The Leap Second

Observations of the sun are the traditional basis for time keeping. Three improvements in clocks have entailed changes in our timekeeping practice, and the leap second is the most recent and smallest change. Solar days (noon-to-noon) vary predictably through the year, and good timekeeping averages-out these effects and defines 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). 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.

The earliest averaging method simply corrected for the seasonal variation due to the Earth's orbital inclination and eccentricity, UT0.

UT0 with the polar wander correction gives UT1, the time scale needed for celestial navigation and surveying.

If the seasonal variation of UT1 is averaged out, UT2 results.

If the rate and time are coordinated through international comparisons organized under the Convention of the Metre, UTC results. 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 (TAI), and leap seconds have been added as required to keep UTC aligned with UT1 within 0.9 seconds.

Three Changes in Timekeeping Practice

By the 1400's, as mechanical clocks became widespread, traditions of 12 daylight "hours" and 12 nighttime "hours", or even the 24 hours from sunset to sunset had to disappear so that the clocks did not need adjustment to suit seasonal variations in "time". A time measurement scheme from southern Germany (where the Black Forest had made sunset observations difficult) became popular. It used 24 hours between successive noontime passages of the sun, divided the day into 12 hours AM and 12 hours PM, and started each new day at midnight. This scheme allowed the convenient use of clocks which were accurate to within a minute per day, and brought convenient timekeeping to cities.

In the 1700's, as pendulum clocks became more accurate, variations in the rate of the sun across the sky were noted, and became troublesome. These variations are due to the differences in the speed of Earth in its orbit around the sun, and to the inclination of the orbit with respect to Earth's rotational axis. Time keeping switched from apparent solar time to mean solar time ("mean" signifying an average position of the sun). Initially the variations due to polar wander did not have to be made (Universal Time 0, or UT0), but to serve for navigation the effects of polar wander needed correcting (Universal Time 1, or UT1). This scheme allowed the convenient use of clocks that were accurate to a few hundredths of a second per day, and with the invention of the marine chronometer, gave a practical solution to determining longitude for safe navigation and maritime commerce, timing Earth's rotation with respect to the sun.

In the mid-1900's, as quartz and atomic clocks became available, variations in the rate of the rotation of Earth were noted, and became troublesome for new advances in science and engineering. In 1957 the rotation of Earth was abandoned as the basis for all science and engineering measurement based on the second. The old basis was replaced first by a predefined fraction of the tropical year 1900, and soon after by observations of cesium atoms. Seasonal variations of UT1 were observed which were similar from year to year, and were removed to form the time scale UT2 (Universal Time 2). Cesium clocks were used to predict UT2 for the coming year, and gave rise to an early UTC (Coordinated Universal Time). In 1967, by international agreement, the second was formally defined as the duration of 9,192,631,770 periods of a rotation of the magnetism of the cesium-133 atom. The civil second was based on the predicted rate of UT2 for the current year, and coexisted with a scientific second, causing unwanted confusion. Every year there was the prospect of corrections to the rate of UT2 and corrections, in 0.1 or .05 s steps, to step UTC back towards the observed UT2. In 1972 the rate of UTC was set to match the cesium definition of the second ("at sea level"). All steering to keep UTC in step with the sun was to be accomplished by the addition (or subtraction if necessary) of integer "leap seconds" just before January 1 at 00:00:00 UTC, or July 1 at 00:00:00 UTC. The goal set in 1972 was to keep UTC within plus or minus nine-tenths of a second of UT1, the time scale used for celestial navigation and astronomical observation. Astronomers were among the most insistent that the UTC must stay in step with UT1. The astronomers' choice of value for the 1957 second has given us only positive leap seconds, spaced by 6 to 30 months. A few astronomers, who are now inconvenienced by this frequency of leap seconds, have proposed their abolition. These astronomers should be using the non-astronomical time scale, International Atomic Time (TAI), which is the basis for UTC, differing only by the addition of leap seconds to TAI to create UTC.

International Atomic Time, TAI (Temps Atomique International), results from the averaging and coordination of several hundred of the best atomic clocks around the world. The averaging and steering of TAI is done by the Bureau international des poids et mesures (BIPM). TAI is not linked to Earth's rotation, so a clock based on this will gradually become out of step with UT1. The 1972 Coordinated Universal Time (UTC) scale was adopted by the scientific community for international use. It is based on TAI with the occasional (6 to 30 months apart) addition of a step, consisting of exactly one second, as necessitated by the irregularities in Earth's rotation, with the objective of keeping UTC within plus of minus nine-tenths of a second of UT1. UTC has been adopted by many countries as the legal basis for time. Since the early 1960's, the official time disseminated for Canada has been UTC. From August 28, 1941 to April 1, 1970 this was done by the Dominion Observatory (Order-in-Council P.C._1970-562). Since then it has been done by the National Research Council of Canada (Order-in-Council P.C._1970-6784). UTC (Coordinated Universal Time) is the modern implementation of GMT (Greenwich Mean Time) that incorporates the averaging properties of atomic clocks in the most coordinated way.

The UTC second is the same length as the TAI second. UTC time is always kept within ±0.9 second of UT1, by the insertion of an extra second (positive leap second) as needed. While it is theoretically possible to have to remove an extra second (negative leap second), it has not happened so far.

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 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 60th second at that moment.

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