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Second of Time

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 $0 \ \mathrm K$.

Second of Arc

The second (of arc) is a measurement of plane angles, symbolized by $''$.

\(\displaystyle \) \(\) \(\displaystyle 1\) second
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 1 {60}\) minute of arc (by definition)
\(\displaystyle \) \(=\) \(\displaystyle \dfrac 1 {60 \times 60} = \dfrac 1 {3600}\) degree of arc

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 arc.

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.