© J R Stockton, ≥ 2012-03-04

Date Miscellany I.

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Our Calendars

The newsgroup sci.astro FAQ part 3/8 gives much date/time information; see also, for instance, at webexhibits, via Calendars. See also the references in Date and Time Index and Links, especially Claus Tøndering's The Calendar FAQ.

Beware : the word "Julian" is applied to several different systems. Day numbers calculated here are correct when local date equals UTC date, but perhaps not otherwise. Proleptic Dates are dates on a calendar before it was actually used.

This page deals largely with the Gregorian Calendar, its ancestry, and derived day counts. For other calendars, see via Liste des Calendriers, including Le Vieux Calendrier Anglais.

The Ancient Egyptian Calendar

This, I think, had 365 days in every year; see Leap Years.


The Romans counted years ab urbe condita - from the founding of the City, nominally in 753 BC - abbreviated to a.u.c. : the current era starts (probably) on 1 January 754 a.u.c. with AD 1.

BC + AUC = 754       AUC = AD + 753

The Julian Calendar

The (previous) Julian Calendar, with a Leap Year intended every four years, was adopted by (Gaius) Julius Caesar in 46 BC (708 a.u.c. (or 709)), for use starting in 45 BC (a Leap Year); but the counting was wrong before 8 AD. Sosigenes did the actual work; extending every fourth year had been suggested by Eratosthenes of Cyrene (275-194).

Year Numbers in Britain

The Gregorian Calendar

The (current) Gregorian Calendar was introduced by Pope Gregory XIII (1572-1585; b. Ugo Buoncompagni [Anglice: Hugo Goodfellow], 1502), on advice from a long Commission (Clavius et al), in 1582 AD, with better Leap Year rules - a Leap year every 4 years, except every 100, except every 400, from 1600; Great Britain made the change in 1752 AD, in the reign of King George II.

The Change

In the calendar changeover from Julian to Gregorian :-

The Old and New Styles

The terms "Old Style" and "New Style" are now commonly used for both the "Start of Year" and "Leap Year" changes (England & Wales: both in 1752; Scotland: 1600, 1752).

I believe that, properly and historically, the "Styles" really refer only to the "Start of Year" change (from March 25th to January 1st); and that the "Leap Year" change should be described as the change from Julian to Gregorian.

Date Validation

To validate Julian or Gregorian Y M D, check that 1≤M≤12 and D>0, then check D against an array or expression for the month-length of an ordinary year. If that passes, good. If it fails, test for D=29 and then for Y is Leap. It is inefficient to evaluate Leapness unless it is already known that D is 29 and M is February.

A.D. Dates Omitted or Duplicated

Includes only some samples of dates omitted at the introduction of the Gregorian Calendar.

Dates OmittedDates Duplicated
or Inserted
LocationPrime Reason
1582-10-05 : 1582-10-14+10Rome & othersCalendar Change
1752-09-03 : 1752-09-13+11Britain & ColoniesCalendar Change
1753-02-18 : 1753-02-28+11Sweden/FinlandCalendar Change
1867-10-07 : 1867-10-17+12-1AlaskaPurchase from Russia
1844-12-31+1PhilippinesCrossing Date Line
1995-??-??+1Eastern KiribatiCrossing Date Line
2011-12-30+1Samoa and TokelauCrossing Date Line
Alaska dates are probable; maybe a day later?

Day Counts

For algorithms, see Date and Day Count.

Resolution B1 of the XXIIIrd General Assembly of the International Astronomical Union (IAU), "On the Use of Julian Dates", gives JD and MJD definitions (and TAI-UTC, 1961-1996).

For GMT, see Greenwich Mean Time and Greenwich Mean Astronomical Time. Here I use the British legal definition of GMT.

Properly, a Day Number is an integer, referring to the whole of a day, and a Date is a real, referring to an instant of time. In practice, Day, Date, Day Number, Date Number are mostly used indiscriminately, the intended meaning being clear from the context.

The following assumes that your system is properly set for locality and time; your computer's clock is used. More can be found in Wikipedia Julian day, "Alternatives".

Absolute Counts

These have the same values world-wide, being based on GMT/UTC.

Julian Date

The Julian Date (JD or JDN) was introduced by the astronomer John Herschel in 1849; see for example Peter Meyer. It is sometimes said to be due to Joseph Scaliger (1540-1609), who introduced the Julian Period of 7980 years from BC 4713-01-01.

Modified Julian Date

The Modified Julian Date (MJD) is given by   MJD = JDN - 2400000.5.

UNIX time_t

UNIX, JavaScript, and others use a base date, with time_t being a seconds count from then.

Local Counts

These change at local midnight.

Chronological Julian Date

The Chronological Julian Day Number is seemingly used by historians and chronologists.

On days when Summer Time begins or ends, one should presumably use for the fractional part the "clock time" rather than the duration since the start of the day.

Chronological Modified Julian Date

The term Chronological Modified Julian Date (CMJD) would be appropriate for a daycount matching MJD but changing at midnight local time. CMJD is the same function of civil Y M D as MJD is of GMT Y M D.


Truncated Julian Date

NASA's Truncated Julian Date (TJD) is given by either   TJD = (JDN - 0.5) mod 10000   or   TJD = JDN - 2440000.5   (I assume the former here; others differ).

Reduced Julian Date

Reduced Julian Date (RJD) is said to be given by   TJD = JDN - 2400000 and is therefore   MJD + 0.5.

Lilian Date

The Lilian Date (LD), named after Dr Luigi Lilio (or Aloysius Lilius) (~1510-1576), a member of the Pope's Commission, is a day-count, with LD 1 being 1582-10-15 Gregorian.

Dublin Julian Date

ASTROCLK p.110 says that the IAU (Dublin 1955) adopted Dublin Julian Date as a count from noon, presumably legal GMT, on 1899-12-31 (a.k.a. 1900-01-00).

1900-01-01.0 is thus DJD 0.5.


RD ("rata dierum"), said to be named by and perhaps for Reingold and Dershowitz (book: "Calendrical Calculations"), is a day-count, with RD 1 being 0001-01-01 Gregorian. I'm not sure whether it is rightly local or GMT.


"Newer variants of COBOL have a way of converting a valid date to a Relative Integer Day number". In the ISO standard since 1989, I'm told.

Other 'Julian' Dates

Another one, often written as YYDDD, YY.DDD, YY-DDD or YY/DDD, is a most unfortunate piece of nomenclature used by IBM and other business; the notation itself is, however, often convenient; ISO 8601 calls it 'Ordinal Day of Year' (OK) / 'Ordinal Date' (Ugh!).

Yet another format, used by U.S. forces in Vietnam, is YDDD; seemingly it is in current use by the USG.

And YYYYDDD can be found - "Long Julian Date".

See in Which Julius?.

The Non-Year Zero


Dionysius Exiguus (Denis the Little), around 525, by fixing the then-current date, fixed the "AD" scale of our present Calendar, which begins with 1 AD, the first Year of the Lord. He thought that Jesus was born during the previous year (current thinking prefers 7-4 BC).

Bede, a couple of centuries later, allegedly first introduced the "BC" scale and fixed its relationship with AD; but general use of BC, it seems, actually dates only from c17. He may have introduced the actual terms AD & BC (though it then seems curions that one comes from Latin and the other from English).

Dave Eastabrook wrote, 1997-09-29 :- How did the calendar go 1997 years ago? Was 1 b.c. followed by 1 a.d, or was there a 0 a.d. - or even a 0 b.c. ?

It went ... 751 AUC, 752 AUC, 753 AUC, 754 AUC, 755 AUC ... oops no, it went ... DCCLI, DCCLII, DCCLIII, DCCLIIII, DCCLV ... , all AUC.

Note : there are only about CCL years (written in AD MCMXCVII) until the Annus MMM AUC, which is itself no great problem; but in the years MMDCCCLXXXVIII the date field will be longer than ever before - I think. Caveat Structor.

The Venerable Bede (672/3-735), in the VIIIth century, did his work, no doubt, in Roman Numerals, so I imagine that he failed to consider the possibility of a Year "", and went ... "II BC", "I BC", "I AD", "II AD" ... Hence, on the present calendar, no year is numbered zero, and 1 AD directly follows 1 BC. The number Zero, as such, was only introduced into the West in the present (2nd) millennium; if BC was not in use until c17, then it really should have been defined more logically, to allow Year 0.

AD is, of course, Anno Domini, "in the Year of The Lord" (or Anno ab incarnatione Domini), and counting ordinally from 1 therefore makes sense; likewise for BC. But what did Bede or Petau actually write where we now use "BC"?

The monk Abbo of Fleury (945-1004) unsuccessfully proposed a Year Null before 1 AD, zero not being then known in Europe.

It is a pity that no room was left for "0 AD", but we must be grateful not to have both of the years "0 BC" and "0 AD".

Some prefer to write CE for AD and BCE for BC, using the same numbers (no Year 0).

Astronomers' Notation

Astronomers prefer to include a year zero (introduced by Jacques Cassini in 1740 and/or G D Cassini (1625-1712), first Director of the Paris Observatory); I suppose that, for them,

..., Year -2 = 3 BC, Year -1 = 2 BC, Year 0 = 1 BC, Year +1 = 1 AD, Year +2 = 2 AD, ...

and therefore they might feel entitled to celebrate the new Millennium at the beginning, rather than the end, of the Year +2000. On the other hand, they could have considered the Year 0 as being half -0, half +0, and celebrated at the end of June, 2000.

See also, of course, the Calendar FAQ.

Century and Millennium

Therefore, if the Century and Millennium are considered to be of the Christian Era, which they are, they each start with a year whose number ends in "01".

Another way of looking at it : for the first 365/6 days after one's birth, one is referred to as being in one's first year, then for the next in one's second, ...; and this is essentially what Anno Domini means.

And in cricket, it is the hundredth run that completes the century.

On earlier occasions, these things were better understood; see The Times of 1799-12-26, for example. The celebrations of the start of the 20th Century were predominantly at the start of 1901 (except for the Kaiser and his Empire). This time, only Cuba, under the learned and conservative Dr Fidel Castro, appears to have got it right (plus, perhaps, China).

Part II of E A Abbott's "Flatland" (text of 1884) is, according to the text of Sections 13-15, set at the 2nd-3rd Millennium rollover, and equally at the 1999-2000 rollover, and since the inhabitants counted 1999 as the 1999th year of the era they can have had no Year 0 within the era. On the other hand in Sec 18, set at the first hour of the first day of the 2000th year (called 2000), it is a millennial anniversary of the "year 1000" and of the "year 0". So confusion in nomenclature is not new to our time. URLs, thanks to Milton Pope, gutenberg, alcyone, ofcn.

The corrections of 1582/1752 made the Julian and Gregorian Calendars match exactly within AD 200-300, so the true start of the Third Millennium, rounded to the nearest day, will be about 250 years * 0.75 days/year different - near enough two days. If I now have the sign and arithmetic correct, we should be celebrating at about 2000-12-30 03:00:00.

1999-09-30 : The ratio of the amount of the 20th Century that remains to the amount of it that people think remains is rapidly increasing. 2000-01-01 : and has now gone through infinity and re-appeared negative. It will pass zero, but never reach unity.

Of course, the Nineteen-Hundreds were 1900-1999, and the Nineties 1990-1999.

The word Millennium is not spelt Millenium, Milenium, or Milennium (but that reference may help bad spellers using search engines!).

It is now Day of the Twenty-First Century and of the Third Millennium of our Era.

See also at ROG and NRC.

See also in my The Calendar Century and Decade.

The First Sunrise of AD 2000

The time and location of the First Sunrise depended on a number of definitions, including that of the International Date Line (Calendar Weeks, RHvG, USNO).

"The US Navy says the first point of land to see a sunrise, at 00:26 a.m. (1326 GMT December 31), will be the unpopulated Balleny Islands in New Zealand's Ross Dependency in Antarctica."

This is a spurious claim, of course; because that "1326 GMT Dec 31" is in the year 1999, by the Proper Time.

At any instant, there is sunrise all along a line (but not a Line of Longitude) between, I suppose and approximately, the Arctic and Antarctic Circles; and the line sweeps around the whole Earth in 24 hours (give or take, here or there, its change of shape). The real question is where this line was, at 2000-01-01 00:00:00 GMT (or UTC).

ISTM that initially it went through (approx) 0° N 90° E, in the 23°-203° direction. But it curved to be tangential to the Circles; the Arctic in the pointy end of Russia, and the Antarctic on the Greenwich Meridian. So the first dry places were perhaps those little French islands (uninhabitable?) to the south of the Indian Ocean, and Burma / China / Siberia.

The Falklands, Mexico, and the bit of Canada that ought to reach the Pacific, had the First Sunset, approximately.

P.S. The Sunday Telegraph, 1999-05-23, reported that the Greenwich Observatory, in agreement, said that the First Sunrise would be much as above, placing it in fact on Katchall Island, in the (Indian) Nicobar Islands.

P.P.S. New Zealand is 13 hours ahead of GMT at year's end.

See also Date Miscellany II, a continuation of this; and The Hebrew Calendar.
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