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

Abstract

(ProQuest: ... denotes formulae omitted.)Perhaps the most striking and surprising feature of the Antikythera mechanism uncovered by recent research is the pin-and-slot device for producing the lunar inequality.1 This clever device, completely unattested in the ancient astronomical literature, produces a back-and-forth oscillation that is superimposed on a steady progress in longitude - nonuniform circular motion.2 Remarkably, the resulting motion is equivalent in angle (but not in spatial motion in depth) to the standard deferent-plus-epicycle lunar theory. Freeth et al. gave a proof of this equivalence, which is, however, a very complicated proof.3 One goal of the present paper is to offer a simpler proof that would have been well within the methods of the ancient astronomers and that, moreover, makes clearer the precise relation of the pin-andslot model to the standard epicycle-plus-concentric and eccentric-circle theories.On the surviving portions of the Antikythera mechanism, only two devices are used to account for inequalities of motion. The first is the pin and slot, used for the lunar inequality. And the second is the nonuniform division of the zodiac scale, which, we have argued, was used to model the solar inequality.4 The second would obviously be of no use in representing planetary inequalities; so a natural question is to ask whether the pin-and-slot mechanism could be modified and extended to the planets, especially to the superior planets, for which the likely mechanical representations are less obvious than they are for the inferior planets. The second goal of this paper, then, is to examine the relation of the pin-and-slot model to the standard concentric-plusepicycle theory for the retrograde motion of the planets. We shall see that, indeed, the pin and slot can be applied to the planets and that this device again gives an exact representation of the motion in angle, though not in depth.Scholars have pondered the various holes and structures on the main solar gear bl, and wondered whether these might represent the remnants of a lost part of the mechanism designed for reproducing planetary motion.5 The evidence is frustratingly sparse. An inscription on the front cover of the mechanism appears to describe planetary phenomena, including stations, and another inscription on the back cover mentions Venus by name,6 but the only hardware surviving is a single wheel of 63 teeth (rl) which has no function in the published reconstruction of the solar and lunar portions of the mechanism. It is not much to go on. That a planetary display could be possible has been shown by Michael Wright, who, in a feat of mechanical virtuosity, constructed one that works and that is based on a full representation of deferent-and-epicycle theory.7 We ourselves published a more modest proposal, in which the mechanism would have offered a display of the key events in the planets' synodic cycles, but not a full -on kinematic display showing the progress of the planets around the zodiac with retrograde motion.8 However, in our view, the realization that the pin-and-slot mechanism could be applied to the planets (when we know that it is in fact used for the Moon) suggests the possibility of a simpler kinematic model. We remain agnostic about whether the Antikythera mechanism offered a full-on kinematic display, or a more modest display of information about planetary phases, or perhaps a display of the mean motions. However, like Hipparchos, we feel it is worth the attention of geometers to investigate the explanation of the same phenomena by means of hypotheses that are so different.9So the third goal of this paper is to present a new approach for the planetary display in the Antikythera mechanism. We will follow the idea proposed by Michael Wright and others, according to which the Antikythera mechanism displayed planetary longitudes on the front dial, using pointers concentric with those of the Moon and Sun and sharing the same zodiac scale. …