On the Pin-and-Slot Device of the Antikythera Mechanism,with a New Application to the Superior Planets

Freeth T. Bitsakis Y. Moussas X. Seiradakis J. H. Tselikas A. Mangou H. Zafeiropolou M. Hadland R. Bate D. Ramsey A. Allen M. Crawley A. Hockley P. Malzbender T. Gelb D. Ambrisco W. Edmunds M. G. , “Decoding the ancient Greek astronomical calculator known as the Antikythera mechanism”, Nature, cdxliv (2006), 587–91. There is substantial “Supplementary information” linked to the online version of the paper at www.nature.com/nature.

Derek de Solla Price drew attention to this slot, but conjectured that it might be the result of an attempt to repair a broken gear. 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 (1974)), 35. M. T. Wright described the pin-and-slot device and its workings and observed that it would suitable for modelling an anomaly, in “Epicyclic gearing and the Antikythera mechanism, part 2”, Antiquarian horology, xxix/1 (September 2005), 51–63.

Freeth , “Decoding” (ref. 1), Supplementary information, 25–7.

Evans J. Carman C. C. Thorndike A. S. , “Solar anomaly and planetary displays in the Antikythera mechanism,” Journal for the history of astronomy, xli (2010), 1–39. The evidence is very simple and comes from matching degree marks on the zodiac scale with day marks on the Egyptian calendar scale. Over a preserved stretch of 69° of the calendar scale, an apparent equation of centre rises steadily to a 2.1° effect, of the right sign and amplitude to represent the Sun's inequality. We shall shortly publish a second study of the zodiac and Egyptian calendar scales, examining this issue in greater detail.

Price , Gears from the Greeks (ref. 2), 21. Wright M. T. , “A planetarium display for the Antikythera mechanism”, Horological journal , cxliv (2002), 169–73 and 193; and “The Antikythera mechanism: A new gearing scheme”, Bulletin of the Scientific Instrument Society, lxxxv, issue of June 2005, 2–7. Freeth , “Decoding” (ref. 1), 590.

Freeth , “Decoding” (ref. 1), Supplementary information, 8–9, with translation on pp. 10–14.

Wright , “A planetarium display” (ref. 5). A film of Wright's reconstruction in motion can be seen at www.youtube.com/watch?v=ZrfMFhrgOFc This film was made in 2008 by the science writer Jo Marchant, who was then working for New scientist.

Evans Carman Thorndike , “Solar anomaly” (ref. 4).

Theon of Smyrna, Mathematical knowledge useful for reading Plato , iii, 26; Dupuis J. , transl., Théon de Smyrne, philosophe platonicien: Exposition des connaissances mathématiques utiles pour la lecture de Platon (Paris, 1892), 269.

We follow the gear names used by translator Freeth . in “Decoding” (ref. 1), which in some cases represent departures from Price's nomenclature in Gears from the Greeks (ref. 2).

The output is by means of a central shaft attached to e6; and this shaft runs inside the hollow pipe to which e5 is attached.

Ptolemy's proof of the equivalence for the Sun is in Almagest iii, 3, and for the Moon at iv, 5. Toomer G. J. , Ptolemy's Almagest (London, 1985), 141–53 and 180–90. Ptolemy's remarks about Apollonios are in Almagest xii, 1 (Toomer, p. 555). The classic argument that Apollonios understood the equivalence of epicycles and eccentrics is Otto Neugebauer, “The equivalence of eccentric and epicycle motion according to Apollonios”, Scripta mathematica, xxiv (1959), 5–21, recapitulated in A history of ancient mathematical astronomy (Berlin and New York, 1975), 149–50, 267–70. But scholars have sometimes questioned the correctness of attributing this understanding to Apollonios. See, most recently, Goldstein Bernard R. , “Apollonios of Perga's contributions to astronomy reconsidered”, Physis , xlvi (2009), 1–14. For Theon of Smyrna's proofs see Dupuis, Théon de Smyrne (ref. 9), 271–9.

Jones Alexander , Astronomical papyri from Oxyrhynchus (Memoirs of the American Philosophical Society, ccxxxiii; Philadelphia, 1999).

See, e.g., Goldstein B. R. , “Descriptions of astronomical instruments in Hebrew”, in King D. A. Saliba G. (eds), Essays in honor of E. S. Kennedy (Annals of the New York Academy of Sciences, d (1987)), 105–41, pp. 106 ff.

The expressions for sin q are the same pair that we get if, in the ordinary eccentric-circle theory, we express q first as a function of the mean anomaly and then as a function of the true anomaly. See Evans James , The history and practice of ancient astronomy (New York, 1998), 233–4.

Freeth , “Decoding” (ref. 1), Supplementary information, 24. We have modified this quotation by multiplying all the frequencies by a minus sign, in order to make the discussion more easily comparable with our diagrams.

This is a distinction in language used by Ptolemy himself (that one sort of anomaly is related to the Sun, and is one related to position in the zodiac), e.g., in Almagest ix, 2; Toomer , Ptolemy's Almagest (ref. 12), 420.

See, for example, Evans , History and practice (ref. 15), 338.

We thank Michael Wright for this suggestion (private communication), as well as for several other comments that helped improve the paper.

Listed in Evans , History and practice (ref. 15), 314. The term ‘goal-year texts’ was introduced by Abraham Sachs, “A classification of the Babylonian astronomical tablets of the Seleucid period”, Journal of cuneiform studies, ii (1970), 271–90.

Price , Gears from the Greeks (ref. 2), 28, speculated that there might have been other lugs fastened to b1.

Edmunds Mike Morgan Philip , “The Antikythera mechanism: Still a mystery of Greek astronomy?”, Astronomy & geophysics, xli, issue of December 2000, 6.10–6.17.

Wright , “A planetarium display” (ref. 5).

See Evans , History and practice (ref. 15), 341.

In arguing that multiple concentric pipes would not be a problem, Wright makes an analogy to surviving fragments of the musical wind instrument called the aulos, in which rotatable sleeves of bronze tube are often seen fitted over a structural tube. Wright M. T. , “In the steps of the master mechanic”, in Ancient Greece and the modern world (Patras, 2003), 86–97.

Evans Carman Thorndike , “Solar anomaly” (ref. 4), 32–3.