Editing Leap second (section)

==History==
[[File:Leapsecond.ut1-utc.svg|thumb|right|300px|Graph showing the difference between UT1 and UTC. Vertical segments correspond to leap seconds.]]
In about AD 140, [[Ptolemy]], the Alexandrian astronomer, [[sexagesimal]]ly subdivided both the mean solar day and the [[true solar day]] to at least six places after the sexagesimal point, and he used simple fractions of both the equinoctial hour and the seasonal hour, none of which resemble the modern second.<ref name=Ptolemy>{{cite book|author=Ptolemy|author-link=Ptolemy|author2=G. J. Toomer|others=Toomer, G. J.|title=Ptolemy's Alemagest|year = 1998|publisher=Princeton University Press|location=Princeton, New Jersey|isbn=978-0-691-00260-6|pages=6–7, 23, 211–216}}</ref>    Muslim scholars, including [[al-Biruni]] in 1000, subdivided the mean solar day into 24 equinoctial hours, each of which was subdivided sexagesimally, that is into the units of minute, second, third, fourth and fifth, creating the modern second as {{nowrap|1= {{frac|1|60}} of {{frac|1|60}} of {{frac|1|24}} = {{frac|1|86,400}}}} of the mean solar day in the process.<ref name="al-Biruni">{{cite book|author=al-Biruni|author-link=al-Biruni|others=Sachau, C. Edward|title=The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past"|url=https://books.google.com/books?id=pFIEAAAAIAAJ|year=1879|publisher=Oriental Translation Fund of Great Britain & Ireland|pages=141–149, 158, 408, 410|url-status=live|archive-url=https://web.archive.org/web/20171114142935/https://books.google.com/books?id=pFIEAAAAIAAJ|archive-date=14 November 2017}} Used for mean new moons, both in [[Hebrew calendar]] cycles and in equivalent astronomical cycles.</ref> With this definition, the second was proposed in 1874 as the base unit of time in the [[CGS system of units]].<ref>{{cite book|title=Illustrations of the centimetre-gramme-second (C.G.S.) system of units|url=https://archive.org/details/illustrationsce00evergoog|year=1875|publisher=Taylor and Francis|page=[https://archive.org/details/illustrationsce00evergoog/page/n99 83]|first1=J. D.|last1=Everett|author-link1=Joseph David Everett}}</ref> Soon afterwards [[Simon Newcomb]] and others discovered that Earth's rotation period varied irregularly,<ref name="Pearce">{{cite journal | last1 = Pearce | first1 = J. A. | year = 1928 | title = The Variability of the Rotation of the Earth | journal = Journal of the Royal Astronomical Society of Canada | volume = 22 | pages = 145–147 | bibcode = 1928JRASC..22..145P }}</ref> so in 1952, the [[International Astronomical Union]] (IAU) defined the second as a fraction of the [[sidereal year]]. In 1955, considering the [[tropical year]] to be more fundamental than the sidereal year, the IAU redefined the second as the fraction {{frac|1|31,556,925.975}} of the 1900.0 [[mean tropical year]]. In 1956, a slightly more precise value of {{frac|1|31,556,925.9747}} was adopted for the definition of the second by the [[International Committee for Weights and Measures]], and in 1960 by the [[General Conference on Weights and Measures]], becoming a part of the [[International System of Units]] (SI).<ref name=Supplement>{{cite book|title=Explanatory Supplement to the Astronomical Almanac|url=https://books.google.com/books?id=WBiqdNy_2KIC|year=1992|publisher=University Science Books|location=Mill Valley, California|isbn=0-935702-68-7|pages=79–80|editor1-first=P. Kenneth|editor1-last=Seidelmann|url-status=live|archive-url=https://web.archive.org/web/20171114142935/https://books.google.com/books?id=WBiqdNy_2KIC|archive-date=14 November 2017}}</ref>

Eventually, this definition too was found to be inadequate for precise time measurements, so in 1967, the [[SI second]] was again redefined as 9,192,631,770 periods of the radiation emitted by a [[caesium]]-133 atom in the transition between the two hyperfine levels of its ground state.<ref name="USNO">{{cite web|title=Leap Seconds|publisher=Time Service Department, [[United States Naval Observatory]]|url=https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/Global-Positioning-System/USNO-GPS-Time-Transfer/Leap-Seconds/|access-date=19 November 2022}}</ref> That value agreed to 1 part in 10<sup>10</sup> with the astronomical (ephemeris) second then in use.<ref>[[William Markowitz|Wm Markowitz]] (1988) 'Comparisons of ET (Solar), ET (Lunar), UT and TDT', in (eds.) A K Babcock & G A Wilkins, 'The Earth's Rotation and Reference Frames for Geodesy and Geophysics', IAU Symposia #128 (1988), at pp 413–418.</ref> It was also close{{quantify|date=January 2022}} to {{frac|1|86,400}} of the mean solar day as averaged between years 1750 and 1892.

However, for the past several centuries, the length of the mean solar day has been increasing by about 1.4–1.7&nbsp;[[millisecond|ms]] per century, depending on the averaging time.<ref>DD McCarthy and AK Babcock (1986), "The Length of the Day Since 1658", Phys. Earth Planet Inter., No. 44, pp. 281–292</ref><ref>RA Nelson, DD McCarthy, S Malys, J Levine, B Guinot, HF Fliegel, RL Beard, and TR Bartholomew, (2001) "The Leap Second: its History and Possible Future" (2001), Metrologia 38, pp. 509–529</ref><ref name=SM1995>{{cite journal | last1 = Stephenson | first1 = F.R. | last2 = Morrison | first2 = L.V. | year = 1995 | title = Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990 | bibcode = 1995RSPTA.351..165S | journal = Philosophical Transactions of the Royal Society of London A | volume = 351 | issue = 1695| pages = 165–202 | doi=10.1098/rsta.1995.0028| s2cid = 120718607 }}</ref> By 1961, the mean solar day was already a millisecond or two longer than {{val|86400}} SI seconds.<ref>{{cite journal | last1 = McCarthy | first1 = D D | last2 = Hackman | first2 = C | last3 = Nelson | first3 = R A | year = 2008 | title = The Physical Basis of the Leap Second | url = https://apps.dtic.mil/sti/pdfs/ADA489427.pdf | archive-url = https://web.archive.org/web/20210312034304/https://apps.dtic.mil/sti/pdfs/ADA489427.pdf | url-status = live | archive-date = 12 March 2021 | journal = Astronomical Journal | volume = 136 | issue = 5 | pages = 1906–1908 | doi = 10.1088/0004-6256/136/5/1906 | bibcode = 2008AJ....136.1906M | doi-access = free | access-date = 26 February 2022}}</ref> Therefore, time standards that change the date after precisely {{val|86400}} SI seconds, such as the [[International Atomic Time]] (TAI), would become increasingly ahead of time standards tied to the mean solar day, such as [[Universal Time]] (UT).

When the [[Coordinated Universal Time]] (UTC) standard was instituted in 1960, based on atomic clocks, it was felt necessary to maintain agreement with UT, which, until then, had been the reference for broadcast time services. From 1960 to 1971, the rate of UTC atomic clocks was offset from a pure atomic time scale by the [[International Time Bureau|BIH]] to remain synchronized with [[UT2]], a practice known as the "rubber second".<ref>{{cite book|title=From Sundials To Atomic Clocks: Understanding Time and Frequency |first1=James |last1=Jespersen |first2=Jane |last2=Fitz-Randolph |publisher=[[National Institute of Standards and Technology]] |url=https://tf.nist.gov/general/pdf/1796.pdf |page=109 |year=1999}}</ref> The rate of UTC was decided at the start of each year, and was offset from the rate of atomic time by −150 parts per 10{{sup|10}} for 1960–1962, by −130 parts per 10{{sup|10}} for 1962–63, by −150 parts per 10{{sup|10}} again for 1964–65, and by −300 parts per 10{{sup|10}} for 1966–1971.<ref name=NBS140>{{citation |editor-last=Blair |editor-first=Byron E. |title=NBS Monograph 140: Time and Frequency: Theory and Fundamentals |url=https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nbsmonograph140.pdf |date=May 1974 |page=8}}</ref> Alongside the shift in rate, an occasional 0.1&nbsp;s step (0.05&nbsp;s before 1963) was needed. This predominantly frequency-shifted rate of UTC was broadcast by [[Time from NPL (MSF)|MSF]], [[WWV (radio station)|WWV]], and [[CHU (radio station)|CHU]] among other time stations. In 1966, the [[ITU-R#CCIR|CCIR]] approved "stepped atomic time" (SAT), which adjusted atomic time with more frequent 0.2&nbsp;s adjustments to keep it within 0.1&nbsp;s of UT2, because it had no rate adjustments.<ref>{{cite book|title=Time: From Earth Rotation to Atomic Physics|edition=second|first1=Dennis D.|last1=McCarthy|first2=P. Kenneth|last2=Seidelmann|quote=For provisional limited use, the CCIR in 1966 approved "Stepped Atomic Time," which used the atomic second with frequent 200&nbsp;ms adjustments made in order to be within 0.1&nbsp;s of UT2.}}</ref> SAT was broadcast by [[WWVB]] among other time stations.<ref name=NBS140/>

In 1972, the leap-second system was introduced so that the UTC seconds could be set exactly equal to the standard SI second, while still maintaining the UTC time of day and changes of UTC date synchronized with those of UT1.<ref name="USNO"/> By then, the UTC clock was already 10 seconds behind TAI, which had been synchronized with UT1 in 1958, but had been counting true SI seconds since then. After 1972, both clocks have been ticking in SI seconds, so the difference between their displays at any time is 10 seconds plus the total number of leap seconds that have been applied to UTC as of that time; {{as of|2024|lc=on}}, 27 leap seconds have been applied to UTC, so the difference is 10 + 27 = 37 seconds. The most recent leap second was on December 31, 2016.