = 2000
 | page = 87
 | url = https://books.google.com/books?id=vCtYnEuW7TIC&pg=PR14
 | isbn = 978-0-306-45880-4
}}</ref>

=== 1602: Galileo's research ===
{{See also|Galileo Galilei#Pendulum}}
Italian scientist [[Galileo Galilei]] was the first to study the properties of pendulums, beginning around 1602.<ref name="Drake">{{cite book
 | last = Drake | first = Stillman
 | title = Galileo at Work: His scientific biography
 | publisher = Courier Dover
 | year = 2003
 | location = USA
 | pages = 20–21
 | url = https://books.google.com/books?id=OwOlRPbrZeQC&pg=PA20
 | isbn = 978-0-486-49542-2
}}</ref> The first recorded interest in pendulums made by Galileo was around 1588 in his posthumously published notes titled ''[[De motu antiquiora|On Motion]]'',<ref>{{cite book |last1=Galilei |first1=Galileo |last2=Drabkin |first2=I.E. |last3=Drake |first3=Stillman |title=On Motion and On Mechanics |date=1960 |publisher=University of Wisconsin |location=Madison |page=108}}</ref><ref> {{cite book | last = Drake | first = Stillman | title = Galileo at Work: His scientific biography | publisher = Courier Dover | year = 2003 | location = USA | page = 17 | url = https://books.google.com/books?id=OwOlRPbrZeQC&pg=PA17
 | isbn = 978-0-486-49542-2}}</ref> in which he noted that heavier objects would continue to oscillate for a greater amount of time than lighter objects. The earliest extant report of his experimental research is contained in a letter to Guido Ubaldo dal Monte, from Padua, dated November 29, 1602.<ref name="Galileo">{{cite book
 | last = Galilei | first = Galileo
 | title= Le Opere di Galileo Galilei, Edizione Nazionale
 | author-link = Galileo Galilei
 | editor-last= Favaro
 | editor-first= Antonio
 | editor-link= :it:Antonio Favaro
 | date = 1909
 | url = https://archive.org/details/leoperedigalile07vivigoog
 | trans-title=The Works of Galileo Galilei, National Edition
 | language=it
 | location = [[Florence]]
 | publisher= Barbera
 | isbn= 978-88-09-20881-0
}}</ref> His biographer and student, [[Vincenzo Viviani]], claimed his interest had been sparked around 1582 by the swinging motion of a chandelier in [[Pisa Cathedral]].<ref>{{cite book
 | last = Murdin | first = Paul
 | title = Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth
 | publisher = Springer
 | year = 2008
 | page = 41
 | url = https://books.google.com/books?id=YUHyhL8MyIQC&pg=PA41
 | isbn = 978-0-387-75533-5
}}</ref><ref>[https://books.google.com/books?id=wq1aAAAAYAAJ La Lampada di Galileo], by Francesco Malaguzzi Valeri, for Archivio storico dell'arte, Volume 6 (1893); Editor, Domenico Gnoli; Publisher Danesi, Rome; Page 215-218.</ref> Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism; the period of the pendulum is approximately independent of the [[amplitude]] or width of the swing.<ref name="GalileoProject">{{cite web
 | last = Van Helden | first = Albert
 | title = Pendulum Clock
 | website = The Galileo Project
 | publisher = Rice Univ.
 | year = 1995
 | url = http://galileo.rice.edu/sci/instruments/pendulum.html
 | access-date = 2009-02-25
}}</ref> He also found that the period is independent of the [[mass]] of the bob, and proportional to the [[square root]] of the length of the pendulum. He first employed freeswinging pendulums in simple timing applications. [[Santorio Santorio|Santorio Santori]] in 1602 invented a device which measured a patient's [[pulse]] by the length of a pendulum; the ''pulsilogium''.<ref>{{Cite journal |last1=Bigotti |first1=Fabrizio |last2=Taylor |first2=David |date=2017 |title=The Pulsilogium of Santorio: New Light on Technology and Measurement in Early Modern Medicine |journal=Societate Si Politica |volume=11 |issue=2 |pages=53–113 |issn=1843-1348 |pmc=6407692 |pmid=30854144}}</ref> In 1641 Galileo dictated to his son [[Vincenzo Gamba|Vincenzo]] a design for a mechanism to keep a pendulum swinging, which has been described as the first pendulum clock;<ref name="GalileoProject" /> Vincenzo began construction, but had not completed it when he died in 1649.<ref>[https://books.google.com/books?id=OwOlRPbrZeQC&pg=PA20 Drake 2003], p.419–420</ref>

=== 1656: The pendulum clock ===
{{multiple image
| align    = left
| direction = horizontal
| footer   = The first pendulum clock
| image1   = Huygens first pendulum clock - front view.png
| width1   = 120
| image2   = Huygens first pendulum clock.png
| width2   = 112
}}{{Main|Pendulum clock}}
In 1656 the Dutch scientist [[Christiaan Huygens]] built the first [[pendulum clock]].<ref>although there are unsubstantiated references to prior pendulum clocks made by others: {{cite book
 | last=Usher | first=Abbott Payson
 | title=A History of Mechanical Inventions
 | year=1988
 | publisher=Courier Dover
 | pages= 310–311
 | isbn=978-0-486-25593-4
 | url=https://books.google.com/books?id=xuDDqqa8FlwC&pg=PA312
}}</ref>  This was a great improvement over existing mechanical clocks; their best accuracy was improved from around 15 minutes deviation a day to around 15 seconds a day.<ref>{{cite book
 | last = Eidson | first = John C.
 | title = Measurement, Control, and Communication using IEEE 1588
 | publisher = Burkhausen
 | year = 2006
 | page = 11
 | url = https://books.google.com/books?id=jmfkJYdEANEC&q=%22accuracy+of+clocks%22&pg=PA11
 | isbn = 978-1-84628-250-8
}}</ref>  Pendulums spread over Europe as existing clocks were [[retrofitted]] with them.<ref>Milham 1945, p.145</ref>

The English scientist [[Robert Hooke]] studied the [[conical pendulum]] around 1666, consisting of a pendulum that is free to swing in two dimensions, with the bob rotating in a circle or ellipse.<ref name="OConnor2002">{{cite web
  | last = O'Connor
  | first = J.J.
  | author2 = E.F. Robertson
  | title = Robert Hooke
  | website = Biographies, MacTutor History of Mathematics Archive
  | publisher = School of Mathematics and Statistics, Univ. of St. Andrews, Scotland
  | date = August 2002
  | url = http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hooke.html
  | access-date = 2009-02-21
  | archive-date = 2009-03-03
  | archive-url = https://web.archive.org/web/20090303081753/http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Hooke.html
  | url-status = dead
}}</ref>  He used the motions of this device as a model to analyze the [[orbital motion]]s of the [[planet]]s.<ref>{{cite conference
  | first = Michael
  | last = Nauenberg
  | title = Robert Hooke's seminal contribution to orbital dynamics
  | book-title = Robert Hooke: Tercentennial Studies
  | pages = 17–19
  | publisher = Ashgate Publishing
  | year = 2006
  | isbn = 0-7546-5365-X
  }}</ref> Hooke suggested to [[Isaac Newton]] in 1679 that the components of orbital motion consisted of inertial motion along a tangent direction plus an attractive motion in the radial direction. This played a part in Newton's formulation of the [[law of universal gravitation]].<ref>{{cite journal
 | last=Nauenberg
 | first=Michael
 | title=Hooke and Newton: Divining Planetary Motions
 | journal=Physics Today
 | year=2004 | volume=57 | issue=2 | page=13
 | url=http://scitation.aip.org/journals/doc/PHTOAD-ft/vol_57/iss_2/13_1.shtml
 | access-date=2007-05-30
 | doi=10.1063/1.1688052 |bibcode = 2004PhT....57b..13N | doi-access=free
 }}</ref><ref>{{cite web
 |author=The KGM Group, Inc. 
 |year=2004 
 |url=http://www.sciencemaster.com/space/item/helio_4.php 
 |title=Heliocentric Models 
 |publisher=Science Master 
 |access-date=2007-05-30 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20070713175810/http://www.sciencemaster.com/space/item/helio_4.php 
 |archive-date=2007-07-13 
}}</ref> Robert Hooke was also responsible for suggesting as early as 1666 that the pendulum could be used to measure the force of gravity.<ref name="OConnor2002" />

During his expedition to [[Cayenne]], [[French Guiana]] in 1671, [[Jean Richer]] found that a [[pendulum clock]] was {{frac|2|1|2}} minutes per day slower at Cayenne than at Paris. From this he deduced that the force of gravity was lower at Cayenne.<ref>{{cite conference
  | first = Victor F.
  | last = Lenzen
  |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}}</ref><ref>{{cite book
 | last=Richer
 | first=Jean
 | year=1679
 | title=Observations astronomiques et physiques faites en l'isle de Caïenne
 | publisher=Mémoires de l'Académie Royale des Sciences | bibcode=1679oaep.book.....R
 }} cited in [https://books.google.com/books?id=A1IqAAAAMAAJ&pg=RA2-PA307 Lenzen & Multauf, 1964], p.307</ref>  In 1687, [[Isaac Newton]] in ''[[Philosophiæ Naturalis Principia Mathematica|Principia Mathematica]]'' showed that this was because the Earth was not a true sphere but slightly [[Oblate spheroid|oblate]] (flattened at the poles) from the effect of [[centrifugal force]] due to its rotation, causing gravity to increase with [[latitude]].<ref>[https://books.google.com/books?id=A1IqAAAAMAAJ&pg=RA2-PA307 Lenzen & Multauf, 1964], p.307</ref>  Portable pendulums began to be taken on voyages to distant lands, as precision [[gravimeter]]s to measure the [[Gravity of Earth|acceleration of gravity]] at different points on Earth, eventually resulting in accurate models of the [[Figure of the Earth|shape of the Earth]].<ref>{{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
  | pages = [https://archive.org/details/bub_gb_TL4KAAAAIAAJ/page/n30 20]–22
  | url = https://archive.org/details/bub_gb_TL4KAAAAIAAJ
  }}</ref>

=== 1673: Huygens' ''Horologium Oscillatorium'' ===
In 1673, 17 years after he invented the pendulum clock, [[Christiaan Huygens]] published his theory of the pendulum, ''[[Horologium Oscillatorium|Horologium Oscillatorium sive de motu pendulorum]]''.<ref>{{cite web
  | last = Huygens
  | first = Christian
  |author2=translated by Ian Bruce
  | title = Horologium Oscillatorium
  | website = 17centurymaths
  | publisher = 17thcenturymaths.com
  | date = July 2007
  | url = http://www.17centurymaths.com/contents/huygenscontents.html
  | format = PDF
  | access-date = 2009-03-01}}</ref><ref>The constellation of [[Horologium (constellation)|Horologium]] was later named in honor of this book.</ref>  [[Marin Mersenne]] and [[René Descartes]] had discovered around 1636 that the pendulum was not quite isochronous; its period increased somewhat with its amplitude.<ref name="Matthews">{{cite book
  | last = Matthews
  | first = Michael R.
  | title = Science Teaching: The Role of History and Philosophy of Science
  | publisher = Psychology Press
  | year = 1994
  | pages = 121–122
  | url = https://books.google.com/books?id=qnwzRqh5jFMC&q=mersenne+isochronous+pendulum&pg=PA121
  | isbn = 978-0-415-90899-3}}</ref>  Huygens analyzed this problem by determining what curve an object must follow to descend by gravity to the same point in the same time interval, regardless of starting point; the so-called ''[[tautochrone problem|tautochrone curve]]''. By a complicated method that was an early use of [[calculus]], he showed this curve was a [[cycloid]], rather than the circular arc of a pendulum,<ref>[http://www.17centurymaths.com/contents/huygens/horologiumpart2b.pdf Huygens, Horologium Oscillatorium], Part 2, Proposition 25</ref> confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings.<ref>{{cite web
 |last=Mahoney 
 |first=Michael S. 
 |date=March 19, 2007 
 |url=http://www.princeton.edu/~mike/articles/huygens/timelong/timelong.html 
 |title=Christian Huygens: The Measurement of Time and of Longitude at Sea 
 |publisher=Princeton University 
 |access-date=2007-05-27 
 |archive-url=https://web.archive.org/web/20071204152637/http://www.princeton.edu/~mike/articles/huygens/timelong/timelong.html 
 |archive-date=December 4, 2007 
 |url-status=dead 
}}</ref>  Huygens also solved the problem of how to calculate the period of an arbitrarily shaped pendulum (called a ''compound pendulum''), discovering the ''[[Center of percussion|center of oscillation]]'', and its interchangeability with the pivot point.<ref>{{cite conference
  | first = Fabio
  | last = Bevilaqua
  |author2=Lidia Falomo |author3=Lucio Fregonese |author4=Enrico Gianetto |author5=Franco Giudise |author6=Paolo Mascheretti
  | title = The pendulum: From constrained fall to the concept of potential
  | book-title = The Pendulum: Scientific, Historical, Philosophical, and Educational Perspectives
  | pages = 195–200
  | publisher = Springer
  | year = 2005
  | url = https://books.google.com/books?id=3GV2NgDwtjMC&pg=PA195
  | isbn = 1-4020-3525-X
  | access-date = 2008-02-26}} gives a detailed description of Huygens' methods</ref>

The existing clock movement, the [[verge escapement]], made pendulums swing in very wide arcs of about 100°.<ref name="Headrick">{{cite journal
 |last=Headrick 
 |first=Michael 
 |year=2002 
 |title=Origin and Evolution of the Anchor Clock Escapement 
 |periodical=Control Systems Magazine, Inst. Of Electrical and Electronic Engineers 
 |volume=22 
 |issue=2 
 |url=http://www.geocities.com/mvhw/anchor.html 
 |access-date=2007-06-06 
 |archive-url=https://web.archive.org/web/20091025120920/http://geocities.com/mvhw/anchor.html
 |archive-date=October 25, 2009
 |url-status=dead
}}</ref> Huygens showed this was a source of inaccuracy, causing the period to vary with amplitude changes caused by small unavoidable variations in the clock's drive force.<ref>"''...it is affected by either the intemperance of the air or any faults in the mechanism so the crutch QR is not always activated by the same force... With large arcs the swings take longer, in the way I have explained, therefore some inequalities in the motion of the timepiece exist from this cause...''",  {{cite book
  | last =Huygens
  | first = Christiaan
  | title = Horologium
  | publisher = Adrian Vlaqc
  | year = 1658
  | location = The Hague
  | url = http://www.antique-horology.org/_Editorial/Horologium/Horologium.pdf
  }}, translation by Ernest L. Edwardes (December 1970) ''Antiquarian Horology'', Vol.7, No.1</ref>  To make its period isochronous, Huygens mounted cycloidal-shaped metal guides next to the pivots in his clocks, that constrained the suspension cord and forced the pendulum to follow a cycloid arc (see [[cycloidal pendulum]]).<ref name="Andrewes1994">Andrewes, W.J.H. [https://books.google.com/books?id=F7wNQk219KMC&pg=PA126 ''Clocks and Watches: The leap to precision''] in {{cite book
  | first = Samuel
  | last = Macey
  | title = Encyclopedia of Time
  | pages = 123–125
  | publisher = Taylor & Francis
  | year = 1994
  | isbn = 978-0-8153-0615-3}}</ref>  This solution didn't prove as practical as simply limiting the pendulum's swing to small angles of a few degrees. The realization that only small swings were [[isochronous]]  motivated the development of the [[anchor escapement]] around 1670, which reduced the pendulum swing in clocks to 4°–6°.<ref name="Headrick" /><ref>[https://books.google.com/books?id=xuDDqqa8FlwC&pg=PA312 Usher, 1988], p.312</ref> This became the standard escapement used in pendulum clocks.

=== 1721: Temperature compensated pendulums ===
[[File:Foucault pendulum animated.gif|thumb|right|The [[Foucault pendulum]] in 1851 was the first demonstration of the Earth's rotation that did not involve celestial observations, and it created a "pendulum mania". In this animation the rate of precession is greatly exaggerated.]]

During the 18th and 19th century, the [[pendulum clock]]'s role as the most accurate timekeeper motivated much practical research into improving pendulums. It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing.<ref name="Milham1945" /><ref name="Beckett1874">{{cite book
|last=Beckett
|first=Edmund
|author-link= Edmund Beckett, 1st Baron Grimthorpe
|year=1874
|title=A Rudimentary Treatise on Clocks and Watches and Bells, 6th Ed
|publisher=Lockwood & Co.
|location=London
|url=https://books.google.com/books?id=OvQ3AAAAMAAJ&pg=PA50
|page=50  }}</ref>  This was solved with the invention of temperature compensated pendulums, the mercury pendulum in 1721<ref name="Graham1726">{{cite journal
  | last = Graham
  | first = George
  | title = A contrivance to avoid irregularities in a clock's motion occasion'd by the action of heat and cold upon the rod of the pendulum
  | journal = Philosophical Transactions of the Royal Society
  | volume = 34
  | issue = 392–398
  | pages = 40–44
  | year = 1726
  | url =https://zenodo.org/record/1432208
  | doi = 10.1098/rstl.1726.0006
  | s2cid = 186210095
  | doi-access = free
  }} cited in {{cite book
  | last = Day
  | first = Lance
  |author2=Ian McNeil
  | title = Biographical Dictionary of the History of Technology
  | publisher = Taylor & Francis
  | year = 1996
  | page = 300
  | url = https://books.google.com/books?id=UuigWMLVriMC&pg=PA300
  | isbn =  978-0-415-06042-4}}</ref> and the [[gridiron pendulum]] in 1726, reducing errors in precision pendulum clocks to a few seconds per week.<ref name="Andrewes1994" />

The accuracy of gravity measurements made with pendulums was limited by the difficulty of finding the location of their [[Center of percussion|center of oscillation]]. Huygens had discovered in 1673 that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot,<ref name="HuygensReciprocity" /> and the distance between the two points was equal to the length of a simple gravity pendulum of the same period.<ref name="HuygensCompound" />  In 1818 British Captain [[Henry Kater]] invented the reversible [[Kater's pendulum]]<ref name="Kater1818">{{cite journal
  | last = Kater
  | first = Henry
  | title = An account of experiments for determining the length of the pendulum vibrating seconds in the latitude of London
  | journal = Phil. Trans. R. Soc.
  | volume = 104
  | issue = 33
  | page = 109
  | year = 1818
  | url = https://books.google.com/books?id=uaQOAAAAIAAJ&q=%22Henry+Kater%22+kater+pendulum&pg=PA83
  | access-date = 2008-11-25}}</ref> which used this principle, making possible very accurate measurements of gravity. For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration.

=== 1851: Foucault pendulum ===
{{Main|Foucault pendulum}}
In 1851, [[Jean Bernard Léon Foucault]] showed that the plane of oscillation of a pendulum, like a [[gyroscope]], tends to stay constant regardless of the motion of the pivot, and that this could be used to demonstrate the  [[rotation of the Earth]]. He suspended a pendulum free to swing in two dimensions (later named the [[Foucault pendulum]]) from the dome of the [[Panthéon, Paris|Panthéon]] in Paris. The length of the cord was {{convert|67|m|abbr =on}}. Once the pendulum was set in motion, the plane of swing was observed to [[precess]] or rotate 360° clockwise in about 32 hours.<ref>{{cite journal|url=https://www.maa.org/sites/default/files/pdf/upload_library/1/1/Oprea-Ford-1996.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.maa.org/sites/default/files/pdf/upload_library/1/1/Oprea-Ford-1996.pdf |archive-date=2022-10-09 |url-status=live|title=Geometry and the Focault Pendulum|publisher= Mathematical Association of America|first=John|last=Oprea|access-date=13 April 2021|date=1995 |journal= The American Mathematical Monthly|volume=102|issue=6|pages=515–522|doi=10.1080/00029890.1995.12004611}}</ref>
This was the first demonstration of the Earth's rotation that did not depend on celestial observations,<ref>Amir Aczel (2003) Leon Foucault: His life, times and achievements, in {{cite book
  | last = Matthews
  | first = Michael R.
  |author2=Colin F. Gauld |author3=Arthur Stinner
  | title = The Pendulum: Scientific, Historical, Educational, and Philosophical Perspectives
  | publisher = Springer
  | year = 2005
  | page = 177
  | url = https://books.google.com/books?id=3GV2NgDwtjMC&pg=PA177
  | isbn = 978-1-4020-3525-8}}</ref> and a "pendulum mania" broke out, as Foucault pendulums were displayed in many cities and attracted large crowds.<ref>{{cite web
 |last=Giovannangeli 
 |first=Françoise 
 |date=November 1996 
 |url=http://www.paris.org/Kiosque/nov96/foucault.html 
 |title=Spinning Foucault's Pendulum at the Panthéon 
 |publisher=The Paris Pages 
 |access-date=2007-05-25 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20070609102153/http://www.paris.org/Kiosque/nov96/foucault.html 
 |archive-date=2007-06-09 
}}</ref><ref>{{cite book
  | last = Tobin
  | first = William
  | title = The Life and Science of Leon Foucault: The man who proved the Earth rotates
  | publisher = Cambridge University Press
  | year = 2003
  | location = UK
  | pages = 148–149
  | url = https://books.google.com/books?id=UbMRmyxCZmYC&pg=PA148
  | isbn = 978-0-521-80855-2}}</ref>

=== 1930: Decline in use ===
Around 1900 low-[[thermal expansion|thermal-expansion]] materials began to be used for pendulum rods in the highest precision clocks and other instruments, first [[invar]], a nickel steel alloy, and later [[fused quartz]], which made temperature compensation trivial.<ref name="BritannicaP540">{{cite EB1911|wstitle= Clock |volume= 06 |last= Penderel-Brodhurst |first= James George Joseph |author-link= James George Joseph Penderel-Brodhurst | pages = 536&ndash;553; see pages 540 and 541 |quote= }}</ref>  Precision pendulums were housed in low pressure tanks, which kept the air pressure constant to prevent changes in the period due to changes in [[buoyancy]] of the pendulum due to changing [[atmospheric pressure]].<ref name="BritannicaP540" />  The best pendulum clocks achieved accuracy of around a second per year.<ref name="Jones2000">{{cite book
  | last = Jones
  | first = Tony
  | title = Splitting the Second: The Story of Atomic Time
  | publisher = CRC Press
  | year = 2000
  | page = 30
  | url = https://books.google.com/books?id=krZBQbnHTY0C&pg=PA30
  | isbn = 978-0-7503-0640-9}}</ref><ref>{{cite book
  | last = Kaler
  | first = James B.
  | title =  Ever-changing Sky: A Guide to the Celestial Sphere
  | publisher = Cambridge Univ. Press
  | year = 2002
  | location = UK
  | page = 183
  | url = https://books.google.com/books?id=KYLSMsduNqcC&pg=PA183
  | isbn = 978-0-521-49918-7}}</ref>

The timekeeping accuracy of the pendulum was exceeded by the [[quartz]] [[crystal oscillator]], invented in 1921, and [[quartz clock]]s, invented in 1927, replaced pendulum clocks as the world's best timekeepers.<ref name="Marrison" />  Pendulum clocks were used as time standards until World War 2, although the French Time Service continued using them in their official time standard ensemble until 1954.<ref>{{cite book
  | last = Audoin
  | first = Claude
  |author2=Bernard Guinot |author3=Stephen Lyle
  | title = The Measurement of Time: Time, Frequency, and the Atomic Clock
  | publisher = Cambridge Univ. Press
  | year = 2001
  | location = UK
  | page = 83
  | url = https://books.google.com/books?id=LqdgUcm03A8C
  | isbn = 978-0-521-00397-1}}</ref>  Pendulum [[gravimeter]]s were superseded by "free fall" gravimeters in the 1950s,<ref name="Torge">{{cite book
  | last = Torge
  | first = Wolfgang
  | title = Geodesy: An Introduction
  | publisher = Walter de Gruyter
  | year = 2001
  | page = 177
  | url = https://books.google.com/books?id=pFO6VB_czRYC&pg=PA177
  | isbn = 978-3-11-017072-6}}</ref> but pendulum instruments continued to be used into the 1970s.