THE LEAP SECOND ------------- John Pazmino NYSkies firstname.lastname@example.org 2005 August 2 initial 2018 July 21 current Introduction ---------- On 2005 July 4 the International Earth Rotation Service announced that the world's time services must insert a leap second into their signals at the end of December 31st. The time marks across that final minute will be: ..., 23:59:58, 23:59:59, 23:59:60, 00:00:00, 00:00:01, ... The last time a leap second was added was at the end of 1998 December 31. During the last seven years many people came on stream in NYSkies, and elsewhere in home astronomy, who likely forgot about or never knew about this queer feature of timekeeping. I give here a basic explanation of the leap second, being the latest part of a vast and fascinating story of timekeeping. Solar Day ------- One of the fundamental justifications for the study of astronomy has been to keep track of time. Since antiquity, time was marked by the daily cycle of night and day, which governed our daily lifes. Even after the deployment of artificial indoor lighting in the 19th century and the growth of 24-hour cultures, the diurnal motion of the Sun was a primal device for telling time. Bye and bye the solar monitoring was refined to careful recording of the meridian transits of the Sun each day. A sundial does this to a reasonable good approximation for ordinary civilian purposes. The interval between successive meridian crossings of the Sun, successive noon moments, was one solar day. It was in ancient eras divided into 24 hours, then into 60 minutes, and finally into 60 seconds. It soon by the Greek era was realized that the Sun's motion across the sky was rather irregular thruout the year. The length of a solar day, as tracked by a water clock (a pot of water dripping into a calibrated jar). However, life was simpler and slower back then and the water clocks could be upset by vibration or tampering. One enduring problem was mischievous kids throwing stones into a public water clock to impede the drips. 'Noon' or '12:00' is the instant when the Sun is centered on the local meridian. It turns out that this hardly ever happens. You can test this by examining an almanac or the weather page of newspapers. Due to the symmetry of the sky east-west across the meridian, the time for the Sun to pass from rising to noon and from noon to setting are the same. That is, the midpoint moment between sunrise and sunset should be 12:00. Try it. You'll find that in general the midpoint is annoying off of 12:00 by several minutes. What's more, this offset varies over the months. I assume you do correct for daylight savings time and for the longitude offset from your timezone's central meridian. Or use an almanac that gives 'local solar time' rather than zone time. Mean Solar Day ------------ When mechanical clocks were developed in the 14th and later centuries, the wandering length of the solar day became too obvious to ignore. Astronomers defined a mean solar day as a day that would prevail by smoothing out the irregular motion of the Sun. This day was then assigned to the mechanical clocks to keep track of time and the clocks were also used to time various celestial events. By 'day' and 'length of day' I mean the span of the whole 24 hours. It's not the length of daylight, from sinrise thru noon to sunset. That varioes widely by season and latitude. More to the heart of the matter, the mean solar day is used to calculate future events. This was on the reasonable premise that mean solar time was a smoothly constant flow of time. It precisely paced the mathematical parameter of time in the calculations. In the earlier centuries when commerce was more localized each town kept its own solar time, like at an observatory or seaport or major business office. An astronomer monitored the Sun's motion, applied the corrections, and sent out time signals for mean solar time. This was usually done for certain hours of the day, typicly noon but likely for a morning and afternoon hour, too. The mean solar day is exactly 86,400 mean solar seconds. Which is to say, there are 24 hours of 60 minutes of 60 seconds in a mean solar day. The presumption was that the mean solar day was a constant of nature, so to speak, so the length of the second would be a constant. Latima te salvat -------------- The terms 'minute' and 'second' are recta mente derived fro latin and the maths of its era. The hour, hora, was the base division of the day. It was divided, thru legacy of the base-60 maths, into 60 minutae partes, minute or small parts. In time the 'partes' was dropped. The next order of division was a second or next minute part or secunda minuta pars or second minute part. In maths we continue into thirds, fourths, and higher order divisions, much like in decimal maths we got hundredths, thousands, millionths and so on. For civil use the second was a small a particle of time that could be sensed in ordinary life. The same logic applied to angular measure. The degree has its minute and second minute parts. From time to time there is an advocance to drop these ancient units and go to straight decimal days and degrees. This never got serious attention from civil authorities or measures & time services. In computations we can use decimals and, optionally, convert to base-60 numbers in the final answer. Universal Time ------------ As commerce and communications globalized in the 19th century and with the realtime telegraphy, time had to be more carefully defined. Eventually, the mean solar time at the Royal Greenwich Observatory was adopted for worldwide, or universal, use. This was called either Greenwich Mean Time or Universal Time. The public employed te former name while astronomers preferred the latter. Ephemerides and observations were cited in Universal Time, UT. The basis of this time was that it banked off of the presumably perfectly smooth and constant rotation of the Earth. After all, there was no indication to hand that the Earth was in some way irregular. And how could it be with so immense a mass with no force large enough to disturb it? As a matter of sheer practicality, astronomers actually monitored the background stars at night, they being orders simpler and more confidently measured than the solitary solar disc by day. The theory of the Sun's own motion within the starry background was sufficiently well known to transfer the star readings to the Sun and thus generate Greenwich Mean Time. With Universal Time and Greenwich Mean Time having the same definition by the early 20th century, the terms were interchangeable, As I explain latter, both 'UT' and 'GMT' no longer have a proper definition any more, but they are still in wide use to mean 'the same kind of time'. Universal Time undergoed a few refinements, resulting in flavors UT0, UT1, and UT2. UT1 is the lineal continuation of UT and is what you record for observations. In this paper I consistently refer to both the old UT and the newer UT1 as 'UT'. The other two UTs are essentially no longer in use. Earth rotation ------------ As the Earth rotates, it carries the stars and Sun round the sky, a phaenomenon that moved humans to use them as time markers. At the same time, people used 'time' as the mathematical parameter to predict future celestial events, like occultations and eclipses. Amazing as it seems, it was in the 17th century that astronomers first noticed that there could be something wrong with our time system. Halley in 1692 discussed how certain eclipses in antiquity seem to occur at hours quite different from what was calculated. This was not caused by mistakes in the maths or the principles of calculation, but to some odd 'accelerated motion' of the Moon. In 1738 Halley confirmed the effect by studying current observations of the Moon. The effing thing keeps running ahead of its calculated position, no matter how carefully he accounted for all the known influences. The Moon's motion displayed a longterm or secular acceleration. Kant in 1754 postulated that the trouble was in the Earth. The Earth, he suggested, is slowing down in its rotation! Our clocks, which are naturally set to the position of the Sun, were slower than they should be! Thus, using slowed clocks, the Moon looks like it is speeding up. He couldn't demonstrate this idea because there was no independent scheme of time keeping and clocks were too crude for longterm running without constant adjustment. By the 1790s the acceleration of the Moon was so well established that it earned specific discussion in astronomy classes and textbooks. Even the public got wind of it thru a treatment of the subject in the Encyclopedia Brittanica of that decade. The phaenomenon of accelerated motion was noticed in the planets and their satellites by the mid 19th century, leading to increasing suspicion that there was real decline in rotation rate of the Earth. But still there was no convincing way to show this. Tidal braking ----------- Can the ponderous globe, so huge and vast, ever be slowed down by any conceivable agent? By the mid 19th century there arose a feeling that since the Moon raises tides on Earth, it must be exchanging energy with Earth. The tides dissipate energy thru the random motion of the water drops and heat radiation into space. Could not this be reflected in a loss of rotational energy, as if the tides were a brake shoe pressing against the wheel of Earth? In 1920 Jeffreys worked out that the tides caused by the Moon dissipate about as much energy as that missing from Earth by a rotational slowing down. But still no firm proof was in hand. The amount of deceleration is tiny, but it accumulates. For the past several centuries the length of the mean solar day is increasing by 1.5 milliseconds per century. This sounds inconsequential but this slivers of time add up. Since just 1900 thru 2000, these slivers of seconds piled up to about 64 full seconds. That is, a clock running on mean solar time in 1900 and now checked against one that was continuously adjusted along the way differ in reading by 64 seconds. In addition to this secular cumulative retardation of the rotation, there are shortterm fluctuations. These, partly appreciated and partly still a mystery, last months to decades. They impose drastic glitches in the underlying slowdoen, This is enough to momentarily arrest the slowdown or to speed it up several times. Some of these brief episodes are due to mass migration of water and ice; others are suspected to be mass migration of fluid in the mantle or core. Both alter the angular momentum of Earth. The end result is that as the day length slowly increases, so does the length of its second. A 'day' is 86,400 'seconds', no matter how 'long' that day happens to be. Irregular time flow ----------------- Time signals sent out by the various time services naturally were Universal Time. In theory, the receiver could check the time with the motion of his local Sun. However, because clocks ticking off UT were fiddled with constantly, their output signals were irregular. From time to time fractions of a second were added or the actual interval between ticks was altered. You could say that leap seconds were always in force, governed in a haphazard erratic manner. For the lifestyle of the early 20th century this didn't matter much. As life grew more complex, information flow around the globe increased, communications and data networks sprang up, the need for a true constant flux of time was crucial. Ephemeris Time ------------ In 1960 the world's time services adopted Ephemeris Time as the new basis for a real smooth and uniform system of time. Ephemeris Time is a theoretical construct based on a certain interval of time that does not stretch out with the slowly increasing length of the mean solar day. First, a new 'second' had to be defined. After much deliberation it was decided to use as the new second of time that derived from the then best set of astronomy theory for the motion of the Sun. This was that of Newcomb, worked up in 1895. Newcomb used data collected from the 19th century and late 18th century. His method for predicting the solar and lunar motion was still in wide use in the mid 20th century. The new second was called the Ephemeris Second. It was declared to be the 31,566,925.9747th part of the year 1900. One common mistake is to claim that 86,400 of these seconds equals the mean solar day IN THAT YEAR. They don't and they can't. The second was averaged out over the whole span of Newcomb's data and it just so happens that this 31+ million of these averaged seconds fit into the year 1900. Phrased an other way, 1900 had slightly FEWER of its OWN seconds. The mean solar day that did really contain 86,400 of these Ephemeric Seconds occurred around 1820. This is near the midpoint of the continuous decline of Earth rotation within the data examined by Newcomb. I give below a table of the deviation of the instant mean solar day from exactly 86,400 Ephemeris Seconds for the span 1623 thru 1990. It is because ET was built from astronomy work of a century earlier that its second is SMALLER than the second of mean solar time prevailing in the mid 20th century. THIS IS IMPORTANT! Second, to calibrate the new time scale, it was declared that ET and UT agree on 1900 January 0 12h UT/ET. 'January 0' is the same as 'December 31'. In astronomy it is OK to extend the day count within a month before the 1st or after the last day. There was later discovered a subtile quirk in the data sources used for the ET and UT comparison. This makes ET 4 seconds AHEAD of UT at the 1900 epoch. We now just live with the error. ET is the argument of calculations. As a matter of sheer practicality, the time used in calculations was ALWAYS an 'ephemeris time' but mislabeled UT. Some of us at that time made a little rubber stamp to overprint 'ET' over the 'UT' in our older almanacs. Initial reactions --------------- The word that a 'new' method of time was invented and put into effect caused a stir among home astronomers. Most never were versed in heavy physics and did not appreciate the underlying theory. They still worked from books and magazines of a decade and more ago, some even from the preWar days. These had no mention of any funny business with timekeeping. On the contrary, they made UT seem so precise and exact. Ephemeris Time is a phantom system, not actually read off of real clocks. When promulgated in 1960, ET was running about 38 seconds AHEAD of UT (including the 4-second booboo). In an honest misunderstanding of what the relation was between the two times, many home astronomers 'corrected' their observational timings, like for occultations, made in UT, to become ET! By a symmetrical mistake, we sometimes 'corrected' the times of predictions, in ET, to render them into UT!! These adjustments were big nonos! The PURPOSE of ET and UT as separate systems was to monitor in a new and objective way the behavior of Earth rotation. Here to fore, home astronomers were out of the loop. Now they were dunked in over their head. I hazard that home astronomy publications in the early 1960s are infected with such erroneous adjustments. Molecular clocks --------------- The gotcha in timekeeping thru the crossing into the 20th century was that we were trying to assay the rotation of the Earth by clocks purposefully ganged to that rotation. Astronomers naturally adjusted their clocks if they drifted from synchronizm with the Sun. They assumed that some mechanical glitch caused the drift. In the 1930s molecular clocks were invented. Time was tracked by electronicly counting the vibrations of a quartz crystal under controlled ambient conditions. A certain number of vibrations added up to one second and this triggered a time pulse distributed to the world. These clocks were immune to the solar motion and were incredibly accurate. In 1936, using the new-fangled molecular clocks, Scheibe and Adelsberger demonstrated conclusively that indeed there is a steady decline in Earth rotation. They also discovered seasonal and midterm variations in the longterm decline, but here I deal only with the secular component. Yet, Universal Time continued as the world time standard both for observation and prediction. You calculated events using UT and labeled the predictions in UT. You then observed the event in UT and recorded the results in UT. Molecular clocks were soon made cheap and simple enough to become consumer items. The molecule is almost always that of quartz, which is artificially grown to exacting standards and then calibrated at the factory. A good quartz clock of today gives precise stable time flow far in excess of what the lay person can ever wish for. But it frees him from the occasional trouble of resetting the watch for mechanical drift. This, and not the extreme precision, is the selling point of these devices. They are 'set and forget' items. Atomic clocks ----------- A molecular clock is vulnerable to ambient conditions, tho orders less so than mechanical ones. The units in time services are maintained in stable settings of temperature, the one main element that affects their vibration rate. Consumer molecular clocks are subject to the seasonal and ambient variations of temperature. The change in rate is, however, slight enough to cause no worry for the owner. Partly as a spinoff of World War II, there were built crude atomic clocks in the mid and late 1940s. These worked by monitoring the energy transitions within, typicly, caesium atoms. Because atomic processes are virtually immune to ambient circumstances, this method provided for the first time in human history a truly perfect system of time independent of any astronomy methods. One early atomic clock was installed at the National Physics Lab, England, in 1955. An other was built at Royal Greenwich Observatory and than at United States Naval Observatory in 1956. Commercial atomic clocks became available by 1958, allowing for quick deployment at many time services and physics labs, There is no one 'master atomic clock', The clocks are by now almost commodities in major physics and geoscience labs, all pretty much ticking right on the money. However, to insure consistency around the world, a set of some 200 of these clocks continuously talk to each other to catch any discrepancies. International Atomic Time ----------------------- By the 1960s enough time centers and observatories had atomic clocks to think about setting up a new time service based on them. The initial impulse was to use the clocks as the mechanism for stable seconds ticks and adjust the actual reading to confirm to Universal Time. The early 'atomic time signals' ended up being little more than a prolongation of the erratic time signals of Universal Time from before the War. After a few false starts, International Atomic Time was adopted in 1971. It was set to agree with UT on 1958 January 1 0h UT/TAI. At that moment, TAI/UT was 32.184 seconds BEHIND ET. The second ticked out by the atomic clocks is the Ephemeris Second, the one that is SHORTER than the second of 1958 (and more so of today!). TAI is NOT the perfect time keeper! Atomic clocks are human made devices which can get out of order like nay other machine. True, the atoms themselfs are free of human influence, so they maintain constant energy transitions. The mechanics and electronics surrounding the caesium tube are susceptible to alteration with ambient conditions. Never the less, TAI is the very best actualization of a stable flux of time humans so far achieved. To hedge against malfunction of any one atomic clock, TAI is a coalition built from about 200 atomic clocks in many countries, all interacting together. Yet, despite TAI being the closest human realization to a uniform time flux, TAI is not casually distributed to the world. You have to be at a time lab to capture it. 'TAI' comes from the French words 'Temps Atomique International'. Many of the time services of Earth still use French for their formal issuances and procedings. SI second ------- The second is one of the base units of the world's system of measures. It was defined as the Ephemeris Second, as realized in International Atomic Time. It is also called the SI Second, after the Systeme International, the world's set of measures. Suggestions were offered that, to lessen the need for leap seconds, the very second should be redimensioned to a more modern value. That is, to lengthen the ET second slightly to more closely equal the second of a mean solar day of the 21st century. While this could be done, it would not be a permanent fix. It would merely shove off the day of reckoning for several more decades. More fundamentally, redimensioning the second, throws off the entire system of measures, not just timekeeping. For example, the meter is defined from the speed of light, which is a declared value and no longer a physicly measured one. A change in the second, for the sake of leap second mitigation, distorts the length of the meter. Using a constant flux of time allows us to see clearly the changing length of the day over the centuries, as a result of tidal braking and other shortterm influences. The table here gives the displacement, in milliseconds, from 86,400 TAI seconds for the day length at ten-year intervals since 1623. year dLOD | year dLOD | year dLOD | year dLOD ------ ---- | ------ ---- | ------ ----- | ------ ---- --- | 1700.5 +0.1 | 1800.5 -0.87 | 1900.5 +3.31 --- | 1710.5 +0.3 | 1810.5 +0.05 | 1910.5 +3.77 1623.5 -11. | 1720.5 +0.2 | 1820.5 -0.65 | 1920.5 +1.48 1630.5 -8. | 1730.5 +0.2 | 1830.5 -1.30 | 1930.5 -0.19 1640.5 -5. | 1740.5 +0.3 | 1840.5 +0.27 | 1940.5 +1.09 1650.5 -3. | 1750.5 +0.4 | 1850.5 +0.36 | 1950.5 +1.15 1660.5 -3. | 1760.5 +0.4 | 1860.5 -0.34 | 1960.5 +1.19 1670.5 -3. | 1770.5 +0.3 | 1870.5 -2.51 | 1970.5 +2.71 1680.5 -2. | 1780.5 +0.2 | 1880.5 -0.23 | 1980.5 +2.30 1690.5 -1. | 1790.5 -0.5 | 1890.5 -0.48 | 1990.5 +1.94 The whacking around of the dLOD comes from the shortterm fluctuations, which are quite stronger than the smooth longterm deceleration. Never the less, there is the trend of the day growing steadily longer during the telescopic era. The dispersion from 1990 thru now, 2005, is still preliminary. It takes some years to digest astronomy observations to see how far off they excurred from their predictions. The predictions are made with a mathematical smooth time parameter, implying a fixed length of the second, and are recorded in the irregular flow of UT. Relativity effects ---------------- I will only make brief mention here, despite my keen interest in Einstein physics. Until the 1950s astronomers for the most part ignored Einstein. They felt that his work had little bearing on astronomy save for isolated peculiar situations. Notable within the solar system was the warping of Mercury's orbit for being in the strongest zone of the Sun's gravity field. With the rise of radio astronomy, whose discoveries could best be explained by applying relativity, astronomers took crash courses in Einstein physics. One aspect of the new science is the behavior of time. The flow of time, seen from a given observer, depends on the strength of the gravity field around and the motion of the clock. Clocks since the dawn of history were on or near the Earth's surface. But they are in a sensible gravity field, to experience gravity redshift, and they are in motion around the rotation axis, causing time dilation. As clocks, specially atomic clocks, improved in precision, the seemingly negligible discrepancies due to these relativity effects showed up. Clearly, a new paradigm was called for in the concept of 'time'. Matters got worse for the space age, where speeds of clocks on satellites were large compared to any previously experienced by humans, and they were passing from one gravity field to an other thru the solar system. Relativity simply could not be ignored! Terrestrial Time -------------- ET was defined for clocks on the surface of Earth, in ignorance of relativity problems. To account for relativity, a new time, Terrestrial Dynamical Time, was invented. This is ET reckoned at the Earth's center. The net gravity field and relative motion is zero there, removing relativity effects. TDT was promulgated in 1984. The name was shortened to Terrestrial Time (or Temps Terrestre) in 1991. TT is the continuation of ET, with the crossover epoch of 1977 January 1 0h TAI. Other relativity-compliant scales were devised, which I pass over here except for one. This is Barycentric Dynamical Time, a time kept on a clock at the barycenter of the solar system. Altho it is no longer an active scheme, being replaced by a simpler one, it is still used by the Jet Propulsion Laboratory in its ephemeris generator programs. The intent was to have a time that is free of all gravity influences of the solar system. Because the barycenter is in the Sun's deep gravity well. there is a gravity redshift which makes TDB gain 489 milliseconds on TT every year. This must be accounted for before processing times in TDB. 'TDB' means 'Temps Dynamique Barycentrique'. Coordinated Universal Time ------------------------ As the 1960s progressed there was the sudden and rapid growth in data, command, control, telcomms systems that required a uniform time flow to operate. The time signals then issued were variable due to the effort to align them with Universal Time. In 1972 a new civil time system was established, Coordinated Universal Time, UTC. 'UTC' is a finagle initial for 'Temps Universal, Coordinee', which is not clean French. UTC was inaugurated in 1972 and was set exactly 10 seconds BEHIND TAI to account for the continuing slowdown of the Earth since TAI began. This was an approximate offset with the idea to fix it later by the leap second scheme. In UTC the time flows at the TAI/ET/TT rate. When ever an adjustment is needed to bring UTC closer in line with UT, a full exact second is added. Because this can be determined a few months in advance, due notice can be issued so time customers can prepare for the change. For example, the leap second to be added in December 2005 was announced in July 2005. The second is added to keep UTC within 0.9 second of UT. UT is still maintained at certain time centers but is no longer distributed as a time service. Only UYC is sent out to the world and all observations are done in UTC, not UT. The extra second, the leap second, is added at the end of December, Then, if necessary, at the end of June. If more are needed, they are added at the end of March and September. In the years when leap second was in force, only the December and June additions were ever used. If for some reason the Earth should speed up, as it can by some unpredictable shortterm glitch, a leap second can be missed out, a NEGATIVE leap second. This so far, as at 2005, never occurred. The leap second corrupts the final minute of the month, say December, like this: December 31 | January 1 ===========-========|=====-=============== no leap second 12:59:58 12:59:59 | 00:00:00 00:00:01 +-- - - - -+ positive (+) 12:59:58 12:59:59 12:59:60 | 00:00:00 +---------------------+ negative (-) 12:59:58 | 00:00:00 00:00:01 00:00:02 For applications requiring a consistent smooth time flux, UTC provides it for the first time in history. So long as the application does not require an absolute time mark, all is well. Many applications rely only on a raw count of seconds without regard to clock reading. Name of the second ---------------- You will hear and read of the official second by several names. All are of exactly the same length, but are zeroed at different epochs and realized in different ways. The Ephemeris Second was the first postWar second, intended as a theoretical mechanism to label prediction by something other than 'UT'. There was no physical clock that ticked Ephemeris Seconds. The Terrestrial Second is a direct continuation of the Ephemeris Second and, also, has no actual clock ticking it off. The International Atomic Second is the actualization, so far as human arts and crafts can achieve, of the Terrestrial Second. Altho the zero point of TAI and TT are different, the rate of the ticks is identical. TAI is not casually available to the public. UTC is distributed in its place. The UTC second is the TAI second. Unlike old UT, it is fixed in length with no slugging or dithering. To keep UTC in line with old UT, integer leap seconds are added or deducted. Thus, the flux of UTC ticks is held at a constant rate. Only the name of a particular one can be altered thru the leap second scheme. We have that ET = TT = TAI = UTC in the length of the second. They differ only in the epoch when they were started. Local practice ------------ The leap second is added (or subtracted) at day's end in UTC clock reading. Due to timezones, this will be a local clock reading, displaced hourly for each zone away from the Greenwich meridian. Technicly, each locality must exercise the leap second action at the local time corresponding to 23:59:59 UTC. In New York City this would be at 19:59:59. As best as I can uncover from assorted time service clients in the City, the leap second was routinely added to the LOCAL 23:59:59. This is the minute before local midnight, not Greenwich midnight. A problem can arise if a timing system is already adjusted from the UTC signal AND THEN is manually set at local midnight. The error will quickly be uncovered but there will be some overlapping period when the clocks of a one system are out of synch with those of an other. With the festivities surrounding December 31st, the leap second is almost always added as part of these celebrations. This is regardless of whether it was already added at the proper local time answering to UTC. The situation arises that for a couple hours, depending on timezone, the local implementation of UTC can be one second off from official UTC. In most cases no one notices or cares. Seeing the leap second -------------------- You can actually see the incidence of a leap second if you got a device that accepts and properly digests a leap second signal. Most ordinary clocks and watches do not. You likely don't even try to manually adjust them for the leap second but wait until the next routine instance of tuning the clock. At that moment the leap second is already embedded in the timing source you set the clock with. You need notice for the next leap second insertion. This comes from the astronomy news media or directly from your country's timekeeping service. Some agencies issue a notice also if there is NO leap second, to be sure all of its clients are in sych. Please actually read the notice! Your device should have a display for seconds, like '17:45:23'. Decimal seconds are optional and are not usually shown on displays meant for monitoring by eye. At the insertion of leap second the final second of the minute will show as '60', which is easy to do with a 7- segment character module. The device may in the stead of showing '60' hold the '59' of the paenultimate second twice. It may blink or change brightness for the final second. Audio signals, by radio broadcasts, like CHU in Canada or WWV in the United States, will beep off an extra second, perhaps with a different tone. A written record, such as a strip chart, will insert an extra tick along the time axis. For all complaint devices the leap second is added at the local equivalent of 0h UTC. Foe New York this is 19h EST and 20h EDST. In just about every gadget I ever saw there is no way to ignore the leap second, specially if the device interacts with other compliant ones. Computer clocks are sometimes reset to a signal from the attached network or Internet so that the leap second correction is eventually in place. You may do this by schedule or manually thru a clock- calendar program. For just about all home astronomy computer functions EXCEPT time stamping realtime celestial observations, you may ignore the leap second for a couple years. Examples of devices that can NOT show leap second properly are * analog clock, one with hands on a dial * digital clock with no means to receive external time signals * public clocks at banks, train stations, towers, similar * sundial, other heliochronical devices * almost all computer clocks, even if tied to network * time marks on files, email, data transfer, money flow * most non-GPS navigation systems UT and GMT -------- Universal Time as such no longer has a proper meaning. The term is a handy one with a honored legacy. Today it is prevalently used as a short form of UTC. That is, when you see a time in UT, it is really a time in UTC. What I consistently have called UT in this article is really named UT1. Yes, there is a UT0 and a UT2 of little interest here. UT1 is what is observed by taking sightings of the Sun. It is the continuation of the former plain UT with the leap second dripping in bit by bit over the years. Similarly for GMT. It started out as the civil time for the zero longitude meridian but now has been set aside for UTC. GMT is merely the 'civilian' word, for UTC. In their prior lifes, UT and GMT were erratic time flows because they were constantly adjusted to keep pace with the Sun. They can not in their former selfs be a competent time system in today's world. GMT is also the name of the civil time in England but the time signals by which clocks are set to GMT are themselfs UTC. With the very slight, for civil purposes, dispersion between the two, likely no one ever caught on. To avoid confusion, the preferred terms for civil time are British Winter Time. when the clocks do read GMT/UTC, and British Summer Time, when the clocks are moved forward one hour. In the daylight savings period, GMT as a world time service is NOT advanced. This emphasizes that GMT is essentially a synonym of UTC. When reading old works, notably before World War II, you may have to dig a bit to learn just what is meant by 'UT' or 'GMT'. Their meaning varied over the decades, until they were formally dropped with the introduction of TAI, ET/TT, and UTC. US legal time ----------- The definition of the legal time system in the United States predates the inauguration of UTC. It prescribes that GMT is the one basis for recording civil time thruout the country, as was in fact true until the startup of UTC. GMT was offset an integral number of hours to produce the 'standard' times within the timezones of America. Eastern Standard Time was GMT minus five hours. It is quite likely that the legal community treats UTC as a new name for GMT or that UTC is sufficiently close to old GMT that it doesn't urge any restatement of the time basis for the country. Yes, UTC is held by the leap second mechanism to within 0.9s of UT/GMT, so for probably all reasonable conceivable legal functions there is no concern. On the other hand, events with resolution of order 1 second may raise questions about how they were timed. I could not learn of any consistent legal opinion on the leap second feature of UTC, even when I reminded that GMT lacked it. GPS Time ------ Shortwave radios once were a must-have among home astronomers in order to receive the official time signals for UT (or now UTC). Now such radios are rare. In their place is the GPS unit, which reads out UTC in a digital form. This output can be feeded into a computer that logs observations, providing accurate complete timings for them. The GPS satellites carry caesium-rhubidium atomic clocks, slugged slightly to account for gravity redshift and time dilation in their orbits. The epoch of GPS is 6 January 1980 0h UTC, when the clocks were set to UTC. GPS time does NOT participate in leap second! It sends down uncorrected UTC, called simply 'GPS Time'. USAF, who runs the GPS network, sends to the satellites a new code when ever a leap second is added. The satellites sends this code in the data stream to Earth. It embeds the number of leap seconds added since the epoch, 13 thru mid 2005. Your GPS unit includes these leap seconds to give proper UTC, labeled as such on the display. GPS processors built as computer programs may have an option to omit this correction. You may want to do this if the application requires only a pure sequence of time marks without interruptions. Perhaps you have to do calendar maths on the timings. The Soviet Union deployed its own GPS network called GLONASS, As at 2004 it is still unfinished under Russian operation, yet it is an appreciated complement to GPS. It sends out Moscow time, which is three hours ahead of UTC. Like GPS, GLONASS has no provision for leap seconds. To keep Moscow time correct, the whole GLONASS system is taken off line for a manual reset of its clocks when ever a leap second was added to UTC. This takes only a couple minutes but it does interrupt the network for navigation and search/rescue work. Network time systems ------------------ Most of the timing sources for running global computer networks are totally ignorant of leap seconds as such. They are synchronized to UTC as the time standard easiest accessible via radio, satellite, and wire. As far as I could uncover, when a leap second was added the network clocks saw it as some localized fault, like a component malfunction or power cut. The last second on record was held in place until the network latched onto UTC again. The result was that the last second of the day to which the leap second was added was a repeated second. That last minute, to the computer, had two 60th seconds. Because computer networks routinely control ongoing processes, there is seldom the need to ask about when a certain operation took place in the past. If the need comes up, to reconstruct the scenario of a power failure several years ago, the clock readings are in error by the number of intervening leap seconds. The timing circuits merely start at the current UTC mark and count backwards along the second ticks WITH NO CONSIDERATION OF LEAP SECONDS. There simply is NO memory of prior leap seconds. I am unaware of any substantial troubles this mechanism of network timing ever caused. I also know of no such system that adds the leap second automaticly from the data taken off of UTC or by specific human intervention at the insertion instant. Table of leap seconds ------------------ Here is a table of all the leap seconds added since the start of the UTC system in January 1972. They were added into the final minute of the day: -------------------------------------------------------- 1972 Jun 30 1972 Dec 31 1973 Dec 31 1974 Dec 31 1975 Dec 31 1976 Dec 31 1977 Dec 31 1978 Dec 31 1979 Dec 31 1981 Jun 30 1982 Jun 30 1983 Jun 30 1985 Jun 30 1987 Dec 31 1989 Dec 31 1990 Dec 31 1992 Jun 30 1993 Jun 30 1994 Jun 30 1995 Dec 31 1997 Jun 30 1998 Dec 31 2005 Dec 31 2008 Dec 31 3012 Jun 30 2015 Jun 30 2016 Dec 31 -------------------------------------------------------- With 27 leap seconds added and the initial 10 at the start of UTC, TAI is AHEAD of UTC by 37 seconds. By parallel reasoning, TT is (32.184)+(37) = 69.184 seconds AHEAD of UTC. Intervals of time ---------------- The leap second feature of timekeeping kicks the hell out of calendar/clock maths. You no longer can simply subtract two moments of time to get a true number of seconds between them. The count is upset by intervening leap seconds, which a maths procedure can not by itself know about. . Because leap seconds are inserted, positive or negative, at human-arbitrated instances, there is no feasible way to prepare for future leap seconds. It is also impossible to reconstruct past leap seconds thru a maths process. A manual look-up is required. This is radicly different from the rules for leapdays, which are added every four year with simple exceptions. Suppose a clock that recognizes leap seconds, having taken part in previous insertions, is run in reverse to a prior moment. Will it catch the earlier leap seconds and yield a correct interval of time? No, it will not. It should be easy to build a clock that stores its leap seconds and counts them into the interval, but so far no such device exists. To measure time intervals correctly we need a signal that is not adjusted for leap seconds. The handiest one for home astronomers is GPS, at least since January 1980 when the GPS clock wfired up. The GPS ground station sends a data byte to the GPS satellite when ever a leap second is added, but it does NOT index the GPS clock. The leap second byte is sent to GPS receivers to locally adjust the displayed time for UTC. There are The receivers that ignore this data byte and take in a stream of pure seconds for timing intervals. Time scales --------- I summarize the relation among the time scales discussed in this article: 00:01:04.184 00:00:32 00:00:13 00:00:00 ET/TT TAI GPS UTC | |<---19----|<---13 (mid 2005)----| |<-----32.184 -----|<--------32 (mid 2005) ---------| |<----------------------64.184----------------------| The 32.184s offset of TT from TAI is fixed, does not change. The offset of UTC and the others alters with the intercalation of leap seconds. The times noted are the simultaneous readings on each time scale at 00:00:00 UTC. UT1 librates around UTC, staying within 0.9 seconds of it due to the leap second. Why so many? ---------- The 1970s thru the 1990s were an orgy of leap seconds. This led to some rather silly discussion among home astronomers! The major debate was that the Earth was slowing down so rapidly that the year now is so many SECONDS longer than in 1972!! If this were ever the case, there would be pandaemonium in every sector of society depending on time services!!! There would be chaos in orbital mechanics within the solar system!!!! While there is consistent secular trend toward a longer solar day, this can not account for the repeated need for leap seconds. The PRINCIPAL cause of the leap second addition is that the second of time in TAI/UTC is actually TOO SHORT to fit today's solar day! From recent reworking of Newcomb's data it turns out that the TAI second was the correct size for the mean solar day in about 1820. That is, a day then did contain exactly 86,400 TAI seconds. I say 'about 1820' because the various articles I found work over the old material in slightly different ways. There is a spread of about 18 months among those I examined. In some cases a date was not explicitly stated; I had to figure it out or graph it up. Since 1820 the day has been stretching due to Earth's decelerated rotation. Now a mean solar day has around 86,400.0025 TAI seconds. If there were NO FURTHER slowdown, the Earth stabilized at its present day length, we STILL would need leap seconds, just to catch up for the annual shortfall using too-short TAI seconds. Options ----- During the long hiatus from 1998 thru mid 2005 there arose debate among astronomers, navigators, time clients about leap seconds. From this dialog came many options for continuing or modifying the current leap second scheme. I describe several of these proposals below. Leave things alone ---------------- We do nothing. Keep the current system of leap seconds as is. This means that single leap seconds will be added (or removed) at irregular unforeseeable intervals. Time clients must wait until such leap seconds are announced before making any preparation to cope with them. The present scheme does keep UTC close enough to UT1 (old UT or GMT) that civil authorities hadn't objected to using UTC. In point of history, the developed countries long ago set its time standard to UT/GMT. I could find none that actually states UTC as its time standard. These include nations derived from older ones and newly formed from colonies. It is possible that due to the long absence of leap seconds until now, many clients simply never dealt with them and are now caught by surprise by the instant notice of the leap second at YE2005. I myself found in my inquiries that some time systems that MUST face up to leap seconds were clueless. Either the crew was too new to remember leap seconds or the system itself was too new. Abandon leap seconds ------------------ The other other extreme is to continue as is in that NO leap seconds are added at all. Let UTC run ahead on UT. The dispersion is about one second every 18 months or a full minute over the rest of the 21st century. For ordinary civil functions, it probably doesn't matter much, as long as there is in fact a world standard for timekeeping. UTC will no longer be 'coordinated' with mean solar time. Already some time clients turned to GPS Time to avoid the hassles of leap second. GPS Time has no leap seconds, but sends out a separate item of data so your receiver can locally add them in. The receiver, particularly if it's a computer program, may simply disregard this item and bank off of the raw GPS clock readings. Altho this option seems now exfenestrate with the forthcoming leap second, it is still a plausible strategy after 2005. Use TAI ----- TAI was zeroed to UTC in 1958 and is right now already over half a minute ahead of UTC. Shifting to TAI would cause a major break in time flow. It would be comparable in social upheaval to the days between the Julian and Gregorian calendars. Going to TAI would terminate once and for all the legacy of Universal Time, being that the new time signals no longer simuate Earth rotation. Because TAI is a somewhat clumsy term, the new time standard should have a short sweet name, World Time or Global Time. For most people, TAI is not readily to hand. The common time service is that based on UTC. What could happen is that in the UTC signals would, at the crossover moment, start citing TAI. Increase the dispersion --------------------- One reason for the frequent issuance of leap seconds is the close tolerance of UTC and UT1, no more than 0.9 second apart. By increasing this to, say, 5 seconds, we put off the leap second addition for about a decade. However, then we must add many leap seconds at once. That last minute has 65 seconds! The interval will still be irregular, only less frequent. There is also the question whether time systems, now having trouble dealing with single leap seconds, will wig out when called on to insert several at once. One interesting variation of this option is to let the dispersion accumulate to one HOUR and then add a leap HOUR. This would hold off any adjustment for many centuries or even a full millennium. The addition could be part of the millennium-crossing celebrations, like leap seconds are now for New Year's eve. The obvious flaw in a leap hour rule is that the world will be so incredibly different hundreds of years from now. The foundations of timekeeping may be completely altered from those of today before we add the initial leap hours! Regular leap seconds ------------------ We declare that with the present slowdown of Earth and the too- short SI second, we go and add a leap second at stated intervals. Perhaps, we make a rule that at the end of December in odd years there is a leap second. Just like that. This parallels the rules for leap days or, in some calendars, the intercalated month. This scheme certainly allows time clients to look ahead to the next leap second. For a simple example, new computer clock chips could automaticly add the second in odd Decembers. This option smooths out the shortterm fluctuations in Earth rotation. In certain years UTC will run ahead of UT1, as it does now. In certain other years UTC will lag UT1! Punctual leap seconds -------------------- We adjust UTC at predetermined intervals, like every four years. The leap second year could just as well be the same as the leapyear. The number of leap seconds in the adjustment answers to the UTC-UT1 relation at each instance. So we WILL do something, but the amount is unpredictable. Such a scheme could prove distressing for ssytems that can tolerate and respond to a one-second glitch or fault, but not one of several seconds duration. Redefine the second ---------------- The root cause of the continual leap seconds is that the very second of time is plain not long enough to fill out the 86,400 required for today's length of the mean solar day. By making the second a bit longer, thru counting off a few more cycles of the atomic clock, we could reduce thee number of leap seconds to perhaps a couple per century. This would be a temporary solution. As the Earth continues its deceleration, the day will lengthen beyond the new second. The whole game begins again, even if many centuries from now. Redefining the second is not a trivial task accomplished by a show of hands among time services. The second is one of the fundamental units in Earth's edifice of measurements. For one thing, it is used in the definition of the meter of length. Alter the second to cure the leap second problem, you may turn the world's measurement system on its ear. What to expect? ------------- After the 1998 leap second, we waited for the next one, perhaps in 1999 or 2000. None were issued. In mid 2000 US Naval Observatory, the time service for the United States, announced that there will be no more leap seconds until further notice. The addition process is suspended, thank you very much. What happened?! There never was a formal explanation but from other sources I learned that there could be valid reasons for suspending the leap second. They derive for the unexpected and explosive growth of digital, satellite, global networks that rely on a truly constant flow of time, with no glitches from leap seconds. Things like computer grids, laser laser ranging. cell phones, synchronized electric power systems, optical interferometry, pulsar astronomy, Internet, communication satellites, GPS, Iridium, planetary spaceprobes, were either embryonic or inconceivable in 1972. These components of our modern life require a predictable sequence of time marks which can not be easily altered to suit a leap second addition. Studies were made but nothing conclusive was announced. We got year after year of 'no leap second this year' notices with no hint of why. In fairness, the Earth did speed up a little, partly offsetting the need for leap second in the 2000s, but that was not the offered explanation. Then, suddenly, on July 4th of 2005 came the word that, bingo!, this year got a leap second!