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In Their Study on Meton of Athens and the Rise of Greek Astronomy, A.C

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In Their Study on Meton of Athens and the Rise of Greek Astronomy, A.C THE EGYPTIAN AND ATHENIAN DATES OF METON’S OBSERVATION OF THE SUMMER SOLSTICE (–431) 1. METON’S SOLSTICE IN THE SOURCES (27 JUNE –431) AND ACCORDING TO COMPUTATION (28 JUNE –431) In their study on Meton of Athens and the rise of Greek astronomy, A.C. Bowen and B.R. Goldstein rightly note that there are «only two reports of dated astronomical observations by any Greek before Alexander the Great». The first is Thales’ ‘prediction’ of a solar eclipse; this is perhaps the eclipse of –584 (that is, 585 B.C.). The sec- ond is Meton’s observation of the summer solstice in Athens in –431 (that is, 432 B.C.)1. Of the two astronomical phemonena involved, only Meton’s solstice can be identified with certainty. Its precise date is this paper’s concern. The two most important sources for the date of Meton’s observation are the Milesian parapegma (end of the second century B.C.) and Ptolemy’s Almagest (middle of the second century A.D.). Ptolemy (Almagest III 1) dates the observation to «sunrise» (prwíav)2 or also 1 A.C. BOWEN - B.R. GOLDSTEIN, Meton of Athens and Astronomy in the Late Fifth Century B.C., in A Scientific Humanist: Studies in Memory of Abraham Sachs, Philadelphia 1988, p. 40. On Meton, see also G.J. TOOMER, Meton, in Dictionary of Sci- entific Biography IX, New York 1974, p. 337–340. I thank David Pingree for making useful comments on an advanced version of this paper. For the conclusions I alone remain responsible. This paper has been written in the margin of two historical works of larger scope: one on the evolution of ancient Egyptian calendars, Civil Calendar and Lunar Calendar in Ancient Egypt (Orientalia Lovaniensia Analecta, 77), Leuven 1997; the other, in progress, on problems of lunar time-reckoning in late period Egypt and its Mediterranean neighbors. Although Meton’s observation occurred in Athens, the dating of the observation is also relevant to the study of ancient Egypt. The Egyptian civil cal- endar features prominently in what follows, as do scholars from Alexandria. The study of Egyptian calendars can otherwise not be isolated from that of the calendars of other ancient peoples. Following a convention of astronomy and of works on its history, I refer to 585 B.C. as –584, counting a year 0. The Julian calendar has no year 0: the day that follows 31 December of 1 B.C. is 1 January of A.D.1. 2 Translation of A.C. BOWEN - B.R. GOLDSTEIN, Meton of Athens, p. 64. Alternative translations are «in the morning» (A.E. SAMUEL, Greek and Roman Chronology, München 1972, p. 47) and «at dawn» (G.J. TOOMER, Ptolemy’s Almagest, New York 1984, p. 138). 28 L. DEPUYDT «around the beginning» (perì t®n ârxßn) of Egyptian 21 Phamenoth at the end of the archonship of Apseudes. Archonships, like Athenian years, last from summer to summer. Apseudes was archon from the sum- mer of –432 to the summer of –431. Ptolemy also specifies that Meton made the observation together with Euctemon. Like Ptolemy, the Mile- sian parapegma mentions 21 Phamenoth and the archonship of Apseudes. It adds the Athenian date, 13 Skirophorion. Skirophorion is the last month of the Athenian year. Diodorus (XII 36) confirms 13 Skirophorion and Apseudes3. The principal problem to emerge from the discussion on Meton’s observation concerns a discordance. On the one hand, the sources state that the summer solstice was observed at sunrise of 21 Phamenoth or Julian 27 June –431. On the other hand, modern computation indicates that the solstice occurred at about 11:30 AM4 of 28 June –431. There is a difference of about a day between these two times. 21 Phamenoth cer- tainly lasted from the morning of 27 June –431 to the morning of 28 June –431. It ended at the latest with sunrise of 28 June. Since Ptolemy states that Meton observed the solstice in the morning, the morning of 27 June must be meant, as is generally accepted. It is remarkable, then, that the sources have the time of day, morning, roughly right while the day date is off by one. This paper is an attempt to answer two questions. First, how was the date of Meton’s summer solstice determined? Second, why is this date a little early? For the sake of simplicity, the answers to these two questions are anticipated in section 3, after the Callippic Cycle has been described in section 2. In section 4, the evidence which, I believe, supports these answers is adduced. Section 5 briefly sum- marizes past research on the problem. A conclusion follows in sec- tion 6. 3 For more details on these sources, see A.E. SAMUEL, Greek and Roman Chronology, p. 44, and G.J. TOOMER, Meton. 4 Thus J.P. BRITTON, Models and Precision: The Quality of Ptolemy’s Observations and Parameters (Sources and Studies in the History and Philosophy of Classical Science, 1), New York 1992, p. 18, rounding off to the nearest tenth of an hour. A.C. BOWEN - B.R. GOLDSTEIN, Meton of Athens, p. 65 with n. 135, using a computer program devel- oped by P.J. HUBER, propose c. 9:15 AM. The exact time of the summer solstice cannot be determined with certainty. All depends on one’s assumptions regarding the length of the solar or tropical year, that is, the time between equinoxes or solstices, and the varia- tions in this length. A difference of one second accumulates to almost an hour over two to three millennia. METON’S OBSERVATION OF THE SUMMER SOLSTICE 29 2. THE CALLIPPIC CYCLE As Geminus observes in Chapter 8 of his Introduction to the Phaenomena (of Aratus), próqesiv … ¥n to⁄v ârxaíoiv toùv mèn m±nav ãgein katà selßnjn, toùv dè êniautoùv kaq’ Ølion, «the ancients had before them the problem of reckoning the months by the moon, but the years by the sun». The problem is that no integer number of months will fit in a year. The astronomical lunar month, that is, the time from one conjunction of sun, moon, and earth to the next, is on average about 29.53059 days long; the tropical solar year, about 365.24220 days. Since, for obvious reasons, time units longer than a day have to consist of whole days, calendrical lunar months are almost always 29 or 30 days long; 29-day months are called hollow, 30-day months full. Modern calendrical solar years are always 365 or 366 days. All this means that 12 lunar months are shorter than a solar year whereas 13 months are longer. But if no integer number of lunar months fits in one year, it may in more than one year. For example, it was noted first by the Babylonians, probably some time in the eighth century B.C., that 235 lunar months are roughly as long as 19 solar years or cycles of the seasons. Indeed, 235 lunar months contain about 6939.68865 days (235 x about 29.53059); 19 solar years, about 6939.6018 days (19 x about 365.24220). On the basis of such observations, the ancients constructed cycles that encompass an integer numbers of lunar months that are together nearly as long as an integer number of solar years. In such cycles, the lunar months are grouped in units of 12 months and units of 13 months. Both units are called years. For example, the cycle of 235 months, which became the calendar of daily life in Babylon and is still used today in the Jewish religious calendar, has 12 ‘years’ of 12 lunar months and 7 ‘years’ of 13 lunar months. Because 235 lunar months are very close to an integer number of solar years, namely 19, the beginnings of lunar months return roughly to the same position in relation to such markers of the solar year as the solstices and the equinoxes after 235 lunar months. Cycles make it possible to use the moon’s revolution around the earth and the earth’s revolution around the sun jointly for the purpose of time- reckoning, even though the two movements are numerically incompati- ble. In the ancient lunar calendars of daily life, as distinct from those used by astronomers, the lengths of lunar months were probably always deter- 30 L. DEPUYDT mined by observation. Since factors such as the weather and the vicissi- tudes of human observation play a role in determining whether a month is hollow or full, 29-day months and 30-day months will alternate rather randomly in observational lunar calendars. Sequences of two, rarely three, 29-day months occur. So do sequences of two or three, even four or five, 30-day months. Such lunar calendars are not suitable for the pur- poses of astronomy. Astronomers need to be able to relate dated obser- vations to one another by counting the days that pass between them. The randomness of the alternation of 29-day and 30-day months in observa- tional lunar calendars forms an obstacle. To relate two astronomical phe- nomena separated by centuries to one another, it is necessary to know about each single intervening lunar month whether it was hollow or full. Accurate records spanning several centuries, with one century alone already containing about 1200 months, are required. In fact, Babylonian records listing exactly this information, probably from the eighth century B.C. onwards, have come to light. They are known as Diaries5. The ear- liest known fragment dates to –651. There is no evidence, however, that the Greeks ever possessed a similar tool.
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