Observations of the sun are the traditional basis for time keeping. Improvements in clock accuracy and stability have entailed changes in our timekeeping practice and the leap second is the most recent and smallest change. Apparent solar time (the time given by sundials) varies predictably through the year for a number of reasons, the most important of which are the Earth's orbital inclination and eccentricity. Good timekeeping averages-out these effects and defines a reference time scale based on the Earth's mean rotation. It has been called variously Universal Time (UT), Zulu Time (Z), and Greenwich Mean Time (GMT). Other seasonal and random effects need to be averaged out, and the phrase "mean time" simply implies that an averaging method is being used. Different methods and names have been applied to the average.

UT0 is the timescale on the prime meridian which results from local, direct measurement of the Earth's rotation angle through observations and timing of the transits of stars and other celestial objects. A mathematical expression is used to convert these observations to mean solar time.

UT1 is the timescale which results if corrections are applied to UT0 to account for the effect on the local observations of the movement of the Earth's axis (polar wander). This is the time scale needed for celestial navigation and surveying.

UT2 is the timescale which results if corrections are applied to UT1 to account for seasonal variations in the Earth's rotational speed.

UTC is the timescale where the rate and time are coordinated through international comparisons organized under the Convention of the Metre . UTC, or Coordinated Universal Time is the modern implementation of GMT and is used as the basis for official time around the world.

Until 1972, the duration of the second for each of these time scales varied slightly (but in different ways) to keep in step with variations of Earth's rotation. Since 1972, the duration of the second for UTC has been fixed at the value established by an average of atomic clocks around the world (International Atomic Time, TAI), and leap seconds have been added to UTC as required to keep it aligned with UT1 within 0.9 seconds.

The International Earth Rotation and Reference System Service (IERS) in Paris is charged with predicting when the next leap second will be needed. It then informs national time laboratories, such as the National Research Council, of the impending leap second. The leap second can be inserted in the last second (UTC) of any month, but preference is given to the ends of June and December. Clocks which can display the leap second will then have a 61st second at that moment and read 23 hr: 59 min: 60 sec. Since 1972, leap seconds have been required approximately every 18 months. It is expected that they will become more frequent due to a gradual slowing of the Earth's rotation. Negative leap seconds, in which the 60th second of the last minute of the last day of the month is removed, are permitted, but have never been required.

Up-to-date information on leap seconds may be found in our BULLETIN TF-B.

## What is a leap second?

With the advent of the first good mechanical clocks, the "sunset to sunset" day was abandoned in favour of the more uniform "noon to noon" day.

As clocks gave rise to chronometers, it became necessary to average-out the predictable variations of the noon-to-noon day and define a reference time scale based on Earth's mean rotation. It has been called variously Universal Time (UT), Zulu time (Z), and Greenwich Mean Time (GMT).

The phrase "mean time" simply implies that an averaging method is being used.

Since the introduction of atomic clocks, which greatly surpass the stability of the rotating Earth, we have technical names for the different averaging methods that address both predictable and random irregularities of Earth's rotation.

### UT

Universal Time, or UT, is the generic name given to mean solar time on the Greenwich meridian. Often UT is used for civil purposes when it is not necessary to specify the method of averaging. Note that clocks keeping UT (or any of its family members listed below) are not ever adjusted for Daylight Saving Time.

### UT0

This was the earliest averaging method and simply corrected for the seasonal variation due to the Earth's orbital eccentricity and inclination, using "the equation of time". UT0 is pronounced "U-T-zero" and is the modern way to refer to the first correction method used historically for Greenwich Mean Time.

### Historical note

Until 1925, two date rollover conventions were used with GMT. For civil purposes the date changed normally, at midnight GMT, but for astronomical purposes it changed at noon (12 hours later) - each convention avoided date changes during its constituency's normal working hours. Historians must be wary about confusing day and night!

### UT1

Adding the polar wander correction to UT0 gives UT1, the time scale needed for the most accurate celestial navigation and surveying. It was the second method used historically for GMT.

### UT2

If the seasonal variation of UT1 is averaged out, UT2 results. It was used briefly as a method for GMT and for predicting the rate of UTC before 1972.

### UTC

If the rate and time are coordinated through international comparisons organized under the Convention of the Metre, UTC results. UTC was used as the final method for GMT by the last time experts at the Royal Greenwich Observatory. UTC, or Coordinated Universal Time is the modern implementation of GMT and is used as the basis for official time around the world.

Until 1972, the duration of the second for each of these time scales varied slightly (but in different ways) to keep in step with variations of Earth's rotation.

### Leap Seconds

Since 1972 the duration of the second for UTC has been fixed at the value established by an average of atomic clocks around the world (TAI), and *leap seconds* have been added as required to keep UTC aligned with UT1 within 0.9 seconds.

The International Earth Rotation Service (IERS) in Paris is charged with predicting when the next leap second will be needed. It then informs national time laboratories, such as the National Research Council, of the impending leap second. The leap second can be inserted in (or - if it were ever necessary - removed from) the last second (UTC) of the day, of June 30 or December 31. Clocks which take advantage of the leap second prediction facility, disseminated by the time laboratories, will then have a minute with 61 (or 59) seconds. With a positive leap second, the normal pattern of times changes from

23:58:57, 23:58:58, 23:58:59, 23:59:00, 23:59:01, 23:59:02... to

23:59:57, 23:59:58, 23:59:59, **23:59:60,** 00:00:00, 00:00:01...

Other clocks report the same time stamp for two seconds (00:00:00 for example), while others (such as NTP software) gradually slew their clock time to avoid the possibility of reversing the order of two time stamps (for example, 23:59:60.9 and 00:00.1 might be recorded as 00:00:00.9 and 00:00:00.1, and construed from these time stamps as having taken place in the wrong order).

Up-to-date information on leap seconds may be found in our BULLETIN TF-B