Lecture 11: The Calendar
Our calendars are based on the motions of the Sun and Moon.
Types of Calendars:
- Lunar Calendars
- Solar Calendars
The Julian & Gregorian Calendars
A.D. and B.C.
The phases of the moon provide a convenient way to keep track
- Phases are easily visible and distinctive.
- 12 lunar months is 354 days, 11 days short of a year of
The oldest recognizable ancient calendars are lunar calendars.
- Common among nomadic peoples and those without written
The Metonic Cycle
A particular difficult of pure lunar calendars is that the 354d
lunar year is 11d short of the 365d solar
This causes the seasons to drift among the months in lunar calendars.
To try to reconcile the lunar calendar and the seasons, the
Babylonians discovered the Metonic Cycle:
- 235 lunar months is almost exactly 19 solar years.
The Babylonians built a complex, but very precise hybrid
luni-solar calendar based on the Metonic Cycle.
Lunar Calendars in use Today
Note: In 2005, the Muslim holy month of Ramadan begins on Oct 4
(yesterday) and runs through Nov 2. For comparison, Ramadan will begin
on September 23 in 2006 and on September 12 in 2007, reflecting how the
purely Lunar calendar is not synchronized with the western Solar
- Purely lunar calendar, 354d in the calendar
- Months occur in different seasons (e.g., Ramadan).
An example of how aspects of the Lunar calendar come into play is the
holiday of Rosh Hashanah, the Jewish New Year, which begins at sunset on
the day of the New Moon that marks the start of the month of Tishri in
the Jewish Calendar. This year (2005) this will occur on Monday, October 3.
- Luni-solar calendar.
- Interpolate an extra 13th month every 2-3
years to keep the calendar aligned with the seasons.
- Repeats on the 19-year Metonic Cycle.
There are also traditional Chinese, Vietnamese, and Japanese lunar
calendars, though these are now primarily used only to set the dates of
traditional holidays (for example: Chinese New Year) since all of these
nations have adopted the Gregorian calendar.
Solar Calendars mark time by the Seasons
- Set the calendar by the Equinoxes and Solstices.
Arrival of seasons often has practical and/or cultural importance:
- Knowing when to plant or harvest.
- Annual flood of the Nile Valley.
- Religious festivals associated with specific seasons
(e.g., Easter, May Day, and Christmas)
Egyptian Solar Calendar
The Egyptians developed the first recorded a solar calendar in about
- Divided year into 12 months of 30d each
- Added an extra 5 days to make up 365d.
- Year began in July when the star Sirius rose exactly
in line with the rising Sun ("Heliacal Rising").
- By 300 BC, they measured the year as 365.25d,
only 11m 14s longer than the true
The Roman Calendar
The Romans had a complex luni-solar calendar tied to important holidays
(fasti) associated with specific seasons:
- 10 lunar months, with extra months and days added to keep
it aligned with the seasons.
- The priests in charge of it were continually tweaking it
for religious and political reasons.
- They usually got it wrong...
The Julian Calendar (46 BC)
Julius Caesar asked the Alexandrine astronomer Sosigenes to reform the
He started with the solar year of 365.25d:
- Year divided in 12 months of 30 and 31d,
(except February which had 29), adding up to 365 days.
- Every 4 years, add a day to February to make 366 days.
- "Leap Year" makes up the difference between
365.25 and 365 days per year.
Caesar started the new calendar in 46 BC:
- Added 80 extra days to 46 BC so that 45 BC would start
correctly aligned with the seasons.
- 46 BC had 445 days in it!
Caesar called 46 BC the ultimus annus confusionis
("The final year of confusion")
Roman wits, however, called it the
annus confusionis ("Year of Confusion").
Missed it by that much...
Sosigenes and the others knew, however, that the year was not exactly
365.25 days long.
- True solar year is about 365.242199 days:
- Calendar gets ahead about 1d every 128 years.
- Causes a slow slip of the seasons against the dates of
the Julian Calendar.
This slip became large during the middle ages.
A Moveable Feast
In 325 A.D., the Council of Nicaea established a formula to compute the
date of Easter.
- Most important holy day in Christianity.
- Important to celebrate it on the correct day.
Council adopted a fixed March 21 equinox:
- Easter is the first Sunday after the first full moon of
the Vernal (Spring) Equinox in the North.
- But, it must not coincide with Passover.
Gregorian Calendar Reform
By the 1570's, the Julian Calendar was out of alignment with the seasons
by 10 days.
- Easter was being computed incorrectly, and so celebrated
on the wrong day.
- Other important holy days were also being celebrated on
the wrong days.
Pope Gregory XIII appointed a commission to develop an improved
A New Leap Year Formula.
An elegant formula was invented by Aloysius Lilius, an Italian
- Keep the Julian formula for leap years, but
- A century year is not a leap year unless it is
divisible by 400.
- 2000 is a leap year, but not 1700, 1800, & 1900
Removes 3 days every 400 years:
- Eliminates all but ~3 hours of error per 400y.
The Lost Ten Days
Pope Gregory XIII instituted the new calendar in 1582. This required
taking 10 days out of October 1582 to realign the calendar with the
seasons. The day after October 4, 1582 was October 15.
The Gregorian Calendar was adopted by Catholic countries within 2
- Some rioting over the "lost days", especially
over payment of wages & rents ("Give us back our 11 days!").
- Adopted all over continental Europe by mid 1700s.
A (nearly) Universal Calendar
Other countries worldwide eventually adopted the Gregorian Calendar:
- England and her American Colonies waited until 1752.
Dropping 11 days triggered riots.
- Japan adopted it in 1873 (Meiji period)
- Soviet Russia adopted it in 1918.
- Communist China adopted it in 1949.
Eastern Orthodox Church still uses a Julian Calendar, and voted as
recently as 1971 to reject switching to the Gregorian Calendar. Some
groups within the Eastern Church have adopted some or all of the
Gregorian solar year, but still compute Easter using the Julian
Calendar. The situation is very complex.
Still off by a little bit...
The Gregorian Calendar formula is equivalent to a year of
- This is ~0.0003 days longer than the length of the true
solar year (about 365.2422 days).
- Gets ahead of the true solar year by 1 day every 3327
The Gregorian Calendar will be ahead of the true solar year by 1 day
in 4909 A.D.
A.D. and B.C.
The Gregorian Calendar uses the Anno Domine (A.D.) system of
- Invented by Dionysus Exiguus (Dennis the Short) in 531
- Starts counting years from the birth of Christ, or 1 A.D.
- Has no year zero (there was no number "zero" in Europe until the
11th or 12th century).
- The year before 1 A.D. was 1 B.C.
B.C. (Before Christ) notation was not introduced until 1627.
In academic history, you will encounter the use of the notation
C.E. (Common Era) for A.D., and B.C.E (Before the Common Era) for B.C.
The story of the development of the calendar can only be covered in its
essential outlines within the scope of one lecture, which is unfortunate
as it is a rich and fascinating topic in itself. For a lively and
engaging history of the calendar, an excellent recent book is
Calendar, by David Ewing Duncan (1998, Avon Books).
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Updated: 2006 September 23
Copyright © Richard W. Pogge, All Rights