Definition:Angular Measure/Second

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Definition

The second (of angle) is a measurement of plane angles.

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


Symbol

$x' '$

The symbol used to denote seconds of angle and seconds of arc is $' '$.

Thus $x' '$ denotes $x$ seconds


The $\LaTeX$ code for \(x' '\) is x' ' .


Also known as

A second of angle is also known as a second of arc, or an arc second.

This term has a specific definition which is subtly different from the concept of a second of angle, and so its use in this context on $\mathsf{Pr} \infty \mathsf{fWiki}$ is discouraged.


Also see

  • Results about seconds of angle can be found here.


Historical Note

The division of the degrees into $60$ and $3600$ subdivisions originates from the Babylonians, who used a sexagesimal (base $60$) system for the purposes of mathematics and astronomy.


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

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