Meton of Athens
Meton of Athens (Greek: Μέτων ὁ Ἀθηναῖος; gen.: Μέτωνος) was a Greek mathematician, astronomer, geometer, and engineer who lived in Athens in the 5th century BC. He is best known for calculations involving the eponymous 19-year Metonic cycle which he introduced in 432 BC into the lunisolar Attic calendar.
Meton was the son of Pausanias, an Athenian from the deme (local subdivision of Attica) Leuconoe. He is dated by his observation of the summer solstice on 27 June 432 b.c.1 He was still active nearly eighteen years later, for the story is told of a ruse whereby he avoided military service either for himself or for his son (the more probable version) on the Athenian expedition to Sicily that set out in 415, by pretending to be mad and setting fire to his house.2 Furthermore, he is introduced as a character in Aristophanes’ comedy The Birds, produced early in 414, and mentioned in Phrynichus’ Monotropos, produced at the same festival as The Birds.3 That is all we know about his life.
No written work by Meton survives; and we have to reconstruct what he did, and its purpose, from a few scattered references in ancient literature. Any such reconstruction involves some guesswork, and there is considerable disagreement on this subject among modern scholars. The following account seems to me to represent the evidence best.
Meton was famous in antiquity for his introduction of a nineteen-year lunisolar calendaric cycle, in ancient times usually called (“nineteenyear period”) and sometimes the “great year” or “year of Meton,” in modern times often called the “Metonic cycle.” In Meton’s time all Greek civil calendars, including the Athenian, were lunisolar. That is, the months were theoretically (although often not in practice) true lunar months, with the new moon occurring on the first of the month. Since the mean synodic month is slightly longer than 29.5 days, calendar months were normally either 30 days long (“full” months) or 29 days long (“hollow” months). The years, on the other hand, were supposed to be solar. Now twelve true lunar months make up only about 354 days. Therefore it was necessary to intercalate a thirteenth month in some years in order to keep the calendar roughly in step with the seasons (the year at Athens, as in most Greek states, began near the summer solstice). All the extant primary evidence (in the form of dated inscriptions and coins) from Athens and elsewhere suggests that at no period was a fixed rule for intercalation of a thirteenth month adopted by any Greek state. Instead, each intercalation was determined by the decision of a magistrate (probably the eponymous archon at Athens) or an official body.
In constructing his nineteen-year cycle Meton used the fact (known before his time) that nineteen solar years correspond very well, on the average, to 235 true synodic months. This means that during one nineteenyear period a thirteenth month has to be intercalated seven times. Meton must have prescribed rules for the places of those seven intercalations, In addition, we are told that his cycle contained precisely 6,940 days.4 This means that 110 of the 235 months in the cycle were hollow and the other 125 full. Thus Meton must also have prescribed rules for the sequence of full and hollow months throughout ihe cycle. Since it is probable that he derived the equation of nineteen years with 235 months from Babylonian practice (see below), it might seem plausible to assume that, like the Babylonians, he intercalated in the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth years of his cycle. There is no evidence whatever for his having adopted this or any other scheme, however, and all modern attempts to reconstruct his intercalation system are futile. The same is true for reconstructions of his sequence of full and hollow months (in this case we cannot even refer to Babylonian practice, since their nineteen-year cycle did not contain a fixed number of days: instead, the length of each month was determined by observation of the new crescent). The only other information we have on the Metonic cycle is that it used the month names of the Athenian civil calendar5 and that the first Metonic cycle began on 27 June 432 b.c., in the archonship of Apseudes at Athens—which was, according to Meton, the day of the summer solstice and the thirteenth day of Skirophorion (the twelfth month) in his calendar.
The evidence for the last statement needs examination. The chief authority is Diodorus, who says; “In the archonship of Apseudes at Athens … Meton the son of Pausanias, who has a reputation in astronomy, set out the so-called nineteen-year period, taking the beginning from the thirteenth of Skirophorion at Athens …” (XII, 36). One might assume that Meton would start his cycle from the beginning of the first month—Hekatombaion 1—and it would be possible to interpret Diodorus as meaning that the first day of Meton’s cycle (his Hekatombaion I) coincided with Skirophorion 13 of the Athenian civil calendar of that year. That this is not so is shown by a fragment of an inscription found at Miletus, probably part of a calendar, which reads; “from the summer solstice in the archonship of Apseudes on Skirophorion 13, which was Phamenoth 21 according to the Egyptians, until the [solstice] in the archonship of Polykleitos on Skirophorion 14, or Pauni 1 according to the Egyptians.”6
The equations with the Egyptian calendar plus the archon years enable us to determine these dates as 27 June 432 b.c. and 26 June 109 B.C., respectively. They are exactly seventeen nineteen-year periods apart; and one can deduce, first, that the second date is not an observed solstice but one computed from the first by means of a fixed calendrical scheme and, second, that the Skirophorion dates must have been taken not from the Athenian civil calendar but from an artificial astronomical calendar. The first is the starting date of Meton’s first cycle. The second must be the date in the current Callippic cycle, for the interval corresponds to 323 years of 3651/4 days.7 The transition from Metonic to Callippic reckoning may also explain the shift of one day (from 13 to 14 Skirophorion) of the date of the solstice after an integer number of nineteen-year cycles. It may seem strange that Meton began his cycle elsewhere than at the beginning of a year (in contrast, when Callippus introduced his “improved” cycle, he began it at a solstice that coincided roughly with a new moon and thus was able to begin the year there too). But one can begin a cycle at an arbitrary point within it, and we know that Meton himself had observed the solstice of 432. No doubt he wished to begin at a point well-established astronomically.
Enormous confusion has arisen over the Metonic cycle because many scholars since Scaliger have assumed that Meton’s purpose was to reform the Athenian civil calendar and that he succeeded (at least in part). Not only is there no evidence for the latter belief, but the former too is not supported by our texts. Instead, we may state confidently that his purpose in publishing the “nineteen-year cycle” was to provide a fixed calendrical scheme for recording astronomical data. Thus, if one was told that event A occurred on day 6 of the month Metageitnion in the second year of the cycle and event B on day 21 of the month Anthesterion of the fourth year, it was possible to determine the exact interval between the two—this was, in general, not possible between dates in the Athenian or any other Greek civil calendar. We can see from references in Ptolemy’s Almagest that the cycle, as reformed by Callippus, was used for astronomical dating as late as Hipparchus (128 b.c.). Ptolemy preferred to use the Egyptian calendar, with a fixed year length of 365 days, for the same purpose.
It is likely that what Meton published was in fact an astronomical calendar for nineteen years. If this assumption is correct, the calendar listed for each year the dates of the solstices and equinoxes, of the morning and evening risings and settings of certain prominent stars and constellations (that is, their first and last appearances just before dawn and just after sunset), and weather predictions associated with the various astronomical phenomena. All of this, except the equinoxes, was traditional Greek “astronomy,”8 but Meton’s observations of the intervals between phenomena may have been more accurate than his predecessors’. There exist a number of astronomical calendars of the type described, both in manuscript and (fragmentarily) on stone,9 but all cover just one year. In these the months are either “zodiacal” (the time taken by the sun to traverse one sign of the zodiac), Egyptian, or Julian.10 All three types are impossible or unlikely for Meton’s time; and it is preferable to assume that he used synodic months and hence, necessarily, a nineteen-year calendar.11 It is certain, at least, that Meton did publish an astronomical calendar. It is one of the authorities listed by Ptolemy,12 and it is referred to by others.
Meton’s chief claim to fame, apart from his cycle, is that he is the first Greek of whom we can say with certainty that he undertook serious astronomical observations. His solstice observations are the earliest that Ptolemy thought worth attention, even if inaccurate. (The only recorded observation is more than a day too early.) We are told that Meton erected an instrument for observing solstices (a ἡλίоτρόπίоν) on the hill of the Pnyx in Athens.13 The form of this instrument is entirely conjectural: but any upright gnomon would serve the purpose, provided one could observe its longest and shortest midday shadow.
It is commonly supposed that Meton also observed equinoxes, since he assumed unequal lengths for the seasons. One source quotes figures for the lengths of the seasons, beginning with the summer solstice, of ninety, ninety, and ninety-two days (and hence, by inference, ninety-three for the fourth).14 But these figures (which are very inaccurate) can equally well be explained by a crude schematic distribution of the times spent by the sun in each of the twelve zodiacal signs into intervals of thirty and thirty-one days.15 This would imply that the equinoxes were not observed. The first Greek of whom we can say with certainty that he determined the lengths of the seasons by observation, and drew the conclusion that the sun has an anomalistic motion, is Callippus (ca. 330 b.c.).
The question of Babylonian influence on Meton is relevant. A standard nineteen-year intercalation cycle was in regular use in the civil calendar of Babylonia from 367 b.c. and seems to have been known there, although not uniformly used, from the early fifth century. We are informed by an early source that Meton derived his nineteen-year cycle from a certain Phaeinos who was a resident alien at Athens.16 It is possible that Phaeinos was an Asian Greek who acted as transmitter of Babylonian astronomical knowledge. A further connection of Meton with Babylonian astronomy is that he put the equinoxes and solstices at 8° of their respective zodiacal signs.17 This is characteristic of “System B” in Babylonian astronomical texts.
Meton is also called a “geometer” in some ancient sources. In Aristophanes’ The Birds he comes on stage equipped with the geometer’s traditional rule and compasses and proceeds to “square the circle” in an absurd manner. It would be hazardous to draw any inference about the real Meton’s mathematical interests from this burlesque. Similarly, we cannot conclude that he engaged in town planning or hydrography from the representations of him in contemporary comedies drawing plans for Cloudcuckooland or drilling wells. He remains an obscure figure; but he and his associate Euctemon were probably of importance in giving an initial impetus to astronomical observation, however crude, in Greece. His cycle, although later superseded by other reference systems, provided the first adequate framework for recording astronomical data.
1. Reported by Ptolemy, Almagest, III, 1.
2. Differing versions in Plutarch, “Nicias,” 13.5; Plutarch, “Alcibiades,” 17.4–5; Aelian, Varia Historia, 10.7.
3. Aristophanes, Birds, 992–1020, with the scholion on 997.
4. Ptolemy, Almagest, III, 1; Geminus, VIII, 51; Censorinus, 18.8.
5. The best evidence for this is that Callippus used them in his cycle, which was a slight modification of Meton’s. See, for instance, Ptolemy, Almagest, VII, 3 (Heiberg, ed., II, 28).
6. Sitzungsberichte der K. Preussischen Akademie der Wissenschaften zu Berlin (1904), no. 1, 96.
7. The Callippic cycle differed from the Metonic in assuming a year length of 3651/4 days. Hence to 76 years it assigned 27,759 days, a day less than the corresponding 4 Metonic cycles (Geminus, VIII, 59–60). Otherwise the Callippic cycle of 76 years was, presumably, identical to 4 consecutive Metonic cycles. The first Callippic cycle began at the summer solstice (probably 28 June) 330 b.c.
8. Found, for example, in Hesiod’s Works and Days, which is some 300 years earlier.
9. Such a calendar, when inscribed on permanent material, was often provided with a hole at each entry to receive a peg to mark the current date. Hence it was called (“that which has a peg beside it”).
10. Examples of the first are Geminus’ calendar (Geminus, Elementa astronomiae, Manitius, ed., 210–232) and the Miletus parapegma (Sitzungsberichte der K. Preussischen Akademie der Wissenschaften zu Berlin , no. 1, 102–111); of the second, Ptolemy’s Phaseis (Calendaria Graeca, Wachsmuth, ed., 211–274); and of the third, the calendar of Clodius Tuscus (Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Phil-hist. Kl., no. 3).
11. A nineteen-year calendar is suggested by the scholion on Aratus, 753 (Maass, ed., Commentariorum in Aratum reliquiae, 478), and by Diodorus, XII, 36.3.
12. Phaseis, in Calendaria Graeca, Wachsmuth, ed., 275.
13. Philochorus, fr. 122, Jacoby, ed.
14. Eudoxi Ars astronomica, Blass, ed., 25. The figures quoted are attributed to Euctemon, but the two are so often coupled in the context of astronomical observations (as by Ptolemy in the passages referred to in notes 1 and 10) that it is plausible to associate Meton with these season lengths too. This is confirmed by Simplicius, In De caelo, Heiberg, ed., 497.
15. See Albert Rehm, “Das Parapegma des Euktemon” (“Griechische Kalender,” F. Boll, ed., III), in Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Phil.-hist. Kl. (1913), no, 3, 9.
16. Theophrastus, De signis, 4.
17. Columella, De re rustica, IX, 14.12.
The principal ancient passages concerning Meton are Ptolemy, Almagest, III, 1 (Claudii Ptolemaei Opera quae exstant omnia, I, Syntaxis mathematica, J. L. Heiberg, ed., pt. 1 [Leipzig, 1898], 205–207); Diodorus, Bibliotheca historica, XII, 36 (F. Vogel, ed. [Leipzig, 1890], II, 395); Geminus, Elementa astronomiae, VIII, 50–56 (K. Manitius, ed. [Leipzig, 1898], 120–122); Censorinus, De die natali, 18.8 (Otto Jahn, ed. [Berlin, 1845], 54); Aristophanes, The Birds, II. 992–1020, with the scholion on 1. 997 (printed as fr. 122 of Philochorus by F. Jacoby, Die Fragmente der Griechischen Historiker, III B [Leiden, 1950], 135); Theophrastus, De signis, 4 (Theophrasti Opera, F. Wimmer, ed. [Leipzig, 1862], III, 116); the scholion on Aratus, 752–753, in Commentariorum in Aratum reliquiae E. Maass, ed. (Berlin, 1898), 478; Ptolemy, Phaseis, 93D, in Calendaria Graeca, C. Wachsmuth, ed. (with Ioannes Lydus, Liber de Ostentis) (Leipzig, 1897), 275 (see also index, 360, under Μέτων); Columella, De re rustica, IX, 14.12 (ibid., 303); Eudoxi Ars astronomica, F. Blass, ed. (Kiel 1887), 25; Simplicius, In Aristotelis De caelo commentaria, J. L. Heiberg, ed. (Commentaria in Aristotelem Graeca, VII) (Berlin, 1894), 497; Plutarch, “Life of Nicias,” 13.5, and “Life of Alcibiades,” 17.4–5 (Plutarch’s Lives, B. Perrin, ed. [Cambridge, Mass., 1916], III, 254–256, and IV, 44–46); and Aelian, Varia Historia, 10.7 and 13.12 (R. Hercher, ed. [Leipzig, 1866], 109, 149).
There is no satisfactory modern account of Meton. Most are vitiated by the belief that the “Metonic cycle” is somehow reflected in the Athenian civil calendar. For a refutation of this belief and a history of scholarly discussion of the question, see W. Kendrick Pritchett, ’The Choiseul Marble,” in University of California Publications. Classical Studies, 5 (1970), 39–97. The fragments of the Miletus parapegma(ta) were published by H. Diels and A. Rehm, “Parapegmenfragmente aus Milet,” in Sitzungsberichte der K. Preussischen Akademie der Wissenschaften zu Berlin (1904), no. 1, 92–111; and by A. Rehm, “Weiteres den milesischen Parapegmen,” ibid., 752–759. For references to other partially preserved ancient parapegmata, see A. Rehm, “Parapegma,” in Pauly-Wissowa, Realencyclopädie der classischen Altertumswissenschaft, 1st ser., XVIII, pt. 2, cols. 1299–1302; for eds. of the Italian ones, with excellent photographs, see Inscriptiones Italiae, XIII, pt. 2, A. Degrassi, ed. (Rome, 1963), 299–313.
Many of the ancient astronomical calendars preserved in MS were collected by C. Wachsmuth in his Calendaria Graeca (see above). See also the series “Griechische Kalender,” F. Boll, ed., in Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Phil.-hist. Kl. (1910), no. 16, (1911), no. 1, (1913), no. 3, (1914), no, 3 and (1920), no, 15. On the nineteen-year cycle in Babylonia, see R. A. Parker and W. H. Dubberstein, Babylonian Chronology 625 b.c.-a.d. 75, Brown University Studies, XIX (Providence, 1956), esp. 1–6. On System B in Babylonian astronomy see O. Neugebauer, Astronomical Cuneiform Texts, 1 (London, 1955), 69–85 (for the vernal point in Aries 8° see 72). A well-informed conjecture about the site of Meton’s instrument for observing solstices on the Pnyx at Athens was adsanced by K. Kouroniotes and Homer A. Thompson, “The Pnyx in Athens,” in Hesperia, 1 (1932), 207–211.
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