The Graeco-Roman sundials in Greece known to this author are to be published in SchaldachK., Die antiken Sonnenuhren 1: Griechenland — Festland und Peloponnes (Frankfurt/M., forthcoming). The importance of this instrument was overlooked by PetrakosB., (Athens, 1997), who published it under no. 359. Further references: MitsosM., in IIAE, 1951, 128, and Bulletin épigraphique, 1965, 122, giving only the first line of the inscription; and GibbsS., Greek and Roman sundials (New Haven and London, 1976), no. 8007, which is based exclusively on Mitsos. The first fragments of the piece were recovered by LeonardosB. in 1886.
2.
The individual parts were found on the square behind the temple. In November 1984 the last fragment was recovered from this very site: cf.Petrakos, op. cit. (ref. 1).
3.
Amphiaraos was one of the seven heroes who, after Oedipus's death, attacked Thebes. After their defeat, Zeus concealed him from his pursuers and had him disappear in a crack. In Antiquity even people like the Lydian king Kroisos and the Persian commander Mardonios came to the sanctuary for consultation.
4.
The given angle is the mean of three measurements: 39°, 40° and 40°.
5.
Another plausible explanation of the shape might be, that room was left for a second device holding the stone on both sides, like crutches.
6.
Besides the adjustment to the north-south line, the exact fixing of the position requires the orientation of the meridian plane of the dial to be perpendicular to the horizontal plane.
7.
As mentioned above, the actual local latitude differs by 1°41′. This difference, however, is of no importance for the ensuing calculations, since it does not influence the fundamental considerations.
8.
NeugebauerO., “On some aspects of early Greek astronomy”, Proceedings of the American Philosophical Society, cxvi/3 (1972), 243–8, p. 243: “In fact we have good evidence from Hipparchos and from Geminus that the ratio 15:9 was considered by Eudoxos, Aratus, and Attalus as representative for Greece in general.” Hipparchus's criticism of this value (cf.ManitiusC., Hipparchi in Arati et Eudoxi Phaenomena commentarius (Leipzig, 1894), 23) looks rather ‘academic’ and has nothing to do with the reality of application, because most Hellenistic sundials of Greece were not constructed according to that value but following the approximate latitudes of the individual places; cf.Schaldach, op. cit. (ref. 1).
9.
JamesEvans, The history and practice of ancient astronomy (New York and Oxford, 1998), 59: “The most ancient value for the obliquity of the ecliptic is the round figure of 24°.”.
10.
We take FwW = 14 mm, which is the difference between MwW (cf. Figure 3) and FwMw, and the relation leads to a gnomon length FwGw of some 13 mm. Both values are possible taking into account that the shadow should reach the stone at the equinoxes. Calculating with a horizontal thickness of the stone of some 31 mm at the top and of some 65 mm at the great circles (cf. Figure 4), we have 34 mm left for both gnomons. For equal lengths of the gnomons on both sides we may conclude that every gnomon should be shorter than 17 mm.
11.
The summer side on the whole seems less well done than the winter side. For instance, the radius of the circle is not constant but increases from 294 mm to 305 mm, the shortest value being close to the meridian (cf. Fig. 3).
12.
On the equatorial ring of Ptolemy see JamesEvans, “The material culture of Greek astronomy”, Journal for the history of astronomy, xxx (1999), 237–307, pp. 274–6.
13.
NeugebauerO., “The astronomical origin of the theory of conic sections”, Proceedings of the American Philosophical Society, xcii/3 (1948), 136–8. As an example of that “rather unpractical dial” he mentioned the equatorial dial with plain surfaces preserved in the British Museum (no. 2546), see also Gibbs, op. cit. (ref. 1), no. 5022G. Its origin and date are unknown. Another dial with an equatorial surface and a gnomon that stood perpendicular to the reclined plane was found on MountGerizim (Jordan) and dates to the Roman or late Roman time, cf.BullR. J., “A tripartite sundial from Rell Er Râs on Mt. Gerizim”, BASOR, no. 219 (1975), 29–37.
14.
Little is known about the origin of the theory. The standard view concerning the beginning of the conics was expressed by Eutokios, who lived about some 700 years later, thus: “After a time, so goes the story, certain Delians, who were commanded by the oracle to double a certain altar, fell into the same quandary as before. They therefore sent over to beg the geometers who were with Plato in the Academy to find them the solution.” See HeathThomas L., A history of Greek mathematics (2 vols, New York, 1981), i, 244f.
15.
Cf.Petrakos, op. cit. (ref. 1).
16.
The θ in line 4 and the Γ in line 6 are unsure. Other probable readings are Ω and Π or E, respectively; cf.Petrakos, op. cit. (ref. 1).
17.
Cf.Heath, op. cit. (ref. 14), i, 320.
18.
HalloW. W., Origins: The ancient Near Eastern background of some modern Western institutions (Leiden, New York and Cologne, 1996), 123; cf. also Rochberg-HaltonF., “Babylonian seasonal hours”, Centaurusxxxii (1989), 146–70, p. 164, where a procedure text is given that speaks of a gnomon used together with “a stone slab”.
19.
Two known pieces are from the Ptolemaic epoch. One found at Luxor is now in Berlin in the Ägyptisches Museum, inv. no. 20322 (Fig. 23 on p. 48 in BorchardtL., Die altägyptische Zeitmessung: Die Geschichte der Zeitmessung und der Uhren, Lieferung B (Berlin, 1920), another in Brussels in the Museés Royaux d'Art et d'Histoire, inv. no. E7330. Both are designed for hanging on a wall or pillar. The oldest known specimen, however, dates from the thirteenth century b.c. It was found at Gezer (Palestine), which in those days was governed by Egypt, and has been also decribed by Borchardt, op. cit., 48.
20.
VitruviusIX, chap, viii, 1. For comments about this passage cf. Vitruve, De l'architecture, livre IX (Paris, 1969), Latin text edited and translated into French by JeanSoubiran, 252f.
21.
Cf.BerggrenJ. L., “The relation of Greek spherics to early Greek astronomy”, Science and philosophy in classical Greece, ed. by BowenA. C. (New York and London, 1991), 227–48.
22.
The Egyptian and Babylonian dials are based on arithmetical notations.
