Decimal time
File:Decimal Clock face by Pierre Daniel Destigny 1798-1805.jpg|right|thumb|French decimal clock from the time of the French Revolution. The large dial shows the ten hours of the decimal day in Arabic numerals, while the small dial shows the two 12-hour periods of the standard 24-hour day in Roman numerals.
Decimal time is the representation of the time of day using units which are decimally related. This term is often used specifically to refer to the French Republican calendar time system used from 1794 to 1800, during the French Revolution, which divided the day into 10 decimal hours, each decimal hour into 100 decimal minutes and each decimal minute into 100 decimal seconds, as opposed to the more familiar standard time, which divides the day into 24 hours, each hour into 60 minutes and each minute into 60 seconds.
The main advantage of a decimal time system is that, since the base used to divide the time is the same as the one used to represent it, the representation of hours, minutes and seconds can be handled as a unified value. Therefore, it becomes simpler to interpret a timestamp and to perform conversions. For instance, 12345 is 1 decimal hour, 23 decimal minutes, and 45 decimal seconds, or 1.2345 decimal hours, or 123.45 decimal minutes or 12345 decimal seconds; 3 hours is 300 minutes or 30,000 seconds.
This property also makes it straightforward to represent a timestamp as a fractional day, so that.54321 can be interpreted as five decimal hours, 43 decimal minutes and 21 decimal seconds after the start of that day, or a fraction of 0.54321 through that day. It also adjusts well to digital time representation using epochs, in that the internal time representation can be used directly both for computation and for user-facing display.
| decimal | 24-hour | 12-hour |
| 0:00 | 00:00 | 12:00 a.m. |
| 1:00 | 02:24 | 2:24 a.m. |
| 2:00 | 04:48 | 4:48 a.m. |
| 3:00 | 07:12 | 7:12 a.m. |
| 4:00 | 09:36 | 9:36 a.m. |
| 5:00 | 12:00 | 12:00 p.m. |
| 6:00 | 14:24 | 2:24 p.m. |
| 7:00 | 16:48 | 4:48 p.m. |
| 8:00 | 19:12 | 7:12 p.m. |
| 9:00 | 21:36 | 9:36 p.m. |
History
Egypt
The decans are 36 groups of stars used in the ancient Egyptian astronomy to conveniently divide the 360 degree ecliptic into 36 parts of 10 degrees. Because a new decan also appears heliacally every ten days, the ancient Greeks called them dekanoi or "tens". A ten-day period between the rising of two consecutive decans is a decade. There were 36 decades, plus five added days to compose the 365 days of a solar based year.China
Decimal time was used in China throughout most of its history alongside duodecimal time. The midnight-to-midnight day was divided both into 12 double hours and also into 10 shi / 100 ke by the 1st millennium BC. Other numbers of ke per day were used during three short periods: 120 ke from 5 to 3 BC, 96 ke from AD 507 to 544, and 108 ke from 544 to 565. Several of the roughly 50 Chinese calendars also divided each ke into 100 fen, although others divided each ke into 60 fen. In 1280, the Shoushi calendar further subdivided each fen into 100 miao, creating a complete decimal time system of 100 ke, 100 fen and 100 miao. Chinese decimal time ceased to be used in 1645 when the Shíxiàn calendar, based on European astronomy and brought to China by the Jesuits, adopted 96 ke per day alongside 12 double hours, making each ke exactly one-quarter hour.Gēng is a time signal given by drum or gong. The character for gēng 更, literally meaning "rotation" or "watch", comes from the rotation of watchmen sounding these signals. The first gēng theoretically comes at sundown, but was standardized to fall at 19:12. The time between each gēng is 1⁄10 of a day, making a gēng 2.4 hours long. As a 10-part system, the gēng are strongly associated with the 10 celestial stems, especially since the stems are used to count off the gēng during the night in Chinese literature.
As early as the Bronze-Age Xia dynasty, days were grouped into ten-day weeks known as xún. Months consisted of three xún. The first 10 days were the early xún, the middle 10 the mid xún, and the last nine or 10 days were the late xún. Japan adopted this pattern, with 10-day-weeks known as jun. In Korea, they were known as sun.
France
Pre-Revolution
In 1754, Jean le Rond d'Alembert wrote in the Encyclopédie:In 1788, Claude Boniface Collignon proposed dividing the day into 10 hours or 1,000 minutes, each new hour into 100 minutes, each new minute into 1,000 seconds, and each new second into 1,000 tierces. The distance the twilight zone travels in one such tierce at the equator, which would be one-billionth of the circumference of the earth, would be a new unit of length, provisionally called a half-handbreadth, equal to four modern centimetres. Further, the new tierce would be divided into 1,000 quatierces, which he called "microscopic points of time". He also suggested a week of 10 days and dividing the year into 10 "solar months".
French Republic
Decimal time was officially introduced during the French Revolution. Jean-Charles de Borda made a proposal for decimal time on 5 November 1792. The National Convention issued a decree on 5 October 1793, to which the underlined words were added on 24 November 1793 :Thus, midnight was called dix heures '', noon was called cinq heures, etc.
Representation
The colon was not yet in use as a unit separator for standard times, and is used for non-decimal bases. The French decimal separator is the comma, while the period, or "point", is used in English. Units were either written out in full, or abbreviated. Thus, five hours eighty three minutes decimal might be written as 5 h. 83 m. Even today, "h" is commonly used in France to separate hours and minutes of 24-hour time, instead of a colon, such as 14h00. Midnight was represented in civil records as "ten hours". Times between midnight and the first decimal hour were written without hours, so 1:00 am, or 0.41 decimal hours, was written as "four décimes" or "forty-one minutes". 2:00 am was written as "eight décimes", "eighty-three minutes", or even "eighty-three minutes thirty-three seconds".As with duodecimal time, decimal time was represented according to true solar time, rather than mean time, with noon being marked when the sun reached its highest point locally, which varied at different locations, and throughout the year.
In "Methods to find the Leap Years of the French Calendar", Jean-Baptiste-Joseph Delambre used three different representations for the same decimal time:
- 0,386
- 0j386
- 3h 86'
Usage
Although clocks and watches were produced with faces showing both standard time with numbers 1–24 and decimal time with numbers 1–10, decimal time never caught on; it was not used for public records until the beginning of the Republican year III, 22 September 1794, and mandatory use was suspended 7 April 1795. In spite of this, decimal time was used in many cities, including Marseille and Toulouse, where a decimal clock with just an hour hand was on the front of the Capitole for five years. In some places, decimal time was used to record certificates of births, marriages, and deaths until the end of Year VIII. On the Palace of the Tuileries in Paris, two of the four clock faces displayed decimal time until at least 1801. The mathematician and astronomer Pierre-Simon Laplace had a decimal watch made for him, and used decimal time in his work, in the form of [|fractional days].Decimal time was part of a larger attempt at decimalisation in revolutionary France and was introduced as part of the French Republican Calendar, which, in addition to decimally dividing the day, divided the month into three décades of 10 days each; this calendar was abolished at the end of 1805. The start of each year was determined according to the day of the autumnal equinox, in relation to true or apparent solar time at the Paris Observatory.
Metric system
In designing the new metric system, the intent was to replace all the various units of different bases with a small number of standard decimal units. This was to include units for length, weight, area, liquid capacity, volume, and money. Initially the traditional second of time equal to 1/86400 day was proposed as the base of the metric system, but this was changed in 1791 to base the meter on a decimal division of a measurement of the Earth, instead. Early drafts of the metric system published in 1793 included the new decimal divisions of the day included with the Republican calendar, and some of the same individuals were involved with both projects.On March 28, 1794, Joseph-Louis Lagrange proposed to the Commission for Republican Weights and Measures on dividing the day into 10 decidays and 100 centidays, which would be expressed together as two digits, counting periods of 14 minutes and 24 seconds since midnight, nearly a quarter hour. This would be displayed by one hand on watches. Another hand would display 100 divisions of a centiday, which is 1/10,000 day, or 8.64 seconds. A third hand on a smaller dial would further divide these into 10, which would be 1/100,000 day, or 864 milliseconds, slightly less than a whole second. He suggested the deciday and centiday be used together to represent the time of day, such as "4 and 5", "4/5", or simply "45".
This was opposed by Jean-Marie Viallon, of the Sainte-Geneviève Library in Paris, who thought that decimal hours, equal to 2.4 old hours, were too long, and that 100 centidays were too many, and proposed dividing two halves of the day into 10 new hours each, for a total of 20 per day, and that simply changing the numbers on watch dials from 12 to 10, he thought, would be sufficient for rural people. For others, there would be 50 decimal minutes per decimal hour, and 100 decimal seconds per decimal minute. His new hours, minutes, and seconds would thus be more similar to the old units.
C.A. Prieur, read at the National Convention on Ventôse 11, year III :
Thus, the law of 18 Germinal An III establishing the metric system, rather than including metric units for time, repealed the mandatory use of decimal time, although its use continued for a number of years in some places. As predicted, it was quickly found to be useful by astronomers, who still use it in the form of fractional days.
Carl Friedrich Gauss recommended the ephemeris second as a metric base unit for time interval in 1832, which eventually became the atomic second in the International System. However, for longer periods of time interval, the old non-decimal units were approved for use.