John Pazmino
 2005 August 2 initial
 2018 July 21 current

    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 
    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. 
    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 
    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 
    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 

  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) ---------|

    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. 

    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. 

    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 
    Then, suddenly, on July 4th of 2005 came the word that, bingo!, 
this year got a leap second!