# Definition:Time/Unit/Second

## Definition

The **second** is the SI base unit of time, and also therefore of the MKS system.

It is also the base unit of time for the FPS and CGS systems.

The **second** is 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 at rest at $0 \ \mathrm K$.

### Symbol

The symbol for the **second** is $\mathrm s$.

## Historical Note

The division of the hour into $60$ minutes, and the minute into $60$ seconds, is a relic of the Babylonian number system, which was a sexagesimal (base $60$) system used mainly for astronomical purposes.

Up until $1967$, the **second** was defined as being $\dfrac 1 {60 \times 60 \times 24}$ the length of a (solar) day.

This appears first to have been used by al-Biruni in the year $1000$ CE.

It had been noted by astronomical observations that the actual (solar) day is gradually lengthening.

In $1960$, therefore, the **second** was redefined as:

- the fraction $\dfrac 1 {31, 556, 925.9747}$ of the tropical year for $1900$ January $0$ at $12$ hours ephemeris time.

However, even the tropical year is not completely unchangeable, and measuring its duration with high accuracy is challenging.

So in $1967$ the definition of the second was changed again, to what it is now.

## Linguistic Note

The word **second**, in the context of the measurement of **time** and of **angle**, derives from the fact that it was originally specified as a **second minute part of an hour** or of a **degree of angle**.

The **minute** had already been defined as a **minute part of an hour**.

The use of the word **second** in English, in this specific context, started near the end of the $16$th century.

## Sources

- 1964: D.E. Rutherford:
*Classical Mechanics*(3rd ed.) ... (previous) ... (next): Chapter $\text I$: Kinematics: $1$. Space and Time - 1966: Isaac Asimov:
*Understanding Physics*... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $2$: Falling Bodies: Free Fall - 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw:
*Data and Formulae for Engineering Students*(2nd ed.) ... (previous) ... (next): $1.$ Units and Abbreviations: $1.2$ SI units $(1)$ Basic units - 1976: Ralph J. Smith:
*Circuits, Devices and Systems*(3rd ed.) ... (previous) ... (next): Chapter $1$: Electrical Quantities: Definitions and Laws: The International System of Units - 1976: Ralph J. Smith:
*Circuits, Devices and Systems*(3rd ed.) ... (previous) ... (next): Chapter $1$: Electrical Quantities: Definitions and Laws: The International System of Units: Table $1$-$1$ Basic Quantities - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**time** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**time** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**second**(time)