Lecture 11: The Calendar

Key Ideas:

Our calendars are based on the motions of the Sun and Moon.

Types of Calendars:

The Julian & Gregorian Calendars

A.D. and B.C.


Lunar Calendars

The phases of the moon provide a convenient way to keep track of time.

The oldest recognizable ancient calendars are lunar calendars.


The Metonic Cycle

A particular difficult of pure lunar calendars is that the 354d lunar year is 11d short of the 365d solar year.

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:

The Babylonians built a complex, but very precise hybrid luni-solar calendar based on the Metonic Cycle.


Lunar Calendars in use Today

Islamic Calendar 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 calendar.

Jewish Calendar

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.

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

Solar Calendars mark time by the Seasons

Arrival of seasons often has practical and/or cultural importance:


Egyptian Solar Calendar

The Egyptians developed the first recorded a solar calendar in about 3000 BC.

The Roman Calendar

The Romans had a complex luni-solar calendar tied to important holidays (fasti) associated with specific seasons:

The Julian Calendar (46 BC)

Julius Caesar asked the Alexandrine astronomer Sosigenes to reform the Roman calendar.

He started with the solar year of 365.25d:


Annus confusionis

Caesar started the new calendar in 46 BC:

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.

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.

Council adopted a fixed March 21 equinox:


Gregorian Calendar Reform

By the 1570's, the Julian Calendar was out of alignment with the seasons by 10 days.

Pope Gregory XIII appointed a commission to develop an improved calendar.


A New Leap Year Formula.

An elegant formula was invented by Aloysius Lilius, an Italian physician:

Removes 3 days every 400 years:


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 years:


A (nearly) Universal Calendar

Other countries worldwide eventually adopted the Gregorian Calendar:

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 365.2425 days.

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 dates:

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.


Further Reading:

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 Reserved.