/kreuh nol"euh jee/, n., pl. chronologies.
1. the sequential order in which past events occur.
2. a statement of this order.
3. the science of arranging time in periods and ascertaining the dates and historical order of past events.
4. a reference work organized according to the dates of events.
[1585-95; CHRONO- + -LOGY]

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      any method used to order time and to place events in the sequence in which they occurred. The systems of chronology used to record human history, which are closely related to calendar systems, vary in scope, accuracy, and method according to the purpose, degree of sophistication, and skills of the peoples using them.

      Scientific chronology, which seeks to place all happenings in the order in which they occurred and at correctly proportioned intervals on a fixed scale, is used in many disciplines and can be utilized to cover vast epochs. Astronomy, for example, measures the sequence of cosmic phenomena in thousands of millions of years; geology and paleontology, when tracing the evolution of the Earth and of life, use similar epochs of hundreds or thousands of millions of years. Geochronology reckons the more distant periods with which it deals on a similar scale; but it descends as far as human prehistoric and even historic times, and its shorter subdivisions consist only of thousands of years. Shortest of all are the chronological scales used in the recording of human events in a more or less systematic and permanent manner. These vary in scope, accuracy, and method according to the purpose, degree of sophistication, and skill of the peoples using them, as do the calendrical systems with which they are inextricably bound up. For further details see the article calendar.

      It is difficult to fix ancient historical chronologies in relation to scientific chronology. The terms of reference of ancient peoples were vague and inconsistent when judged by modern standards, and many of their inscriptions and writings have inevitably disappeared. The gaps in their records are increasingly filled in and their inconsistencies removed by the results of archaeological excavation. Guided by these findings, scholars can confirm, refute, or amend chronological reconstructions already tentatively made. Astronomical calculation and dating by radioactive-carbon content are also helpful in the work of fixing ancient chronologies.

      Chinese legendary history can be traced back to 2697 BC, the first year of Huang Ti (Chinese: Yellow Emperor), who was followed by many successors and by the three dynasties, the Hsia, the Shang, and the Chou. Recent archaeological findings, however, have established an authentic chronology beginning with the Shang dynasty, though the exact date of its end remains a controversial topic among experts. The so-called oracle-bone inscriptions of the last nine Shang kings (1324–1122 BC) record the number of months up to the 12th, with periodical additions of a 13th month, and regular religious services on the summer and winter solstice days, all of which indicates the adjustment of the length of the lunar year by means of calculations based on the solar year. Individual days in the inscriptions are named according to the designations in the sexagenary cycle formed by the combination of the 10 celestial stems and 12 terrestrial branches. Every set of 60 days is divided into six 10-day “weeks.” Also recorded are numerous eclipses that can be used to verify the accuracy of the Shang chronology. In the oracular sentences of the last Shang king, Chou (Zhou dynasty) Hsin, the year of his reign is referred to as “the King's nth annual sacrifice.”

      From the beginning of the following (Chou) dynasty, the word year was etymologically identical with “harvest.” Thus, “King X's nth harvest” meant the nth year of his reign. The lunar month was then divided into four quarters—Ch'u-chi, Tsai-sheng pa, Chi-sheng pa and Chi-szu pa—and the practice of using the 60 cyclical names for the days was continued. Thus, in the inscription on a Chou bronze vessel, a typical date would read: “In the King's nth harvest, in the nth quarter of the nth month, on the day X-y, etc.”

      The tradition of recording events by referring to the king's regnal year continued until 163 BC, when a new system, nien-hao (nianhao) (“reign-period title”), was introduced by Emperor Han Wen Ti (Wendi) of the Former Han dynasty (206 BC–AD 8). Thereafter, every emperor proclaimed a new nien-hao for his reign at the beginning of the year following his accession (sometimes an emperor redesignated his nien-hao on special occasions during his reign). A typical date in the nien-hao system might read, “the third year of the Wan-li reign period” (Wan-li san nien). In order to date any event in Chinese history, it is necessary to convert the year in the period of the designated nien-hao into the Western calendar.

      During the Chou dynasty the civil year began with the new moon, which occurred before or on the day of the winter solstice. This “first month” of the Chou year (Chou cheng) was equivalent to the 11th month of the Hsia year (Hsia cheng) or to the 12th month of the Shang year. The first emperor, Shih Huang-ti, of the short-lived Ch'in dynasty (Qin dynasty) (221–206 BC) made the year begin one month earlier—i.e., with the lunation (the period of time between one new moon and the next) before the one in which the winter solstice occurred. The Ch'in year was continuously used until 104 BC, when Emperor Han Wu Ti (Wudi) promulgated the T'ai-ch'u calendar by reverting to the Hsia cheng—i.e., by taking the third month of the Chou year, or the second lunation after the winter solstice, as the first month of the civil year. This lunar year (or Hsia cheng) was used till the last day of the Ch'ing, or Manchu, dynasty (1644–1911/12). When in 1911 the first republic was founded, the solar year was officially adopted, but successive governments kept the nien-hao tradition by referring any date to the number of years since the establishment of the republic—e.g., 1948 was chronicled “the 37th year of the republic.” In 1949, when the People's Republic of China was proclaimed, the old system was replaced by the Gregorian calendar.

Wu Shih-ch'ang

      The principal chronicles describing the origins of Japanese history are the Nihon shoki (“Chronicle of Japan”) and the Koji-ki (Kojiki) (“Record of Ancient Matters”). The Nihon shoki (compiled in AD 720) assembled information in a chronological order of days, months, and years starting several years before 660 BC, which was the year of the enthronement of the first Japanese emperor, who was posthumously named Jimmu. The Koji-ki (compiled in AD 712) related events under the reign of each emperor without a strict chronological order. Sometimes the Koji-ki gave the years of emperors' deaths and their ages at death. This information is different from that recorded in the Nihon shoki.

      Native Japanese scholars since Fujiwara Teikan in the 18th century have realized that the Nihon shoki was historically inadequate and different from the Koji-ki, at least insofar as the chronological information is concerned. They have suggested that the foundation year of Japan was 600 years later than stated in the Nihon shoki. Naka Michiyo (late 19th century) argued with minute detail about the question of Japanese chronology. His ideas were supplemented by those of other Japanese scholars, who pointed out that: (1) the reigns of the earlier Japanese emperors as stated in the Nihon shoki are unnaturally long; (2) the date of the enthronement of the emperor Jimmu should be reconsidered; (3) a chronological gap exists between the Nihon shoki and contemporary Chinese and Korean chronicles. In comparison with Korean chronicles, they argued, the Nihon shoki has created an intentional expansion of chronology—i.e., the entries about the empress Jingō and the emperor Ōjin can be identified with historical facts relating to the Korea of the 4th and 5th centuries and therefore must be placed 120 years later than mentioned in the Nihon shoki. When comparing the Nihon shoki with Chinese chronicles, one finds the chronological gap somewhat reduced. The Chinese chronicles provide information about the tributes sent individually by five Japanese “kings” to Liu-Sung and Southern Ch'i during the 5th century. There are still questions about the identification of these kings, but it is generally accepted that the “king” written in Chinese character as Wu must be the Japanese emperor Yūryaku. By the late 5th century the gap between Japanese and Korean records, on the one hand, and Japanese and Chinese, on the other hand, disappears.

      The intentional expansion of the chronology of the Nihon shoki was adopted by its compilers, who identified Queen Himiko (Pimihu) of Yamatai of the chronicle of Wei China with the Empress Jingō of Japanese legend.

      The method of designating a year by the kan-shi (sexagenary cycle) appears to have begun about the reign of Emperor Yūryaku, when, as mentioned above, the gap between the continental and Japanese chronologies was bridged. The inscription on remarkable copper images of Buddha cast just after the period of Prince Shōtoku's regency (AD 593–621) bears a nengō (nien-hao, or reign-year title), although not a strictly authorized one. It was at this time that the Chinese luni-solar calendar system was adopted. The first official nengō was Taika, which was adopted by the imperial court in 645. Since 701, when the second title, Taihō, was adopted, the reign-year system has been continuously used in relation to the emperors' reigns up to the present day. In medieval times Japanese chronology underwent a remarkable evolution: (1) when the Imperial dynasty split into two courts (1336–92), two series of nengō began to be used; (2) during the Ashikaga period some private nengō again appeared; (3) some dates of the authorized “central” calendars did not correspond with those of locally compiled calendars. Moreover, military leaders would not accept some of the new nengō. Minamoto Yoritomo, for example, did not use the nengō that was adopted by the emperor Antoku and the Taira regime, and Ashikaga Mochiuji and Ashikaga Shigeuji did not use the official, respectively Eikyō and Kōshō, nengō.

      In the Tokugawa period (1603–1867), gaps between central and provincial calendars disappeared, especially after the establishment of the Jōkyō calendar, the first native calendar compiled in Japan, instead of the Chinese-based one that was in use until this period. On January 1, 1873, Emperor Meiji (Meiji Restoration) adopted the Gregorian calendar in use in the West and at the same time adopted the “Japanese Era,” with Emperor Jimmu as its founder, in addition to the nengō system.

Hiroyuki Momo

      Two kinds of chronological systems have been used in India by the Hindus (Hinduism) from antiquity. The first requires the years to be reckoned from some historical event. The second starts the reckoning from the position of some heavenly body. The historical system, the more common in modern times, exists side-by-side with Muslim and international systems successively introduced.

Reckonings dated from a historical event
      The inscriptions of the Buddhist king Aśoka (Ashoka) (c. 265–238 BC) give the first epigraphical evidence of the mode of reckoning from a king's consecration (abhiṣeka). In these inscriptions (Middle Indian language in India or Greek and Aramaean in what is now Qandahār, Afghanistan) the dates are indicated by the number of complete years elapsed since the king's consecration. But the earlier existence of a reckoning of duration of reigns and dynasties is evidenced by the testimony of the Greek historian Megasthenes, who in 302 BC was the ambassador of Seleucus I Nicator, founder of the Seleucid Empire, to the court of Candragupta (Chandra Gupta) Maurya, Aśoka's grandfather. According to Megasthenes, the people of the Magadha kingdom, with its capital Pāṭaliputra ( Patna), kept very long dynastic lists, preserved in the later Sanskrit Purāṇas (legends of the gods and heroes) and later Buddhist and Jain chronicles. They generally indicate, in years or parts of years, the duration of each reign.

      Similar records of other periods and regions exist, and a relative chronology may be established. Unfortunately, it is not always possible to connect them with any absolute chronology, the precise dates of the reigns given being still unsettled. For example, in the Scythian period of the history of northern India, several inscriptions are dated from the beginning of the reign of Kaniṣka (Kaniska), the greatest king of the Asian (Kushān) invaders, but his dates are still uncertain (AD 78, 128–129, 144, etc., have been suggested for the beginning of a Kaniṣka era).

      Other records give regnal years that can be linked with absolute chronology through other data—e.g., those of several rulers of the Rāṣṭrakūṭa of the Deccan.

      The dynastic eras, founded by several rulers and kept up or adopted by others, are also numerous. The most important were the Licchavi era (AD 110), used in ancient Nepal; the Kalacuri (Kalacuri Dynasty) era (AD 248), founded by the Abhūrī king Īśvarasena and first used in Gujarāt and Mahārāshtra and later (until the 13th century) in Madhya Pradesh and as far north as Uttar Pradesh; the Valabhī era (AD 318, employed in Saurāṣṭra) and the Gupta era (AD 320), used throughout the Gupta Empire and preserved in Nepal until the 13th century. Later came the era of the Thakuri dynasty of Nepal (AD 395), founded by Aṃśuvarman; the Harṣa era (AD 606), founded by Harṣa (Harṣavardhana), long preserved also in Nepal; the western Cālukya (Chalukya dynasty) era (AD 1075), founded by Vikramāditya VI and fallen into disuse after 1162; the Lakṣmaṇa era (AD 1119), wrongly said to have been founded by the king Lakṣmaṇasena of Bengal and still used throughout Bengal in the 16th century and preserved until modern times in Mithilā; the Rājyabhīṣekasaka or Marāthā (Marāṭhā) era (1674), founded by Śivājī but ephemeral.

      Later, instead of the beginning of a reign or of a dynasty, the death of a religious founder was adopted as the starting point of an era. Among Buddhists (Buddhism) the death of the Buddha and among the Jains (Jainism) the death of the Jina were taken as the beginning of eras. The Jain era (vīrasaṃvat) began in 528 BC. Several Buddhist sects (no longer existing in India) adopted different dates for the death (Nirvāṇa) of the Buddha. The Buddhist era prevailing in Ceylon and Buddhist Southeast Asia begins in 544 BC.

      Historical events, now obscure, were the basis of the two most popular Indian eras: the Vikrama and the Śaka.

      The Vikrama era (58 BC) is said in the Jain book Kālakācāryakathā to have been founded after a victory of King Vikramāditya over the Śaka. But some scholars credit the Scytho-Parthian ruler Azes with the foundation of this era. It is sometimes called the Mālava era (Hindu calendar) because Vikramāditya ruled over the Mālava country, but it was not confined to this region, being widespread throughout India. The years reckoned in this era are generally indicated with the word vikramasaṃvat, or simply saṃvat. They are elapsed years. In the north the custom is to begin each year with Caitra (March–April) and each month with the full moon. But in the south and in Gujarāt the years begin with Kārttika (October–November) and the months with the new moon; in part of Gujarāt, the new moon of Āṣāḍha (June–July) is taken as the beginning of the year. To reduce Vikrama dates to dates AD, 57 must be subtracted from the former for dates before January 1 and 56 for dates after.

      The Śaka, or Salivāhana, era (AD 78), now used throughout India, is the most important of all. It has been used not only in many Indian inscriptions but also in ancient Sanskrit inscriptions in Indochina and Indonesia. The reformed calendar promulgated by the Indian government from 1957 is reckoned by this era. It is variously alleged to have been founded by King Kaniṣka or by the Hindu king Salivāhana or by the satrap Nahapāna. According to different practices, the reckoning used to refer to elapsed years in the north or current years in the south and was either solar or luni-solar. The luni-solar months begin with full moon in the north and with new moon in the south. To reduce Śaka dates (elapsed years) to dates AD, 78 must be added for a date within the period ending with the day equivalent to December 31 and 79 for a later date. For Śaka current years the numbers to be added are 77 and 78. The official Śaka year is the elapsed year, starting from the day following that of the vernal equinox. A normal year consists of 365 days, while the leap year has 366. The first month is Chaitra, with 30 days in a normal year and 31 in a leap year; the five following months have 31 days, the others 30.

      A Nepalese era (AD 878) of obscure origin was commonly used in Nepal until modern times. The years were elapsed, starting from Kārttika, with months beginning at new moon. Another era, the use of which is limited to the Malabār Coast (Malabar Coast) (Malayalam-speaking area) and to the Tirunelveli district of the Tamil-speaking area, is connected with the legend of the hero Paraśurāma, an avatar (incarnation) of the god Vishnu. It is called the Kollam era (AD 825). Its years are current and solar; they start when the Sun enters into the zodiacal sign of Virgo in north Malabār and when it enters into Leo in south Malabār. It is sometimes divided into cycles of 1,000 years reckoned from 1176 BC. Thus, AD 825 would have been the first year of the era's third millennium.

Eras based on astronomical speculation
      During the period of elaboration of the classical Hindu astronomy, which was definitively expounded in the treatises called siddhāntas and by authors such as Āryabhaṭa I (Aryabhata I) (born AD 476), Varāhamihira, Brahmagupta (7th century AD), etc., the ancient Vedic (Veda) notions on the cycle of years, embracing round numbers of solar and lunar years together, were developed. On the one hand, greater cycles were calculated in order to include the revolutions of planets, and the theory was elaborated of a general conjunction of heavenly bodies at 0° longitude after the completion of each cycle. On the other hand, cosmologists speculated as to the existence of several successive cycles constituting successive periods of evolution and involution of the universe. The period calculated as the basis of the chronology of the universe was the mahāyuga, consisting of 4,320,000 sidereal years. It was divided into four yugas (yuga), or stages, on the hypothesis of an original “order” (dharma) established in the first stage, the Kṛta Yuga, gradually decaying in the three others, the Tretā, Dvāpara, and Kali yugas. The respective durations of these four yugas were 1,728,000, 1,296,000, 864,000, and 432,000 years. According to the astronomer Āryabhaṭa, however, the duration of each of the four yugas was the same—i.e., 1,080,000 years. The basic figures in these calculations were derived from the Brahmanical reckoning of a year of 10,800 muhūrta (see calendar: The Hindu calendar (calendar)), together with combinations of other basic numbers, such as four phases, 27 nakṣatras, etc. The movement of the equinoxes was at the same time interpreted not as a circular precession but as a libration (periodic oscillation) at the rate of 54 seconds of arc per year. It is in accordance with these principles that the calculation of the beginning of the Kali Yuga was done in order to fix for this chronology a point starting at the beginning of the agreed world cycle. Such a beginning could not be observed, since it was purely theoretical, consisting of a general conjunction of planets at longitude 0°, the last point of the nakṣatra Revati (Pisces). It has been calculated as corresponding to February 18, 3102 BC (old style), 0 hour, and taken as the beginning of the Kali era. In this era, the years are mostly reckoned as elapsed and solar or luni-solar.

      In Hindu tradition the beginning of the Kali era was connected with (1) events of the Mahābhārata war; (2) King Yudhiṣṭhira's accession to the throne; (3) 36 years later, King Parikṣit's consecration; and (4) the death of Lord Krishna. Years of the era are still regularly given in Hindu almanacs.

      An era resting upon a fictitious assumption of a complete 100-year revolution of the Ursa Major, the Great Bear (saptarṣi), around the northern pole was the Saptarṣi, or Laukika, era (3076 BC), formerly used in Kashmir and the Punjab. The alleged movement of this constellation has been used in Purāṇa compilations and even by astronomers for indicating the centuries.

      Two chronological cycles were worked out on a basis of the planet Jupiter's revolutions, one corresponding to a single year of Jupiter consisting of 12 solar years and the other to five of Jupiter's years. The second, the bṛhaspaticakra, starts, according to different traditions, from AD 427 or from 3116 BC. Before AD 907 one year was periodically omitted in order to keep the cycle in concordance with the solar years. Since 907 the special names by which every year of the cycle is designated are simply given to present years of the almanac.

      Side-by-side with Hindu and foreign eras adopted in India, several eras were created in the country under foreign influence, chiefly of the Mughal emperor Akbar: Bengali San (AD 593), Amli of Orissa and Vilayati (AD 592), Faṣlī (AD 590, 592, or 593 according to the district), and Sursan of Mahārāshtra (599).

Jean L.A. Filliozat

      At the end of the 4th millennium BC, when King Menes, the first king of a united Egypt, started his reign, the ancient (Egypt, ancient) Egyptians began to name each year by its main events, presumably to facilitate the dating of documents. These names were entered into an official register together with the height of the Nile during its annual inundation. Short notes at first, the year names developed into lengthy records of historical and religious events, especially of royal grants to the gods. These lists grew into annals, which were kept during the entire history of Egypt so that later kings could, after important events, consult the annals and ascertain whether a comparable occurrence had happened before. Unfortunately, these annals are lost. Only fragments from the 1st to the 5th dynasty (c. 3100–c. 2345 BC) are preserved, copied on stone. These fragments, however, are in such poor condition that they raise more chronological problems than they solve.

      The Egyptian priests of the Ramesside period (c. 1300 BC) copied the names and reigns of the kings from Menes down to their time from the annals, omitting all references to events. Even this king list would have given a safe foundation of an Egyptian chronology, but the only extant copy, on a papyrus now kept at the Museo Egizio in Turin (Turin Papyrus), has survived only in shreds, entire sections having been lost. Extracts from this king list, which name only the more important kings, are preserved in the temples of the kings Seti I and Ramses II at Abydos and on the wall of a private tomb at Ṣaqqārah (now in the Egyptian Museum), but they give little help in chronological matters.

      When the Greeks began to rule Egypt after the conquest of Alexander the Great, King Ptolemy II Philadelphus, hoping to acquaint the new ruling class with the history of the conquered country, commissioned Manetho, an Egyptian priest from Sebennytus, to write a history of Egypt in the Greek language. As Manetho had access to the ancient annals, he added some of their entries to his list of kings and reigns, especially during the first dynasties. The more he progressed in time, the more he added semihistorical traditions and stories as they were composed by the Egyptian priests to discuss moral problems in the disguise of a historical “novel.” There had been, undoubtedly, fewer historical facts in Manetho's history than one might expect. But Manetho's work, too, is lost except for some excerpts used by Sextus Julius Africanus and Eusebius in writing their chronicles. These, in turn, represented the material used in part by George Syncellus in the 8th century AD. During copying and recopying, Manetho's text clearly suffered many changes, unintentionally or on purpose. The figures of the reigns, especially of the older dynasties, for instance, were enlarged when some of the early Christian historians tried to equate King Menes with Adam. In addition, the excerpts were done carelessly. Therefore, Manetho's work, as handed down to us, is short of useless. Nevertheless, together with the fragments of the annals and of the king list of Turin, they create a framework of Egyptian chronology; so the division into dynasties was taken over from Manetho. But to achieve a continuous history of Egypt and to bridge the gaps left by the fragmentary state of the extant chronological material, scholars must turn to other means, particularly astronomical references found in dated texts. These are related principally to the rising of Sothis and to the new moon.

      Theoretically, the Egyptian (Egyptian calendar) civil year began when the Dog Star, Sirius (Egyptian Sothis), could first be seen on the eastern horizon just before the rising of the Sun (i.e., 19/20 of July). As the civil calendar of the ancient Egyptians consisted of 12 months (each of 30 days) and five odd days (called epagomenal days), the civil year was a quarter of a day too short in relation to the rising of Sothis, so that the new year advanced by one day every four years. New Year's Day and the rising of Sothis coincided again only after approximately 1,460 years, the so-called Sothic cycle. Dated documents mentioning the rising of Sothis can be translated into the present calendar by multiplying the number of days elapsed since the first day of the year by four and subtracting this sum from the date of the beginning of the particular Sothic cycle. The dates for the start of each Sothic cycle are fortunately known because the Roman historian Censorinus fixed the coincidence of New Year's Day and heliacal rising of Sothis in AD 139. Taking into account a slight difference between a Sothic year and a year of the fixed stars, the years 1322, 2782, and 4242 BC are taken as starting points of a Sothic cycle.

      There are six ancient Egyptian documents extant giving Sothis dates, but only three of these are of value. The oldest is a letter from the town of Kahun warning a priest that the heliacal rising of Sothis will take place on the 16th day of the 8th month of year 7 of a king who, according to internal evidence, is Sesostris III of the 12th dynasty. This date corresponds to 1866 BC, according to the corrected Sothic cycle. The next date is given by a medical papyrus written at the beginning of the 18th dynasty, to which a calendar is added, possibly to ensure a correct conversion of dates used in the receipts to the actual timetable. Here it is said that the 9th day of the 11th month of year 9 of King Amenhotep I was the day of the heliacal rising of Sothis—i.e., 1538 BC. This date, however, is only accurate provided that the astronomical observations were taken at the old residence of Memphis; if observed at Thebes in Upper Egypt, the residence of the 18th dynasty, the date must be lowered by 20 years—i.e., 1518 BC. The third Sothis date shows that Sirius rose heliacally sometime during the reign of Thutmose III, which lasted for 54 years, on the 28th day of the 11th month; so year 1458 BC (point of observation at Memphis) or 1438 BC (point of observation at Thebes) must have belonged to the reign of this king. From these dates it is possible to calculate the absolute dates for the reigns of the 12th dynasty, as the durations of most of the reigns of the kings belonging to this dynasty are preserved on the king list of the Turin Papyrus. On the other hand, chronologists are able to compute the reigns of the kings of the 18th dynasty by utilizing the highest dates of their documents and the figures preserved by Manetho. Historians are also helped by the fact that the Egyptians sometimes identified a certain day as “exactly new moon”; they reckoned new moon (lunar calendar) from the morning after the last crescent of the waning moon had become invisible in the east just before sunrise. As there is a 25-year lunar cycle, such ancient Egyptian moon dates could be calculated with a fair amount of certainty but of course only if the ancient Egyptians themselves observed this celestial phenomenon accurately. There is some doubt, however, as it is shown by the attempts of very competent scholars to convert these moon dates. Sometimes even moon dates given by the same papyrus contradict themselves; in another case, the date given by a document had to be amended to achieve a reasonable result. These and other examples show that ancient Egyptian statements on celestial phenomena, especially on new moons, tend to be inaccurate because of faulty or inexact observations. Therefore, every date given for a fixed reign should be used with caution as the astronomical observation on which it is based may be inexact. Sometimes they are controlled by synchronism with Babylonian, Assyrian, or Hittite king lists or, later on, by the close interconnections between Greek and Egyptian history. Sometimes even biographical data are helpful. The statements found on small stelae inside the burial ground of the holy bulls of Memphis (Apis) register the dates of birth, enthronement, and death of these animals accurately. But the more time recedes, the more the chronology of the Egyptian history becomes uncertain, even when astronomical data are available. Up till now even carbon-14 data are of no great help, as uncertainties are mostly not greater than the standard deviations to be expected in a carbon-14 calculation.

      Nevertheless, Egyptologists believe themselves to be on fairly firm ground when dating the beginning of the Ancient Kingdom (1st and 2nd dynasty) about 3090 BC, the beginning of the 11th dynasty at 2133 BC, and of the Middle Kingdom (12th dynasty) at 1991 BC. The New Kingdom started at 1567 or 1552 BC, depending on a choice for the first year of Ramses II of either 1290 BC or 1304 BC—one lunar cycle earlier. The following centuries still pose many chronological questions down to 664 BC, when Greek historiography took over.

Wolfgang Helck

Babylonian and Assyrian

Mesopotamian chronology, 747 to 539 BC
      The source from which the exploration of Mesopotamian chronology started is a text called Ptolemy's Canon. This king list covers a period of about 1,000 years, beginning with the kings of Babylon (Babylonia) after the accession of Nabonassar in 747 BC. The text itself belongs to the period of the Roman Empire and was written by a Greek astronomer resident in Egypt. Proof of the fundamental correctness of Ptolemy's Canon has come from the ancient cuneiform tablets excavated in Mesopotamia (art and architecture, Mesopotamian), including some that refer to astronomical events, chiefly eclipses of the Moon. Thus, by the time excavations began, a fairly detailed picture of Babylonian chronology was already available for the period after 747 BC. Ptolemy's Canon covers the Persian and Seleucid periods of Mesopotamian history, but this section will deal only with the period up to the Persian conquest (539 BC).

      The chief problem in the early years of Assyriology was to reconstruct a sequence for Assyria for the period after 747 BC. This was done chiefly by means of limmu, or eponym, lists, several of which were found by early excavators. These texts are lists of officials who held the office of limmu for one year only and whom historians also call by the Greek name of eponym. Annals of the Assyrian kings were being found at the same time as eponym lists, and a number of these annals, or the campaigns mentioned in them, were dated by eponyms who figured in the eponym lists. Moreover, some of the Assyrian kings in the annals were also kings of Babylonia and as such were included in Ptolemy's Canon.

      Good progress was therefore being made when, soon after 1880, two chronological texts of outstanding importance were discovered. One of these, now known as King List A, is damaged in parts, but the end of it, which is well preserved, coincides with the first part of Ptolemy's Canon down to 626 BC. The other text, The Babylonian Chronicle, also coincides with the beginning of the canon, though it breaks off earlier than King List A. With the publication of these texts, the first phase in the reconstruction of Mesopotamian chronology was over. For the period after 747 BC, there remained only one serious lacuna—i.e., the lack of the eponym sequence for the last 40 years or so of Assyrian history. This had not been established by the early 1970s.

Assyrian chronology before 747 BC
      German excavations at Ashur, ancient capital of Assyria, yielded further eponym lists. By World War I the full sequence of eponyms was known from about 900 to 650 BC. A further fragmentary list carried the record back to about 1100 BC, and on this basis Assyrian chronology was reconstructed, with little error, back to the first full regnal year of Tiglath-pileser I in 1115 BC. Without another eponym list, a king list was needed for substantial further progress. King lists found at Ashur proved disappointing. Those fairly well preserved did not include figures for the reigns, and those with figures were very badly damaged.

      In 1933, however, an expedition from the University of Chicago discovered at Khorsabad, site of ancient Dur Sharrukin, an Assyrian king list going back to about 1700 BC. But for the period before 1700 BC the list is damaged and otherwise deficient, and Assyrian chronology prior to this date is still far from clear.

      Before 747 BC it was the custom of the Assyrian kings to hold eponym office in their first or second regnal year. Thus, in an eponym list, the number of names between the names of two successive kings usually equals the number of years in the reign of the first of the two kings. It would have been easy to compile a king list from an eponym list, and there is evidence that this Assyrian king list was compiled from an eponym list probably in the middle of the 11th century BC. As an eponym list is a reliable chronological source, since omission of a name entails an error of only one year, the king list, if based on one, will have preserved much of the structure of older eponym lists now lost. (Except for one fragment, no known eponym list goes back further than the beginning of the 11th century BC.)

Babylonian chronology before 747 BC
      In the long interval between the fall of the last Sumerian dynasty c. 2000 BC and 747 BC there are two substantial gaps in chronology, each about two centuries long. The earlier gap is in the 2nd millennium, from approximately 1600–1400 BC, the later gap in the 1st millennium, from c. 943–747 BC. During these gaps the names of most of the kings are known, as well as the order, but usually not the length of their reigns.

      A means of checking the reliability of the Babylonian king list is provided by the chronicles, annals, and other historical texts that show that a given Assyrian king was contemporaneous with a given Babylonian king. There are no fewer than 15 such synchronisms between 1350 and 1050 BC, and, when the Babylonian and Assyrian king lists are compared, they all fit in easily. Only one of them, however, provides a close approximate date in Babylonian chronology. This synchronism shows that the two-year reign of the Assyrian king Ashared-apil-Ekur (c. 1076–c. 1075 BC) is entirely comprised within the 13-year reign of the Babylonian king Marduk-shapik-zeri. The Assyrian's dates are probably correct to within one year. Thus, if Marduk-shapik-zeri is dated so that equal proportions of his reign fall before and after that of Ashared-apil-Ekur, a date is obtained for the former that should not be in error more than six years. This synchronism constitutes a key to the structure of Babylonian chronology by providing the base date for all the reigns in the interval c. 1400–943 BC for which the Babylonian king list gives figures. All the dates thus obtained are subject to the six-year margin of error.

      These synchronisms between Assyrian and Babylonian kings continue throughout the period that corresponds to the second gap in the Babylonian king list—from c. 943–747 BC. Since the Assyrian chronology in that period is firmly established, these synchronisms provide a useful framework for the structure of Babylonian chronology in that period.

      The gap in the 2nd millennium BC, however, is not as easy to fill. The fact that the magnitude of the gap is uncertain constitutes the main problem in the chronology of the 2nd millennium BC and also affects the chronology of the preceding Sumerian (Sumer) period. The problem is not yet solved. Observations of the planet Venus made during the reign of King Ammisaduqa, less than 50 years before the end of the 1st dynasty of Babylon, permit only certain possible dates for his reign. Translated into dates for the end of the dynasty, the three most likely possibilities are 1651, 1595, and 1587 BC. The evidence is not yet conclusive and leaves uncertain what choice should be made among the three. The chronology adopted here is based on the second of these dates for the end of the 1st Babylonian dynasty—i.e., 1595 BC.

      Prior to this gap in the 2nd millennium BC, there is a period of five centuries with a well-established chronological structure. All the kings in the major city-states are known, as well as their sequence and the length of their reigns. Which sets of dates should be assigned to these reigns, however, depends on the date adopted for the 1st dynasty of Babylon. This period of five centuries extends from the beginning of the 3rd dynasty of Ur to the end of the 1st dynasty of Babylon—i.e., on the chronology adopted here, 2113–1595 BC. During this period the Babylonians dated their history not by regnal years but by the names of the years. Each year had an individual name, usually from an important event that had taken place in the preceding year. The lists of these names, called year lists or date lists, constitute as reliable a source in Babylonian chronology as the eponym lists do in Assyrian chronology. One of the events which almost invariably gave a name to the following year was the accession of a new king. Hence, the first full regnal year of a king was called “the year (after) NN became king.” In Assyria the number of personal names in an eponym list between the names of two successive kings normally equalled the number of years in the reign of the first king, and, similarly, in Babylonia the number of year names between two year names of the above kind nearly always equalled the number of years in the reign of the first king. Just as in Assyria, the eponym lists are almost certainly the source of the king lists, so in Babylonia the king lists are based on the year lists. Several of these king lists, compiled at a time when the year lists were still in use, survive. One gives the 3rd dynasty of Ur and the dynasty of Isin; another gives the dynasty of Larsa. Both may be school texts.

      The 3rd dynasty of Ur and the dynasty of Isin also figure in the Sumerian king list, which reaches far back into the Sumerian period. The original version probably ended before the 3rd dynasty of Ur, but later scribes brought it up to date by adding that dynasty as well as the dynasty of Isin.

Michael B. Rowton

      The era at present in vogue among the Jews, counted from the creation of the world ( anno mundi; abbreviated to AM), came into popular use about the 9th century AD. Traceable in dates recorded much earlier, this era has five styles conventionally indicated by Hebrew letters used as numerals and combined into mnemonics, which state the times of occurrence of the epochal mean conjunctions of moladim (see calendar: The Jewish calendar (calendar)) or the orders of intercalation in the 19-year cycle or both. The respective epochs of these styles fall in the years 3762–3758 BC, inclusive. By about the 12th century AD the second of the mentioned styles, that which is in use at present, superseded the other styles of the era anno mundi.

      The styles of this era arise from variations in the conventional rabbinical computation of the era of the creation. This computation, like hundreds of other calculations even more variable and no less arbitrary, is founded on synchronisms of chronological elements expressed in the terms of biblical and early postbiblical Jewish eras.

      The biblical (Bible) era anno mundi underlies the dating of events (mainly in the book of Genesis) prior to the Exodus from Egypt. This period of biblical chronology abounds in intractable problems caused by discrepancies between the Jewish and Samaritan Hebrew texts and the Greek version known as the Septuagint, by apparent inconsistencies in some of the synchronisms, and by uncertainties about the method of reckoning.

      During the period from the Exodus to the founding of Solomon's Temple, the only continuous biblical era (chiefly in the remaining books of the Pentateuch) is the era of the Exodus. With regard to a crucial date expressed in this era—“In the four hundred and eightieth year after the people of Israel came out of the land of Egypt, in the fourth year of Solomon's reign over Israel, in the month of Ziv, which is the second month, he began to build the house of the Lord” (I Kings 6:1)—there is again a discrepancy between the Hebrew text and the Septuagint. Other problems to be met with during this period are due to the obscurity of chronological data in the book of Judges and in I and II Samuel.

      During the following period, the Bible uses the eras of the regnal years of monarchs (the kings of Judah, Israel, and Babylon) and of the Babylonian Exile. This period of biblical chronology likewise poses numerous problems, also the result of apparent inconsistencies of the synchronisms—e.g., in the period from the accession of Rehoboam of Judah and of Jeroboam of Israel to the fall of Samaria “in the sixth year of Hezekiah [of Judah], which was the ninth year of Hoshea king of Israel” (II Kings 18:10) the reigns of the southern kingdom exceed those of the northern kingdom by 25 years.

      The biblical data might be easier to harmonize if the occurrence of coregencies were assumed. Yet, as an ever-variable factor, these evidently would not lead to the determination of the true chronology of this period. Scholars therefore seek additional information from sources outside the Bible—e.g., inscriptions on Assyrian monuments, which are dated by the so-called eponym lists. Substantial use also has been made of the data in the king list known as Ptolemy's Canon (compiled in the 2nd Christian century) commencing in 747 BC with the reigns of the Babylonian kings (see above Babylonian and Assyrian (chronology)). Scholars differ widely, however, in their interpretation of details, and numerous chronological problems remain unsolved. Only a few dates in this period can be fixed with any degree of confidence.

      After the Babylonian Exile, as evidenced by the data in the Bible and the Aswān papyri, the Jews reckoned by the years of the Persian kings. The chronological problems of this period are caused by the apparent disorder in the sequence of events related in the biblical books of Ezra and Nehemiah and by the difficulty of identifying some of the Persian kings in question. For example, the King Artaxerxes of these books may stand for Artaxerxes I Longimanus (465–425 BC), for Artaxerxes II Mnemon (404–359/358 BC), or in the case of Ezra at any rate, for Artaxerxes III Ochus (359/358–338/337 BC).

      From the Grecian period onward, Jews used the Seleucid (Seleucid kingdom) era (especially in dating deeds; hence its name Minyan Sheṭarot, or “Era of Contracts”). In vogue in the East until the 16th century, this was the only popular Jewish era of antiquity to survive. The others soon became extinct. These included, among others, national eras dating (1) from the accession of the Hasmonean princes (e.g., Simon the Hasmonean in 143/142 BC) and (2) from the anti-Roman risings (“era of the Redemption of Zion”) in the years 66 and 131 of the Common (Christian) Era. Dates have also been reckoned from the destruction of the Second Temple (le-ḥurban ha-Bayit). The various styles of the latter, as also of the Seleucid era and of the era anno mundi, have often led to erroneous conversions of dates. The respective general styles of these eras correlate as follows: 3830 AM = year 381 of the Seleucid era = year 1 of the Era of the Destruction = year 69/70 of the Common (Christian) Era.

      The earliest Jewish chronologies have not survived. Of the work of the Alexandrian Jew Demetrius (3rd century BC), which deduced Jewish historical dates from the Scriptures, only a few fragments are extant. In the Book of Jubilees (Jubilees, Book of), events from the creation to the Exodus are dated in jubilee and sabbatical cycles of 49 and 7 years, respectively. Scholars differ as to the date and origin of this book. The era of the creation therein is unlikely to have been other than hypothetical.

      The earliest and most important of all Jewish chronologies extant is the Seder ʿolam rabbaʾ (“Order of the World”), transmitted, according to Talmudic tradition, by Rabbi Yosi ben Halafta in the 2nd century AD. The author was possibly the first to use the rabbinic Era of the Creation. His chronology extends from the creation to Bar Kokhba in the days of the Roman emperor Hadrian (2nd century AD); but the period from Nehemiah to Bar Kokhba (i.e., from Artaxerxes I or II to Hadrian) is compressed into one single chapter. The Persian phase shrinks to a mere 54 years. The smaller work Seder ʿOlam zuṭaʾ completes the Rabbaʾ. It aims to show the Babylonian exilarchs as lineal descendants of David.

      Megillat taʿanit (“Scroll of Fasting”), although recording only the days and months of the year without the dates of the years, is nevertheless an important source for Jewish chronology. It lists events on 35 days of the year that have been identified with events in five chronological periods: (1) pre-Hasmonean, (2) Hasmonean, (3) Roman (up to AD 65), (4) the war against Rome (65–66), and (5) miscellaneous. The authors, or rather the last revisers, are identified with Zealots guided by Hananiah ben Hezekiah ben Gurion and his son Eliezer.

E.J. Wiesenberg

      As the cities of ancient Greece (ancient Greek civilization) progressed to their classical maturity, the need arose among them for a chronological system on a universally understood basis. In the Archaic period, genealogies of local monarchs or aristocrats sufficed for the historical tradition of a given area, and events were associated with the lifetimes of well-known ancestors or “heroes.” The synoikismos (founding of the united city) of Athens took place “in the time of Theseus”; the Spartan ephorate (chief magistracy) was established “in the reign of King Theopompus.” When the city-states adopted annual magistracies, the years were designated by the eponymous officials—“in the archonship of Glaucippus” or “when Pleistolas was ephor.” This was the local usage throughout classical and Hellenistic Greece, the title of the magistrate varying in different cities. Sometimes tenure of a priesthood provided the chronological basis, as at Argos, where years were dated as the nth of the (named) priestess of Hera. The correctness of the series was a matter first of memory and later of careful record. The list of annual archons (archon) at Athens was known back to 683 BC (in modern terms). Lists of dynasties also amounted to recorded folk memory, and in all genealogical reckoning there is a point, for modern critics, at which acceptable tradition shades into myth. Corruption of the records was introduced through error or political design, and traditions often conflicted.

      Chronology became subject to systematization when cities felt a national need for accurate clarification of their past. In literature the growth of historiography initiated a search for a method of dating that could be universally applied and acknowledged. In the 5th and 4th centuries, local historians used local magistracies as their framework; research was devoted to rationalization of conflicting traditions and production of definitive lists. Charon of Lampsacus, perhaps in the early 5th century, compiled a record of Spartan magistrates; Hellanicus of Lesbos, author of the earliest history of Athens, wrote on the priestesses of Argos. Lists of victors in the great Olympic games were valid for all Greece, pointing the way to the widely accepted reckoning by Olympiads. The Athenian Philochorus was the latest (early 3rd century BC) of compilers of Olympionikai.

      The 5th-century historian Herodotus relied for his chronology principally upon the reckoning by generations used by his informants, conventionally accepted as showing three generations to a century. In some cases a 40-year, or other, reckoning was used, and varying traditions sometimes produced difficulty of synchronism. Thucydides, writing “contemporary” history, recognized the chronological problems involved. He dated the beginning of the Peloponnesian War by the Athenian, Spartan, and Argive systems and thenceforward marked the passage of time by seasonal indications. Synchronization was not helped by the fact that the official year began at different times in different cities. In later historical writing the impossibility of accurately coordinating the Athenian and Roman years resulted in serious chronological difficulties.

      The system of dating by Athenian (Greek calendar) archons came to be recognized outside Attica as of wider value, but, in the Hellenistic (Hellenistic Age) period, Alexandrian scholarship, represented especially by Eratosthenes of Cyrene, the “father of chronology,” was instrumental in promoting the use of the Olympiads as an acceptable system, reckoning a four-year period from each celebration of the Olympic Games. Timaeus of Tauromenium (c. 356–260 BC) was the first historian to employ it, but it was little used outside historical writing. Aristotle had been concerned to identify the generation of the first Olympiad, accepted as 776 BC on modern reckoning. For convenience, the beginning of the Olympic year was equated with the summer solstice, when the Athenian year also began. This makes it generally necessary for a Greek year to receive a double date in modern terms (e.g., the death of the philosopher Epicurus in 271/270 BC). Eratosthenes' system produced tables of dates, from which, for example, the fall of Troy could be dated to 1184/83 BC. The “Parian Marble (Parian Chronicle)” of 264/263 BC is an inscribed record of events from the time of Cecrops, first king of Athens, reckoning years between the date of the inscription, fixed by the Athenian archon, and each event concerned. Some cities inscribed lists of their eponymous magistrates; the Athenians were the first to do so c. 425 BC. A list from Sicilian Tauromenium originally spanned some 300 years. The regnal years of the Hellenistic monarchs or the count from a fixed event (a city foundation or refoundation) also provided acceptable chronological reckoning often useful for more than contemporary or local purposes.

      The use of these chronological possibilities is best seen in historians using the annalistic method, of whom Diodorus Siculus is most notable. In the Christian period, Eusebius (Eusebius of Caesarea), followed by St. Jerome, began the work of reconciling all these indications to the Judaic tradition and produced the foundation of chronology in terms of the Julian calendar upon which modern historians have constructed their framework.

      For modern scholarship the problem, in E.J. Bickerman's words, is “how we know Caesar was assassinated on March 15, 44 BC.” Before 480 BC, no date can be precise in terms of the Julian calendar (Roman republican calendar) unless confirmed by astronomical phenomena. Archaic chronology relies upon the typology of Corinthian pottery in relation to the foundation dates for Greek colonies in Sicily implicit in Thucydides, book vi. Julian dates given for this period (e.g., for the tyranny of Peisistratus in Athens) stem from a complex combination of ancient chronographic tradition with modern archaeology, acceptable only with appropriate reserve. Literary tradition gives the succession of Athenian archons from 480 to 294 BC. The regnal, era, and Olympiad years also provide dates within a 12-month period. Closer dating is seldom possible unless the sources give precise information in calendric terms, as occasionally in literature and regularly in Athenian and Egyptian public documents. Even these are not translatable into Julian months and days unless coordinated with knowledge of contemporary solar or lunar phenomena and of possible official interference with the calendar.

A. Geoffrey Woodhead

      The establishment of a sound chronology for Roman history, as for Greek, depends on the assessment of the evidence available, which falls into two categories—literary and archaeological.

Literary evidence
      Although by the late 3rd century BC the Greek mathematician Eratosthenes was working on the systematization of chronography and a series of learned historians had used the documentary method—e.g., for Roman history, Timaeus of Tauromenium, to whom are probably due many of the synchronizations of Roman history with the Greek Olympiads—unfortunately this tradition of documentation and concern for chronology did not immediately pass over into Roman historiography. According to Cicero (Cicero, Marcus Tullius) in De oratore, the earliest Roman historians did no more than “compile yearbooks”—for example, Fabius Pictor (Fabius Pictor, Quintus) in the late 3rd century BC, Lucius Calpurnius Piso in the 2nd, and the so-called Sullan annalists in the 1st. Of these authors it is possible to judge only at second hand, and only those of the 1st century were much used directly by the historians whose work survives in any quantity, notably Livy, Dionysius of Halicarnassus, and Diodorus Siculus. In these authors, as in other 1st-century historians such as Sallust, there is little concept of documentation or research other than comparison of literary sources; for none was chronology a direct concern, and in many cases dramatic effectiveness took priority over fidelity to truth. Apart from the Greek Polybius, who treated the rise of Roman power in the Mediterranean from 264 to 146 BC, it was not until Cicero's time that the conception of historical scholarship developed in Rome. Cicero's friend Atticus (Atticus, Titus Pomponius) not only was concerned to draw up a chronological table in his Liber annalis but had undertaken research to that end, and the great scholar Marcus Terentius Varro (Varro, Marcus Terentius) and a little later the learned Marcus Verrius Flaccus (Verrius Flaccus, Marcus) produced a vast body of erudite work, nearly all lost. To this source must probably be ascribed the fasti Capitolini, a list of magistrates from the earliest republic to the contemporary period, set up near the regia (the office and archive of the pontifices, or high priests), perhaps on the adjacent Arch of Augustus, at the end of the 1st century BC. This work, since it is based on inscriptions, is sometimes given precedence over literary evidence, but, since it is a compilation, it is still subject to serious error.

Sources used by Roman (Roman law) historians
      The traditionally early extant bodies of law, such as the Twelve Tables (Twelve Tables, Law of the) from the early republic, were of little chronological value, and juristic commentarii were liable to mislead through their zeal for precedent, while Cicero, in spite of Polybius' claim to have inspected early treaties preserved in the Capitol definitely states that there were no public records of early laws. A source frequently referred to is the Annales maximi, a collection made about 130 BC of the annual notices displayed on a white board by the pontifices and containing notes of food prices, eclipses, etc. Dionysius of Halicarnassus implied that they gave a date for the foundation of the city but was reluctant to accept their authority; and one of the eclipses is referred to by Cicero as being mentioned also by Ennius, but unfortunately the number of the year “from the foundation of the city” is corrupt in the text. Although it is possible to calculate the dates of eclipses astronomically in terms of the modern era, it is difficult to link these to Roman chronology because of the uncertainty of the figures and because of the confused state of the Roman calendar before the Julian reform (see calendar: The early Roman calendar (calendar)). Another difficulty is that the early records may have been burned in 390 BC when Celtic tribes sacked the city; also they would probably have been largely unintelligible if authentic.

      Livy quoted the 1st-century annalist Gaius Licinius Macer as having found in the temple of Juno Moneta “linen rolls” giving lists of magistrates; but he also said that Macer and Quintus Aelius Tubero both cited the rolls for the consuls of 434 but gave different names. In any case, it is unlikely that the list could have been older than the temple, which dates from 344 BC. It is clear that the chief sources for the lists were the pedigrees of prominent Roman families, such as the Claudii Marcelli, Fabii, and Aemilii, drawn up by Atticus; but Cicero and Livy agree that tendentious falsifications had in many cases corrupted the records, and other suspicious facts are the appearance of obviously later or invented cognomina, or third names, and of plebeian gentile names for the earliest period, when only patricians bore them. Many scholars, however, accept the general authenticity of the lists—one reason being the appearance in them of extinct patrician families—but prefer Livy's version to that of the Capitoline lists, which show signs of late revision, often give names in incorrect order, and contain other anomalies.

      The question, therefore, remains whether Roman chronography was dependent on the lists of magistrates or whether these were adapted to fit other known datings. The apparent advantages of the existence of a terminal date, the “foundation of the city,” is illusory for Roman chronology, since it depended on back reckoning and was not agreed even in antiquity. Various ancient scholars each assumed a different date. Each computed his date by adding a different number of years of kingly rule from the foundation of the city to his estimate of the date of the foundation of the republic. This, in turn, was presumably computed by counting back over the yearly lists of magistrates. There may have been traditions about the intervals between certain events in early Roman history, but the frequently accepted reckoning of 244 years of kingly rule seems to be a calculation based only on the conventional 35-year generation for the rule of the seven legendary kings. Polybius claimed that the dating of the first republican consulship to 508/507 BC could be substantiated by an extant copy of a contemporary treaty. Combined with the traditional kingly period, this would give a foundation date of 751–750, reckoned inclusively, and 752–751, exclusively (Cato's date). The chronological scheme worked out by Varro added two years of nonconsular rule, thus the foundation of Rome was put in 754/753 and the beginning of the republic in 510/509. Varro's dates became standard for later Romans and are sometimes also used by modern scholars in a purely conventional sense. But it remains uncertain whether the dating depended on the magistrate lists or whether these were “doctored” to synchronize with given dates or intervals, whether these were traditional or calculated in some other way. Anomalies such as Livy's five-year anarchy 15 years after the Gallic invasion, Diodorus' repetition of magistrates' names, and the “dictator years” in the lists are perhaps attempts to synchronize the various pedigrees.

Contribution of archaeology
      Archaeology can provide many dates useful to the detailed study of Roman history, especially from coins and inscriptions, but, for the general scheme of early chronology, its value is largely negative. It shows, for example, that Rome evolved over a lengthy period and was not really “founded,” though a “foundation” date might perhaps refer to the first common celebration of the Septimontium, or festival of the seven hills; again, if that dating is dependent on the seven kings, archaeology shows that the tradition about them, though it may preserve genuine names and events, is largely legendary.

Datings after the 1st century BC
      In this better documented period, datings to consul years, or later to the years of tribunician power of the emperors, are normally intelligible, despite a few notorious cruxes, although up to the Julian reform the state of the calendar has always to be taken into account. In parts of the empire, however, different eras were used—e.g., that of the Seleucids—and from the 4th century AD dates were often calculated in terms of the years of the indiction, a 15-year cycle connected with the levying of taxes, a method that continued in use for many centuries in spite of difficulties, such as lack of synchronization among the various provinces.


Christian (Christianity)
      The Christian Era is the era now in general use throughout the world. Its epoch, or commencement, is January 1, 754 AUC (ab urbe condita—“from the foundation of the city [of Rome]”—or anno urbis conditae—“in the year of the foundation of the city”). Christ's birth was at first believed to have occurred on the December 25 immediately preceding. Years are reckoned as before or after the Nativity, those before being denoted BC (before Christ) and those after by AD (anno Domini, “in the year of the Lord”). Chronologers admit no year zero between 1 BC and AD 1. The precise date of commencing the annual cycle was widely disputed almost until modern times, December 25, January 1, March 25, and Easter day each being favoured in different parts of Europe at different periods.

      The Christian Era was invented by Dionysius Exiguus (c. AD 500–after 525), a monk of Scythian birth resident in Italy; it was a by-product of the dispute that had long vexed the churches as to the correct method of calculating Easter. Many churches, including those in close contact with Rome, followed 95-year tables evolved by Theophilus, bishop of Alexandria, and by his successor, St. Cyril; but some Western churches followed other systems, notably a 532-year cycle prepared for Pope Hilarius (461–468) by Victorius of Aquitaine. In 525 (Middle Ages), at the request of Pope St. John I, Dionysius Exiguus prepared a modified Alexandrian computation based on Victorius' cycle. He discarded the Alexandrian era of Diocletian, reckoned from AD 284, on the ground that he “did not wish to perpetuate the name of the Great Persecutor, but rather to number the years from the Incarnation of Our Lord Jesus Christ.”

      Somehow Dionysius reckoned the birth of Christ to have occurred in 753 AUC; but the Gospels state that Christ was born under Herod the Great—i.e., at the latest in 750 AUC. Dionysius' dating was questioned by the English saint Bede (Bede the Venerable, Saint) in the 8th century and rejected outright by the German monk Regino of Prüm at the end of the 9th. Nevertheless, it has continued in use to the present day, and, as a result, the Nativity is reckoned to have taken place before the start of the Christian Era.

      The new chronology was not regarded as a major discovery by its author; Dionysius' own letters are all dated by the indiction (see below). The use of the Christian Era spread through the employment of his new Easter tables. In England the Christian Era was adopted with the tables at the Synod of Whitby (Whitby, Synod of) in 664. But it was the use, above all by Bede, of the margins of the tables for preserving annalistic notices and the consequent juxtaposition of historical writing with calendrical computations that popularized the new era. Outside Italy it is first found in England (in a charter of 676) and shortly afterward in Spain and Gaul. It was not quickly adopted in royal diplomas and other solemn documents, however, and in the papal chancery it did not replace the indiction until the time of John XIII (965–972). The Christian Era did not become general in Europe until the 11th century; in most of Spain it was not adopted until the 14th and in the Greek world not until the 15th.

      Of the alternative chronologies used by Christians, the most important were: (1) the indiction, (2) the Era of Spain, and (3) the Era of the Passion. The indiction was a cycle of 15 years originally based on the interval between imperial tax assessments but during the Middle Ages always reckoned from the accession of Constantine, in 312. Years were given according to their place in the cycle of 15, the number of the indiction itself being ignored. This chronology was the most widespread in the early Middle Ages, but its use diminished rapidly in the 13th century, although public notaries continued to use it until the 16th. The Era of Spain was based on an Easter cycle that began on January 1, 716 AUC (38 BC), marking the completion of the Roman conquest of Spain. First recorded in the 5th century, it was in general use in Visigothic Spain of the 6th and 7th centuries and, after the Arab invasions, in the unconquered Christian kingdoms in the north of the Iberian Peninsula. It was abolished, in favour of the Era of the Incarnation, in Catalonia in 1180, in Aragon in 1350, in Castile in 1383, and in Portugal in 1422. The Era of the Passion, commencing 33 years after that of the Incarnation, enjoyed a short vogue, mainly in 11th-century France.


      Unlike earlier chronological systems in use before Islam (Islāmic world), Islamic chronology was instituted so soon after the event that was to be the beginning of the Muslim era that no serious problems were encountered in its application. According to the most reliable authorities, it was Umar Iʿ, the second caliph (reigned 634–644), who introduced the era used by the Muslim world. When his attention was drawn by Abū Mūsā al-Ashʿarī to the fact that his letters were not dated, ʿUmar consulted with men at Medina and then ordered that the year of the Hijrah (Hegira (Hijrah)), the Prophet's flight from Mecca to Medina, be taken as the beginning of an era for the Muslim state and community. According to the Muslim calendar, the Hijrah took place on 8 Rabīʿ I, which corresponds to September 20, 622 (AD), in the Julian calendar. But, as Muḥarram had been already accepted as the first month of the lunar year, ʿUmar ordered that (Friday) 1 Muḥarram (July 16, 622) be the beginning of the reckoning. It is generally accepted that this was done in AH 17 (anno Hegirae, “in the year of the Hijrah”).

      There are a few points in connection with this that deserve mention: first, there is no real agreement on the exact date of the Hijrah—other dates given include 2 and 12 Rabīʿ I; second, the year in which ʿUmar issued the order is a point of contention—the years 16 and 17 are sometimes given; third, some people have ascribed the use of the chronology to the Prophet himself. According to some sources, the Hijrah date was first used by Yaʿlā ibn Umayyah, Abū Bakr's governor in Yemen. This sounds somewhat plausible because Yemenis were probably used to affixing dates to their documents. There is, however, a consensus among workers in the field that 8 Rabīʿ I was the day of the Hijrah, that ʿUmar instituted the use of the date for the new era, and that this was done in AH 17. The choice of the Hijrah as the beginning of the epoch has two reasons. On the one hand, its date had been fixed; on the other, ʿUmar and his advisers must have recognized the importance of the migration—Islam had become, as a result, a religion and a state.

      Before the introduction of the new epoch, the Arabs (Arabia, history of) had been acquainted with chronologies used by their neighbours, the Seleucids and the Persians. In Yemen the practice of dating had been perfected to the extent that inscriptions show the day, the month, and the year. In Mecca the “year of the Elephant,” supposedly coinciding with the birth of the Prophet, had been in use. For the period between the migration and the institution of the new epoch, the Muslims of Medina resorted to naming the year after local events—“the year of the order of fighting” and “the year of the earthquake,” etc.

      The lunar year was adopted by the Muslims for the new chronology. In this there was hardly any innovation insofar as Arabia was concerned.

      The chronology introduced by ʿUmar was adopted throughout the Muslim world, although earlier epochs continued in use in outlying provinces. Muslim historians, annalists, and chroniclers met with difficulties when writing their books on pre-Islamic history. No practice had as yet developed for pre-Hijrah dating; therefore, when writing about the history of various lands in pre-Islamic times, authors resorted to the use of chronologies previously in existence there (e.g., Persian, Indian, Seleucid, Alexandrian). For the histories of the area under Islam, writers used only Muslim chronology, while non-Muslim authors (e.g., Bar Hebraeus) used the Seleucid and the Hijrah dates when discussing events pertaining to provinces that had been Byzantine and therefore still had fairly large groups of Christians.

      The era of the Hijrah is in official use in Saudi Arabia, Yemen, and in the Persian Gulf area. Egypt, Syria, Jordan, Morocco, Algeria, Libya, and Tunisia use both the Muslim and the Christian eras. Many Muslim countries, such as Turkey, Nigeria, and Pakistan, use the Christian Era.

      Within the general uniformity of applying the Hijrah era proper, there existed differences, some of which were the result of earlier pre-Islamic practices; others were the result of continuous contacts of Muslim countries with their European neighbours, with whom they had economic as well as political relations. An example of the former was the work of the ʿAbbāsid caliph al-Muʿtaḍid (Muʿtaḍid, al-), who brought the Nowrūz (Persian New Year's Day) back to date in keeping with the agricultural activities of the community. Maḥmūd Ghāzān (Ghāzān, Maḥmūd) introduced the Khānian era in Persia (Iran) in AH 701, which was a reversion to the regnal chronologies of antiquity. It continued in use for some generations, then the ordinary Hijrah era was reintroduced. A similar step was taken by Akbar when he established the Ilāhī era, which began on Rabīʿ II 963 (February 13, 1556), the date of his accession; the years were solar.

      Two Muslim countries, Turkey and Iran, introduced more drastic changes into their chronology because of European influences.

      In Turkey (Ottoman Empire) the Julian calendar was adopted in AH 1088 (AD 1676–77) and used solar months with Hijrah dating. The year was officially called the Ottoman fiscal year but was popularly known as the marti year, after mart (Turkish for March), which was the beginning of the year. Under Mustafa Kemal Atatürk (Atatürk, Kemal), the Gregorian calendar and the Christian Era were officially adopted in Turkey (1929). Iran also adopted a solar year; the names of the months in its calendar are Persian, and the era is still that of the Hijrah.

Nicola Abdo Ziadeh

Pre-Columbian American

      The lowland Maya (Mayan calendar) had a 365-day year formed of 18 “months.” Each month consisted of 20 days, plus five “nameless” days, which the Maya considered an extremely dangerous and unlucky period and during which activities were kept to a minimum. Leap days were not intercalated.

      Reckoning was not by those years but by tuns (360 days) and their multiples of 20: katuns (20 tuns), baktuns (400 tuns), pictuns (8,000 tuns), calabtuns (160,000 tuns), and kinchiltuns (3,200,000). In practice, the last three were seldom used. The tun comprised 18 uinals, each of 20 kins (days), but these did not coincide with the equivalent divisions of the 365-day year. The Maya normally carved or wrote these in descending order; students transcribe them in Arabic numerals—e.g., represents nine baktuns, ten katuns, six tuns, five uinals, nine kins.

      With this system, current dates were related to the start of the Maya era, which, because of the Maya system of re-entering cycles, marked both the end of 13 baktuns (written and the start of another cycle of baktuns and perhaps commemorated a re-creation of the world, the baktun about to enter being numbered 1, not 14. Because of the construction of the calendar, this start of the era happened to be day 4 Ahau falling on the eighth day of the month Cumku.

      Such reckonings are called Initial Series, or Long Counts, the former because they usually stand at the start of an inscription (see calendar: The Mayan calendar (calendar)). For example, the combination day 8 Muluc, falling on second of Zip (third month), recurs every 52 years, but the Initial Series (here 8 Muluc 2 Zip) pinpoints its position. The next occurrence, 52 years later, would be 8 Muluc 2 Zip. Each unit had its own glyph (or symbolic character), with appropriate number (normally a dot for 1 and bar for 5) attached.

      A shorter dating system was by “Period Endings”—that is, by recording the ending of the current baktun, katun, or tun. Thus, day 13 Ahau and month position 13 Muan with 13 tuns added is an abbreviation of 13 Ahau 13 Muan, a combination that will not repeat for over 900 years (949 tuns). A still shorter but less precise method was to give the day and its number ending the current katun.

      Several Maya dates were commonly linked to Initial Series or Period Endings by series of additions or subtractions—a glyph signifying count indicated forward or backward by secondary attachments.

      Dates were normally reckoned from the 4 Ahau 8 Cumku base, nearly 4,000 years before most inscriptions, but some calculations ranged far into the past and a few into the distant future. One reaches backward nearly 1,250,000 years, but the deepest probings of eternity are embodied in texts that seemingly record positions respectively 90,000,000 and 400,000,000 years ago. Although the interpretation of these last computations is disputable, the Maya certainly thought in millions of years a millennium before Europe discarded the view that the world was only some 6,000 years old.

      The Maya conceived of time as a journey through eternity in which each deified number—all time periods and their numbers were gods—carried his period on his back supported by a tump line. Each evening the procession rested. Next morning, carriers whose period was completed were replaced. For instance, if the uinal and kin numbers were 15 and 19 respectively, the new carriers would be the deified 16 and 0 (the latter because kin numbers go no higher than 19). Other period numbers would journey on until it came time to change the tun carrier. Much ritual and imagery grew out of this concept of the march of time; sculpture illustrates bearers lowering their burdens at journey's end.

      Correlation of the Maya calendar with ours depends on several factors. First, the 260-day almanac still functions in some Maya villages in the Guatemalan highlands. As there is excellent evidence it has neither gained nor lost a day since the Spanish conquest, despite strong Spanish efforts to suppress it, one may reasonably assume no break under the more favourable pre-Columbian conditions. Lunar and other data support such a view. Second, month positions in Yucatán and southern Petén at the Spanish conquest also are reliably correlated to the day with the present Western calendar. Third, the combined day and month parts of the Maya calendar are in day-for-day agreement with the present Western calendar within a 52-year span (after that given day and month positions repeat). The katun (specifically, 13 Ahau) current at the Spanish conquest is, however, known, thereby fixing any day and month position in a longer range of 260 years because a named katun repeats only after 260 tuns. Those conditions produce a correlation of the two calendars that is either correct to the day or is 260 or even 520 years wrong, since historical evidence does not specify which particular katun 13 Ahau coincided with the Spaniards' arrival. Fourth, such factors as astronomy (Maya records of heliacal risings of Venus and of many dates with moon age stated), pottery sequences, architectural changes (less reliable), and data from neighbouring areas govern choice of the applicable katun 13 Ahau. Weight of evidence led to wide acceptance of the Goodman–Martínez–Thompson correlation that equates 4 Ahau 8 Cumku, start of the Maya era, with August 10, 3114 BC, and the Classic period with AD 300 to 900. Fifth, when the carbon-14 dating technique was first applied to the problem, various difficulties attendant on the use of new techniques and failure to take into account that a tree dies year by year from its centre outward (so that a sample from the core might give a date well over a century before felling) distorted readings, producing results favourable to the correlation making Maya dates 260 years earlier. Now, with better technique and averaging of many “runs” of samples of latest growth from beams at Tikal with secure Maya dates, carbon-14 readings overwhelmingly support the Goodman–Martínez–Thompson correlation.

      The only other Middle American calendar with a known era is that of the Cakchiquel of highland Guatemala. The system was vigesimal: kih, day; uinak, 20 days; a, 400 days; and may, 8,000 days. The 400-day “year” ran concurrently with the 260-day almanac, which, in turn, synchronized with all other Maya almanacs. Like the 360-day tun of the lowlands, the 400-day a was the counting unit, for reckoning was always in multiples of the a, never by days, as in our Julian calendar. May signifies twenty, and is so named because it comprised 20 a. At the arrival of the Spaniards, reckoning was from a revolt in AD 1493. Earlier eras may be postulated, but inscribed calendrical texts are lacking in Cakchiquel territory.

      The Aztec and related peoples of central Mexico employed the cycle of 52 years, constructed, like its Maya equivalent, of concurrent 365-day years and 260-day cycles, any position of the former coinciding with a given position of the latter only at 52-year intervals. Again leap days were not used. At completion of the 52 years, known as “binding of the years,” elaborate ceremonies were held to avert destruction of the world expected on that occasion. The last occurrence before the Spanish conquest was in AD 1507. Although the last creation of the world was designated by a day name, neither that nor any other was in general use in central Mexico as the start of an era. Aztec reckoning is normally from their arrival in the Valley of Mexico, supposedly the year 1 Flint (AD 1168).

      There is much confusion in placing events in Mexican history because no system of distinguishing one 52-year cycle from another was employed except by writing every year glyph throughout the period covered, a clumsy arrangement. Each year was named for either its last day (omitting the five-day unlucky period) or for the last day of the fifth month (both choices have distinguished supporters). In either case, only four day names (House, Rabbit, Cane, and Flint), each with its accompanying numeral, could designate a year. The Spanish conqueror Hernán Cortés seized the Aztec capital in 1521, year 3 House, but some past event, also assigned to a year 3 House but unlocated in a full sequence of years, might refer to AD 1261, 1313, or 1365, etc. Month positions were rarely given in chronological statements.

Peoples of Oaxaca and the Isthmus of Tehuantepec
      Pictorial books of the Mixtec of Oaxaca record events in the lives of ruling families covering seven centuries, but, again, happenings are fixed only by the day on which each occurred and the year in which the day fell. Sequence is usually clear, but at times there is doubt as to which 52-year period is meant when parenthetical material, such as life histories of secondary characters, is inserted.

      No era is recognizable. A clouded entry concerning the descent to Earth of the Sun and Venus, perhaps assignable to AD 794, is a logical starting point, but other entries are earlier.

      Little is known of the calendar of the Zapotec, neighbours of the Mixtec. Years began on a different set of days, and glyphs differ from those of Mixtec and Aztec. Months are not recorded on monuments, which are numerous, and no chronological system has survived. Most Zapotec texts are early.

      Rare inscriptions in western Chiapas, southern Veracruz, and the Guatemalan Pacific coast resemble the abbreviated lowland Maya Initial Series used in script and on a single sculpture in that numerical bars and dots are in a vertical column with period glyphs and month signs suppressed, clearly place numeration, that is, the value of each unit was shown by its position in the column. The linguistic affiliation of their sculptors is unknown.

      All texts are either fragmentary or damaged; the two complete ones, unlike Maya Initial Series, open with days signs (and different ones at that). If, as one may reasonably assume, the series of bars and dots departed from those day signs, a fixed era is questionable. Nevertheless, some scholars postulate use of the Maya era ( 4 Ahau 8 Cumku). This little understood system may have been ancestral to the Maya Initial Series, the Maya perhaps developing a fixed era, for they alone seem to have been interested in an exact chronological system.

Sir Eric Thompson

Additional Reading
James C. MacDonald, Chronologies and Calendars (1897); Alfred E. Stamp, Methods of Chronology (1933); R.L. Poole, Studies in Chronology and History, collected and ed. by A.L. Poole (1934, reprinted 1969).On the astronomical basis of Chinese calendrical systems, see Joseph Needham, Science and Civilisation in China, vol. 3, pp. 390–408 (1959). A standard reference for conversion between Chinese and Western calendars is Mathias Tchang, Synchronismes chinois (1905).Robert Sewell and S.B. Dikshita, The Indian Calendar (1896), describes the various systems of calendars in India, with tables of concordance and a useful index; Robert Sewell, The Siddhantas and the Indian Calendar (1924), a study of the Hindu astronomical system as a basis for the traditional calendar; Swamikannu Pillai, An Indian Ephemeris, 6 vol. (1922), tables of concordance of Hindu, Muslim, and modern calendars; Jean Filliozat, “Notions de chronologie,” in Louis Renou and Jean Filliozat, Inde classique, vol. 2 (1953), a general summary and list of different eras used in India.Richard A. Parker, The Calendars of Ancient Egypt (1950), a basic work providing valid solutions to most of the problems of Egyptian chronology; “Lunar Dates of Thutmose III and Ramesses II,” J. Near Eastern Stud., 16: 39–43 (1957), an analysis of the more important lunar dates of the New Kingdom; M.B. Rowton, “Manetho's Date for Ramesses II,” J. Egyptian Archaeol., 34:57–74 (1948), and “Comparative Chronology at the Time of Dynasty XIX,” J. Near Eastern Stud., 19:15–22 (1960), two articles that deal with the date for the accession of Ramses II (1290 or 1304 BC); Erik Hornung, Untersuchungen zur Chronologie und Geschichte des Neuen Reiches (1964), the most up-to-date synthesis of the chronological problems of the New Kingdom; I.E.S. Edwards, “Absolute Dating from Egyptian Records and Comparison with Carbon-14 Dating,” Phil. Trans. R. Soc., Series A, 269:11–18 (1970), includes a complete list of all radiocarbon dates taken from Egyptian samples.The most complete general work on the chronology of Western Asia, including Mesopotamia, is P.E. van der Meer, The Chronology of Ancient Western Asia and Egypt, 2nd rev. ed. (1955); however, it should be used with caution. For the general chronology of ancient Western Asia, with special reference to Mesopotamia, see M.B. Rowton in The Cambridge Ancient History, 3rd ed., vol. 1, pp. 193–237 (1970), and the extensive literature quoted there (up to 1959). For a discussion of the gap in the 2nd millennium BC, see A. Goetze, “The Kassites and Near Eastern Chronology,” J. Cuneiform Stud., 18:97–101 (1964); and B.L. van der Waerden, Die Anfänge der Astronomie, pp. 28–49 (1966). For the chronology of the late 2nd millennium BC and the chronological gap in the 1st millennium BC, see J.A. Brinkman, A Political History of Post-Kassite Babylonia, 1158–722 B.C., pp. 37–85 (1968).B. Ratner, Seder Olam Rabba: Die grosse Weltchronik (1897), the authoritative edition, carefully annotated and with a detailed introduction, of the oldest rabbinic chronology extending from the earliest records to the first century of the current era; E. Mahler, Handbuch der jüdischen Chronologie (1916), the only comprehensive work on Jewish chronology, covering all aspects and summarizing most previous works on the subject; S. Zeitlin, Megillat Taanit As a Source for Jewish Chronology and History in the Hellenistic and Roman Periods (1922), removes all discrepancy in I and II Maccabees' and Josephus' chronological data in the Hasmonean phase of Jewish history, thus reinvesting their statements with historical significance and authority.Alan E. Samuel, Greek and Roman Chronology: Calendars and Years in Classical Antiquity (1972), a fundamental work; Henry Fynes Clinton, Fasti Hellenici, 3 vol. (1834), still useful in providing the sources for the framework of Greek chronology; W. Kubitschek, Grundriss der antiken Zeitrechnung (1928), the standard handbook but unreliable; A.E. Samuel, Ptolemaic Chronology (1962); E.J. Bickerman, Chronology of the Ancient World (1968), a summary survey to be used judiciously; W. Den Boer, Laconian Studies, pt. 1, “The Struggle for the Chronological Pattern” (1954), on ancient attempts to systematize archaic chronology; A.G. Woodhead, The Greeks in the West, pp. 69–72 (1962), on dates in the archaic period.E.J. Bickerman, Chronology of the Ancient World (1968), an excellent short manual, unfortunately marred by a number of factual errors; Agnes Kirsopp Michels, The Calendar of the Roman Republic (1967), contains much valuable information on chronology as well as the calendar—probably the best book ever written on the Roman calendar; F.K. Ginzel, Handbuch der mathematischen und technischen Chronologie das Zeitrechnungswesen der Völker, 3 vol. (1906–14), the standard work of reference on its subject.F.K. Ginzel, Handbuch der mathematischen und technischen Chronologie das Zeitrechnungswesen der Völker, 3 vol. (1906–14), still the fundamental work; Jack Finegan, Handbook of Bible Chronology (1964), the best for its subject; E.J. Bickerman, Chronology of the Ancient World (1968), very thorough and complete.Al-Biruni, The Chronology of Ancient Nations, Eng. trans. by C. Edward Sachau (1879), useful source material on the Muslim knowledge of chronology down to the 10th century AD; see especially pp. 16–82. For actual tables of Muslim chronological information and comments, the following may be consulted: E. Lacoine, Tables de concordance des dates des calendriers . . . (1891); C.L. Ideler, Handbuch der mathematischen und technischen chronologie, 2 vol. (1825–26); S. Lane-Poole, The Mohammedan Dynasties (1894); and C.E. Bosworth, The Islamic Dynasties (1967). See also articles on calendar, chronology, and “Hidjra” in the Encyclopaedia of Islam. An extensive collection of conversion tables is given in Frank Parise (ed.), The Book of Calendars (1982).S.G. Morley, “An Introduction to the study of the Maya Hieroglyphs,” Bull. U.S. Bur. Am. Ethnol., no. 57 (1915, reprinted 1968), a clear exposition of Maya chronology; J. Eric S. Thompson, Maya Chronology: The Correlation Question (1935) and Maya Hieroglyphic Writing: Introduction (1950, reprinted 1971); H.J. Spinden, The Reduction of Maya Dates (1924), a presentation of earlier correlation; L. Satterthwaite and E.K. Ralph, “New Radiocarbon Dates and the Maya Correlation Problem,” Am. Antiq., 26:165–184 (1960).

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