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Second: The Unit of Time in the Metric System

In this article, you will learn about the second (symbol s), which is the unit of time in the metric system, i.e., in the International System of Units (SI).

We will first explore how the definition of the second evolved over time and then see the common multiples and submultiples of the second.

Definition of the second over time

The definition of the second evolved over time to be more convenient and to more precisely define the duration of the second.

The second was first defined in terms of the mean solar day, then in terms of the tropical year, and finally, in terms of the period of cesium vibration.

As we will now go through each definition, an important thing to keep in mind is that with every redefinition of the second, one of the main goals was to change the duration of the second as little as possible.

Mean solar day definition

Earth completing a rotation relative to the Sun.

The second was historically defined as 186 400 of the mean solar day.

The mean solar day is the average time needed for the Earth to complete a rotation relative to the Sun.

The mean solar day is computed over the course of one year. This is because the speed of rotation of the Earth, relative to the Sun, changes throughout the year.

If you wonder where the 86 400 comes from, it is from the subdivision of the mean solar day into 24 hours, of an hour into 60 minutes, and of a minute into 60 seconds.

So, the mean solar day has 24 × 60 × 60 = 86 400 seconds, which is why the second was defined as 186 400 of the mean solar day.

Tropical year definition (1960)

Earth completing a revolution around the Sun.

At a later point, it was discovered that the speed of rotation of the Earth, relative to the Sun, was slowly decreasing.

This meant that the duration of the mean solar day was slowly increasing, and thus the duration of the second was also slowly increasing.

To keep the duration of the second fixed, in 1960 the second was redefined as 131 556 925.9747 of the tropical year 1900.

Period of cesium vibration definition (1967)

Vibrating sphere.

With the development of atomic clocks, which measure time by counting the vibrations of an atom or molecule, it was possible to redefine the second very precisely and more conveniently, as the amount of time during which a chosen atom or molecule vibrates a specific number of times.

In 1967, the second was redefined as the amount of time during which a cesium atom vibrates 9 192 631 770 times.

If you wonder why 9 192 631 770 was chosen, it is simply because, as we said, with every redefinition of the second, one of the main goals was to change the duration of the second as little as possible.

So, when measurements were performed, it was found that in one second, as defined in terms of the tropical year, a cesium atom vibrates 9 192 631 770 times.

A clock that measures time by counting the vibrations of a cesium atom is called a cesium atomic clock.

Modern cesium atomic clocks are very precise; they won't lose or gain more than 1 second in the course of millions of years.

Multiples and submultiples of the second

The commonly used multiples and submultiples of the second consist of decimal submultiples (e.g. millisecond and microsecond) and non-decimal multiples (e.g. minute and hour):

Common multiples and submultiples of the second
NameSymbolValue
yeara365.25 d = 31 557 600 s
dayd24 h = 86 400 s
hourh60 min = 3 600 s
minutemin60 s
millisecondms10−3 s
microsecondμs10−6 s
nanosecondns10−9 s
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