### History of the unit of time

#### The unit of time before 1956

The natural measure of time of man is the day defined by the rotation of the earth. Due to the obliquity of the ecliptic and the elliptical shape of the earth's orbit, the duration of the true solar day (the interval between two successive meridian transits of the sun at the same place) is not at all constant. What is more strictly proportional to the earth's rotational angle and thus much more constant is the mean solar time at a fixed place. The corresponding time unit is the mean solar day *d*_{m}. With the aid of clocks, *d*_{m} is further divided into 24 hours of 60 minutes, each minute being in turn divided into 60 seconds. The definition of the duration of the second as the 86400th part of the mean solar day basically was arbitrary, and part of our tradition. There has never been a formal definition of the second as a binding measure of time in the sense of the International System of Units. The mean solar time related to the zero meridian is referred to as *U*niversal *T*ime (UT); the original name still popular today was *G*reenwich *M*ean *T*ime (GMT).

The comparison between the earth's rotation and the orbits of planets and of the moon showed that the duration of the mean solar day is changing continuously. The earth's rotation is gradually slowed down by tidal friction (400 million years ago one year amounted to 400 days), and there are additional unpredictable rotational fluctuations (by a relative amount of a few 10^{-8}) which are attributed to mass shifts inside the earth's body. This phenomenon was noted for the first time at the end of the19th century, and definite proof of it was established in the mid-thirties of the 20th century. Approximately at the same time, Scheibe and Adelsberger of the Physikalisch-Technische Reichsanstalt demonstrated with the aid of their quartz clocks that the earth's rotation is subject also to seasonal fluctuations. The observations of the earth's rotation are continued today by application of different modern techniques, using atomic clocks as time references. The results are documented by the International Earth Rotation Service.

#### The SI second between 1956 and 1967

Following a proposal made by astronomers, in 1956 the International Committee of Weights and Measures defined the SI second as a specific fraction of the tropical year. The tropical year is the interval between two successive passages of the "mean sun" through the "mean spring equinox". As the duration of the tropical year varies, the definition was based on the differential tropical year of the 31st^{ }of December 1899 at 12:00pm Universal Time. This fraction of the tropical year was selected from a calculation made in 1895 by Simon Newcomb, who evaluated astronomical observations made in the course of several centuries and determined the ratio of the mean periods of the earth's rotation and the earth's orbit. Since at that time the earth still rotated a little faster than today, the "ephemeris second" defined in 1956 is shorter than today's Universal Time second by about 3^{.}10^{-8} s. Today's mean solar day is, consequently, almost 3 ms longer than 86 400 ephemeris seconds.

Since points in time can be determined only rather inaccurately from the earth's orbit, in practice the ephemeris second was to be determined by the position of the moon. After long-term comparisons with the earth's orbit, the lunar orbit was regarded as a "calibrated secondary standard" which allowed points in time to be determined much more accurately than with the aid of the earth's orbit. On account of deficiencies of the theory of the moon's motion, and considering the superiority of atomic time standards - the small uncertainty and the unproblematic availability of the second defined as an atomic unit - the concept of the ephemeris second was finally abandoned.

#### The 1967 definition of the second

*The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the ^{133}Cs atom.*

As early as 1955, the British physicist Essen had suggested using the transition frequency between hyperfine levels in the ground state of the caesium atom (non-radioactive isotope ^{133}Cs) for the redefinition of the second. In the years that followed, in particular the ammonia beam maser and the hydrogen maser were investigated for their suitability as a frequency standard, but finally it was the transition in the Cs atom proposed by Essen which proved to be particularly suitable for the redefinition of the second. The transition frequency was determined by a comparison between the atomic frequency standard of the National Physical Laboratory (UK) and quartz clocks, whose seconds were compared in several steps with the ephemeris second defined above. Between 1956 and 1958, the NPL and the United States Naval Observatory, Washington, co-operated in this project. According to these investigations, the duration of an ephemeris second is 9 192 631 770 ± 20 periods of the radiation corresponding the transition between two ground-state levels of ^{133}Cs. It is likely that the real uncertainty of this measurement was considerably greater because the duration of an ephemeris second can not be exactly determined, as explained above. The measurement result was nevertheless taken as the basis of the redefinition of the second. The definition of the SI second adopted by the 13th General Conference on Weights and Measures was given above and is still valid today.

The number of periods stated in this definition corresponds exactly to the original measurement result given above. This ensured that the duration of the new second was approximately that of the ephemeris second.