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General: DECIMAL TIME (FRENCH REPUBLICAN CALENDAR) NOVEMBER 24TH 1793
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Decimal time
| At 12:06:34 UTC 29 March 2025 (update) |
| Format | Decimal time | Zone |
| French |
5h 11m 5s |
Paris MT |
| Fraction |
0.50456 d |
GMT/UTC |
| Swatch .beats |
@546 |
BMT/CET |
Times are in different time zones.
 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 in France 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 (100,000 decimal seconds per day), 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 (86,400 SI seconds per day).
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, 1h23m45s 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 2025-03-29.54321 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 (54.321%) through that day (which is shortly after traditional 13:00). 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.
 Paper dial to convert a 12-hour clock face to decimal time, presented to the Revolutionary Committee of Public Instruction by Hanin.
| 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. |
The decans are 36 groups of stars (small constellations) 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 (that is, every ten days, a new decanic star group reappears in the eastern sky at dawn right before the Sun rises, after a period of being obscured by the Sun's light), the ancient Greeks called them dekanoi (δεκανοί; pl. of δεκανός dekanos) or "tens". A ten-day period between the rising of two consecutive decans is a decade. There were 36 decades (36 × 10 = 360 days), plus five added days to compose the 365 days of a solar based year.
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 (traditional Chinese: 時辰; simplified Chinese: 时辰; pinyin: shí chén) and also into 10 shi / 100 ke (Chinese: 刻; pinyin: kè) by the 1st millennium BC.[1][2] Other numbers of ke per day were used during three short periods: 120 ke from 5 to 3 BC, 96 ke from 507 to 544 CE, 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 (Season Granting) calendar further subdivided each fen into 100 miao, creating a complete decimal time system of 100 ke, 100 fen and 100 miao.[3] 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.[4]
Gēng (更) 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 (2 hours 24 minutes). 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 (旬). Months consisted of three xún. The first 10 days were the early xún (上旬), the middle 10 the mid xún (中旬), and the last nine or 10 days were the late xún (下旬). Japan adopted this pattern, with 10-day-weeks known as jun (旬). In Korea, they were known as sun (순,旬).
 Astronomical table from the Almanach national de France using decimal time
In 1754, Jean le Rond d'Alembert wrote in the Encyclopédie:
- It would be very desirable that all divisions, for example of the livre, the sou, the toise, the day, the hour, etc. would be from tens into tens. This division would result in much easier and more convenient calculations and would be very preferable to the arbitrary division of the livre into twenty sous, of the sou into twelve deniers, of the day into twenty-four hours, the hour into sixty minutes, etc.[5][6]
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 (older French for "third"). 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".[7]
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 (4 Frimaire of the Year II):
- VIII. Each month is divided into three equal parts, of ten days each, which are called décades...
- XI. The day, from midnight to midnight, is divided into ten parts or hours, each part into ten others, so on until the smallest measurable portion of the duration. The hundredth part of the hour is called decimal minute; the hundredth part of the minute is called decimal second. This article will not be required for the public records, until from the 1st of Vendémiaire, the year three of the Republic. (September 22, 1794) (emphasis in original)
Thus, midnight was called dix heures ("ten hours"), noon was called cinq heures ("five hours"), etc.
 3 different representations of 3 hours 86 minutes decimal time by Delambre (9:15:50 a.m.)
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 (0.8333) 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 (comma is the decimal sign in French)
- 0j386 ("j" is for jour, day in French)
- 3h 86' (apostrophe is for minutes)
 Marriage certificate for Napoleon's sister, dated 12 floreal l'An V "à Sept heures Cinq Decimes" (May 1, 1797, at 6:00 pm).
Sometimes in official records, decimal hours were divided into tenths, or décimes, instead of minutes. One décime is equal to 10 decimal minutes, which is nearly equal to a quarter-hour (15 minutes) in standard time. Thus, "five hours two décimes" equals 5.2 decimal hours, roughly 12:30 p.m. in standard time.[8][9] One hundredth of a decimal second was a decimal tierce.[10]
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 (18 Germinal of the Year III). 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.[11] In some places, decimal time was used to record certificates of births, marriages, and deaths until the end of Year VIII (September 1800). On the Palace of the Tuileries in Paris, two of the four clock faces displayed decimal time until at least 1801.[12] 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 (which also included decimalisation of currency and metrication) 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.
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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.[13]
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.[14]
C.A. Prieur (of the Côte-d'Or), read at the National Convention on Ventôse 11, year III (March 1, 1795):
- 1) As it does not offer almost all of the nation any marked advantage, it would only throw a disadvantage on the new system of measures and the decimal method, which is however very useful;
- 2) Since the hourly compilation is not a commercial object or susceptible to a police regulation, the old uses would be maintained by the immense force of habit;
- 3) This habit would be further consolidated by the fear of confusion. It would be necessary, to prevent it, to take new names that have not yet been indicated, and that it would be very difficult to introduce into common language, especially for so many people who do not write, who do not calculate, and who appreciate time only by a routine based on common opinion;
- 4) The expense of changing the clocks would be enormous;
- 5) Finally, citizens and watchmakers would be infinitely dismayed, some to change their watches, others to lose the ability to sell those that are already made. This truth is acquired by the result of the contest which took place recently, under the decree on watchmaking movements.
- But by asking that the decimal division of the day is not a condition of rigor, there is no disagreement that there are several circumstances where it has advantages. We know that in several objects of the Navy service, in astronomical or trigonometric calculations, and for delicate experiments, the decimal division of time is more convenient. It will therefore be good to reserve it for these cases, until the use can spread more generally, which will happen by itself imperceptibly.
Thus, the law of 18 Germinal An III (April 7, 1795) 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.
 French timepiece with 12-hour (upper) and decimal (lower) faces, 1793–94
At the International Meridian Conference of 1884, the following resolution was proposed by the French delegation and passed nem con (with 3 abstentions):
- VII. That the Conference expresses the hope that the technical studies designed to regulate and extend the application of the decimal system to the division of angular space and of time shall be resumed, so as to permit the extension of this application to all cases in which it presents real advantages.
In the 1890s, Joseph Charles François de Rey-Pailhade, president of the Toulouse Geographical Society, proposed dividing the day into 100 parts, called cés, equal to 14.4 standard minutes, and each divided into 10 decicés, 100 centicés, etc. The Toulouse Chamber of Commerce adopted a resolution supporting his proposal in April 1897. Although widely published, the proposal received little backing.[15]
The French made another attempt at the decimalization of time in 1897, when the Commission de décimalisation du temps was created by the Bureau des Longitudes, with the mathematician Henri Poincaré as secretary. The commission adopted a compromise, originally proposed by Henri de Sarrauton of the Oran Geographical Society, of retaining the 24-hour day, but dividing each hour into 100 decimal minutes, and each minute into 100 seconds. The plan did not gain acceptance and was abandoned in 1900.
 A Swatch watch showing .beat time in the bottom part of the display
On 23 October 1998, the Swiss watch company Swatch introduced a decimal time called Internet Time for its line of digital watches, which divided the day into 1,000 ".beats", (each 86.4 seconds in standard time) counted from 000–999, with @000 being midnight and @500 being noon standard time in Switzerland, which is Central European Time (one hour ahead of Universal Time).
Although Swatch did not specify units smaller than one .beat, third party implementations extended the standard by adding "centibeats" or "sub-beats", for extended precision: @248.00. Each "centibeat" was a hundredth of a .beat and was therefore equal to one French decimal second (0.864 seconds).[16][17]
When using .beats and centibeats, Swatch Internet Time divided the day into 1,000 French decimal minutes and each decimal minute into 100 decimal seconds. So 9pm was 21:00:00 in standard time and @875.00 in extended Swatch Internet Time.
Swatch no longer markets digital watches with Internet Time.
There are exactly 86,400 standard seconds (see SI for the current definition of the standard second) in a standard day, but in the French decimal time system there were 100,000 decimal seconds in the day; thus, the decimal second was 13.6% shorter than its standard counterpart.
| Unit | Seconds (SI) | Minutes | Hours | h:mm:ss.sss |
| 1 Decimal second |
0.864 |
0.0144 |
0.00024 |
0:00:00.864 |
| 1 Decimal minute |
86.4 |
1.44 |
0.024 |
0:01:26.400 |
| 1 Décime |
864 |
14.4 |
0.24 |
0:14:24.000 |
| 1 Decimal hour |
8,640 |
144 |
2.4 |
2:24:00.000 |
"Decimal hour" redirects here. For measurement of angle, see hour angle. Another common type of decimal time is decimal hours. In 1896, Henri de Sarrauton of the Oran Geographical Society proposed dividing the 24 hours of the day each into 100 decimal minutes, and each minute into 100 decimal seconds.[18] Although endorsed by the Bureau des Longitudes, this proposal failed, but using decimal fractions of an hour to represent the time of day instead of minutes has become common.
Decimal hours are frequently used in accounting for payrolls and hourly billing. Time clocks typically record the time of day in tenths or hundredths of an hour. For instance, 08:30 would be recorded as 08.50. This is intended to make accounting easier by eliminating the need to convert between minutes and hours.
For aviation purposes, where it is common to add times in an already complicated environment, time tracking is simplified by recording decimal fractions of hours. For instance, instead of adding 1:36 to 2:36, getting 3:72 and converting it to 4:12, one would add 1.6 to 2.6 and get 4.2 hours.[19]
The time of day is sometimes represented as a decimal fraction of a day in science and computers. Standard 24-hour time is converted into a fractional day by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including the following, all of which refer to the same moment in time:
As many decimal places may be used as required for precision, so 0.5 d = 0.500000 d. Fractional days are often calculated in UTC or TT, although Julian Dates use pre-1925 astronomical date/time (each date began at noon = ".0") and Microsoft Excel uses the local time zone of the computer. Using fractional days reduces the number of units in time calculations from four (days, hours, minutes, seconds) to just one (days).
Fractional days are often used by astronomers to record observations, and were expressed in relation to Paris Mean Time by the 18th century French mathematician and astronomer Pierre-Simon Laplace, as in these examples:[20]
... et la distance périhélie, égale à 1,053095; ce qui a donné pour l'instant du passage au périhélie, sept.29j,10239, temps moyen compté de minuit à Paris.
Les valeurs précédentes de a, b, h, l, relatives à trois observations, ont donné la distance périhélie égale à 1,053650; et pour l'instant du passage, sept.29j,04587; ce qui diffère peu des résultats fondés sur cinq observations.
— Pierre-Simon Laplace, Traité de Mécanique Céleste
Fractional days have been used by astronomers ever since. For instance, the 19th century British astronomer John Herschel gave these examples:[21]
Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0d·286003, or at 6h 51m 50s·66 Greenwich Mean Time ... For example, at 12h 0m 0s Greenwich Mean Time, or 0d·500000...
— John Herschel, Outlines of Astronomy
Fractional days are commonly used to express epochs of orbital elements. The decimal fraction is usually added to the calendar date or Julian day for natural objects, or to the ordinal date for artificial satellites in two-line elements.
Decimal multiples and fractions of the second
[edit]
The second is the International System of Units (SI) unit of time duration. It is also the standard single-unit time representation in many programming languages, most notably C, and part of UNIX/POSIX standards used by Linux, Mac OS X, etc.; to convert fractional days to fractional seconds, multiply the number by 86400. Fractional seconds are represented as milliseconds (ms), microseconds (μs) or nanoseconds (ns). Absolute times are usually represented relative to 1 January 1970, at midnight UT. Other systems may use a different zero point (like Unix time).
In principle, time spans greater than one second may be given in units such as kiloseconds (ks), megaseconds (Ms), gigaseconds (Gs), and so on. Occasionally, these units can be found in technical literature, but traditional units like minutes, hours, days and years are much more common, and are accepted for use with SI.
It is possible to specify the time of day as the number of kiloseconds of elapsed time since midnight. Thus, instead of saying 3:45 p.m. one could say (time of day) 56.7 ks. There are exactly 86.4 ks in one day (each kilosecond being equivalent to 16 minutes and 40 seconds worth of conventional time). However, this nomenclature is rarely used in practice.
Scientific decimal time
[edit]
Scientists often record time as decimal. For example, decimal days divide the day into 10 equal parts, and decimal years divide the year into 10 equal parts. Decimals are easier to plot than both (a) minutes and seconds, which uses the sexagesimal numbering system, (b) hours, months and days, which has irregular month lengths. In astronomy, the so-called Julian day uses decimal days centered on Greenwich noon.
- Seconds in a decimal minute
Since there are 60 seconds in a minute, a tenth part represents 60/10 = 6 seconds.
Conversion between decimal minutes and seconds
| Decimal minutes |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
| Second |
6s |
12s |
18s |
24s |
30s |
36s |
42s |
48s |
54s |
60s |
- Minutes in a decimal hour
Since there are 60 minutes in an hour, a tenth part represents 60/10 = 6 minutes.
Conversion between decimal hours and minutes
| Decimal hours |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
| Minutes |
6m |
12m |
18m |
24m |
30m |
36m |
42m |
48m |
54m |
60m |
- Hours in a decimal day
Since there are 24 hours in a day, a tenth part represents 24/10 = 2.4 hours (2 hours and 24 minutes).
Conversion between decimal day and hours/minutes
| Decimal days |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
| Hours/minutes |
2h 24m |
4h 48m |
7h 12m |
9h 36m |
12h |
14h 24m |
16h 48m |
19h 12m |
21h 36m |
24h |
- Length of a decimal year
Since there are about 365 days in a year, there are about 365/10 = 36.5 days in a tenth of a year. Hence the year 2020.5 represents the day 2 July 2020.[22] More exactly, a "Julian year" is exactly 365.25 days long, so a tenth of the year is 36.525 days (36 days, 12 hours, 36 minutes).
Conversion between decimal years and date (in a common year)
| Decimal years |
0.0 |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
1.0 |
| Days |
0 |
36.525 |
73.050 |
109.575 |
146.100 |
182.625 |
219.150 |
255.675 |
292.200 |
328.725 |
365.250 |
Date
Time |
1 Jan
00:00 |
6 Feb
12:36 |
15 Mar
01:12 |
20 Apr
13:48 |
27 May
2:24 |
1 Jul
15:00 |
8 Aug
03:36 |
13 Sep
16:12 |
20 Oct
04:48 |
25 Nov
17:24 |
1 Jan
06:00 |
These values, based on the Julian year, are most likely to be those used in astronomy and related sciences. A Gregorian year, which takes into account the 100 vs. 400 leap year exception rule of the Gregorian calendar, is 365.2425 days (the average length of a year over a 400–year cycle), resulting in 0.1 years being a period of 36.52425 days (3155695.2 seconds; 36 days, 12 hours, 34 minutes, 55.2 seconds).
Other decimal times
[edit]
Numerous individuals have proposed variations of decimal time, dividing the day into different numbers of units and subunits with different names. Most are based upon fractional days, so that one decimal time format may be easily converted into another, such that all the following are equivalent:
- 0.500 day
- 5 heures décimales
- @500.beats Swatch Internet Time (see above)
- 50.0 kes or cés (centidays)
- 500 millidays
- 50.0% time as a percentage of the day
- 12:00 standard time
Some decimal time proposals are based upon alternate units of metric time. The difference between metric time and decimal time is that metric time defines units for measuring time interval, as measured with a stopwatch, and decimal time defines the time of day, as measured by a clock. Just as standard time uses the metric time unit of the second as its basis, proposed decimal time scales may use alternative metric units.
In the fictional Star Trek universe, each stardate increment represents one milliyear, with 78 years in 2401, counted from 2323. The decimal represents a fractional day. Thus, stardates are a composition of two types of decimal time.[citation needed] In 2023, 78 years earlier would be 1945.
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For centuries we have used the sexagesimal system of measuring time, where each day is divided into 24 hours, each hour into 60 minutes and each minute into 60 second. Why do we do this? Is it out of habit, or is there any inherent advantage of measuring time by base 60?
The ancient Greeks were the first to introduce the concept of hour after Horae, the goddesses of the seasons and the natural portions of time. The number of Horae varied according to different sources, and while the most common is three, by Late Antiquity, their numbers had inflated to twelve, from which came the idea of dividing the day and the night into 12 hours each. The division of the hour into 60 minutes and of the minute into 60 seconds came from the Babylonians who used a sexagesimal system for mathematics and astronomy. The Babylonians divided the day into 360 parts, because that was their estimate for the number of days in a year. Diving a circle into 360 degrees was also their idea.
“Apollo with the Hours” by Georg Friedrich Kersting (1822)
The Egyptians also used 12 hour days, possibly because there are twelve lunar cycles in a year, or probably they were easier to count on the 12 finger joints on each hand. In any case, these systems were adopted throughout the world and are now the standards of measuring time. But what if we change the standards?
Decimal Time
In 1754, French mathematician Jean le Rond d'Alembert proposed that all units of time should be divisible by ten:
It would be very desirable that all divisions, for example of the livre, the sou, the toise, the day, the hour, etc. would be from tens into tens. This division would result in much easier and more convenient calculations and would be very preferable to the arbitrary division of the livre into twenty sous, of the sou into twelve deniers, of the day into twenty-four hours, the hour into sixty minutes, etc.
In 1788, Claude Boniface Collignon, a French attorney, proposed dividing the day into 10 hours, each hour into 100 minutes, each minute into 1000 seconds, and each second into 1000 tierces. He also suggested a week of 10 days and dividing the year into 10 "solar months".
Jean-Charles de Borda modified the proposal, and based on this foundation the French Parliament decreed that “from midnight to midnight, is divided into ten parts, each part into ten others, and so forth until the smallest measurable portion of duration.”
Decimal time clock. Photo: Kcida10/Wikimedia Commons
The system officially went into force on November 24, 1793. Midnight began at zero hours (or 10 hours), and noon arrived at 5 hours. Each metric hour thus became 2.4 conventional hours long. Each metric minute became equivalent to 1.44 conventional minutes, and each metric second became 0.864 conventional second. Calculations became easier. Time could be written fractionally, for example, 6 hours 42 minutes became 6.42 hours and both meant that same thing.
To help people transition to the new time format, clock manufacturers began producing clocks with faces showing both decimal time and the old time. But the people never did transition to the new time. On the contrary, decimal time proved to be so unpopular that it was scrapped 17 months after it was introduced.
Decimal time was part of a larger attempt at decimalisation of everything by the French revolutionaries, which also included decimalisation of currency and metrication, 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. Since this only accounted for 360 days, the five extra days required to approximate the solar year were placed at the end of each year without being count in any month. This calendar too was abolished at the end of 1805, and the entire plan was buried before it had time to fly.
Clocks from the French Revolution
After the decimal time fiasco, you would have expected that the French would never talk about it again, yet in the 1890s, Joseph Charles François de Rey-Pailhade, president of the Toulouse Geographical Society, once again proposed dividing the day, this time into 100 parts, called cés, each equal to 14.4 standard minutes, and each divided into 10 decicés, 100 centicés, etc. Worse still, the Toulouse Chamber of Commerce adopted a resolution supporting his proposal. Fortunately, sanity prevailed and the proposal received little backing outside the Chamber of Commerce.
Finally, a last ditch attempt was made in 1897 by the French scientific committee Bureau des Longitudes, with the mathematician Henri Poincaré as secretary. Poincaré adopted a compromise of retaining the 24-hour day, but dividing each hour into 100 decimal minutes, and each minute into 100 seconds. Again, the plan did not gain acceptance and decimal time was abandoned in 1900 for good. Nobody has dared to touch the clock again.
References:
# Why are there 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day? Who decided on these time divisions?, The Guardian
# Why are there 24 hours in a day?, ABC Science
# Wikipedia
https://www.amusingplanet.com/2021/06/that-time-when-french-divided-day-into.html |
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History of the observatory
The decimal clock
A curiosity in Abbadia: all measurements are in decimal system. This may seem normal since we are at the end of the nineteenth century but it concerns measures of both angles and timings.
- For angle measurements, graduations are not in degrees but in grades (from 0 to 100 degrees instead of 0 to 90 degrees for latitudes). This system is not common on an astronomical instrument but is much more so on IGN maps. D'Abbadie defies the traditions of astronomers by thinking that he is ahead of his epoch.
- For the measurement of time, it is much more surprising: the clocks are not graduated on 12 hours but on 10! And one day is not 24 hours but 10 hours divided into 100 parts. This system proposed with the metric system at the time of the French Revolution, has never been used by scientists or by the general public. The change in habits was there too much. Decimal clocks and watches have been built but without success. Yet, nearly a century after the revolution, D'Abbadie still believed that the decimal system will eventually prevail for the measurement of time as well. The future will give him wrong.
one of the decimal clocks of AbbadiaCredit : JEA
If ancient Egypt and China were already using decimal measures of time, it was not the same for peoples under the Babylonian influence: the sexagesimal system for angles and hours had the advantage of having many of divisor. The decimal system did not even allow division by 4 in integers, which did not go well on the clocks. This is probably the cause of the abandon of decimal hours but of the conservation - which will not be universal - of grades for angles.
Let's explain the decimal system of time:
-the day of 24h is divided into 10 hours, each hour being divided into 100 decimal minutes divided into 100 decimal seconds. One day contains 1000 decimal minutes (instead of 1440 sexagesimal minutes) and 100 000 decimal seconds (instead of 86400 sexagesimal seconds).
The decimal time was officially introduced in France during the Revolution by the decree of the 4th Frimaire of Year II (November 24, 1793) but was abolished in 1795! It should be noted that astronomers use a decimal time with the Julian period where each day is numbered from January 1, -4712 at noon and each moment noted by its decimal fraction of a day.
https://abbadia.imcce.fr/en/deci-en.html |
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Tiempo decimal
Se denomina tiempo decimal a la expresión de la extensión del día utilizando unidades que se encuentran relacionadas mediante un sistema decimal. Este término es utilizado para referirse específicamente al tiempo revolucionario francés, el cual divide al día en 10 horas decimales, cada hora decimal en 100 minutos decimales y cada minuto decimal en 100 segundos decimales, en contraposición al tiempo estándar usual, en el cual el día se divide en 24 horas, cada hora en 60 minutos y cada minuto en 60 segundos.
 Reloj decimal francés de la época de la Revolución francesa.
El tiempo decimal fue utilizado en China a lo largo de casi toda su historia junto con el tiempo duodecimal. Hacia el año 1000 a. C. el día que se extendía desde una medianoche a la medianoche siguiente se encontraba dividido en 12 horas dobles (chino tradicional: 時辰; chino simplificado: 时辰; pinyin: shíchen) y 100 ke (Hanzi: 刻; Pinyin: kè).[1] Durante tres períodos breves se utilizaron un número diferente de kes por día, 120 ke durante 5–3 A.d. C., 96 ke durante 507–544, y 108 ke durante 544–565. Varios de los casi 50 calendarios chinos también dividieron cada ke en 100 fen, aunque en otros cada ke era dividido en 60 fen. En 1280, el calendario Shoushi (Season Granting) subdividió a cada fen en 100 miao, creando un sistema decimal completo de 100 ke, 100 fen y 100 miao.[2] El tiempo decimal chino dejó de ser utilizado en 1645 cuando el calendario Shixian (Constant Conformity), basado en la astronomía europea llevada a China por los jesuitas, adoptó 96 ke por día junto con 12 horas dobles, con lo cual cada ke corresponde exactamente a un cuarto de hora.[3]
En tiempos modernos, el tiempo decimal fue introducido durante la Revolución francesa por un decreto promulgado el 5 de octubre de 1793:
- XI. Le jour, de minuit à minuit, est divisé en dix parties, chaque partie en dix autres, ainsi de suite jusqu’à la plus petite portion commensurable de la durée.
- XI. El día, desde medianoche hasta la medianoche siguiente, se divide en diez partes, cada parte a su vez se compone de diez partes, y así sucesivamente hasta la duración de tiempo más pequeña que se pueda medir.
Se les dio nombre a estas partes el 24 de noviembre de 1793 (4 Frimario del Año II). Las divisiones primarias se denominaron horas, y se agregó:
- La centième partie de l'heure est appelée minute décimale; la centième partie de la minute est appelée seconde décimale. (énfasis en el original)
- La centésima parte de una hora es denominada minuto decimal; la centésima parte de un minuto es denominada segundo decimal.
Por lo tanto, medianoche correspondía a la hora 10, mediodía a la hora 5, etc. Si bien se fabricaron relojes con cuadrantes mostrando el tiempo estándar con los números 1–24 y el tiempo decimal con los números 1–10, el tiempo decimal nunca contó con gran aceptación; no fue utilizado de manera oficial hasta comienzos del año Republicano III, 22 de septiembre de 1794, y el uso obligatorio fue suspendido el 7 de abril de 1795 (18 Germinal del Año III), mediante la misma ley que introdujo el sistema métrico original. Por lo tanto, inicialmente el sistema métrico no poseía una unidad de tiempo, y versiones posteriores del sistema métrico utilizan el segundo, igual a 1/86400 de día, como unidad de tiempo métrico.
El tiempo decimal fue introducido como parte del calendario republicano francés, en el cual además de dividir el día en forma decimal, dividió al mes en tres décadas de 10 días cada una; este calendario fue abolido a finales del 1805. El comienzo de cada año era determinado según el día en él tenía lugar el equinoccio de otoño, en relación con el tiempo solar aparente o verdadero en el Observatorio de París. El tiempo decimal habría sido expresado también según el tiempo solar aparente, dependiendo de la posición desde la cual se lo registraba, como ya era la costumbre general para ajustar los relojes.
En 1897 los franceses realizaron otro intento de decimalizar el tiempo, cuando se creó la Commission de décimalisation du temps en el Bureau des Longitudes, siendo secretario el matemático Henri Poincaré. La comisión propuso un compromiso, al mantener el día de 24 horas, pero dividir cada hora en 100 minutos decimales, y cada minuto en 100 segundos. El plan no tuvo buena acogida y fue abandonado en 1900.
Hay exactamente 86.400 segundos estándar (véase SI para una definición actual del segundo estándar) en un día estándar, pero en el sistema de tiempo decimal francés hay 100.000 segundos decimales en un día, por lo que el segundo decimal es más corto que su contraparte.
| Unidad decimal | Segundos | Minutos | Horas | h:mm:ss |
| Segundo decimal |
0,864 |
0,0144 |
0,00024 |
0:00:00,9 |
| Minuto decimal |
86,4 |
1,44 |
0,024 |
0:01:26,4 |
| Hora decimal |
8640 |
144 |
2,4 |
2:24:00,0 |
Son los científicos y los programadores de computadoras lo que utilizan en forma más asidua el tiempo decimal del día en forma de día fraccional. El tiempo estándar de 24 horas es convertido en un día fraccional simplemente mediante dividir el número de horas pasadas desde la medianoche por 24 para obtener una fracción decimal. Por lo tanto medianoche es 0,0 día, mediodía es 0,5 d, etc., lo cual se puede componer con cualquier tipo de fecha, tales como:
Es posible utilizar tantos sitios decimales como sea necesario de acuerdo a la precisión requerida, de forma que 0,5 d = 0,500000 d. Los días fraccionarios a menudo son expresados en UTC o TT, aunque las fechas Julianas utilizan fecha/tiempo astronómico anterior a 1925 (cada fecha comenzaba en el 0h por lo tanto ".0" = mediodía) y Microsoft Excel utiliza la zona de tiempo local de la computadora. El uso de días fraccionarios reduce el número de unidades utilizadas en cálculos de tiempo de cuatro (días, horas, minutos, segundos) a una sola (días). A menudo los astrónomos utilizan días fraccionarios para registrar sus observaciones, y fueron indicados haciendo referencia al Paris Mean Time por el matemático y astrónomo francés del siglo xviii Pierre-Simon Laplace en su libro, Traité de Mécanique Céleste, tal como en estos ejemplos:
... et la distance périhélie, égale à 1,053095 ; ce qui a donné pour l'instant du passage au périhélie, sept.29,10239, temps moyen compté de minuit à Paris.
Les valeurs précédentes de a, b, h, l, relatives à trois observations, ont donné la distance périhélie égale à 1,053650; et pour l'instant du passage, sept.29,04587; ce qui diffère peu des résultats fondés sur cinq observations.
Días fraccionales fueron utilizados durante el siglo xix por el astrónomo británico John Herschel en su libro, Outlines of Astronomy, como se ilustra en estos ejemplos:
Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0 d•286003, or at 4 h 51 m 50 s •66 Greenwich Mean Time ... For example, at 12 h 0 m 0 s Greenwich Mean Time, or 0 d•500000...
En general el sistema de segundos fraccionales es más utilizado que el de días fraccionales. En efecto, esta es la representación en una única unidad que utilizan numerosos lenguajes de programación, incluidos C, y parte de los estándares UNIX/POSIX utilizados por Mac OS X, Linux, etc.; para convertir días fraccionales en segundos fraccionales, multiplican el número por 86400. Tiempos absolutos son a menudo expresados relativos a la medianoche del 1 de enero de 1970. Otros sistemas pueden utilizar un punto cero distinto, pueden contar en milisegundos en vez de segundos, etc.
Tiempo de Internet Swatch
[editar]
El 23 de octubre de 1998, la compañía fabricante de relojes Suiza, Swatch, presentó un tiempo decimal denominado Swatch Internet Time, el cual divide al día en 1000 beats (cada uno 86,4 s) contados en el rango 000–999, con @000 medianoche y @500 mediodía CET (UTC +1), en contraposición al UTC.[4] La empresa ha vendido relojes que indican el Tiempo de Internet.
Internet Time ha sido criticado por utilizar un origen diferente al utilizado por el Horario universal, tergiversar CET al presentarlo como "Biel Mean Time", y por no tener unidades más precisas, aunque ciertas organizaciones han propuesto los "centibeats" (864 ms) y "milibeats" (86.4 ms).
Otros tiempos decimales
[editar]
Distintas personas han propuesto un rango de variaciones al tiempo decimal, dividiendo al día en diferente número de unidades y subunidades con diversos nombres. La mayoría están basados en días fraccionarios, de forma que un formato de tiempo decimal puede ser fácilmente convertido en otro, de forma tal que todos estos son equivalentes:
- 0,500 día fraccional
- 5h 0m tiempo decimal francés
- @500 Swatch Internet Time
- 50,0 centidía
- 500 milidía
- 50,0% Tiempo porcentual
- 12:00 Standard Time
Algunas propuestas de tiempo decimal están basadas en unidades de medidas alternativas del tiempo métrico. La diferencia entre el tiempo métrico y el tiempo decimal es que en el tiempo métrico se definen las unidades para medir intervalos de tiempo, tal como se lo mide con un cronómetro, mientras que el tiempo decimal define el tiempo del día, tal como lo mide un reloj. Así como el tiempo estándar utiliza como base el segundo la unidad métrica de tiempo, las escalas de tiempo decimal propuestas pueden utilizar otras unidades métricas.
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