# Leap seconds

The rotation of the earth about its axis defines our natural measure of time, the length of the day. If the length of a day averaged over a year is divided by 86400, the so-called Universal Time (UT) second is obtained. Until 1956, this was the official unit of time. On the other hand, it was recognised that the earth rotates in a rather non-uniform way. In particular, the long-time average of the rotating velocity decreases, i.e. the length of the day increases. One cause of this is the influence of the tides (tidal friction). Therefore after 1956, the ephemeris second (defined as a fraction of the time the earth takes to revolve about the sun) was adopted as the unit of time because it was supposed to be more stable. Its duration should be equivalent to the mean value obtained by Simon Newcomb based on data obtained in the time period from 1750 to 1892 of the UT second. Due to the slowing-down of the earth's rotation, it was shorter than the UT second of 1956, since the value actually referred to the year approximately1820.

In the following years, however, the actual duration of the ephemeris second could be stated only with an accuracy of 10-8 s so that the advantage over the UT second was not significant. It was therefore decided to link up the unit of time with an atomic fundamental constant. In 1967, a time interval was defined as the atomic second (SI second) which was matched to the ephemeris second and thus was also slightly shorter than the UT second of 1967. The difference is on average about 2.4·10-8 s, which in the course of a year would add up to a difference between UT and atomic time of about 0.75 seconds (365·24·60·60·2.4·10-8 s).

Now we are using three time systems in parallel, each of which is discussed in detail:

Astronomical time UT1

International Atomic Time TAI

And Coordinated Universal Time UTC

The unit of the time scale UTC agrees with that of the time scale TAI and represents seconds as defined as one of the base unit in the International Sysatem of Units SI. UTC is kept in agreement with UT1 by the insertion of leap seconds such that the difference between both scales never exceeds +0.9 s. Leap seconds are thus not inserted following a fixed schedule but instead on the basis of observations of the earth's rotation with respect to the system of quasars, with respect to the constellation of GPS satellites and with respect to other satellites which are flown for scientific purposes. The observations are collected and evaluated by IERS (International Earth Rotation and Reference Systems Service).

Usually, leap seconds are inserted at the end or in the middle of a year. This happens at the same instant all over the world either at the end of the last minute of the 31st December or of the 30th June in the time scale UTC. In Central Europe this corresponds to the end of the first hour of January 1 in CET or the end of the second hour of July 1 in CEST, respectively. On January 1, 1972, the starting point of the UTC scale, the difference TAI-UTC was set to 10 seconds. The first leap second was inserted in summer 1972.

In compliance with the IERS directive the 22nd leap second was inserted on January 1, 1999. After seven years the 23rd leap second was inserted on January 1, 2006, and after another three years the 24th . This indicates that the earth's rotation has for a while been slightly faster than its long-term average but has now decelerated again somewhat. It will be interesting to watch the evolution of this process.

The program of the PTB time code transmitter DCF77 (Working Group 4.42) provides an "annunciator bit" (second marker 19). This bit is set as an additional second marker one hour before a leap second is inserted.

Leap seconds are also taken into account in the time information transmitted via telephone modem (telephone number +49(0)531-512038). Here the insertion of a leap second is announced several days in advance.

Different software solutions have been implemented in the various servers providing time over the Internet via NTP protocol, and not all have always functioned well. The PTB servers have been carefully tested and should be available without interruption.

Clocks which take their time of day information from GPS signals can also correctly handle the leap seconds since the actual number of leap seconds is part of the GPS signal in space data content.

### Leap seconds in UTC since its introduction in 1972

After the introduction of UTC, the first leap second (n-n0)=1 was inserted on 1972-07-01 one second before 01:00 CET. At the introduction of UTC, the difference between TAI and UTC had been set to n0=10. In the table shown below, (n-n0) is the sum of leap seconds inserted in UTC since 1972-01-01, and n is the corresponding time scale difference between TAI and UTC. Leap seconds were inserted as shown in the following table.

Link to table leap seconds in UTC

Table leap seconds in UTC
Calendar date in CET Time of insertion of the leap second Number of leap seconds inserted
1972-01-01 1s before 1 h CET (n - n0) = 1
1973-01-01 1s before 1 h CET (n - n0) = 2
1974-01-01 1s before 1 h CET (n - n0) = 3
1975-01-01 1s before 1 h CET (n - n0) = 4
1976-01-01 1s before 1 h CET (n - n0) = 5
1977-01-01 1s before 1 h CET (n - n0) = 6
1978-01-01 1s before 1 h CET (n - n0) = 7
1979-01-01 1s before 1 h CET (n - n0) = 8
1980-01-01 1s before 1 h CET (n - n0) = 9
1981-07-01 1s before 2 h CEST (n - n0) = 10
1982-07-01 1s before 2 h CEST (n - n0) = 11
1983-07-01 1s before 2 h CEST (n - n0) = 12
1985-07-01 1s before 2 h CEST (n - n0) = 13
1988-01-01 1s before 1 h CET (n - n0) = 14
1990-01-01 1s before 1 h CET (n - n0) = 15
1991-01-01 1s before 1 h CET (n - n0) = 16
1992-07-01 1s before 2 h CEST (n - n0) = 17
1993-07-01 1s before 2 h CEST (n - n0) = 18
1994-07-01 1s before 2 h CEST (n - n0) = 19
1996-01-01 1s before 1 h CET (n - n0) = 20
1997-07-01 1s before 2 h CEST (n - n0) = 21
1999-01-01 1s before 1 h CET (n - n0) = 22
2006-01-01 1s before 1 h CET (n - n0) = 23
2009-01-01 1s before 1 h CET (n - n0) = 24
2012-07-01 1s before 2 h CEST (n - n0) = 25
2015-07-01 1s before 2 h CEST (n – n0) = 26
2017-01-01 1s before 1 h CET (n - n0) = 27