# On the epoch of the Antikythera mechanism and its eclipse predictor

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## Abstract

The eclipse predictor (or Saros dial) of the Antikythera mechanism provides a wealth of astronomical information and offers practically the only possibility for a close astronomical dating of the mechanism. We apply a series of constraints, in a sort of sieve of Eratosthenes, to sequentially eliminate possibilities for the epoch date. We find that the solar eclipse of month 13 of the Saros dial almost certainly belongs to solar Saros series 44. And the eclipse predictor would work best if the full Moon of month 1 of the Saros dial corresponds to May 12, 205 BCE, with the exeligmos dial set at 0. We also examine some possibilities for the theory that underlies the eclipse times on the Saros dial and find that a Babylonian-style arithmetical scheme employing an equation of center and daily velocities would match the inscribed times of day quite well. Indeed, an arithmetic scheme for the eclipse times matches the evidence somewhat better than does a trigonometric model.

## Notes

### Acknowledgments

We are grateful to James Bernhard for a discussion of statistical issues. Alexander Jones generously shared preliminary results of his own unpublished research which disclosed the existence of a lunar equation of center embedded in the Antikythera mechanism eclipse times. This turned out to be crucial for our project—it is the lunar anomaly that allows one to unambiguously identify a particular solar Saros series. Dennis Duke gave valuable help in calculation and programming. We thank John Steele for answering our questions about the Babylonian Saros schemes. We thank Paul Iversen and John Morgan for their lively and helpful discussion of previous versions of the paper. The Antikythera Mechanism Research Project has, as always, been extremely generous in sharing images and data. James Evans expresses his thanks to the University of Puget Sound for research funds that helped make this work possible. Christián Carman would like to express his thanks for the support of Research Project PICT-2010-0319 of the Agencia Nacional de Promoción Científica y Tecnológica of Argentina. While we were in the last stages of completing our manuscript, an article by Tony Freeth was published that focuses on some of the same issues that we have studied (Freeth 2014), but it appeared too late for us to make any use of it. The work published here is independent of Dr. Freeth’s study.

## References

- Aaboe, A., J.P. Britton, J.A. Henderson, O. Neugebauer, and A.J. Sachs. 1991. Saros cycle dates and related Babylonian astronomical texts.
*Transactions of the American Philosophical Society, New Series*81(6): 1–75.CrossRefGoogle Scholar - Anastasiou, M., J.H. Seiradakis, C.C. Carman, and K. Efstathiou. 2014. The Antikythera mechanism: The construction of the Metonic pointer and the back plate dials.
*Journal for the History of Astronomy*45:1–26.Google Scholar - Bickerman, E.J. 1980.
*Chronology of the ancient world*. Ithaca: Cornell University Press.Google Scholar - Britton, John P. 1989. An early function for eclipse magnitudes in Babylonian astronomy.
*Centaurus*32: 1–52.CrossRefMATHMathSciNetGoogle Scholar - Espenak, Fred. Eclipses and the Saros. http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html.
- Espenak, Fred. NASA Eclipse Web Site. NASA Five-Millennium Catalog of Lunar Eclipses. http://eclipse.gsfc.nasa.gov/LEcat5/LE-0099-0000.html.
- Espenak, Fred. NASA Eclipse Web Site. Five-Millennium Catalog of Solar Eclipses. http://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html.
- Espenak, Fred. NASA Eclipse Web Site. Javascript Solar Eclipse Explorer. http://eclipse.gsfc.nasa.gov/JSEX/JSEX-index.html.
- Espenak, Fred. NASA Eclipse Web Site. Six Millennium Catalog of Phases of the Moon. http://eclipse.gsfc.nasa.gov/phase/phasecat.html.
- Evans, James, and Christián Carlos Carman. 2013. On the epoch of the Antikythera Mechanism (PowerPoint presentation). http://www.lorentzcenter.nl/lc/web/2013/570/presentations/index.php3?wsid=570&type=presentations&venue=Oort.
- Evans, James, and Christián Carlos Carman. 2014. Mechanical astronomy: A route to the ancient discovery of epicycles and eccentrics. In
*From Alexandria, through Baghdad: Surveys and studies in the ancient Greek and medieval Islamic mathematical sciences in honor of J. L. Berggren*, ed. Nathan Sidoli, and Glen Van Brummelen, 145–174. heidelberg: springer.CrossRefGoogle Scholar - Evans, James, Christián Carlos Carman, and Alan S. Thorndike. 2010. Solar anomaly and planetary displays in the Antikythera Mechanism.
*Journal for the History of Astronomy*41: 1–39.Google Scholar - Evans, James, and J. Lennart Berggren. 2006.
*Geminos’s introduction to the phenomena: A translation and study of a Hellenistic survey of astronomy*. Princeton: Princeton University Press.Google Scholar - Fox, John. 2008.
*Applied regression analysis and generalized linear models*. Los Angeles: Sage.Google Scholar - Freeth, Tony. 2014. Eclipse prediction on the Antikythera Mechanism. PLOS One (Public Library of Science). http://dx.plos.org/10.1371/journal.pone.0103275.
- Freeth, Tony, et al. 2006. Decoding the ancient Greek astronomical calculator known as the Antikythera Mechanism.
*Nature*444. doi: 10.1038/nature05357. Supplementary Information is linked to the online version of the paper at www.nature.com/nature. - Freeth, Tony, Alexander Jones, John M. Steele, and Yanis Bitsakis. 2008. Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism.
*Nature*454. doi: 10.1038/nature07130. Additional information is available in the “Supplementary Notes” at www.nature.com/nature. - Iversen, Paul. 2013. http://apaclassics.org/annual-meeting/151iversen.
- Meeus, Jean. 2009.
*Astronomical algorithms*, 2nd ed. Richmond: Willmann-Bell.Google Scholar - Morgan, John D. 2013. The season of Karneios. (A presentation at the conference The Antikythera Mechanism: Science and innovation in the ancient world, held in Leiden). A PDF of the presentation is posted at the conference web site. http://www.lorentzcenter.nl/lc/web/2013/570/presentations/index.php3?wsid=570&type=presentations&venue=Oort.
- Neugebauer, O. 1975.
*A history of ancient mathematical astronomy*. Berlin, Heidelberg, New York: Springer.CrossRefMATHGoogle Scholar - Ramsey, Fred, and Daniel Schafer. 2002.
*The statistical sleuth: A course in methods of data analysis*, 2nd ed. Belmont, CA: Brooks/Cole, Cengage Learning.Google Scholar - Price, Derek de Solla. 1974. Gears from the Greeks: The Antikythera mechanism—A calendar computer from ca. 80 B.C.
*Transactions of the American Philosophical Society*, n.s., lxiv/7.Google Scholar - Smart, W.M. 1977.
*Textbook on spherical astronomy*, 6th ed. Cambridge: Cambridge University Press.Google Scholar - Steele, John M. 2000a. Eclipse prediction in Mesopotamia.
*Archive for History of Exact Sciences*54: 421–454.CrossRefMathSciNetGoogle Scholar - Steele, John M. 2000b.
*Observations and predictions of eclipse times by early astronomers*. Dordrecht, Boston: Kluwer Academic Press.CrossRefMATHGoogle Scholar - Toomer, G.J. 1984.
*Ptolemy’s Almagest*. London: Duckworth.MATHGoogle Scholar