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  - If year X is the third year after a leap year, you can reuse its
    calendar in years X+11, X+22, and X+28.

Note that the expression X+28 occurs in all four items above. So you
can always reuse your calendar every 28 years.

But if you also want your calendar's indication of Easter and other
Christian holidays to be correct, the rules are far too complex to be
put to a simple formula. Sometimes calendars can be reused after just
six years. For example, the calendars for the years 1981 and 1987 are
identical, even when it comes to the date for Easter. But sometimes a
very long time can pass before a calendar can be reused; if you happen
to have a calendar from 1940, you won't be able to reuse it until the
year 5280!


2.7. What is the Roman calendar?
--------------------------------

Before Julius Caesar introduced the Julian calendar in 45 BC, the
Roman calendar was a mess, and much of our so-called "knowledge" about
it seems to be little more than guesswork.

Originally, the year started on 1 March and consisted of only 304 days
or 10 months (Martius, Aprilis, Maius, Junius, Quintilis, Sextilis,
September, October, November, and December). These 304 days were
followed by an unnamed and unnumbered winter period. The Roman king
Numa Pompilius (c. 715-673 BC, although his historicity is disputed)
allegedly introduced February and January (in that order) between
December and March, increasing the length of the year to 354 or 355
days. In 450 BC, February was moved to its current position between
January and March.

In order to make up for the lack of days in a year, an extra month,
Intercalaris or Mercedonius, (allegedly with 22 or 23 days though some
authorities dispute this) was introduced in some years. In an 8 year
period the length of the years were:
        1: 12 months or 355 days
        2: 13 months or 377 days
        3: 12 months or 355 days
        4: 13 months or 378 days
        5: 12 months or 355 days
        6: 13 months or 377 days
        7: 12 months or 355 days
        8: 13 months or 378 days
A total of 2930 days corresponding to a year of 366 1/4 days. This
year was discovered to be too long, and therefore 7 days were later
dropped from the 8th year, yielding 365.375 days per year.

This is all theory. In practice it was the duty of the priesthood to
keep track of the calendars, but they failed miserably, partly due to
ignorance, partly because they were bribed to make certain years long
and other years short. Furthermore, leap years were considered unlucky
and were therefore avoided in time of crisis, such as the Second Punic
War.

In order to clean up this mess, Julius Caesar made his famous calendar
reform in 45 BC. We can make an educated guess about the length of the
months in the years 47 and 46 BC:

                47 BC          46 BC
January          29             29
February         28             24
Intercalaris                    27
March            31             31
April            29             29
May              31             31
June             29             29
Quintilis        31             31
Sextilis         29             29
September        29             29
October          31             31
November         29             29
Undecember                      33
Duodecember                     34
December         29             29
                ---            ---
Total           355            445

The length of the months from 45 BC onward were the same as the ones
we know today.

Occasionally one reads the following story:
        "Julius Caesar made all odd numbered months 31 days long, and
        all even numbered months 30 days long (with February having 29
        days in non-leap years). In 44 BC Quintilis was renamed
        'Julius' (July) in honour of Julius Caesar, and in 8 BC
        Sextilis became 'Augustus' in honour of emperor Augustus. When
        Augustus had a month named after him, he wanted his month to
        be a full 31 days long, so he removed a day from February and
        shifted the length of the other months so that August would
        have 31 days."
This story, however, has no basis in actual fact. It is a fabrication
possibly dating back to the 14th century.


2.7.1. How did the Romans number days?
--------------------------------------

The Romans didn't number the days sequentially from 1. Instead they
had three fixed points in each month:
        "Kalendae" (or "Calendae"), which was the first day of the month.
        "Idus", which was the 13th day of January, February, April,
                June, August, September, November, and December, or
                the 15th day of March, May, July, or October.
        "Nonae", which was the 9th day before Idus (counting Idus
                 itself as the 1st day).

The days between Kalendae and Nonae were called "the 5th day before
Nonae", "the 4th day before Nonae", "the 3rd day before Nonae", and
"the day before Nonae". (There was no "2nd day before Nonae". This was
because of the inclusive way of counting used by the Romans: To them,
Nonae itself was the first day, and thus "the 2nd day before" and "the
day before" would mean the same thing.)

Similarly, the days between Nonae and Idus were called "the Xth day
before Idus", and the days after Idus were called "the Xth day before
Kalendae (of the next month)".

Julius Caesar decreed that in leap years the "6th day before Kalendae
of March" should be doubled. So in contrast to our present system, in
which we introduce an extra date (29 February), the Romans had the
same date twice in leap years. The doubling of the 6th day before
Kalendae of March is the origin of the word "bissextile".  If we
create a list of equivalences between the Roman days and our current
days of February in a leap year, we get the following:

        7th day before Kalendae of March        23 February
        6th day before Kalendae of March        24 February
        6th day before Kalendae of March        25 February
        5th day before Kalendae of March        26 February
        4th day before Kalendae of March        27 February
        3rd day before Kalendae of March        28 February
        the day before Kalendae of March        29 February
        Kalendae of March                        1 March

You can see that the extra 6th day (going backwards) falls on what is
today 24 February. For this reason 24 February is still today
considered the "extra day" in leap years (see section 2.3). However,
at certain times in history the second 6th day (25 Feb) has been
considered the leap day.

Why did Caesar choose to double the 6th day before Kalendae of March?
It appears that the leap month Intercalaris/Mercedonius of the
pre-reform calendar was not placed after February, but inside it,
namely between the 7th and 6th day before Kalendae of March. It was
therefore natural to have the leap day in the same position.


2.8. What is the proleptic calendar?
------------------------------------

The Julian calendar was introduced in 45 BC, but when historians date
events prior to that year, they normally extend the Julian calendar
backward in time. This extended calendar is known as the "Julian
Proleptic Calendar".

Similarly, it is possible to extend the Gregorian calendar backward in
time before 1582. However, this "Gregorian Proleptic Calendar" is
rarely used.

If someone refers to, for example, 15 March 429 BC, they are probably
using the Julian proleptic calendar.

In the Julian proleptic calendar, year X BC is a leap year, if X-1 is
divisible by 4. This is the natural extension of the Julian leap year
rules.


2.9. Has the year always started on 1 January?
----------------------------------------------

For the man in the street, yes. When Julius Caesar introduced his
calendar in 45 BC, he made 1 January the start of the year, and it was
always the date on which the Solar Number and the Golden Number (see
section 2.12.3) were incremented.

However, the church didn't like the wild parties that took place at
the start of the new year, and in AD 567 the council of Tours declared
that having the year start on 1 January was an ancient mistake that
should be abolished.

Through the middle ages various New Year dates were used. If an
ancient document refers to year X, it may mean any of 7 different
periods in our present system:

- 1 Mar X to 28/29 Feb X+1
- 1 Jan X to 31 Dec X
- 1 Jan X-1 to 31 Dec X-1
- 25 Mar X-1 to 24 Mar X
- 25 Mar X to 24 Mar X+1
- Saturday before Easter X to Friday before Easter X+1
- 25 Dec X-1 to 24 Dec X

Choosing the right interpretation of a year number is difficult, so
much more as one country might use different systems for religious and
civil needs.

The Byzantine Empire used a year starting on 1 Sep, but they didn't
count years since the birth of Christ, instead they counted years
since the creation of the world which they dated to 1 September 5509 BC.

Since about 1600 most countries have used 1 January as the first day
of the year. Italy and England, however, did not make 1 January official
until around 1750.

In England (but not Scotland) three different years were used:
- The historical year, which started on 1 January.
- The liturgical year, which started on the first Sunday in advent.
- The civil year, which
        from the 7th to the 12th century started on 25 December,
        from the 12th century until 1751 started on 25 March,
        from 1752 started on 1 January.


2.10. Then what about leap years?
---------------------------------

If the year started on, for example, 1 March, two months later than
our present year, when was the leap day inserted?

[The following information is to the best of my knowledge true. If
anyone can confirm or refute it, please let me know.]

When it comes to determining if a year is a leap year, since AD 8 the
Julian calendar has always had 48 months between two leap days. So, in
a country using a year starting on 1 March, 1439 would have been a
leap year, because their February 1439 would correspond to February
1440 in the January-based reckoning.


2.11. What is the origin of the names of the months?
---------------------------------------------------

A lot of languages, including English, use month names based on Latin.
Their meaning is listed below. However, some languages (Czech and
Polish, for example) use quite different names.

January     Latin: Januarius. Named after the god Janus.
February    Latin: Februarius. Named after Februa, the purification
            festival.
March       Latin: Martius. Named after the god Mars.
April       Latin: Aprilis. Named either after the goddess Aphrodite or
            the Latin word "aperire", to open.
May         Latin: Maius. Probably named after the goddess Maia.
June        Latin: Junius. Probably named after the goddess Juno.
July        Latin: Julius. Named after Julius Caesar in 44 BC. Prior
            to that time its name was Quintilis from the word
            "quintus", fifth, because it was the 5th month in the old
            Roman calendar.
August      Latin: Augustus. Named after emperor Augustus in 8
            BC. Prior to that time the name was Sextilis from the
            word "sextus", sixth, because it was the 6th month in the
            old Roman calendar.
September   Latin: September. From the word "septem", seven, because
            it was the 7th month in the old Roman calendar.
October     Latin: October. From the word "octo", eight, because it
            was the 8th month in the old Roman calendar.
November    Latin: November. From the word "novem", nine, because it
            was the 9th month in the old Roman calendar.
December    Latin: December. From the word "decem", ten, because it
            was the 10th month in the old Roman calendar.

--- End of part 1 ---

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