Representation of the time of day using decimally related units
At
14:22:10
UTC 25 May 2024 (
update
)
|
Format
|
Decimal time
|
Zone
|
French
|
6
h
5
m
21
s
|
Paris MT
|
Fraction
|
0.59872 d
|
GMT/UTC
|
Swatch .beats
|
@640
|
BMT/CET
|
Times are in different time zones.
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, 1
h
23
m
45
s
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 2024-05-25.54321 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.
decimal
|
24-hour
|
12-hour
|
0 (
Midnight
)
|
00:00
|
12:00 a.m.
|
1
|
02:24
|
2:24 a.m.
|
2
|
04:48
|
4:48 a.m.
|
3
|
07:12
|
7:12 a.m.
|
4
|
09:36
|
9:36 a.m.
|
5 (
Noon
)
|
12:00
|
12:00 p.m.
|
6
|
14:24
|
2:24 p.m.
|
7
|
16:48
|
4:48 p.m.
|
8
|
19:12
|
7:12 p.m.
|
9
|
21:36
|
9:36 p.m.
|
History
[
edit
]
Egypt
[
edit
]
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
(δεκανο?; pl. of δεκαν??
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.
China
[
edit
]
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
:
?辰
;
pinyin
:
shi chen
) and also into 10 shi / 100
ke
(
Chinese
:
刻
;
pinyin
:
ke
) 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
Shixian 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]
G?ng (更) is a time signal given by drum or gong. The character for g?ng 更, literally meaning "rotation" or "watch", comes from the rotation of watchmen sounding these signals. The first g?ng theoretically comes at sundown, but was standardized to fall at 19:12. The time between each g?ng is 1?10 of a day, making a g?ng 2.4 hours?or 2 hours 24 minutes?long As a 10-part system, the g?ng are strongly associated with the 10 celestial stems, especially since the stems are used to count off the g?ng during the night in Chinese literature.
As early as the Bronze-Age Xia dynasty, days were grouped into ten-day weeks known as xun (旬). Months consisted of three xun. The first 10 days were the early xun (上旬), the middle 10 the mid xun (中旬), and the last nine or 10 days were the late xun (下旬). Japan adopted this pattern, with 10-day-weeks known as jun (旬). In Korea, they were known as sun (順,旬).
France
[
edit
]
Pre-Revolution
[
edit
]
In 1754,
Jean le Rond d'Alembert
wrote in the
Encyclopedie
:
- 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]
French Republic
[
edit
]
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
decades
...
- 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 Vendemiaire, 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.
Representation
[
edit
]
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 decimes." or "forty-one minutes". 2:00 am (0.8333) was written as "eight decimes," "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)
- 0
j
386 ("j" is for jour, day in French)
- 3
h
86' (apostrophe is for minutes)
Sometimes in official records, decimal hours were divided into tenths, or
decimes
, instead of minutes. One
decime
is equal to 10 decimal minutes, which is nearly equal to a quarter-hour (15 minutes) in standard time. Thus, "five hours two decimes" 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]
Usage
[
edit
]
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
decades
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
[
edit
]
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 refuted by Jean-Marie Viallon, of the Sainte-Genevieve 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 Cote-d'Or), read at the National Convention on Ventose 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.
Later proposals
[
edit
]
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 Francois de Rey-Pailhade, president of the Toulouse Geographical Society, proposed dividing the day into 100 parts, called
ces
, equal to 14.4 standard minutes, and each divided into 10
decices
, 100
centices
, 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 decimalisation du temps
was created by the
Bureau des Longitudes
, with the mathematician
Henri Poincare
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.
Switzerland
[
edit
]
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.
Conversions
[
edit
]
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 Decime
|
864
|
14.4
|
0.24
|
0:14:24.000
|
1 Decimal hour
|
8,640
|
144
|
2.4
|
2:24:00.000
|
Decimal hours
[
edit
]
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]
Fractional days
[
edit
]
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 (all of which refer to the same moment):
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 perihelie, egale a 1,053095; ce qui a donne pour l'instant du passage au perihelie, sept.29
j
,10239, temps moyen compte de minuit a Paris.
Les valeurs precedentes de a, b, h, l, relatives a trois observations, ont donne la distance perihelie egale a 1,053650; et pour l'instant du passage, sept.29
j
,04587; ce qui differe peu des resultats fondes sur cinq observations.
?
Pierre-Simon Laplace, Traite de Mecanique Celeste
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 0
d
·286003, or at 6
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...
?
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. 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
|
6
s
|
12
s
|
18
s
|
24
s
|
30
s
|
36
s
|
42
s
|
48
s
|
54
s
|
60
s
|
- 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
|
6
m
|
12
m
|
18
m
|
24
m
|
30
m
|
36
m
|
42
m
|
48
m
|
54
m
|
60
m
|
- 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
|
2
h
24
m
|
4
h
48
m
|
7
h
12
m
|
9
h
36
m
|
12
h
|
14
h
24
m
|
16
h
48
m
|
19
h
12
m
|
21
h
36
m
|
24
h
|
- 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 (
3
155
695
.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 decimales
- @500.beats
Swatch Internet Time
(
see above
)
- 50.0
kes
or
ces
(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. In 2023, 78 years earlier would be 1945.
See also
[
edit
]
References
[
edit
]
Notes
[
edit
]
- ^
Nachum Dershowitz
,
Edward M. Reingold
,
"
Calendrical Calculations
"
, page 207
- ^
Joseph Needham, Ling Wang, and Derek John de Solla Price
Heavenly clockwork: the great astronomical clocks of medieval China
(Cambridge: Cambridge University Press, 1986) 199-202,
ISBN
0-521-32276-6
.
- ^
Jean-Claude Martzloff, "Chinese mathematical astronomy", in
Helaine Selin
, ed.,
Mathematics across cultures
(Dordrecht: Kluwer, 2000) 373?407, p. 393,
ISBN
0-7923-6481-3
.
- ^
K. Yabuuti [Kiyoshi Yabuuchi], "Astronomical tables in China, from the Wutai to the Ch'ing dynasties", in
Japanese Studies in the History of Science
no. 2 (1963) 94?100.
- ^
Vera, Hector (2009).
"Decimal Time: Misadventures of a Revolutionary Idea, 1793?2008"
.
KronoScope
.
9
(1?2). Brill: 31?32.
doi
:
10.1163/156771509X12638154745382
.
ISSN
1567-715X
.
[
permanent dead link
]
- ^
d'Alembert, Jean le Rond (1754).
Encyclopedie
. Archived from
the original
on 2012-12-15.
- ^
Collignon, Claude Boniface (1788).
Decouverte d'etalons justes, naturels, invariables et universels
. Chez l'auteur. pp. 39?40.
- ^
Jean Nicolas (1989).
La Revolution francaise dans les Alpes: Dauphine et Savoie, 1789-1799
. Privat. p. 256.
ISBN
9782708953529
.
- ^
Carrigan, Richard A. (May?June 1978). "Decimal Time: Unlike the metric system of measurements, decimal time did not survive the French Revolution. But is dividing the day by tens a possibility for the future?".
American Scientist
.
66
(3): 305?313.
JSTOR
27848641
.
- ^
"Instruction sur l'ere de la Republique, a la suite du decret du 3 brumaire, an II"
(PDF)
.
Universite de Toulouse
.
- ^
Matthew Shaw (2011).
Time and the French Revolution: The Republican Calendar, 1789-year XIV
. Boydell & Brewer Ltd. pp. 132?3.
ISBN
978-0-86193-311-2
.
- ^
Ernest Leroux, ed. (1900).
Bulletin de geographie historique et descriptive, annee 1899
. Paris: Comite des travaux historiques et scientifiques. p. 142.
- ^
Commission des poids et mesures (1793). Hauy, Rene-Just (ed.).
Instruction abregee sur les mesures deduites de la grandeur de la Terre, uniformes pour toute la Republique, et sur les calculs relatifs a leur division decimale; par la Commission temporaire des poids & mesures republicaines, en execution des decrets de la Convention nationale. Edition originale
(in French). France: de l'imprimerie nationale executive du Louvre (A Paris).
- ^
Proces-verbaux du Comite d'instruction publique de la Convention nationale
. Imprimerie nationale. 1897. p. 605.
- ^
Bulletin of the International Railway Congress
(English ed.). 1899. p. 784.
- ^
"Nucleus Plugin: NP_InternetTime"
.
TeRanEX Wiki
. 2005-11-23. Archived from
the original
on 2007-08-07.
- ^
"iBeat"
. Archived from
the original
on 2008-12-24.
- ^
Sarrauton, Henri de (1896).
L'Heure decimale et la division de la circonference
, Oran: Fouque
- ^
"Pilot Log Books"
.
Civil Aviation Safety Authority
. Archived from
the original
on 2012-03-21
. Retrieved
2012-06-23
.
- ^
Laplace, Pierre Simon de (1823).
Traite de Mecanique Celeste
.
- ^
Outlines of Astronomy
.
- ^
Campbell, Wallace Hall (2003).
Introduction to geomagnetic fields
(2 ed.). Cambridge University Press. p. 316.
ISBN
0-521-52953-0
.
ISBN
978-0-521-52953-2
Sources
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]
External links
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]