Leap second

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Screen capture of the UTC clock from time.gov during the UTC leap second, on June 30, 2012, 23:59:60.

A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC) in order to keep its time of day close to the mean solar time. Without such a correction, time reckoned by Earth rotation drifts away from atomic time because of irregularities in the Earth's rate of rotation. Since this system of correction was implemented in 1972, 25 such leap seconds have been inserted. The most recent one happened on June 30, 2012 at 23:59:60 UTC.[1]

The UTC time standard, which is widely used for international timekeeping and as the reference for civil time in most countries, uses the international system (SI) definition of the second, based on atomic clocks. Like most time standards, UTC defines a grouping of seconds into minutes, hours, days, months, and years. However, the duration of one mean solar day is slightly longer than 24 hours (86400 SI seconds). Therefore, if the UTC day were defined as precisely 86400 SI seconds, the UTC time-of-day would slowly drift apart from that of solar-based standards, such as Greenwich Mean Time (GMT) and its successor UT1. The purpose of a leap second is to compensate for this drift, by occasionally scheduling some UTC days with 86401 or 86399 SI seconds.

Specifically, a positive leap second is inserted between second 23:59:59 of a chosen UTC calendar date (the last day of a month, usually June 30 or December 31) and second 00:00:00 of the following date. This extra second is displayed on UTC clocks as 23:59:60. On clocks that display local time tied to UTC, the leap second may be inserted at the end of some other hour (or half-hour or quarter-hour), depending on the local time zone.

A negative leap second would suppress second 23:59:59 of the last day of a chosen month, so that second 23:59:58 of that date would be followed immediately by second 00:00:00 of the following date. However, since the UTC standard was established, negative leap seconds have never been needed.

Because the Earth's rotation speed varies in response to climatic and geological events, UTC leap seconds are irregularly spaced and unpredictable. Insertion of each UTC leap second is usually decided about six months in advance by the International Earth Rotation and Reference Systems Service (IERS), when needed to ensure that the difference between the UTC and UT1 readings will never exceed 0.9 second. Between their adoption in 1972 and June 2012, 25 leap seconds have been scheduled, all positive. The rate at which leap seconds have been inserted has been decreasing.


Graph showing the difference between UT1 and UTC. Vertical segments correspond to leap seconds.

About 140 AD Ptolemy, the Alexandrian astronomer, sexagesimally 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.[2] 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 160 of 160 of 124 = 186400 of the mean solar day in the process.[3] With this definition, the second was proposed in 1874 as the base unit of time in the CGS system of units.[4] Soon afterwards Simon Newcomb and others discovered that Earth's rotation period varied irregularly,[5] so in 1952 the International Astronomical Union (IAU) defined the second as a fraction of the sidereal year. Because the tropical year was considered more fundamental than the sidereal year, in 1955 the IAU redefined the second as the fraction 131,556,925.9747 of the 1900.0 mean tropical year, which was adopted in 1956 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).[6]

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.[7] That value agreed to 1 part in 1010 with the astronomical (ephemeris) second then in use.[8] It was also close to 186400 of the mean solar day as averaged between 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 ms per century, depending on the averaging time.[9][10][11] By 1961 the mean solar day was already a millisecond or two longer than 86400 SI seconds.[12] Therefore, time standards that change the date after precisely 86400 SI seconds, such the International Atomic Time (TAI), will get increasingly ahead of time standards tied to the mean solar day, such as Greenwich Mean Time (GMT).

When the Coordinated Universal Time standard was instituted in 1961, based on atomic clocks, it was felt necessary to maintain agreement with the GMT time of day, which until then had been the reference for broadcast time services. Thus, from 1961 to 1971, the rate of (some) atomic clocks was constantly slowed to remain synchronised with GMT. During that period, therefore, the "seconds" of broadcast services were actually slightly longer than the SI second and closer to the GMT seconds.

In 1972 the leap-second system was introduced so that the broadcast UTC seconds could be made 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 (the solar time standard that superseded GMT).[7] 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 readouts at any time is 10 seconds plus the total number of leap seconds that have been applied to UTC (35 seconds in July 2012).

Insertion of leap seconds[edit]

Announced leap seconds to date
Year Jun 30 Dec 31
1972 +1 +1
1973 0 +1
1974 0 +1
1975 0 +1
1976 0 +1
1977 0 +1
1978 0 +1
1979 0 +1
1980 0 0
1981 +1 0
1982 +1 0
1983 +1 0
1984 0 0
1985 +1 0
1986 0 0
1987 0 +1
1988 0 0
1989 0 +1
1990 0 +1
1991 0 0
1992 +1 0
1993 +1 0
1994 +1 0
1995 0 +1
1996 0 0
1997 +1 0
1998 0 +1
1999 0 0
2000 0 0
2001 0 0
2002 0 0
2003 0 0
2004 0 0
2005 0 +1
2006 0 0
2007 0 0
2008 0 +1
2009 0 0
2010 0 0
2011 0 0
2012 +1 0
2013 0 0
2014 0 0
Year Jun 30 Dec 31
Total 10 15
Current TAI − UTC

The scheduling of leap seconds was initially delegated to the Bureau International de l'Heure (BIH), but passed to the International Earth Rotation and Reference Systems Service (IERS) on January 1, 1988. IERS usually decides to apply a leap second whenever the difference between UTC and UT1 approaches 0.6 s, in order to keep the difference between UTC and UT1 from exceeding 0.9 s.

The UTC standard allows leap seconds to be applied at the end of any UTC month, but as of July 2012 all of them have been inserted either at the end of June 30 or December 31. IERS publishes announcements every six months, whether leap seconds are to occur or not, in its "Bulletin C". Such announcements are typically published well in advance of each possible leap second date — usually in early January for June 30 and in early July for December 31. [13][14] Some time signal broadcasts give voice announcements of an impending leap second.

Between 1972 and 2012 a leap second has been inserted about every 18 months, on the average. However, the spacing is quite irregular and apparently increasing: there were no leap seconds in the seven-year interval between January 1, 1999 and December 31, 2005, but there were 9 leap seconds in the 8 years 1972–1979.

Unlike leap days, UTC leap seconds occur simultaneously worldwide; for example, the leap second on December 31, 2005 23:59:60 UTC was December 31, 2005 18:59:60 (6:59:60 p.m.) in U.S. Eastern Standard Time and January 1, 2006 08:59:60 (a.m.) in Japan Standard Time.

Not all clocks implement leap seconds in the same manner as UTC. Leap seconds in Unix time are commonly implemented by repeating the last second of the day. Network Time Protocol freezes time during the leap second. Other experimental schemes warp time in the vicinity of a leap second.[15]

Slowing rotation of the Earth[edit]

Deviation of day length from SI based day, 1962–2010
Main article: ΔT

Leap seconds are irregularly spaced because the Earth's rotation speed changes irregularly. Indeed the Earth's rotation is quite unpredictable in the long term, which explains why leap seconds are announced only six months in advance.

A mathematical model of the variations in the length of the solar day was developed by F. R. Stephenson and L. V. Morrison,[11] based on records of eclipses for the period 700 BC to 1623 AD, telescopic observations of occultations for the period 1623 until 1967 and atomic clocks thereafter. The model shows a steady increase of the mean solar day by 1.70 ms (± 0.05 ms) per century, plus a periodic shift of about 4 ms amplitude and period of about 1500 yr.[11] Over the last few centuries, the periodic component reduced the rate of lengthening of the mean solar day to about 1.4 ms per century.[16]

The main reason for the slowing down of the Earth's rotation is tidal friction, which alone would lengthen the day by 2.3 ms/century.[11] Other contributing factors are the movement of the Earth's crust relative to its core, changes in mantle convection, and any other events or processes that cause a significant redistribution of mass. These processes change the Earth's moment of inertia, affecting the rate of rotation due to conservation of angular momentum, sometimes increasing earth's rotational speed (decreasing the solar day and opposing tidal friction). For example, glacial rebound shortens the solar day by 0.6 ms/century and the 2004 Indian Ocean earthquake is thought to have shortened it by 2.68 microseconds.[17]

Proposal to abolish leap seconds[edit]

The irregularity and unpredictability of UTC leap seconds is problematic for several areas, especially computing. For example, to compute the elapsed time in seconds between two given UTC past dates requires consulting a table of leap seconds, which needs to be updated whenever a new leap second is announced. Moreover, it is not possible to compute accurate time intervals for UTC dates that are more than about six months in the future.

On July 5, 2005, the Head of the Earth Orientation Center of the IERS sent a notice to IERS Bulletins C and D subscribers, soliciting comments on a U.S. proposal before the ITU-R Study Group 7's WP7-A to eliminate leap seconds from the UTC broadcast standard before 2008. (The ITU-R is responsible for the definition of UTC.) The Wall Street Journal noted that the proposal was considered by a U.S. official to be a "private matter internal to the ITU", as of July 2005.[18] It was expected to be considered in November 2005, but the discussion has since been postponed.[19] Under the proposal, leap seconds would be technically replaced by leap hours as an attempt to satisfy the legal requirements of several ITU-R member nations that civil time be astronomically tied to the Sun.

A number of objections to the proposal have been raised. Dr. P. Kenneth Seidelmann, editor of the Explanatory Supplement to the Astronomical Almanac, wrote a letter[20] lamenting the lack of consistent public information about the proposal and adequate justification. Steve Allen of the University of California, Santa Cruz cited the large impact on astronomers in a Science News article.[21] He has an extensive online site[22] devoted to the issues and the history of leap seconds, including a set of references about the proposal and arguments against it.[23]

At the 2014 General Assembly of the International Union of Radio Scientists (URSI), Dr. Demetrios Matsakis, the US Naval Observatory's Chief Scientist for Time Services, presented the reasoning in favor of the redefinition and rebuttals to the arguments made against it.[24] He stressed the practical inability of software programmers to allow for the fact that leap seconds make time appear to go backwards, particularly when most of them do not even know that leap seconds exist. The possibility of leap seconds being a hazard to navigation was presented, as well as the observed effects on commerce.

The United States formulated its position on this matter based upon the advice of the National Telecommunications and Information Administration [25] and the Federal Communications Commission (FCC), which solicited comments from the general public.[26] This position is in favor of the redefinition.[27] The FCC has posted its received comments, which can be found using their search engine for proceeding 04-286 and limiting the "received period" to those between January 27 and February 18, 2014 inclusive.[28]

In 2011, Chunhao Han of the Beijing Global Information Center of Application and Exploration said China had not decided what its vote would be in January 2012, but some Chinese scholars consider it important to maintain a link between civil and astronomical time due to Chinese tradition. The 2012 vote was ultimately deferred.[29] At an ITU/BIPM-sponsosred workshop in the leap second, Dr. Han expressed his personal view in favor of abolishing the leap second,[30] and similar support for the redefinition was again expressed by Dr. Han, along with other Chinese timekeeping scientists, at the URSI General Assembly in 2014.

Arguments against the proposal include the unknown expense of such a major change and the fact that universal time will no longer correspond to mean solar time. It is also answered that two timescales that do not follow leap seconds are already available, International Atomic Time (TAI) and Global Positioning System (GPS) time. Computers, for example, could use these and convert to UTC or local civil time as necessary for output. Inexpensive GPS timing receivers are readily available and the satellite broadcasts include the necessary information to convert GPS time to UTC. It is also easy to convert GPS time to TAI as TAI is always exactly 19 seconds ahead of GPS time. Examples of systems based on GPS time include the CDMA digital cellular systems IS-95 and CDMA2000. In general, computer systems use UTC and synchronize their clocks using NTP (Network Time Protocol). Systems that cannot tolerate disruptions caused by leap seconds can base their time on TAI and use PTP (Precision Time Protocol). However the BIPM has pointed out that this proliferation of timescales leads to confusion,[31] and examples of how leap seconds have adversely affected GPS and NTP are given elsewhere in this article.

At the 47th meeting of Civil Global Positioning System Service Interface Committee in Fort Worth, Texas in September 2007, it was announced that a mailed vote would go out on stopping leap seconds. The plan for the vote was:[32]

  • April 2008: ITU Working Party 7A will submit to ITU Study Group 7 project recommendation on stopping leap seconds
  • During 2008, Study Group 7 will conduct a vote through mail among member states
  • October 2011: The ITU-R released its status paper, Status of Coordinated Universal Time (UTC) study in ITU-R, in preparation for the January 2012 meeting in Geneva; the paper reported that, to date, in response to the UN agency's 2010 & 2011 web based surveys requesting input on the topic, it had received 16 responses from the 192 Member States with "13 being in favor of change, 3 being contrary."[33]
  • January 2012: The ITU makes a decision.

In January 2012, rather than decide yes or no per this plan, the ITU decided to postpone a decision on leap seconds to the World Radio Conference in 2015. France, Italy, Japan, Mexico and the US were reported to be in favor while Canada, China, Germany and the UK were reportedly against.[34] Others including Nigeria, Russia and Turkey called for more study. The BBC states the ITU decided further study of broader social implications was needed.[35]

In May 2014 David Willetts, the ex-UK Minister State for Universities and Science[36], expressed opposition to the abolition of leap seconds. He indicated that as a layman, he wanted to keep "the link between time and people’s everyday experience of day and night." He also wanted to keep Greenwich Mean Time in Britain, and "warned" that it would drift towards the United States.[37] An article in the Times science section suggested that the abolition of leap seconds would mean the demise of Britain's role in timekeeping.[38]

Most if not all of the objections to the proposed change have been answered by its opponents. Dr. Felicitas Arias, who as Director of the International Bureau of Weights and Measures (BIPM)'s Time, Frequency, and Gravimetry Department, is responsible for generating UTC noted in a press release[39] that the drift of about one minute every 60–90 years could be compared to the 16-minute annual variation between true solar time and mean solar time, the one hour offset by use of daylight time, and the several-hours offset in certain geographically extra-large time zones. This value was computed using the pre-21st century slow-down rate; if the current slow-down rate prevails, it could take two centuries for a one-minute drift to develop. It is frequently noted that if the proposal passes, civil time could be adjusted by the sovereign nations simply by changing the offset between their civil time and UTC, and that those users who require the difference between solar time (GMT-equivalent) and UTC can obtain it several ways, including from the IERS via the internet, and that GPS upgrade plans include broadcasting this information.

Examples of problems caused by the leap second[edit]

A number of organizations reported computer problems following the June 30, 2012, leap second. Among the sites which reported problems were reddit (Apache Cassandra), Mozilla (Hadoop),[40] Qantas Airlines,[41] and various sites running Linux.[42]

Older versions of Motorola Oncore VP, UT, GT, and M12 GPS receivers had a bug that would cause a single timestamp off by a day if no leap second was scheduled for 256 weeks. On November 28, 2003 this actually happened. At midnight the receivers with this firmware reported November 29, 2003 for one second and then reverted to November 28, 2003.[43][44]

Older Trimble GPS receivers would insert a leap second immediately after the GPS constellation started broadcasting the next leap second insertion time (some months in advance of the actual leap second), rather than waiting for the next leap second to happen. This left the receiver's time off by a second in the interim.[45]

The NTP packet includes a leap second flag, which informs the user that a leap second is imminent. This among other things allows the user to distinguish between a bad measurement that should be ignored and a genuine leap second that should be followed. It has been reported that never, since the monitoring began in 2008 and whether or not a leap second should be inserted, have all NTP servers correctly set their flags on a December 31 or June 30.[46] This is one reason many NTP servers broadcast the wrong time for up to a day after a leap second insertion,[47] and it has been suggested that hackers have exploited this vulnerability.[48][49]

Workarounds for leap second issues[edit]

Instead of inserting a leap second at the end of the day, Google servers implement a leap smear, extending seconds slightly over a time window prior to the leap second.[50]

It has been proposed that media clients using the Real-time Transport Protocol inhibit generation or use of NTP timestamps during the leap second and the second preceding it.[51]

It has been proposed that, in the event the ITU resolution passes and leap seconds are no longer inserted, special Network Time Protocol and other time servers could be set up that provide UT1 rather than UTC.[52] Those astronomical observatories and other users that require UT1 could run off that time - although in many cases these users already download UT1-UTC from the IERS, and apply corrections in software.[53]

See also[edit]

  • Clock drift, phenomenon where a clock gains/loses time compared to another clock
  • Leap year, a year containing one extra day
  • Unix time, a common representation of time for computer systems
  • Delta-T (ΔT), the time difference obtained by subtracting Universal Time from Terrestrial Time
  • Shortwave radio stations that continuously broadcast UTC



  1. ^ IERS 2013
  2. ^ Ptolemy; G. J. Toomer (1998). Ptolemy's Alemagest. Toomer, G. J. Princeton, New Jersey: Princeton University Press. pp. 6–7, 23, 211–216. ISBN 978-0-691-00260-6. 
  3. ^ al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past". Sachau, C. Edward. Oriental Translation Fund of Great Britain & Ireland. pp. 141–149, 158, 408, 410.  Used for mean new moons, both in Hebrew calendar cycles and in equivalent astronomical cycles.
  4. ^ Everett, J. D. (1875). Illustrations of the centimetre-gramme-second (C.G.S.) system of units. Taylor and Francis. p. 83. 
  5. ^ Pearce, J. A. (1928), "The Variability of the Rotation of the Earth." Journal of the Royal Astronomical Society of Canada, volume 22, pages 145–147
  6. ^ Seidelmann, P. Kenneth, ed. (1992). Explanatory Supplement to the Astronomical Almanac. Mill Valley, California: University Science Books. pp. 79–80. ISBN 0-935702-68-7. 
  7. ^ a b "Leap Seconds". Time Service Department, United States Naval Observatory. Retrieved December 27, 2008. 
  8. ^ 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.
  9. ^ DD McCarthy and AK Babcock (1986), "The Length of the Day Since 1658", Phys. Earth Planet Inter., No. 44, pp. 281-292
  10. ^ 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
  11. ^ a b c d F.R. Stephenson, L.V. Morrison. "Long-term fluctuations in the Earth's rotation: 700 BC to AD 1990". Philosophical Transactions of the Royal Society of London, Series A 351 (1995) 165–202.
  12. ^ D D McCarthy, C Hackman and R A Nelson (2008), "The Physical Basis of the Leap Second". Astronomical Journal, vol. 136, pages 1906–1908
  13. ^ Gambis, Daniel (July 4, 2008). "Bulletin C 36". Paris: IERS EOP PC, Observatoire de Paris. Retrieved April 18, 2010. 
  14. ^ Andrea Thompson (December 8, 2008). "2008 Will Be Just a Second Longer". Live Science. Retrieved December 29, 2008. 
  15. ^ Kevin Gross (March 2014), RTP and Leap Seconds, RFC 7164 
  16. ^ Steve Allen (June 8, 2011). "Extrapolations of the difference ( TI - UT1 )". ucolick.org. Retrieved December 9, 2011. 
  17. ^ Cook-Anderson, Gretchen; Beasley, Dolores (January 10, 2005). "NASA Details Earthquake Effects on the Earth". National Aeronautics and Space Administration (press release). 
  18. ^ Why the U.S. Wants To End the Link Between Time and Sun by The Wall Street Journal
  19. ^ Leap second talks are postponed by BBC News
  20. ^ UTC redefinition or change by Kenneth Seidelmann
  21. ^ Cowen 2006
  22. ^ UTC might be redefined without Leap Seconds by Steve Allen
  23. ^ Proposed US Contribution to ITU-R WP 7A
  24. ^ http://tycho.usno.navy.mil/papers/ts-2014/Matsakis-LeapSecondComments.URSI-2014.pdf
  25. ^ http://www.ntia.doc.gov/page/us-proposals
  26. ^ https://apps.fcc.gov/edocs_public/attachmatch/DA-14-88A1.pdf
  27. ^ http://www.ntia.doc.gov/files/ntia/publications/sitt-stit-357221-v1-citel_presentation_for_regional_meetings_on_wrc-15-r2.ppt
  28. ^ http://apps.fcc.gov/ecfs/comment_search/input?z=li5rw
  29. ^ Merali 2011
  30. ^ https://www.itu.int/dms_pub/itu-r/oth/0a/0e/R0A0E0000960001PDFE.pdf
  31. ^ CCTF Strategy Document, International Bureau of Weights and Measures, July 29, 2013, pp. 19–24 
  32. ^ "47th CGSIC Meeting - Timing Subcommittee" (PDF). September 25, 2007. p. 9. Retrieved November 18, 2007. 
  33. ^ "WP7D - Status of Coordinated Universal Time (UTC) study in ITU-R" (Word 2007). International Telecommunication Union – Radiocommunication Sector (ITU-R) Release: Pg.2 (Pgs.2). October 4, 2011. Retrieved October 24, 2011. "To date, the BR received replies from 16 different Member States for the latest survey (out of a total of 192 Member States, 55 of which participate in the formation of UTC) - 13 being in favor of the change, 3 being contrary." 
  34. ^ "Wait a second: leap-second verdict goes into extra time". Ottawa Citizen. January 19, 2012. 
  35. ^ "Leap second decision is postponed". BBC News. January 19, 2012. 
  36. ^ O'Leary, Miles. (July 14, 2014). "Havant MP to stand down at next General Election after more than two decades." Portsmouth News.
  37. ^ Swinford, Steven. (May 15, 2014). "Greenwich Mean Time could drift to the US, minister warns." The Telegraph.
  38. ^ Whipple, Tom. (September 22, 2013). Rogue Second May Mean Time is up for Britain". London: The Times.
  39. ^ http://www.bipm.org/utils/en/pdf/Press_Release_UTC_13October.pdf
  40. ^ "‘Leap Second’ Bug Wreaks Havoc Across Web". Wired. July 1, 2012. 
  41. ^ "'Leap second crashes Qantas and leaves passengers stranded'". News Limited. July 1, 2012. 
  42. ^ "Anyone else experiencing high rates of Linux server crashes during a leap second day?". Serverfault.com. 
  43. ^ "256-Weak Leap Second Bug". July 2, 2013. 
  44. ^ "Motorola Oncore receivers and Leap Second bug". July 2, 2013. 
  45. ^ "Leap-second problem with older GPS receivers". July 2, 2013. 
  46. ^ Dr. David Malone, http://www.maths.tcd.ie/~dwmalone/time/leaps/
  47. ^ http://www.satsignal.eu/ntp/ntp-events.htm
  48. ^ http://lists.ntp.org/pipermail/questions/2012-August/033671.html
  49. ^ https://groups.google.com/forum/#!topic/comp.protocols.time.ntp/vhVlH4ENsJQ
  50. ^ Christopher Pascoe (September 15, 2011). "Time, technology and leaping seconds". Google. Retrieved July 2, 2012. 
  51. ^ Kevin Gross (June 21, 2012). "RTP and Leap Seconds". Internet Engineering Task Force. Retrieved July 2, 2012. 
  52. ^ Wallace, Patrick (2003). "The UTC Problem and its Solution". Proceedings of Colloquium on the UTC Time Scale. Torino. 
  53. ^ Luzum, Brian (2013). "The Role of the IERS in the Leap Second". BIPM/ITU Workshop on the Future of the International Time Scale. 


Further reading[edit]

External links[edit]

UTC redefinition