# Second

Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

The second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time.

SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g., the millisecond (one thousandth of a second) and nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second (such as “kilosecond,” or one thousand seconds), such units are rarely used in practice. More commonly encountered, non-SI units of time such as the minute, hour, and day increase by multiples of 60 and 24 (rather than by powers of ten as in the SI system).

## International second

Under the International System of Units, the second is currently defined as

 “ 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 caesium 133 atom.[1] ”

This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero). The ground state is defined at zero magnetic field. The second thus defined is equivalent to the ephemeris second, which was based on astronomical measurements. (See History below.)

The international standard symbol for a second is s[2] (see ISO 31-1)

The realization of the standard second is described briefly in NIST Special Publication 330; Appendix 2, pp. 53 ff, and in detail by National Research Council of Canada.

## Equivalence to other units of time

1 international second is equal to:

## History

The Egyptians had subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence their hours varied seasonally. The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdivided the day sexagesimally and also used a mean hour (​124 day), but did not use distinctly named smaller units of time. Instead they used simple fractions of an hour.

The day was subdivided sexagesimally, that is by ​160, by ​160 of that, by ​160 of that, etc., to at least six places after the sexagesimal point by the Babylonians after 300 BC, but they did not sexagesimally subdivide smaller units of time. For example, six fractional sexagesimal places of a day was used in their specification of the length of the year, although they were unable to measure such a small fraction of a day in real time. As another example, they specified that the mean synodic month was 29;31,50,8,20 days (four fractional sexagesimal positions), which was repeated by Hipparchus and Ptolemy sexagesimally, and is currently the mean synodic month of the Hebrew calendar, though restated as 29 days 12 hours 793 halakim (where 1 hour = 1080 halakim).[3] They did not use the hour, but did use a double-hour, a time-degree lasting four of our minutes, and a barleycorn lasting 3⅓ of our seconds (the helek of the modern Hebrew calendar).[4]

In 1000, the Muslim scholar al-Biruni gave the times of the new moons of specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.[5] In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates.[6] Although a third for ​160 of a second remains in some languages, for example Polish (tercja) and Arabic (ثالثة), the modern second is subdivided decimally.

The second first became measurable with the development of pendulum clocks keeping mean time (as opposed to the apparent time displayed by sundials), specifically in 1670 when William Clement added a seconds pendulum to the original pendulum clock of Christian Huygens.[7] The seconds pendulum has a period of two seconds, one second for a swing forward and one second for a swing back, enabling the longcase clock incorporating it to tick seconds. From this time, a second hand that rotated once per minute in a small subdial began to be added to the clock faces of precision clocks.

In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun, which provides a formula for the motion of the Sun at the epoch 1900 based on astronomical observations made between 1750 and 1892.[8] The second thus defined is

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.[8]

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. The tropical year in the definition was not measured, but calculated from a formula describing a mean tropical year which decreased linearly over time, hence the curious reference to a specific instantaneous tropical year. Because this second was the independent variable of time used in ephemerides of the Sun and Moon during most of the twentieth century (Newcomb's Tables of the Sun were used from 1900 through 1983, and Brown's Tables of the Moon were used from 1920 through 1983), it was called the ephemeris second.[8]

With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the revolution of the Earth around the Sun.

Following several years of work, Louis Essen from the National Physical Laboratory (Teddington, England) and William Markowitz from the United States Naval Observatory (USNO) determined the relationship between the hyperfine transition frequency of the caesium atom and the ephemeris second.[8] Using a common-view measurement method based on the received signals from radio station WWV,[9] they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock. As a result, in 1967 the Thirteenth General Conference on Weights and Measures defined the second of atomic time in the International System of Units as

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 caesium-133 atom.[8]

During the 1970s it was realized that gravitational time dilation caused the second produced by each atomic clock to differ depending on its altitude. A uniform second was produced by correcting the output of each atomic clock to mean sea level (the rotating geoid), lengthening the second by about 1×10−10. This correction was applied at the beginning of 1977 and formalized in 1980. In relativistic terms, the SI second is defined as the proper time on the rotating geoid.[10]

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement

This definition refers to a caesium atom at rest at a temperature of 0 K.

The revised definition would seem to imply that the ideal atomic clock would contain a single caesium atom at rest emitting a single frequency. In practice, however, the definition means that high-precision realizations of the second should compensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate and extrapolate accordingly to the value of the second as defined above.

For approximately twenty years, it has been possible to confine an ion to a region of space smaller than one cubic micron (10-6 m)3. Such an ion is almost completely isolated from the surrounding environment and suggests a frequency or time standard with a reproducibility and stability several orders of magnitude superior to the best caesium time standards. Such standards are under development. See magneto-optical trap and "Trapped ion optical frequency standards". National Physical Laboratory.

## Approximations

It is a common belief that saying one one thousand, two one thousand three one thousand...... can be used to time events in seconds (one mississippi, two mississippi is another common sequence)

## SI multiples

SI prefixes are commonly used to measure time less than a second, but rarely for multiples of a second, instead the non-SI units minutes, hours and days are used.

SI multiples for second (s)

Submultiples Multiples
Value Symbol Name Value Symbol Name
10–1 s ds decisecond 101 s das decasecond
10–2 s cs centisecond 102 s hs hectosecond
10–3 s ms millisecond 103 s ks kilosecond
10–6 s µs microsecond 106 s Ms megasecond
10–9 s ns nanosecond 109 s Gs gigasecond
10–12 s ps picosecond 1012 s Ts terasecond
10–15 s fs femtosecond 1015 s Ps petasecond
10–18 s as attosecond 1018 s Es exasecond
10–21 s zs zeptosecond 1021 s Zs zettasecond
10–24 s ys yoctosecond 1024 s Ys yottasecond
Common prefixes are in bold

Look up second in Wiktionary, the free dictionary.

## References

1. Official BIPM definition
2. ISO 31-1
3. Neugebauer Otto (1975). A history of ancient mathematical astronomy. Berlin: Springer.
4. Neugebauer Otto (1949). "The astronomy of Maimonides and its sources". Hebrew Union College Annual. 22: 325. More than one of `|pages=` and `|page=` specified (help)
5. al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past". Translated by Sachau C Edward. London: W.H. Allen. pp. 147–149. OCLC 9986841.
6. Bacon Roger (2000). The Opus Majus of Roger Bacon. Translated by Burke Robert Belle. Philadelphia: University of Pennsylvania Press. p. table facing page 231. ISBN 9781855068568. Unknown parameter `|originalyear=` ignored (help)
7. Long Case Clock: Pendulum
8. "Leap Seconds". Time Service Department, United States Naval Observatory. Retrieved 2006-12-31.
9. Leschiutta Sigfrido (2005-06-07). "The definition of the 'atomic' second". Metrologia. 42 (3): S10–S19. doi:10.1088/0026-1394/42/3/S03.
10. Nelson RA et al., (2000). "The leap second: its history and possible future" (PDF 381KB). Metrologia. 38: 515. More than one of `|pages=` and `|page=` specified (help)