ΔT vs. time from 1657 to 1984
Deviation of day length from international
standard second-based day, 1962–2010
Aztec Calendar Stone
Leap seconds are irregularly spaced because the Earth's rotation speed changes
irregularly. Indeed the Earth's rotation is quite unpredictable in the long term, which
explains why leap seconds are announced only six months in advance.

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

Graph showing the difference between
UT1 (succesor to GMT) and UTC
(Coordinated Universal Time). Vertical
segments correspond to leap seconds.
Collier Smith - A Man with Time on His Hands
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1.  The Leap Second
2.  To keep Universal Time the same as XXX
3.  30 Dec 2008
Answer to Quiz #358
July 1, 2012
1. What recent event?
2.  Why did it happen?
3.  When was the previous occasion this occurred?
Comments from Our Readers
It's nice to know that I'm not alone.  The Earth and I are as one, we are both slowing

Carol Farrant

Very interesting. I have of course heard of leap days, but I don't think I ever knew they
did that kind of tinkering on the second level.

Robert Austin

The last increase was Jan. 1, 2009.

Christine Walker

If anyone gets this wrong, we'll give them a second chance.

- Q. Gen.

I'd do another puzzle in a New York minute.

Christine Walker

BTW, the last addition of the Leap Second was Dec 31, 2008, delaying the start of
the New Year.  We'll let it go this time....

- Q. Gen.

When I got the time listed correctly, I got San Francisco's webpage which mentioned
the leap second. Very timely quiz. Interesting that the leap seconds are necessary to
keep out time correct.

I did not change my wristwatch or any of the house clocks. My computer is run off of
the country's time signals and probably made the addition Sunday morning.

Arthur Hartwell

What did you do with all that extra time on Saturday?  I tried to eat as much ice
cream as possible because I heard that whatever you consumed during the leap
second didn't have any calories.

- Q. Gen.

I did all that extra genealogy research while eating licorice in that extra time - those
calories don't count either.....

Marcelle Comeau

I'll bet you got an ice cream headache from eating that fast.

Ellen Welker

I've been indexing the 1940 census like crazy. Glad I stopped in for a peek at the
puzzle.   Thanks.

Jinny Collins

Too bad the Big Indexing Day was scheduled for July 1 and not June 30.  Imagine
how many more records could have been indexed with all that extra time available.  
People could have pooled their extra second and donated to a fund that could have
been used by a volunteer who otherwise would not have had time to participate.

- Q. Gen.

I would have had no idea except that the leap second managed to crash (or so they say)
the entire QANTAS booking system. That said, a post knowledge Google for '4:59:60'
+ time brought up leap second stories, so I guess I would have picked it anyway.

Ben Hollister

It was way back on 31 December 2008 that I was last able to enjoy that extra sleep due
to a leap second being added.  Of course, since that was New Years Eve and I was
partying a bit, I wasn't sleeping anyway.

Marty Guidry

Time is on my side - Deus.

Mike Dalton

My leap second was spent relaxing!  Making up for "lost" time.  Ha ha ha.

Audrey Nicholson
Congratulations to Our Winners!

Collier Smith                Janice Kent-MacKenzie
Arthur Hartwell                Judy Bradley
Robert Austin                Alan Lemm
Christine Walker                Judy Bradley
Peter Norton                Claudio Trapote
Anne-Marie Laberge                Marcelle Comeau
Daniel Jolley                Jinny Collins
Sharon Martin                Jessie Hagan
Nelsen Spickard                Maureen O'Connor
Margaret Paxton                Audrey Nicholson
Ellen Welker                Ellen Rohr                Dennis Brann
Jim Kiser                Marty Guidry
Angel Esparza                Elaine C. Hebert
Carol Farrant                Mike Dalton
Joshua Kreitzer                Donna Jolley
Richard Wakeham                Diane Burkett
I have a major advantage on this one: I worked as a public affairs specialist from 1969
to 2002 at the NIST Boulder Labs, where the atomic clock is housed, and wrote all the
press releases during that time concerning the introduction and implementation of "leap
seconds". I also edited books on this general subject, and wrote a number of pamphlets
on it, as well.

So, the answers are:

1. -- Leap second (probably the one on Saturday, 6/30/12, but it could have been
any of the 25 we have had).

2. -- Leap seconds are needed to make our modern time, which is kept by atomic
clocks and is very constant in rate, and astronomical time, which is based on the
spinning earth, in synch. Without adding (or subtracting) leap seconds from time to
time, the two kinds of time would gradually drift apart, and in the very long term
(thousands of years), we would find our clocks saying it was noon while the sun was
rising or setting. NIST's current clock system provides time so constant that it gains or
loses less than a second per 100 million years.

3. -- Leap seconds have been added 23 times since the first two in 1972.

Leap Seconds Inserted into the UTC Time Scale

(Always at 23:59:60 UTC -- the last second of the day, usually on Dec. 31 or
June 30)

UTC is Universal Coordinated Time, the modern replacement for Greenwich Mean
Time for most of the world. Pacific Daylight Time is 7 hours earlier than UTC,
hence the leap second occurs at 4:59:60 pm PDT.

More info at:

It is in analogy to the extra day added during leap years to keep our calendars in step
with the seasons. Just as an extra "leap day" is added every 4 years (approximately), we
add an extra "leap second" in about 5 out of 8 years to keep our clocks in step with the

I won't bore you with all the other material on leap seconds, atomic clocks, and the
history of timekeeping in my files.  But here is a brochure I co-wrote and revised many
times between 1970 and 1995 on the topic, and adapted to the Web:

In the 1840s a railway standard time for all of England, Scotland, and Wales evolved,
replacing several "local time" systems. The Royal Observatory in Greenwich began
transmitting time telegraphically in 1852 and by 1855 most of Britain used Greenwich
time. Greenwich Mean Time (GMT) subsequently evolved as an important and
well-recognized time reference for the world.

In 1830, the U.S. Navy established a depot, later to become the U.S. Naval Observatory
(USNO), with the initial responsibility to serve as a storage site for marine
chronometers and other navigation instruments and to "rate" (calibrate) the
chronometers to assure accuracy for their use in celestial navigation. For accurate
"rating," the depot had to make regular astronomical observations. It was not until
December of 1854 that the Secretary of the Navy officially designated this growing

Yesterday, June 30 2012, a 'leap second' was added to clocks around
the world in order to account for the slowing of the Earth's rotation,
making the day one second longer than a normal Saturday. Although
the extra second went unnoticed by most, a few internet companies
had trouble dealing with unusual change to the atomic clocks.

Wired reports that web operators at Reddit, Mozilla and several other
internet companies experienced brief technical issues Saturday night,
when their software programs tripped up on the 'leap second' Wired
goes on to say that a lot of computing systems utilize the Network
Time Protocol to keep themselves lined up with the world's atomic
clocks. Last night, when a 'leap second' was added to the atomic
clocks, several computing systems weren�t sure how to respond.

At 6:41pm, Reddit confirmed via Twitter that they were having
technical issues due to the 'leap second'. 'We are having some
Java/Cassandra issues related to the leap second at 5pm PST. We're
working as quickly as we can to restore service,' Reddit Status

Reported by Jim Kiser
Big Ben
New Year's Eve Ball
Times Square, NYC
Peace Clock Tower
Jens Olsen Clock
Atomic Clock at NIST
World Time Scales
Did You Know That...
Leap seconds can be positive (one second added) or negative
(one second omitted) - at least in theory: so far, all leap seconds
were positive, and given the slowing of the Earth's rotation it is
unlikely that a negative leap second will ever occur.

The speed of the Earth's rotation differs from day to day and
from year to year, so the difference between UT1 and TAI
varies accordingly. For example, the accumulated discrepancy
over one year was 0.28 seconds in 2011, but only 0.02 seconds
in 2001 (based on data from IERS).

Not only do days become longer, but the rate at which day
lengths increase also grows over time – but only by about two
thousandths of a second per century, according to Dr Bruce
Warrington, from Australia’s National Measurement Institute
(NMI). This means that at the moment days are 0.002 seconds
longer than the sum of 86,400 seconds measured by atomic
clocks; in 100 years, they are expected to be 0.004 seconds “too

Some scientists suggest abolishing leap seconds, effectively
redefining the way we measure time.
Workarounds for leap second issues

Instead of inserting a leap second at the
end of the day, Google servers implement
a leap smear, extending seconds slightly
over a time window prior to the leap
institution as the "United States Naval
Observatory and Hydrographic Office."
Through all of the ensuing years, the
USNO has retained timekeeping as one of
its key functions.

With the advent of highly accurate atomic
clocks, scientists and technologists
recognized the inadequacy of timekeeping
based on the motion of the Earth, which fluctuates in rate by a few thousandths of a
second a day. The redefinition of the second in 1967 had provided an excellent
reference for more accurate measurement of time intervals, but attempts to couple
GMT (based on the Earth's motion) and this new definition proved to be highly
unsatisfactory. A compromise time scale was eventually devised, and on January 1,
1972, the new Coordinated Universal Time (UTC) became effective internationally.

UTC runs at the rate of the atomic clocks, but when the difference between this atomic
time and one based on the Earth approaches one second, a one second adjustment (a
"leap second") is made in UTC. NIST's clock systems and other atomic clocks located
at the USNO and in more than 25 other countries now contribute data to the
international UTC scale coordinated in Paris by the International Bureau of Weights and
Measures (BIPM). As atomic timekeeping has grown in importance, the world's
standards laboratories have become more involved with the process, and in the United
States today, NIST and USNO cooperate to provide official U.S. time for the nation.
You can see a clock synchronized to the official U.S. government time provided by
NIST and USNO at
Slowing Down of the Earth
the rate of lengthening of the mean
solar day to about 1.4 ms per century.

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

ΔT, Delta T, delta-T, deltaT, or DT is the time difference obtained by subtracting
Universal Time (UT) from Terrestrial Time (TT): ΔT=TT−UT.

Universal Time is a time scale based on the Earth's rotation, which is somewhat
irregular over short periods (days up to a century), thus any time based on it cannot
have an accuracy better than 1 : 108. But the principal effect is over the long term: over
many centuries tidal friction inexorably slows Earth's rate of rotation by about +2.3
ms/day/cy. However, there are other forces changing the rotation rate of the Earth. The
most important one is believed to be a result of the melting of continental ice sheets at
the end of the last glacial period. This removed their tremendous weight, allowing the
land under them to begin to rebound upward in the polar regions, which has been
continuing and will continue until isostatic
equilibrium is reached. This "post-glacial
rebound" brings mass closer to the rotation
axis of the Earth, which makes the Earth
spin faster (law of conservation of angular
momentum)[clarification needed]: the rate
derived from models is about −0.6
ms/day/cy. So the net acceleration (actually
a deceleration) of the rotation of the Earth,
or the change in the length of the mean solar
day (LOD), is +1.7 ms/day/cy. This is
indeed the average rate as observed over the
past 27 centuries.

All values of ΔT before 1955 depend on
observations of the Moon, either via eclipses
or occultations. Conservation of angular
momentum in the Earth-Moon system
requires that the angular momentum lost by the Earth due to tidal friction be transferred
to the Moon, increasing its angular momentum, which means that its moment arm (its
distance from the Earth) is increased (for the time being about +3.8 cm/year), which
via Kepler's laws of planetary motion causes the Moon to revolve around the Earth at a
slower rate. The cited values of ΔT assume that the lunar acceleration (actually a
deceleration = a negative acceleration) due to this effect is dn/dt = −26"/cy2, where n is
the mean sidereal angular motion of the Moon. This is close to the best estimate for
dn/dt as of 2002 of −25.858±0.003"/cy2 so ΔT need not be recalculated given the
uncertainties and smoothing applied to its current values. Nowadays, UT is the
observed orientation of the Earth relative to an inertial reference frame formed by extra-
galactic radio sources, modified by an adopted ratio between sidereal time and solar
time. Its measurement by several observatories is coordinated by the International Earth
Rotation and Reference Systems Service (IERS).
Ancient Sun Clock
Types of Ancient Clocks

Read Collier Smith's NIST brochure.

Also click on links below each of
the following images.
Ancient Persian waterclock and
waterclock manager