Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism
Previous research on the Antikythera Mechanism established a highly complex ancient Greek geared mechanism with front and back output dials. The upper back dial is a 19-year calendar, based on the Metonic cycle, arranged as a five-turn spiral. The lower back dial is a Saros eclipse-prediction dial, arranged as a four-turn spiral of 223 lunar months, with glyphs indicating eclipse predictions. Here we add surprising findings concerning these back dials. Though no month names on the Metonic calendar were previously known, we have now identified all 12 months, which are unexpectedly of Corinthian origin. The Corinthian colonies of northwestern Greece or Syracuse in Sicily are leading contenders—the latter suggesting a heritage going back to Archimedes. Calendars with excluded days to regulate month lengths, described in a first century bc source, have hitherto been dismissed as implausible. We demonstrate their existence in the Antikythera calendar, and in the process establish why the Metonic dial has five turns. The upper subsidiary dial is not a 76-year Callippic dial as previously thought, but follows the four-year cycle of the Olympiad and its associated Panhellenic Games. Newly identified index letters in each glyph on the Saros dial show that a previous reconstruction needs modification. We explore models for generating the unusual glyph distribution, and show how the eclipse times appear to be contradictory. We explain the four turns of the Saros dial in terms of the full moon cycle and the Exeligmos dial as indicating a necessary correction to the predicted eclipse times. The new results on the Metonic calendar, Olympiad dial and eclipse prediction link the cycles of human institutions with the celestial cycles embedded in the Mechanism’s gearwork.
Remarks on the Theoretical Treatment of Eclipses in Antiquity
It has been a recurring problem in the history of early astronomy to discover how eclipses, and particularly solar eclipses, might be predicted by astronomers whose theories seemed clearly insufficient for the task. In the fully developed Babylonian arithmetical astronomy of the last four centuries B.C., which we now control very well, we find excellent account made of the motions of the Sun in longitude and of the Moon, in longitude as well as in latitude, on which basis solid predictions of lunar eclipses were given.' But it is not really until Ptolemy that we encounter an understanding and control of lunar daily parallax which suffice for predictions of solar eclipses for a given locality. Yet we have accounts from Antiquity of predictions of solar eclipses, most notoriously Herodotus'S report that Thales predicted "the loss of daylight for the year" of the battle between the Lydians and the Medes.s It is particularly this passage which has generated much speculation and discussion." The proposed solutions of the problem have very often been sought in eclipse cycles, most notably the 'Saros' period of 18 years or, more precisely, 223 lunations (about 65851 days). These attempts were doomed to failure for though there are excellent cycles for lunar eclipses (here the triple Saros, or Exeligmos, of 669 lunations is particularly good)! there are no such cycles or periodic recurrences of solar eclipses for a given location on Earth. A more realistic and fruitful approach to the dilemma, I shall suggest, follows from the assumption that what was predicted was something for which the theory at the time was sufficient. It is, indeed, quite a simple matter to point to those conjunctions at which an obviously necessary condition for solar eclipses-that the conjunction happen near a lunar node-is satisfied, thus isolating conjunctions at which a solar eclipse might happen from those at which eclipses are entirely excluded.
The Accuracy of Eclipse Times Measured by the Babylonians
L'etude comparative de la date et de la duree des eclipses solaires et lunaires determinees par les Babyloniens et des methodes de calculs modernes montrent la precision des mesures effectuees par les Babyloniens