Calendar Basics

About prehistoric Calendar Basics not much is known, and even the old calendar of literate cultures can often only  reconstructed incomplete. However, a comparison with various known types of calendars can historically classify calendars. This is a supplementary draft is an overview of the calender development in North Africa, Middle East (including Egypt and Mesopotamia), Persia, Asia Minor, Europe, India, China and Mesa-America from 3000 B.C. to 2000 A.D.

Timeline

Time of no calendars

The history of time – Measurement and Calendars – is closely interconnected with the  cultural and sociological state of the society. The development of the concept of time and of calendars is remarkably similar in all societies around the world, but remarkable different between hunter-gatherer societies and societies that have agriculture, political hierarchies, and class systems.

When human were gatherers and hunters the real and imaginary world was interchangeable and only present exists. There was no memorized past and empiric observed future, no regular events, therefore no need of calendars.  Shamanism, humanity’s most ancient spiritual practice was the first magic to gain control over powers not understood essentially only living in the present. Shamans’ development involves a death-and-rebirth experience and the acquisition of spirit or animal allies that provide powers to heal, control but not predict future, assist in hunting, and engage in fights to harm others. Charismatic social leaders, shamans hold all-night ceremonies in which the entire community dances, drums, and chants. Shamans are not normally possessed by spirits; rather they control spirits.

On a side note, shamanistic practices disappeared under the onslaught of ritualized spirituality, feudalism, capitalism, communism. Today’s highly complex global world ironically travels in reverse, creates new ignorance, consumerism discards  future and past and thus, emerging reinventions of shamanism of different pattern re-appear for example the masters of the monetary system and new charismatic leaders. Shamanism has been in a way also used for prophecy, to plan how to deal with the unknown by sensing and  intuition.

Nature and weather calenders

When societies moved on to farming and raising animals, the need to understood weather and regular a events. A new class  of woman and men was employed to manage past and future – priests, mediums and healers. Healers and mediums share many characteristics with shamans, but differ from shamans in some important ways. They are subordinated to the first religious practitioners called priests. Mediums are predominantly female but unlike shamans, mediums do not hold a high leadership role. Healers are almost exclusively male, and generally of high economic status and holding political power and generally work in collaboration with priests. As the society become complex with political hierarchies, with regular economic pattern and a need of writing and administration the priests class came up together with the first calendars. The simplest calendar is the nature and weather calendar with entirely on one count which divides the year into phenomena. For instance, in the Bay of Bengal is the year has been divided into : Dryness – South West monsoon – Southeast Monsoon – Northeast wind.

 Direct observation calendars

A more challenging are the direct observation calendar. For them the months or year are determined by direct lunar and solar observation in the beginning by observing the moon. Any time you can specify how many days since the last appearance of the moon have passed , and when the next one appears. Observing the sun marks , special buildings and sticks were used determining the seasons and in particular the solstices. When a striking point was reached, with the moon usually the first light of the crescent moon, with the sun usually the shortest length of the shadow, the new month and or new year was proclaimed . The word calendar comes from the Latin calendae (to call out ) with the root word calare ( call ) the new moon. There were other direct observations (which led to calculated calendars) which were sidereal (position or rising position of stars)  for instance Sirius or elliptic (position or rising position of planets) for instance Mars or Venus. The latter two obviously needs good astronomy conditions like in Mesa-America or Middle East.

Calculated Calendars

As societies became moved from matriarchy to patriarchy most moved from lunar calendars to solar calendars (pure solar, lunar-solar or solar-lunar). However the correlation may be more cultural and mythological. Anthropological female (and goodness) are often associated with the moon and lunar energies in many of the world’s myths, most Goddesses also have correlations with the moon, or phenomenon related to the moon such as ocean tides.  Consider the connection between the movements of the moon and the menstrual cycle. As such these cultures tended to follow lunar cycles and build their calender around them, as such these societies had a tendency to value women, and their influences in culture and political discourse, as such they have lunar calendars because of associations of woman with the moon. However, a shift from lunar to solar is very evident in the Egypt culture in which the woman had an important role. You find the shift in the famous myth of Isis ans Osiris from 360 days to 365 days (see in part III).

There is no direct correlation as may be matriarchy without having a lunar calenders and currently rather patriarchal cultures and systems do have lunar calendars.Agricultural needs,  trading, ritualized religion and administration created  societies a complexity which clearly resulted in a initiative to move to a solar synchronized calendar, be it just for reasons of practicability.

There are six principle calendars in current use. These are the Gregorian, Jewish, Islamic, Indian, Chinese, and Julian Calendars. Six types of calendars replicate astronomical cycles according to fixed rules:

• Pure lunar calendar which  has no connection to the solar year and the seasons as the Islamic calendar. A true lunar calendar is synchronized with the exact time in which it takes the moon to fully orbit the earth and return to the same exact location in relation to the earth that it was at the beginning of the previous month. This is known as a Synod Orbit. A lunar calendar will very quickly shift with respect to a solar calendar.
• Pure solar calendar as the ancient Egyptians  can indicate the position of Earth on its revolution around the sun (and seasons) well  — the time it takes for the Earth to return to the same place in its orbit of the Sun. A solar year has 365.242199 days. Solar calendars are based on the progression through seasons as the Earth revolves around the Sun, but neglect any attempt to keep the months synchronous with the lunar phases.
• Lunisolar calendar used, for example, in Judaism with a leap month to synchronize to the solar year.Lunisolar calendars may be regarded as solar calendars, although their dates additionally indicate the moon phase. A lunisolar calendar year is made up of lunar months. They try to remain synchronous with both the solar year and the moon phases. Without  adjustment the seasons will steadily drift through the months. Only a long-term synchronization between months and years is every 19 years possible (Meton equal to 235 lunar months), since a solar year does not contain an integral number of days or an integral number of lunar months. To compensate for this, many luni-solar calendars adjust the length of their years and months.
• Solar-lunar calendar like our Gregorian calendar counts. This is actually a solar calendar, but has one reference to the lunar year for religious reasons (Easter).
• Sidereal time calendars based on fixed stars or star patterns e.g. (Sirius Egypt, and Mayas Pleiades and Orion)
• Calendars based on planets typically Venus (Mayan) or Mars.

All these calendars follow special rules that make them more or less exactly match the astronomical facts. Unfortunately, with the accuracy of the calendar increases the complexity of the switching rules. The peak of accuracy and therefore also on complexity form the astronomical calendar, based on astronomical formulas , such as the French Revolutionary calendar and the ancient Chinese calendar.

Pure lunar calendar which  has no connection to the solar year and the seasons

• Ancient Roman calendar until 450 BC – then replaced by lunisolar
  
  Islamic Calendar

Pure solar calendar

• Christian Church calendar : Liturgical Calendar ( Roman Catholic)
• Ethiopian Calendar – Ethiopia in common
• Greek Orthodox calendar
• Julian Calendar – still only some Orthodox churches ( in the Altkalendariern ) and used in the Historical Sciences
• Coptic calendar or Alexandrian calendar – used in the Coptic Orthodox Church
• Berber calendar – used widely throughout North Africa (a consequence of the Julian calendar )
• Juche calendar – used in North Korea
• Modern Japanese calendar or Gengo Calendar – common in Japan
• Soviet revolutionary calendar
• French Revolutionary Calendar
• Suriyakati Calendar – common in Thailand
• Minguo calendar – in the Republic of China ( Taiwan ) are common
• Armenian calendar
• Aztec Calendar
• Hindu solar calendar
• Indian National Calendar or Saka calendar – in India partly in use
• Iranian Calendar or Jalali calendar – used in Iran and Afghanistan
• Mayan Calendar: Haab cycle – in Mexico and Guatemala partially in use
• Sikh calendar or Nanakschahi calendar – in the religion of the Sikhs partially in use
• Tamil Calendar
• Zoroastrian Parsi calendar or calendar – in the Parsi religion common

Lunisolar calendar  with a leap month

• Attic Calendar
• Babylonian lunar calendar
• Bikram Sambat – in Nepal partially in use
• Burmese calendar
• Chantarakati Calendar – common for Buddhist festivals in Thailand
• Chinese calendar – in China used to determine traditional festivals
• Germanic calendar or Rune Calendar
• Hindu lunisolar calendar
• Japanese lunisolar – replaced by solar calendars
• Jewish Calendar – common in Jewish societies and Israel
• Celtic Calendar – Calendar of Coligny
• Khmer calendar
• Korean calendar

Solar-lunar calendar

• Gregorian Calendar – the world’s most -used calendar (Solar adjusted to the moon for Easter)

Sidereal time calendars aligned on fixed stars or star patterns

• Egyptian calendars, nature calendars with stellar alignment
• Egyptian lunar calendar, hybrid of Stellar and Nature Calendar
• Babylonian calendar , originally based Calendar stars , later replaced by lunisolar
• Assyrian calendar as Babylonian calendar
• Inca Calendar
• Loango calendar – one based on lunar cycles calendar and Sirius at the West African nation of Loango

Calendars based on planets

• Mayan Calendar: Tzolkin cycle 260 days of Venus

Our calendar is composed of the units day, week, month and year. With the exception of the week all other parts are based on astronomical basics. The smallest basic unit is the day. For the calendar of the mean solar day is crucial. The length of the day varies by about ± 15 min during the year and increases by 1.7 milliseconds per century . The month has its origins while in lunar orbit , but the months of our calendar have lost this regard since antiquity . Only the Easter (and Ramadan) calculation still depends on it. Phases of the moon are determining the calendar. This so-called synodic (from the Greek synodos = meeting ) with an average of 29.53059 days but large variation.
Of the four different astronomic years  determines the tropical (from the Greek tropos = turn ) years the course of the seasons , and thus also to our calendar. The tropical year has a duration of 365.242199 days. The exact duration of the tropical year was for a long time unknown due to the lack of exact watches and the precession (the circular motion of Earth’s axis) through 25800 years. Since this moves the equinox in 1000 years at least 360 ° / 25800 * 1000 ~ 14 ° records of the ancient astronomers only of  limited use. Anonther crucial problem for all calendars arises because the days are counted only with integers , while the orbital periods of sun and moon, planets or stars can be specified only inaccurate in whole days. As a solution , the only way to combine the fractions of a day over several years to whole days and capture it in the calendar by a long-term periodic switched single ” leap days ” or added five days (supplementary days). In order to ensure the predictability of the date in the past and in the future, this could not be done arbitrarily, but by a fixed rules – a mathematically formulated algorithm.

Calendars of ancient Times

Sumerian calendar

Sumerian culture, without prehistoric periods, spans from the 3rd millennia BC, ending with the downfall of the Third Dynasty of Ur around 2004 BC, followed by a transitional period of Amorite states before the rise of Babylonia in the 18th century BC. They were theocratic states, Kings were also Priests. Uruk was2700 BC  the first major city in history ruled by King Gilgamesh.  The Sumerian civil lunar year of 354 was divided a year into 12 lunar months of 29 or 30 days. Each month began with the sighting of a new moon. There occasionally a leap month to synchronize with the real (tropical year).

Besides many others, Sumerians (Chaldean actually) had an astronomical motivated calender, with 360 days as normal year equals with the 360 degrees of the epileptic divided by 12 sectors, we still use today. It could be connected to the Sumerian civil lunar year of 354 days. On a side note, the Mesopotamians used the first mathematical position system i.e, an sexgesimal arithmetic, which is method of comutation  by 360 used in dividing a full circle and hours in minutes and seconds by sixty. 12 (Jupiter completing a full cycle through the epileptic), 7 (visible planets),  60 (Jupiter 5 and Saturn 2 full cycles, together 7 through the epileptic) where meaningful numbers. So was 6,  a sacred number, which was used earlier to divide the year in six moths with 60 days. The 7 was used for the week. The Sumerians had the first star catalog with 66 stars which documented for 34 the heliacal rising of fixed stars measured accurate  the year’s length. The Babylonians we owe the 12 / 24 hours and the Chaldean the 12 animal signs in the epileptic.

Egyptian calendar

The ancient Egyptians began numbering their years when the star Sirius rose at the same place as the Sun (4241 and 2773 BC). There was no leap year. This Egyptian civil calendar, base of the Roman Julian and today’s Gregorian calendar, was the first  solar calendar known to use a year of 365 days, approximately equal to the tropical year. The Egyptians added 5 days to the schematic (astronomical) year of 30 x 12 = 360 days,  the astronomical calendar used by the Sumerians from 2400 BC on.There was a simultaneously maintained lunar calendar in Egypt, the older of the two systems,  consisted of twelve months whose duration differed according to the length of a full lunar cycle (normally 28 or 29 days). Each lunar month began with the first visible new moon. Since the lunar calendar was 10 or 11 days shorter than the solar year, a 13th month (called Thoth) was intercalated every several years to keep the lunar calendar in rough correspondence with the agricultural seasons and their feasts. New Year’s Day was signaled by the annual heliacal rising of the star Sothis (Sirius), when it could be observed on the eastern horizon just before dawn in midsummer; the timing of this observation would determine whether or not the intercalary month would be employed.

The names of the Eras

Armenian Calendar

Coptic Calendar

This calendar is derived from the Egyptian. He used the Julian switching and Easter calculation. Leap year if the year is divided by 4 the rest of 3 results. His era begins on 29 August 284 with the accession of Diocletian and is also called martyrs era..

Ethiopian Calendar

Derived from the Coptic calendar, it has just another era (August 29, 8, incarnation of Christ) and has its own month names.

 The names of the months

Persian / Iranian calendar

 The names of the months

The Gelálkalender

The calendar , named after the Grand Sultan Melik Shah Jelaleddin , was introduced by a calendar Commission , at the Omar Chaijám was involved. The circuit rules are handed down contradictory. The sources speak of :

6 * every 4 years and 1 * after 5 years.
7 * every 4 years and 1 * after 5 years.
8 * every 4 years and 1 * after 5 years.

The panel turn in a cycle of 62 years, 6 * 4 + 1 * 5 and 7 * 4 + 1 * 5 The year therefore has 365.2419355 days and achieved an accuracy of 1 day in 3795 years. Start is at the beginning of spring 3/15/1079 (JD = 2115236 ). The structure of the calendar follows the Jazdagird, the leap year has 6 additional days .

The Jazdagird Calendar

The calendar is set up like the old Egyptian calendar . 12 months of 30 days and 5 days without additional circuitry. The era begins on 16.6.632 (JD = 1952063 ) . The extra days were before the year 376 after the Aban (8th month ) and then inserted after the Isfandarmud (12th month). The era depends on the throne of the last Persian king Jezdegerd III . After two lost battles against Caliph Omar , he was 652 killed and no longer carried on the circuit of the ancient Persian calendar , from which this calendar was launched.

The Kurdish calendar

The Kurdish calendar follows the modern Persian calendar.

 The names of the months

 The Chinese Calendar

The official calendar in China since 1912 is the Gregorian calendar, which is a solar calendar. However, Tthe civil calendar in much of China is the Han calendar, which is a lunisolar calendar. It is used for selecting the day of a wedding or funeral, for opening a venture, or a relocation. Muslims living in  northern China use the Islamic calendar, which is a mean moon lunar calendar, as their civil calendar. The civil calendar for Tibet is the Tibetan calendar, which is a lunisolar calendar. There are actually two Chinese calendars, a solar calendar and the han lunarsolar calendar. Both calendars depend on the times of certain astronomical events, such as dark moons and winter solstices. For at least several centuries (according to some scholars, since the 5th C. BCE) the times of these events have been ascertained not by observation but rather by calculation, so these calendars can be classified as calculated or rule-based.

The Han calendar is a lunisolar calendar, which indicates both the moon phases and the solar terms. In Han calendar, a year usually begins on the second dark moon after the winter solstice but occasionally on the third dark moon after the winter solstice.

Chinese calender uses such astromical events

• A dark moon occurs when the Sun and the Moon are astronomically conjunct (or more exactly, when either the Moon’s center lies on the line joining the centers of the Earth and the Sun or the plane defined by the Sun, Earth and Moon is perpendicular to the Earth’s orbital plane).  A dark moon describes the Moon during that time that it is invisible against the backdrop of the Sun in the sky. The duration of a dark moon is between 1.5 and 3.5 days, depending on the orientation of the Earth and Sun
• The term “new moon” is not used here, since it is ambiguous. It can mean either a dark moon or the phase of the Moon when a crescent is first visible (in which sense a month in the Muslim calendar begins at new moon). Originally “new moon” referred to the crescent on the first night it is visible, one or two days after conjunction. Maritime records from the nineteenth century distinguish the dark moon (no moon) from the new moon.
• A lunation is a passage of the Moon from one dark moon to the next. A lunation begins at the dark moon (astronomical conjunction of Sun and Moon), and the next dark moon marks the beginning of the next lunation.
• An equinox occurs when the angle formed at the Earth’s center between its axis of rotation and the line joining the Earth to the Sun is a right angle. At such a point in the Earth’s orbit the length of day and night is almost equal (but not exactly equal, due to atmospheric refraction of the Sun’s rays near the horizon and the practice of measuring the start and end of the day from the first or last appearance of the Sun). The northern vernal equinox occurs around March 20th of each year, and the northern autumnal equinox occurs around September 21st.
• A solstice occurs when this angle reaches a maximum or a minimum. At such a point the duration of the day and the night is either longest or shortest. The northern winter solstice occurs around December 21st of each year, and the northern summer solstice occurs around June 21st.

The Chinese Solar Calendar

The Chinese solar calendar consists of a sequence of solar years which are not divided into months but rather into 24 periods which begin at the “solar terms” (see below). The Chinese lunar calendar consists of a sequence of lunar years which are divided into 12 or 13 lunar months. A solar year begins at the (northern) winter solstice, which is on or around December 22 in the Common Era Calendar. A lunar month begins on the day of a dark moon. The beginning of a lunar year (i.e, lunar new year’s day) is more difficult to define (but see below); it always begins from about January 20th to about February 20th, i.e., about a month or so after the start of the Chinese solar year.

The Chinese Calendar uses cycles of sixty years. A year within a cycle is designated by a combination of an element name (e.g., “Water”) and an animal name (e.g. “Serpent”):

Wood     Fire     Earth     Metal     Water

Rat     Ox     Tiger     Rabbit     Dragon     Snake     Horse     Sheep     Monkey     Chicken     Dog     Pig

For the order in which the various element-animal-designated years occur within a cycle of sixty years (Wood-Rat, Wood-Ox, Fire-Tiger, …) see Interconverting Chinese and Western Years.

A Chinese year is uniquely determined by an element name, an animal name and a cycle number, e.g., the Water-Dragon year in the 21st cycle.

Since the years of the Chinese Calendar run concurrently with the years of the Common Era Calendar (although they do not overlap exactly) each year at a certain position in a certain cycle in the Chinese Calendar can be uniquely associated with a year in the Common Era Calendar provided that one such correlation is known. Actually two such correlations are used by different scholars: The first year in the first cycle is correlated either with -2696 CE (i.e., 2697 BC) or with -2636 CE (i.e., 2637 BC). 2004 is a Wood-Monkey year in Cycle 79 (according to the first correlation) or in Cycle 78 (according to the second)

The Chinese Calendar assumes a prime meridian of 120 degrees East (120°E). This means that a day (or rather, a nychthemeron, a day and a night) is taken to run from midnight Beijing standard time (BST = CCT = GMT+8) to the next midnight BST. This is in contrast to the Common Era Calendar, where a nychthemeron runs from midnight Greenwich Mean Time (GMT) to the next midnight GMT. The time difference between Beijing and London is eight hours, so nychthemerons (or nychthemera) in the Chinese Calendar begin eight hours earlier than nychthemerons in the Common Era Calendar

The Chinese solar year always begins at the winter solstice. It may be thought of either (i) as running from the exact moment of a winter solstice to the exact moment of the next winter solstice or (ii) as running from midnight (Beijing time) at the start of the day during which the winter solstice occurs to the midnight (Beijing time) of the start of the day during which the next winter solstice occurs. We could call these “astronomical” and “calendrical” solar years.

The astronomical solar year is divided into 24 periods. The times of the start and end of these are called “solar terms”. These are denoted by the symbols J1, Z1, J2, Z2, …, J12, Z12. The two (northern) solstices and the two equinoxes coincide with four of these solar terms, as follows:

•     vernal equinox (VE)    Z2
•     summer solstice (SS)    Z5
•     autumnal equinox (AE)    Z8
•     winter solstice (WS)    Z11

The Z’s and J’s
The other eight Z’s (the “major solar terms”, also known as “zhong qi”)) occur at equal (or nearly equal) intervals between these four Z’s. The major solar terms thus are like the hour numbers on a clock face, with the vernal equinox at 2 o’clock, etc. (and the minor solar terms, the J’s, marking the half-hours).

There are two variations on the Chinese solar calendar. It used to be defined so that the period from each solar term to the next was exactly 1/24th of an astronomical solar year, i.e., approximately  15.22 days. This is called the “Mean Sun” variation.

Revised Solar Calendar

In the 17th Century Chinese calendricists adopted calculations based on the true motions of the Earth and Sun, and in this variation of the solar calendar each solar term consists of the time required for the Earth to move exactly fifteen (= 360/24) degrees in its orbit (starting from a solstice or an equinox). This is called the “True Sun” variation. Since the Earth moves at slightly different speeds at different places in its orbit (it moves slightly faster when it is closer to the Sun) this implies that in the True Sun variation the period from one solar term to the next is not always the same.

Strictly speaking, solar terms are points in time, namely, the times at which the Sun (as seen from the Earth to be travelling along the ecliptic) reaches 0°, 15°, 45°, …, measured from a solstice or an equinox. A solar term may also be understood as a period of time, namely, the period between two such solar terms. We can thus say that (in this sense) the solar year is divided into 24 solar terms.

Although there are 12 pairs of adjacent solar terms, a pair of solar terms cannot be regarded as a ‘month’. The solar year is divisible into solar terms, but not into months. An attempt to do so (as is done in Wikipedia) flounders on the astronomical facts underlying why the lunar year sometimes has 12 months and sometimes has 13 months.

Just as “solar year” has two meanings, an astronomical and a calendrical, so a “solar term” may be thought of either (i) as running from the exact moment of a solar term as defined above to the exact moment of the next solar term (an “astronomical solar term”) or (ii) as running from midnight (Beijing time) at the start of the day during which the solar term (in the first sense occurs) to the midnight (Beijing time) of the start of the day during which the next solar term occurs (a “calendrical solar term”).

The day on which a calendrical solar term begins in the Chinese solar calendar is the day in which the astronomical solar term occurs. E.g., if a winter solstice occurs at 23:03 then the calendrical solar term Z2 begins at midnight (Beijing time) at the start of that day.

The 24 calendrical solar terms in a calendrical solar year are numbered 1 – 24 (1 = Z11, 2 = J12, 3 = Z12, 4 = J1, 5 = Z1, and so on). Within a calendrical solar term the days are numbered 1, 2, …  Thus a date in the solar calendar may be represented by a quadruple of the form cycle-position-solarterm-day, where c-p-s-d denotes day d (1-16) of solar term s (1-24) of the year at position p (1-60) in cycle c. Thus a sequence of dates in the Chinese solar calendar looks like this:

1-59-24-14, 1-59-24-15, 1-60-01-01, …, 1-60-24-16, 2-01-01-01, …

As noted in the preceding section each position-in-cycle is associated with a unique element-animal combination, so, e.g., “1-59-24-14” can also be expressed as “The 14th day of the last solar term of the Water-Dog year in the 1st cycle.”

Dates in the Chinese solar calendar may be marked by CHS, as in “2-01-01-01 CHS”.

  The Chinese Lunar Calendar

The definition of the lunar calendar depends on the definition of the solar calendar, but not vice-versa.

The first day of a lunar month begins at midnight (Beijing time) on the day in which the dark moon occurs. Thus a lunar month always runs from the day of the dark moon up to but not including the day of the next dark moon. It is thus tautologous (and hence true) to say that the dark moon always occurs on the first day of the lunar month.

This series of lunar months is partitioned into lunar years, which consist of either twelve or thirteen lunar months. Months are labelled with a numeral from “1” through “12” or (when a year contains a thirteenth month) with a numeral-plus-asterisk, e.g., “9*”.

The way the series of lunar months is partitioned into lunar years is as follows:

A nian is the period of a whole number of lunar months making up a lunar year, beginning with month “1”. A nian consists of 12 or 13 months. A related concept is a sui, which is a period of a whole number of lunar months such that the first month of the period contains the winter solstice. A sui also consists either of 12 or 13 lunar months. A sui largely overlaps the solar year, but can begin up to nearly a month before the solar year begins (when the winter solstice occurs close to the end of the first month of the sui).

Consider the series of lunar months partitioned into suis. Consider a particular sui. If it has twelve months then the months are to be numbered “11”, “12”, “1”, “2”, …, “10”. The third month will thus be the first month of the nian which largely overlaps this sui.

Suppose, on the other hand, that there are thirteen months in the sui. A sui can contain only twelve major solar terms (the Z’s, or zhong qi’s, described above), so at least one of the months does not contain a major solar term. The first month which does not contain a major solar term is distinguished as a “leap” month (a.k.a. an “intercalary” month). The first month in the sui cannot be a leap month because it contains the solar term Z11. The twelve non-leap months are numbered “11”, “12”, “1”, …, “10”. The leap month has the same number as its preceding month. Leap months are distinguished by an asterisk or a plus sign, so that, e.g., month “4” may be followed by leap month “4*” (or “+4” or “4+”), which is followed by month “5”.

A date in the Chinese lunar calendar may be represented by a quadruple of the form cycle-position-month[*]-day, where c-p-m[*]-d denotes day d (1-30) of month s (1-12) — a leap month if this is s* — of the year at position p (1-60) in cycle c. Thus a sequence of dates in the Chinese lunar calendar looks like this:

1-59-11-29, 1-59-11-30, 1-59-11*-01, …, 1-59-11*-29, 1-59-12-01, …, 1-59-12-30, 1-60-01-01, …

As with solar dates the position-in-cycle number can be replaced by an element-animal combination.

Dates in the Chinese lunar calendar may be marked by CHL, as in “1-60-01-01 CHL”.

Overseas Chinese number years sequentially, as in the Gregorian Calendar, with Chinese year 4709 corresponding to Gregorian year 2011. Thus the Overseas Chinese date “4709-07-13 CHL” denotes the same day as the cycle-position date “79-28-07-13 CHL”.

Comparison with the Gregorian Calendar

• New Year’s Day in the Chinese Lunar Calendar can occur on any date in the Gregorian Calendar from January 21 to February 21 (though not all dates are equally likely).
• New Year’s Day in the Gregorian Calendar always occurs about a week after the northern winter solstice, whereas on average New Year’s Day in the Chinese Calendar occurs approximately midway between that solstice and the northern vernal equinox.
• A year in the Gregorian Calendar always has 12 months, whereas a year in the Chinese Calendar usually has 12 but in about one year in three it has 13 months.
• A month in the Gregorian Calendar may have any number of days from 28 through 31. A month in the Chinese Calendar always has either 29 or 30 days.
• A month in the Chinese Calendar always begins at the dark moon, and the full moon always occurs in mid-month. In the Gregorian Calendar the dark moon and full moon can occur at any time during a month.

Traditionally associated with (although not formally a part of) the Gregorian Calendar is a cycle of 7 days (“the week”). There is no such cycle in the Chinese Calendar; instead there are cycles of 60 days, 60 months and 60 years.  Each day, month and year in the Chinese Calendar is traditionally associated with one of twelve animals and one of five elements. There is no such association in the Gregorian Calendar, although months are loosely connected with astrological signs of the zodiac (whose periods are offset from the months by about nine days). The Gregorian Calendar is rule-based, whereas the Chinese Calendar depends on exact calculation of the times of dark moons and solar terms (which must be done by calendrical experts using astronomical methods and data).

Mesoamerican systems

Every 52 years the so called called Sheaf and synchronized the 52 solar calendar years with 73 forward advance of Venus. The 52 x 365.256363 Earth-Pleiades Cycle was susceptible to precession. This Galactic Alignment occurs only once every 26,000 years, but the ancient Maya pointed to it with their 2012 end-date of  the cycle part the Long Count. This alignment occurs as a result of the precession of the equinoxes.  Precession is caused by the earth wobbling very slowly on its axis and shifts the position of the equinoxes and solstices one degree every 71.5 years. Because the sun is one-half of a degree wide, it will take the December solstice sun 36 years to precess through the Galactic equator.  The precise alignment of the solstice point (the precise center-point of the body of the sun as viewed from earth) with the Galactic equator was calculated to occur in 1998 (Jean Meeus, Mathematical Astronomy Morsels, 1997).  Thus, the Galactic Alignment “zone” is 1998 +/- 18 years = 1980 – 2016. This is “era-2012.” According to some, the  special version of the Mayan  Long Count (called Katun) End Date (13.0.0.0.0 – 13x20x20x18x20 or 1 872 000 days) represents the rare alignment of the Winter Solstice Sun crossing through the Galactic Equator along the dark band of stars at the center of the Milky Way Galaxy, and the Ecliptic (the path of the Sun) that will occur exactly 11:11 AM Greenwich Mean Time.

The Long Count

As a date was only unique in a 52 year period the Mayan but not the Aztec) introduced the perodic Long Count with its zero date (4 Ahau, 8 Cumhu according to Morely in Tzolkin/Haab notation) preceding their earliest record by up to 3440 years (first record 8.14.3.1.12). Those main calendar, the Tzolkin, the Haab and the Long Count can be seen was three parts, but are actually three separate calendars. This Long Count was used by the Mayans in the classical period. The Aztecs used only the Tzolkin called Tonalpohualli) and the Haab called Xihuitl. The Mayan Long Count Calendar was developed around 200 B.C.E. in Izapa, Mexico, using data calculated over hundreds of years. The era of the Long Count is controversial. E. Foerstemann worked out the initial long count 1887 from the Dresden codices, 1897 acknowledged by G.D. Goodman. Thirty years later, in 1927, eminent Maya scholar J. Eric Thompson revived Goodman’s work and tested it against astronomical data in hieroglyphic texts from the Maya Classic Period. Putting it all together in a 1937 land mark publication, Thompson proposed the GMT (Goodman Martinez Thompson) Correlation, also known as the 584283 correlation which received wide acceptance and corresponds to the zero point of the Aztec calendar. According to GMT, the last Mayan Long Count cycle began on August 11th, 3114 B.C and the target end date will be on December 21st, 2012 AD. So the Maya and Western calendars are correlated by using a Julian day number (JDN) of the starting date of the current creation – 13.0.0.0.0, 4 Ahau, 8 Cumhu . Using the GMT correlation, the current creation started on September 6, 3114 BC in the Julian Calendar or August 11 in the Gregorian calendar. The number 584283 is the number of days one has to count from Julian Day Number 0 to arrive at August 11, 3114 BC. The Julian Day Number System, not to be confused with the Julian Calendar, was established by Joseph Justus Scaliger in the 16th Century, specifically to correlate non-western calendar dates. In order to accommodate the most ancient calendars known at that time, he arbitrarily began the JDN count at Greenwich, at 12 o’clock noon, on January 1, 4713 B.C

The evidence for the GMT correlation is therfore historical, astronomical, and archaeological:

• Historical: Calendar Round dates with a corresponding Julian date are recorded in Diego de Landa’s Relación de las cosas de Yucatán (written circa 1566), the Chronicle of Oxcutzkab and the books of Chilam Balam. Oxcutzkab and de Landa record a date that is a Tun ending in the Short Count.
• Astronomical: Any correct correlation must match the astronomical content of classic inscriptions. The GMT correlation does an excellent job of matching the lunar data in the so called supplementary series.  This Long Count is also compliant with the eclipse table of the Dresden Codex and the Venus table which records the heliacal risings of Venus by less than half a day difference.
• Archaeological: Various items that can be associated with specific Long Count dates have been isotope dated.

The Long Count itself was assumed earlier by historians consisting of five parts,  given the fifth order (Baktun) given initially the name cyle by researchers. There are also four rarely used higher-order periods above the Bakton  as shown below. All these words are inventions of Mayanists.

The Katun replaced at the end of the Classic Maya culture in northern Yucatan, the Long Count. Whenever an act of the value reached 00 and the katun was incremented by one, the day of the Tzolkin certain the name of the Katun. This results in a period of 20 results Kin * 18 * 20 Uinal days = 7200 days, depending Katun. The count itself is repeated after 13 Katun and thus has a cycle of 93,600 days, giving rise to the 2012 doomsday theory. The Long Count date not only includes the five digits of the main five digit Long Count, but the 2-character Tzolk’in and the two-character Haab’ dates as well. The five digit Long Count can therefore be confirmed with the other four characters (the “calendar round date”). According to creation accounts known to the K’iche’ Maya of the Colonial-era highlands, we are living in the fourth world. The Popol Vuh describes the first three creations that the gods failed in making and the creation of the successful fourth world where men were placed. The third creation ended on a Long Count of 12.19.19.17.19. the next (fifth) 12.19.19.17.19 occurred on December 20, 2012 (Gregorian Calendar).

The Greek Athenian calendar

The Greek Athenian calendar was a lunisolar calendar with 354 day years, consisting of twelve months of alternating length of 29 or 30 days known as the Metonic calendar. This calendar showed that 235 lunar months made up almost exactly 19 solar years. This 19-year cycle became known as the Metonic cycle.

A variant of the Greek calendar is the Attic Delphic Oktaeteris . In a cycle of 8 years , there are five normal years with 354 days each and three leap years of 384 days. Leap years are the 3rd, 5th and 8 Year cycle. The leap month is inserted in the middle of the year and has the name ” Poseidon II ” and the number 7 The months are divided into three decades. The last decade counting backwards. The year begins in the summer (July / August) , the solar year is assumed to be 365.25 days. Epoch is the Neulicht 19 July 264 BC . (JD = 1625179 ) . The calendar gives way after 8 years to 1.528409916 days from the astronomical lunar orbit from and to 0.062408 days from the orbit around the sun .
The Olypiads

In addition to the names of the archons and the Olypiads was expressed as total annual number in the Greek historians. As an example, the year ” Ol.695 , 1″ what 1 Year of 695 Olympics and corresponding falls in the year 2001/2002. The Olympics bill was introduced probably by the historian Timaeus of Tauromenion (around 350-255 BC . ) . First conversions can be found but already the Sicilian politician and historian Philistus .
The beginning of a new year is defined according to in retrospect by historians as the full moon of the first New Moon follows after the summer solstice. In the calendar of the Athenians would be the 14th Hekatombaion . The victory of Coroebus around the summer solstice 776 BC . considered the beginning epoch of the Olympics count.

 The names of the months

The names of the days

Roman Calendar

The Romans had originally with the old calendar an eight-day market week Nundinae.  Over time, the market week was replaced by the seven-day planetary week (Hebdomas , septimana ), which after the Council of Nicaea (325 ) became the Judeo-Christian week. The calendar was calculated “from the founding of the city” of Rome, or ab urbe condita (AUC 750 BC). This old Roman year had 304 days divided into 10 months, beginning one the 21 April with extra months as stop-gaps.

The Julian calendar

The internal structure of the Julian calendar is derived from the ancient Roman lunisolar calendar. This began with the month martius and ended with the februarius. The Julian calendar consisted of cycles of three 365-day years (January until 31 December) followed by a 366-day leap year.  Augustus introduced the concept of the “leap year” and that Julian calendar.
In the 6th century, a Christian monk Dionysius Exiguus devised the Anno Domini system, dating from the Incarnation of Jesus. It was used until until 1582 in Europe although rival calendar to Anno Domini remained in use in Christian Europe

Start of the year

The names of the eras (creation date)

Named after Julius Caesar was introduced in the year 45 BC after he came back from Cleopatra. It has been scientifically supported by an Egyptian named Sosigenes . The calendar was a pure, solar calendar, derived from the Egyptian calendar with a length of 365 days in general and 366 days in a leap year inserted every 4 years. The beginning of the year was moved from March to January . The official beginning of spring was laid on the 25th March , although it astronomically occurred at the 23rd. They had measured imprecisely in the determination.  The internal structure of the Julian calendar is derived from the former Roman lunisolar calendar (which became a mess). The month are preserved until today counting names of months of September ( 7) to December ( 10). Leap ( bissexto ) in the Julian calendar was the 25th February (actually extended to February 24 to 48 hours). This was in addition to religious reasons, probably the leap month of the old calendar which every two years, has been added. This was done alternately on 23 and 24 February .  The month Quinctilis was renamed 44 BC in honor of the Caesar Julius and the Sextilis  in honor of Augustus. Whether the latter cost February one day so that Augustus had not less days than Julius is controversial.

As of 1582 , the Julian calendar was gradually replaced by the Gregorian calendar. Today, you can still use it in the Orthodox Church and historic times (and astronomy)

Christian Calenders

Although the early church held on to 1st January as a fixed beginning  and New Year the Council of Tours ( 576 ) as changed that as antiquus error. This still lives in the Coptic calendar. During the Middle Ages , the  Christian era,  the rule that leap years rule whose annual figures divided by 4 result as remainder is 0. In the late Middle Ages began the first January to be recognized again recognized (1691) in papal bulls . Nevertheless, additionally to the 1 January,  the church year begins on 1 Advent.
In principle, one should not overestimate the broad impact of the historical calendar and therefore also that of the Julian calendar .

For both Christians and Jews, the prime historical date was the Year of Creation, or Annus Mundi.

• Th Byzantine Church fixed the date of Creation at 5509 BC.which remained until modern times.
• The Coptic Church fixed on 5500 BC.
• The Church of England preferred 3761 BC as the date of creation,which forms the basis of the modern Jewish calendar.

The Easter calculation (computus paschalis ) based its historical roots lie on a lunar calendar in the Babylonian calendar. This was the model of the Jewish lunisolar calendar, which directed the date of Passover. Celebrating Easter in turn depends indirectly on Passover, even though it after a decree of Pope Victor I (reigned about 189-198 / 199) it was not allowed to coincide with Passover, The first Ecumenical Council , held in Emperor Constantine in the Summer Palace in Nicaea wanted to unify the date of Easter. After the feast of Easter should not be celebrated before the Passover and on a Sunday.  Preparations for the Passover begin on 14 Nisan in the Jewish calendar , the date of the vernal full moon. Hence the rule:

Easter should be celebrated on that Sunday , the first follows on the full moon of spring .
Does the full moon with a Sunday together , as Easter is to celebrate until the following Sunday.

To publicize the date of Easter time , unlike the Jewish calendar based on direct observation the Christian Easter was calculated it in advance. There were to be several calculation methods the Roman and the Alexandrian. The Roman method retained the historic beginning of spring on 25 March in and calculated the phase of the moon in a cycle of 84 years  the Alexandrian Computus with the (correct) 21 March and a nineteen -year cycle which was more accurate. The calculation was laid based on an average lunar orbit and designed as with an background lunar calendar t0 the Julian year. The nineteen- year lunar cycle , also called meton cycle was already known to the Babylonians and base of their calendar. It describes fact that the phases of the moon fall into its expiry after 19 years relatively accurate to the same dates in a solar year .

Since an orbit of the moon takes 29.53059 days to complete
and a solar year lasts 365.242199 days ,
requires the moon 365.242199 / 29.53059 = 12.36826623 rounds for a year.
A lunar year lasts 29.53059 * 12 = 354.36708 days .
The moon is so every year around 365.242199 to 354.36708 = 10.875119 days older.
There are for the Julian calendar, according to 365.25 to 354.36708 = 10.88292 days . To determine the age of the moon at the beginning of each year in the cycle, only this difference needs to multiplied by the corresponding year.

However the Julian lunar caledar hat some flaws.  The monthly length is  a 6939.75 / 235 = 29.53085106 days . The lunar month is thus an average of 29.53085106-29.53059 = 0.00026106 days too long. In 19 years, the 235 * 0.00026106 = 0.0613491 days or per Julian year = 0.0613491 / 19 = 0.0032289 days . This results in an error of one day in 1 / 0.0032289 = 309.7029948 years.

Also, the Julian solar year is inaccurate. Average has such a year (365 * 3 + 366) / 4 = 365.25 days . The solar year is 365.242199 days , however, with around 365.25 to 365.242199 = 0.007801 days shorter. Add 1 / 0.007801 = 128.1886938 years adds up the errors to a day.

When Nicholas Copernicus presented in 1514 with his book Commentariolus his heliocentric worldview, he was asked by the church immediately for proposals of an calendar reform . He refused. Pope Gregory XIII (1502 – 1585) then put a calendar Commission and reformed on 02.24.1582 with the Bull Inter gravissimas the calendar. The reform was based on the font Compendium novae rationis restituendi calendarium of the physician and astronomer Aloysius Lilius (actually Luigi Lilio 1510-1576 ) and the Jesuit astronomer Christoph Clavius:

Easter should come back to the astronomically determined by the Council of Nicaea place .
The beginning of spring should be back on the set of the Alexandrian Computisten 21 March fall .
The mean tropical year should be taken as closely as possible in the rules.
The existence of the old calendar should remain possible get .

To do justice to the switching rules of the solar year were extended as follows :

A year whose year number without a remainder is divisible by 4 is a leap year.
The leap year falls out when the year is divisible by 100 without remainder is .
If the year without a remainder is divisible by 400 , the year also by Rule 2 is a leap year .

The Gregorian reform had adapted the outer structure of the calendar with three simple switching rules fairly accurate to the sun’s path. The other hand, the internal structure of the calendar, still drags the ballast of the Roman lunisolar calendar. In 1923, therefore, considered the League of Nations 185 calendar proposals of different radicalism but all these attempts ended 1954 with proposals to the UN but did not materialize. Just the begin of the week was changed from Sunday to Monday by the European Union in essences an pagan and history-ignorant bureaucracy.

The Jewish Calendar

The switching rules and adjournments of the Jewish calendar lead to six different lengths of years . One year may be deficient in common or surplus and is either a joint or a leap year. The annual lengths are accordingly: 353 , 354, 355 and 383 , 384, 385 days . In 19 years 7 leap years of 13 months each are inserted according to the Metonzyklus .
The epoch of the calendar is JD = 347 998 ( the 7.10.3761 BC . ) , As era is considered the foundation of the world .
The molad

The year of the calendar is based on a monthly average length of 29 days, 12 hours and 793 khalakim , which corresponds to 29.5305941235 days. The beginning of the year is from the derived molad , the Jewish new moon determined . The first was on 29 molad Elul in 0 by 23 clock 11 minutes and 20 seconds ( CET) (5 clock and 204 parts of Jewish time).
The beginnings of the year

The civil year begins on 1 Tishri , as well as the Shmitah and the Joweljahr . In contrast, the religious year begins on 1 Nissan the month of the cyclical spring full moon and the Passover . The for determining traditional method of counting the months indicated in the table below in parentheses. In addition , there is the New Year for Trees 15 Shevat and the calculation of the tithes from the cattle on 1 Elul . The counting of the years following the civil calendar and replaced on 1 Tishri .

The names of the months

For religious reasons, the beginning of the new year is often postponed or adjourned.

The Chinese Calendar

The calendar is astronomically defined what a historical dating more difficult because the calendar is not based on reproducible rules, but , on partly erroneous , tables. Because of the consequent variations of the calendar of astronomical events of the calendar often had to be adjusted . Thus, the Chinese calendar look back until today to more than 50 reforms. The epoch begins at 8.3 in 2637 BC . in the 61st Year of the Emperor Hoang -ti .

The day begins at midnight.
The months are numbered from 1 to 12. ( Beginning of year = # 1 )
The month begins at the day of the astronomical new moon in Beijing. (Length = -116 ° 24 ‘ , latitude 39 ° 56’ time zone + 8 hours , before 1929 the Beijing local time + 7 hrs 46 min)
The month of sweeps over the beginning of winter , always assigned the number 11
Lying between two winter beginnings 13 new moons , a leap month is inserted.
Leap month is the first month between the two winter starts, which is within a divisible by 30 solar position. The leap month is assigned the number of the previous month with the addition of tan .
Examples:
On 21 March 2004 in Beijing new moon, when the Sun ‘ is at 0 ° 39 . The next new moon the sun is at 29 ° 49 ‘ , it is a 29 -day intercalary month inserted.
On 23 July 2017 , the sun is at 120 ° 44 ‘, 30 days later, on 22 August at 148 ° 53 ‘ , which is a leap month of 30 days conditionally .

The calendar consists of one cycle sixties for the day and the year. They are based on the numbers 10 and 12 is the least common multiple of 60 . Each number is assigned a name , so that each day and each year has a double name .
example:
the ” 1.5.40.76 ” (27 May 1903) is , therefore, 1 Day on the 5th Month on the 40th Year of the 76th Cycle lake. The day is named ” timber – Hare ” , the year is called ” source – Hare ” .

The names of the years

The Chinese year is divided into 24 parts corresponding to the astronomical position of the sun in steps of 15 °. The organization calls itself tSIE-k’i. Where tSIE for the odd numbers and k’i stands for the even numbers.

Seasons

The French Revolutionary Calendar

The French Revolutionary calendar was from 24/11/1793 to 12/31/1805 in use. His era will begin on 22 September 1792 , the first day of the French Republic. Thus began the first Years of the Republican era. On this day also the autumnal equinox in Paris, which was henceforth regarded as the year fell . The calendar follows in its construction to the Coptic ( Egyptian ) calendar with 12 months of 30 days each and 5, in leap year 6 additional days. The names of the months were directed only to agriculture in the French heartland. The annual figures were given in Roman notation.
An outlook

Later was also , at the suggestion of the astronomer Jean Baptiste Joseph Delambre’s out of planned Gilbert Romme a departure from the astronomical defined circuit . But should an extended firing rule of the Gregorian calendar , introduced by the failure of a leap day every 4000 years. For this revision , however no longer came . Before them decency in the Convention for discussion Romme was arrested and committed suicide. Later attempts failed due to the negative attitude of the Convention.

The names of days and months

The month was divided into three decades with 10 days , the days were numbered were: Primedi , Duodi , Tridi , Quartidi , Quintidi , Sextidi , Septidi , Octidi , Nonodi and Decadi . In practice, however, by days were counted 1-30 . As a rest day and day of public holidays (decade festivals) the Decadi was used. In addition, still got each day in its own name. These were the names of animals , plants, minerals or agricultural equipment . The naming of days and months was elaborated by Philippe -François- Nazaire Fabre . He wanted to bring his naming the people the basics of agriculture close . Four consecutive years ( three normal and leap years ) were referred to as Franciade .

The names of the months

The names of the months

It circulates in the Anglo-Saxon countries and has German names. It was designed by the novelist and anarchist Robert Anton Wilson. The year is divided into five parts with him, each 73 days. Each part has a specific name. The 29 February shall not be counted. The epoch of the calendar is 4000 BC.

The names of the months

The Islamic calendar

With a revelation in the second year of the Hegira , the Prophet Muhammad adopted a pure lunar calendar and lifted the old Arab moon – on the solar calendar . Especially so that the insertion of leap months was unnecessary. The calendar moves through the seasons so because it lacks 11 or 12 days a year.

The beginning of the month of the calendar was originally fixed on the basis of direct observation of the first crescent moon. This is true for the holidays and the beginning of Ramadan until today , being resorted to determine the month beginning also in part to astronomical calculations.
The history

The calendar itself was under Caliph Omar II (r. 634-644 ) established to allow a precise dating . There are two variants :

the civil calendar, which begins on 16.7.622 and
the astronomical calendar , with the 15.7.622 as the start date .

As one era put the emigration of Muhammad from Mecca to Medina , the Hijra , firm, which took place in September 622.

The calendar is based on a 30-year cycle in which 10 leap days are added . These are divided by 30 years the residues 2 , 5, 7 , 10, 13 , 15 or 16 , 18, 21 , 24 and 29 result . The remainder being 15, on astronomical , the rest 16 on the other hand for the civil year . Thus, deviations of up to two days between the two variants are possible .
The months are alternately recorded with 30 and 29 days. Their names , their transliteration from Arabic is very different, go back to the pre-Islamic calendar.

The names of the months

Bibliography

• “The exact Science in Antiquity”  O. Neugebauer, Dover Edition 1989
• “Cosmos An illustrated History of Astronomy and Cosmology”. John North 2008
• Universalgeschichte der Zeit Hans Lenz Matrix Verlag GmbH, Wiesbaden 2005
• The Religion of Ancient Egypt Sir W. M. Flinders (William Matthew Flinders) Petrie
• Geschichte des Morgenlandes im Altertum: Hertzberg, G.F.: Verlag: Berlin, Historischer Verlag Baumgärtel (ca. 1904), 1904
• Prophyläen der Weltgeschichte, Golo Mann, Ullstein 1961
• The Religions of Ancient Egypt and Babylonia, by A. H. (Archibald Henry) Sayce
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• Heritage Sites of Astronomy and Archaeoastronomy in the context of the UNESCO World Heritage Convention: A Thematic Study. Other. ICOMOS,  2010 Paris
• World of Astrology, Dorling Kindersley
• Handbuch der mathematischen und technischen Chronologie  Das Zeitrechnungswesen der Völker,  F. K. Ginzel
  
  J. C. HINRICHS’sche BUCHHANDLUNG Band 1 1906, Band 2 1911 und Band 3 1914.
  
  Band 1: Zeitrechnung der Babylonier, Ägypter, Mohammedaner, Perser, Inder, Südostasiaten, Chinesen,
  
  Japaner und Zentralamerikaner
  
  Band 2: Zeitrechnung der Juden, der Naturvölker, der Römer und Griechen sowie Nachträge zum I. Bande
  
  Band 3: Zeitrechnung der Makedonier, Kleinasier und Syrer, der Germanen und Kelten, des Mittelalters,
  
  der Byzantiner (und Russen), Armenier, Kopten, Abessinier, Zeitrechnung der neueren Zeit, sowie Nachträge zu den drei Bänden

Appendix

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