# Metric time

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Metric time is the measure of time interval using the metric system, which defines the second as the base unit of time, and multiple and submultiple units formed with metric prefixes, such as kiloseconds and milliseconds. It does not define the time of day, as this is defined by various time scales, which may be based upon the metric definition of the second. Other units of time, the minute, hour, and day, are accepted for use with the modern metric system, but are not part of it.

## History

Although part of the decimal metric system, the second derives its name from the sexagesimal system, which originated with the Sumerians and Babylonians, and divides a base unit into sixty minutes, minutes into sixty seconds, seconds into sixty tierces,[1] etc. The word "minute" comes from the Latin pars minuta prima, meaning first small part, and "second" from pars minuta secunda or second small part. Angular measure also uses these sexagesimal units; in that field, it is the degree that is subdivided into minutes and seconds, while in time, it is the hour.

When the metric system was introduced in France in 1795, it included units for length, area, dry volume, liquid capacity, weight or mass, and even currency, but not for time. Decimal time of day had been introduced in France two years earlier, but was set aside at the same time the metric system was inaugurated, and did not follow the metric pattern of a base unit and prefixed units. James Clerk Maxwell and Elihu Thomson (through the British Association for the Advancement of Science - BAAS) introduced the Centimetre gram second system of units (cgs) in 1874, in order to derive electric and magnetic metric units, following the recommendation of Carl Friedrich Gauss in 1832.

The ephemeris second (defined as 1/86400 of a mean solar day) was made one of the original base units of the modern metric system, or International System of Units (SI), at the 10th General Conference on Weights and Measures (CGPM) in 1954. Because the planet Earth's rotation is slowly decelerating at an irregular rate and was thus unsuitable as a reference point for precise measurements, the SI second was later redefined more precisely 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. The international standard atomic clocks use caesium-133 measurements as their main benchmark.

## Alternative units

Numerous proposals have been made for alternative base units of metric time. On March 28, 1794, the president of the commission which developed the metric system, Joseph Louis Lagrange, proposed in a report to the commission the names déci-jour and centi-jour (deciday and centiday in English).[2] Base units equivalent to decimal divisions of the day, such as 1/10, 1/100, 1/1000, or 1/100,000 day, or other divisions of the day, such as 1/20 or 1/40 day, have also been proposed, with various names, and multiple and submultiple units formed with metric prefixes. Such alternative units have not gained any notable acceptance.

A decimal second = 1/100,000 of a day = 0.864 s is an obvious alternative. Any redefinition of the second, however, creates conflicts with anything based on its precise current definition.

Swatch Internet Time introduced a time unit called .beat, equal to the French decimal minute, with 1,000 decimal minutes in a day. In the French decimal time system there are 100 decimal seconds in a decimal minute. As there are 100,000 decimal seconds in the day, the decimal second is shorter than its counterpart. See Decimal time#Conversions.

Another unit for time, more familiar than some other suggestions, could be 14.4 minutes, i.e. a shorter quarter of an hour, or a centiday, as proposed by Lagrange. The centiday (called in Chinese) was used in China for thousands of years.

In the 19th century, Joseph Charles François de Rey-Pailhade proposed using the centiday, abbreviated , divided into 10 decicés, 100 centicés, 1000 millicés.[3] and 10000 dimicés.[4][5]

In 1897, the Commission de décimalisation du temps was created by the French Bureau of Longitude, with the mathematician Henri Poincaré as secretary. The commission proposed making the standard hour the base unit of metric time, but the proposal did not gain acceptance and was eventually abandoned.[6]

## Alternative meaning

Metric time is sometimes used to mean decimal time. Metric time properly refers to measurement of time interval, while decimal time refers to the time of day. Standard time of day is usually measured by the 24-hour clock or its closely related derivative, the 12-hour clock. These measurement systems are now based on the metric base unit of time, the second. Some proposals for alternative units of metric time are accompanied by decimal time scales for telling the time of day. Other proposals called "metric time" refer only to decimal time and are therefore not truly metric.

French decimal time is sometimes called "metric time" because it was introduced around the same time as the metric system and both were decimal. The April 7, 1795 decree creating the original metric units and prefixes actually suspended decimal time, which had named its units the (decimal) hour, minute and second instead of using metric prefixes.

## In computing

In computing, at least internally, metric time gained widespread use for ease of computation. Unix time gives date and time as the number of seconds since January 1, 1970, and Microsoft's FILETIME as multiples of 100ns since January 1, 1601.[7] VAX/VMS uses the number of 100ns since November 17, 1858 and RISC OS the number of centiseconds since January 1, 1900.

None of these systems is strictly linear, as they each have discontinuities at leap seconds.

## Fractions of a second

While larger metric prefixes of a second are rarely used, subdivision prefixes are well established within science and technology. Milliseconds, microseconds and smaller units (but not centiseconds) are well established.

## Problems

One problem lies in the size of time units created using metric prefixes. The International System of Units has developed prefixes to express units as exponential multiples or sub-multiples. The first three multiples would be viable for use within a metric time system; they are:

Multiple Name of Unit Seconds Minutes
101 decasecond 10 0.166
102 hectosecond 100 1.666
103 kilosecond 1 000 16.666

However, the next multiples are:

Multiple Name of Unit Seconds Minutes Hours Days Years
106 megasecond 1 000 000 16 666.666 277.777 11.574 0.032
109 gigasecond 1 000 000 000 16 666 666.666 277 777.777 11 574.074 31.688

Such lengths of time are relatively impractical for measuring human activities.

For decimal multiples of the metric time unit to be practical, standard units and prefixes would need to be developed or revived for the 4th and 5th exponents so that it becomes viable for measuring human life. Historically, the metric system included a myria- prefix to represent 104 (and a counterpart dimi- prefix for 10−4), but SI (introduced in 1960) omitted the prefixes and prohibited using multiple prefixes such as decahecto-, a workaround also in use prior to the SI, leaving no way to name those orders of magnitude. 105 was represented using various ad hoc solutions; 100 000 meters composed a grade, 100 000 pascals composed a bar, and 100 000 dynes composed a newton; most of these conversions stem from compatible units that were used in the SI (and its predecessor, MKS) and the CGS system of units. Meteorologists currently use a unit of 100 000 seconds (a quantity on the order of a day) to quantify atmospheric vorticity at the synoptic scale; the unit, however, does not have a formal name.

The only way to express a nonstandard order of magnitude as an SI unit is to combine two prefixed SI derived units whose component base units cancel out; for example, units of 105 seconds could be expressed as kilojoules per centiwatt (kJ/cW) or hectocoulombs per milliampere (hC/mA). Such misuse of SI derived units can create a cognitive dissonance; to do so requires the invocation of units not directly related to the quantity being measured (coulombs and amperes, for example, quantify electricity, making it awkward to combine the two in a way that creates a unit of time with no electrical component).

Multiple Name of Unit Seconds Minutes Hours Days
104 "myriasecond" 10 000 166.6 2.777 0.116
105 No formal name 100 000 1 666.6 27.77 1.157

## References

1. ^ "What does tierce mean". findwords.info. Retrieved 2016-03-23.
2. ^ Procès-verbaux du Comité d'instruction publique de la Convention nationale by James Guillaume
3. ^ Histoire d'heure - Fractionnement du temps Archived 2015-05-22 at the Wayback Machine.
4. ^ AJB, Volume 9, 1907
5. ^ Report of the Sixth International Geographical Congress: Held in London, 1895
6. ^ Einstein's Clocks, Poincare's Maps: empires of time By Peter Louis Galison
7. ^ FILETIME documentation on MSDN
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