Reference / Paper · 2025

Reconstructing the Antikythera Mechanism's Central Front Dial Parts — Division and Placement of the Zodiac Dial Ring

Journal of Astronomical History and Heritage 28(1), 257–279.

Author: A. Voulgaris et al.
Year: 2025
Type: Reference / Paper
Credit: JAHH (arXiv:2505.08484)

antikythera
front dial
zodiac

Journal of Astronomical History and Heritage, 28(1), 257– 279 (2025). RECONSTRUCTING THE ANTIKYTHERA MECHANISM’S CENTRAL FRONT DIAL PARTS – DIVISION AND PLACEMENT OF THE ZODIAC DIAL RING Aristeidis Voulgaris City of Thessaloniki, Directorate of Culture and Tourism Thessaloniki, GR-54625, Greece. E-mail: [email protected] Christophoros Mouratidis Merchant Marine Academy of Syros, GR-84100, Greece. E-mail: [email protected] and Andreas Vossinakis Thessaloniki Astronomy Club, Thessaloniki, GR-54646, Greece. E-mail: [email protected] Abstract: In this paper we analyze, discuss and present the design of the Antikythera Mechanism’s central front parts. Based on the aligned and visual images of the same scale of Fragment C front/back face and X-ray CT scans, we designed and reconstructed in bronze, the four independent parts comprising the central front dial. We then correlated the zodiac dial ring with 365 equal subdivisions/days and we investigated the number of days per astronomical season and per zodiac month. Then, we adopted a specific number of equal subdivisions/days per zodiac month and we engraved these on the bronze zodiac month ring. The different number of days per zodiac month created 12 unequal central angles on the zodiac dial ring and therefore the solar anomaly and the unequal time span of the astronomical seasons were well represented on the Antikythera Mechanism. In this way, the functionality of the central front dial of the Mechanism was achieved by adopting the minimum number of hypotheses. Keywords: Antikythera Mechanism; Fragment C; square front plate; zodiac dial ring; Egyptian dial ring; zodiac month. 1 INTRODUCTION Today the Mechanism is partially preserved in seven relatively large fragments and 75 smaller ones. During its 2000 years underwater, the bronze material (an alloy of ~94% copper and ~6% tin, Price, 1974) of the Mechanism (density 8.87gr/cm 3) was transformed into atacamite (see Voulgaris et al., 2019b). Atacamite is a copper halide mineral with a significantly lower density (3.76gr/cm3) than bronze (http://webmineral.com/data/Atacamite.shtml). The Antikythera Mechanism is a complex geared device, which was constructed for timemeasuring calculations and astronomical predictions based on the luni-solar cycle. The results were calculated by means of a large number of engaged gears and pointers which rotated on their corresponding scales. The Mechanism could calculate the (timed) position of the Sun on the Ecliptic, the phases of the Moon, solar and lunar eclipses,1 the Metonic month (Anastasiou et al., 2016; Freeth et al., 2006), the hour when eclipses occurred 2 (Voulgaris et al., 2023b) and the starting date of the athletic Games (Freeth et al., 2008). The procedures of the Mechanism were presented versus time and were mostly based on the lunar synodic cycle, except for the Egyptian and zodiac dials, which were based on the solar cycle (see Table 1). The hypothesis that the planets’ indication gearing on the Antikythera Mechanism presented the motion of the planets with rotated spheres is highly doubtful because it is not in accordance with the Construction Protocol for a Research Quality Bronze Reconstruction of the Antikythera Mechanism, presented in the Appendix (Section 8) at the end of this paper. Owing to the significant change in the material density, as well as to corrosion and gravity, the Mechanism’s parts suffered irregular alterations in shape, volume and position. With time, the fragile corroded pieces of the Mechanism started to collapse inside the Mechanism’s rotten box.3 An additional strong deformation of the Mechanism happened when in 1901 it was removed from the bottom of the sea near Antikythera Island: the abrupt dehydration of the Mechanism and the dry atmosphere further contributed to the irregular deformation, displacement, shrinkage and change of volume (dimensions and shape) of the Mechanism’s parts (Voulgaris et al., 2019b), e.g. see the strong deformation of Fragment C shown in Figure 1E. ~ 257 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Table 1: The preserved dials of the Antikythera Mechanism and their corresponding units. The type of measurement for each scale is the same: Units of time (the units of the zodiac dial ring are analyzed in this work). The nature of the units in a measuring instrument defines the kind of instrument and what physical quantity it counts. Any measuring instrument has calibrated scales that present relevant or associated measurements. Measuring Dial Egyptian dial ring Parapegma plates 1, 2 Lunar phases sphere Metonic spiral Saros spiral Exeligmos dial Athletic Games dial Zodiac dial ring Antikythera Mechanism Scale Egyptian Year of 365.0 Days 1 Year = 2 Plates = 4 Columns 1 Column = 1 Season = 3 months Each parapegma event corresponds to a specific date = 1 day per index letter The lunar phases are measured in days (e.g. Full Moon = 15d Moon, not Moon at 180°) 19 Years/235 synodic months 18.03 Years/223 synodic months 54.09 = 3  Saros (= 3  223 synodic months) 4 years (= alternately 49/50 synodic months) Full circle corresponds to one solar tropical year Scale Units/ Subdivisions 1 day/subdivision Event/day and index letter/day Type of Measurement Time Time Colors: black, white, half black/half white 1 synodic month/cell 1 synodic month/cell 18.03 years/⅓ sector 1 year/quadrant 360 degrees or 365 days Time Time Time Time Time Space or time Figure 1(A) and (C): Fragment C (back and front faces) captured in 1903 by an anonymous photographer and included in Rehm (1906; cf. Rehm 1905). Around 1905, the two parapegma plates were better preserved than they currently are. (B and D): The current condition of Fragment C, back and front faces. Credits: National Archaeological Museum, Athens, first author, Copyright Hellenic Ministry of Culture & Sports/Archaeological Receipts Fund. (E): A 3-D reconstruction of Fragment C based on the AMRP X-Ray Raw Volume,4 Top Coronal view of Fragment C. The permanent strong deformation of Fragment C (bent and twisted) is evident. X-ray Volume process by the authors, via REAL3D VolViCon software. Therefore, all modern measurements are approximate, since these measurements are applied to the deformed parts—not to the original bronze prototype—and in many cases they are not representative (e.g. see the graphs in Voulgaris et al., 2022: Figure 8). More realistic approaches for the parts’ dimensions can be deduced by taking into account the symmetry of the design and the ideal/correct positions for the best operation and functioning of the Mechanism’s parts. Today, the fragments are totally (or deeply) corroded inside (see Voulgaris et al., 2021: Figure 1) and their degree of X-ray absorption (darkening) is almost everywhere equal to the atacamite absorption (Ramsey, 2012; Voulgaris et al., 2018c; 2021; also, see Figure 1). The front face of the Mechanism consists of three independent sectors: the two parapegma plates 1 and 2 (PP1-top and PP2bottom) and the central front dial (Anastasiou et al., 2013; Bitsakis and Jones, 2016a). Today, the main part of the front face is partially preserved as Fragment C: the central front dial (~20%) and a part of parapegma plates 1 and A large number of cracks in the material are visible to the naked eye, in the radiographs and in the computed tomography (CT) scans. ~ 258 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis 2 (see Figure 1).5 (1st day of Capricorn–Winter Solstice; Voulgaris et al., 2023a)8 in 365.25 days (van der Waerden, 1953). The zodiac dial ring is divided into 12 zodiac sectors, one for each of the twelve Ecliptic constellations. The pointer of the golden sphere (ΗΛΙΟΥ ΑΚΤΙΝ; Bitsakis and Jones, 2016a) traverses each of the zodiac sectors, representing the motion of the Sun as it is projected on the sky. The Sun traverses each zodiac sign of 30° over an unequal number of days due to the solar anomaly (discussed in Section 2.2). The central front dial of the Antikythera Mechanism is the main cadran (dial) of the Mechanism. This cadran gives important information for time measuring based on the lunar sidereal/synodic cycles and the solar tropical year: the synodic lunar cycle (via the lunar pointer which travels around the Ecliptic and is either aligned with or points opposite to the golden sphere, New Moon/Full Moon),6 the sidereal cycle (when the lunar pointer points to the same position of a zodiac constellation), the phases of the Moon (via the Moon phases sphere located at the lunar cylinder’s perimeter) and the solar tropical year/cycle (via the solar pointer of the ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ, golden sphere,7 which also travels along the Ecliptic). For the reconstruction of the square front plate (design, parts and scales) the authors used their own photographs of Fragment C. The photographs were captured by an optomechanical system dedicated to this project and designed and constructed by the first author (Voulgaris et al., 2018a). Photographs taken by K. Xenikakis and Polynomial Texture Maps (PTMs) also made in 2004 were used to test the results. Images of the front and back faces of the fragments were captured at the same scale in pixels/mm (ibid.). All preserved parts of the front dial are relatively thin (~2mm), so simultaneous inspection of the front and back faces of Fragment C can provide us with information about their geometrical characteristics and positioning. Aligned photographs of the fragment’s front and back faces allow their juxtapositioning by mirroring one of them. The Ecliptic and the 12 zodiac constellations are represented on the zodiac month ring. Encircling the zodiac dial ring, a second outer ring represents the Egyptian (year) calendar (Price, 1974). For several astronomical events, Ptolemy refers to their dates in the Metonic (also in Dionysius, see footnote 23) and the Egyptian calendars (Heiberg, 1898: 1.341, 1.342, 2.25, 2.28, 2.29, 2.32, 2.268, 2.419; Toomer, 1984). This practice must have been widespread during the Hellenistic era, since Greece, Egypt and Babylon were considered as one state and their administrations, policies, cultures and knowledge were interconnected (Voulgaris et al., 2023c). According to Figure 2, the central front dial of the Antikythera Mechanism consists of four totally independent parts (see Voulgaris et al., 2018a): 2 THE DESIGN OF THE ANTIKYTHERA MECHANISM FRONT DIAL PLATE (1) The square, or almost square, front plate, with a width of ~174mm according to Voulgaris et al. (2019b: Table 1; Allen et al., 2016); 9 (2) The bearing base ring with 365 holes in a circular distribution (at present about 80 are preserved, Evans et al., 2010), which is stabilized on the back face of the square plate; (3) The free-to-rotate Egyptian dial ring, which is placed above the bearing base ring; and (4) The zodiac dial ring, which is also free to rotate clockwise and counterclockwise (similar results were obtained by applying the same process to the 2004 photographs obtained by K. Xenikakis and the PTM images). 2.1 Analysis of the Design of the Front Plate Parts The central front plate is comprised of the two dial scale rings, the Egyptian and the zodiac, which are homocentric to each other, as well as to the lunar cylinder and b1 gear. The Egyptian dial ring represents the Egyptian year (Price, 1974), which had a constant duration of 365.0 days/year, breaking down into 12 months  30 days + 5 ΕΠΑΓΟΜΕΝΑΙ epagomenal days, dedicated to the birthdays of Osiris, Horus, Seth/Typhon, Isis and Nephthys (Maravelia, 2018b; Theodosiou and Danezis, 1995). The Egyptian calendar was ahead by one day every four solar tropical years or one month every 120 years, as Geminus mentions (Evans and Berggren, 2006; Manitius, 1880, viii, 18– 24). Figure 3 shows the reconstruction of the central front dial plate parts of Fragment C in bronze, by applying the symmetry options to the design (Voulgaris et al., 2022). The zodiac dial ring on the Mechanism is directly correlated with the solar tropical year, in which the Sun returns to its starting position By applying a middle-horizontal/vertical/ ~ 259 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 2: Composite image of same-scale aligned front/back faces of Fragment C. On the front face of Fragment C, the Egyptian and the zodiac dial rings are at the same level on the square front plate. The bearing base (black arrows) is visible on the back face of the fragment (see also Voulgaris et al., 2018a). The bearing base is partially covered by the lunar cylinder (its round contour is shown by the white arrows). The color balance of the righthand photograph was deliberately altered to increase contrast and improve visibility compared to the left-hand photograph. Images processed by the authors. The sliding catch is visible on the top-right edge of the Fragment (Bitsakis and Jones, 2016a). (Credits: National Archaeological Museum, Athens, first author, Copyright Hellenic Ministry of Culture & Sports/Archaeological Receipts Fund). The square front plate as well as the two parapegma plates are based on the internal wooden casement (Voulgaris et al., 2019b). Since the square front plate is detachable via the four sliding catches, the two parapegma plates must have been stabilized on the internal wooden casement, probably with pins (see Figure 5). mirror/central symmetry, it was deduced that this plate must have been almost, or exactly, square in shape (see also Allen et al., 2016). It is difficult to discern the bearing base ring as a separate part on the radiographs and the CT scans, since it is corroded, worn out and stuck to the Egyptian dial ring, with the two of them essentially forming one piece. However, in the X-ray imaging the two stuck plates can be seen as independent, since there is a thin layer of air between them and air exhibits very weak absorption in X-rays (Day and Taylor, 1948; Voulgaris et al., 2018c); otherwise these two plates merely appear to be one thicker plate. The precise positioning of the square front plate was very critical, so that the rotational centers of the lunar cylinder and the golden sphere coincided precisely with the geometrical centers of the Egyptian and zodiac dial rings (preventing errors of eccentricity). For this reason, the ancient craftsman made four small square holes on the corners of the square front plate (only one is preserved at present), which were the holes for the locking position of the plate. Originally square pin-drivers in these square holes were attached to the internal wooden casement (see Figure 5(B) and (C)). In the X-ray and CT scans of Fragment C about 80 of the ~0.7mm –0.8mm diameter 365 holes are visible.10 The holes are clogged with petrified silt, but since the X-ray absorption for silt is very low relative to atacamite the holes are easily visible on the radiographs and the CT scans. As Figure 4 illustrates, the authors also captured some of the preserved holes on photographs, using a specifically positioned digital single lens reflex (DSLR) camera. On Fragment F, which is a part of the Saros spiral, also present is a corner of a plate with a thumb button, a sliding catch and its driver with a Ω-shape. This part is stuck above ~ 260 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 3: The four parts of the central front dial plate, reconstructed of bronze (94%Cu + 6%Sn). (A) The square front plate of the Mechanism. The ancient craftsman adapted four sliding catches on the small oblong holes, so that he could easily detach the square front plate to have a direct look at the moving parts inside (i.e. the gears and axles). (B) The bearing base ring (fourth part/third ring). The outer perimeter/arc limits of the bearing base ring are cut to match the square shape of the central square plate. On the bearing base ring, the ancient craftsman drilled 365 holes in a circular distribution. For the drilling of the holes on the reconstructed model, common electric tools were used, not computer-controlled machines. (C) The bearing base ring is stabilized on the back face of the central square plate. In this way two uneven levels are created. (D) The front dial of the Antikythera Mechanism: The central square front plate with the two independent and homocentric rings of the Egyptian and zodiac calendars. The bearing base ring is beneath the Egyptian dial ring. Bronze parts construction (photographs: the authors). the Saros spiral parts and is surrounded by petrified silt (see Figure 6). box; see the current position of the lunar disk in Figure 1B).11 The strong similarity to the design of the preserved corner of the square front plate of Fragment C is evident in Figure 2 (see also Figure 3.3 in Bitsakis and Jones, 2016b: 76– 77). According to its geometry, this piece must have been at the top left corner of the square front plate or at the bottom right (due to its proximity to the preserved Fragment F; note that due to corrosion, some components or parts of it collapsed inside the Mechanism’s 2.2 The Zodiac Dial Ring of the Antikythera Mechanism and its Units The zodiac dial ring of the Antikythera Mechanism represents the Ecliptic, which is the line in the middle of the 12° wide zodiac belt, as Geminus mentions in V.51–53 (see also van der Waerden, 1953).12 In one full turn of the golden sphere–Sun, the Sun pointer travels through the 12 zodiac signs which is equal to ~ 261 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 4(A): A composite image of a photograph and the AMRP radiograph, shown to scale (the aligning of the two images was based on the fragment’s boundary and on the pins of the sliding catch). The limit between the Egyptian and zodiac dial rings is visible in the radiographs. The lower limit of the bearing base ring is clearly visible in the photograph. (B): The small holes in the bearing base ring were also detected in the photographs of Fragment C2. As the holes are filled with petrified silt they are visible as small pits (indicated by the black arrows). (Image by the first author. Credits: National Archaeological Museum, Athens, first autor, Copyright Hellenic Ministry of Culture & Sports/ Archaeological Receipts Fund). Figure 5(A): The bearing base ring is stabilized on the back face of the central square plate. In this way, the Egyptian dial ring and the zodiac month rings are located at the same level as the central square plate (see also Voulgaris et al., 2018a: Figure 4). (B): The square driver pin (missing and represented here) is fixed on the internal wooden casement of the Mechanism (Voulgaris et al., 2019b). (C) The driver pin enters its corresponding square locking hole, so that the central square plate is precisely positioned on the internal wooden casement. This method guarantees a high degree of accuracy when repositioning the plate. ~ 262 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 6(A): The front face of Fragment F on which the eclipse events are engraved (only visible in the CT scans). A corner of a plate (noted by the white lines) with a sliding catch is located about 5–7 mm above the fragment’s surface (see Note 10). Fragment F and this plate were mostly surrounded by calcareous encrustation, even after their first (?) cleaning (around 1903 –1905), created by deposits of marine carbonates, salts, dead microorganisms, etc. (Voulgaris et al., 2019b). The pin that connects the thumb button and the sliding catch is visible (image by the first author. Credits: National Archaeological Museum, Athens, first author, Copyright Hellenic Ministry of Culture & Sports/Archaeological Receipts Fund). (B): CT scan coronal view of Fragment F, specifically the area of the sliding catch (the slice aligned to the corner plate surface). (C): The thumb button of the sliding catch. (D): The plate’s surface. (E): The sliding catch with its Ω-shaped driver, which is stabilized on the plate with pins. (F): A digital restoration of the sliding catch (CT scans processed by the authors via REAL3D VolViCon). (G) and (H): A ‘modern’ sliding catch from a 70year old wooden storage cupboard (images: the authors). one tropical year (and one full turn of the lunar cylinder around the Ecliptic equals one sidereal month of 27.321 days). iac month (see Rehm, 1913; 1941; 1949). If the 365.25 days were represented by dividing the zodiac dial ring in (rounded) 365 equal subdivisions/days,13 then each zodiac month did not have an equal number of days, since this varied according to the total days the Sun needed to traverse each zodiac sign. This value depended on the solar anomaly phase, i.e. perihelion/aphelion position (see also Voulgaris et al., 2018a). This division was in accordance with the Mechanism’s operation and measurements, eliminating the need for any complex assumptions (see the Appendix at the end of this paper). Price (1974) suggested the subdivision of the zodiac dial ring into 360 degrees (see also Bitsakis and Jones, 2016a; Carman and Evans, 2014; Freeth et al., 2006; Wright, 2006). Price’s assumption was based on measuring the (well) preserved subdivisions of the complete month of ΧΗΛΑΙ (Claws–Libra) and ΣΚΟΡΠΙΟΣ (Scorpion) which both have 30 subdivisions (see also Bitsakis and Jones, 2016a), and he also argued that all the other months were also divided into 30 subdivisions, i.e. 360 subdivisions/degrees in the ring. In order to represent the solar anomaly, these 360 subdivisions/ degrees should be engraved at unequal distances from each other: larger distances for the months Gemini/Cancer (slower angular velocity) and shorter distances for the months Sagittarius/Capricorn (faster angular velocity)— see Evans et al. (2010). Additionally, it was faster and easier to construct and divide the zodiac dial ring into 365 parts than to produce the Egyptian dial ring and the bearing base ring, both of which had to be divided into 365 parts but also have holes drilled correspondingly. That said, the division of these two rings could be done simultaneously by an ancient craftsman. It seems that the Antikythera Mechanism was a device that measured time (see Table 1), and this paper examines the scenario that the zodiac dial ring was divided into units of time, in 365 subdivisions-days (instead of arc degrees, which are units for angle/space measurement). Thus, star risings and settings on the parapegma were measured in days (units of time) and they were classified for each zod- 2.3 Dividing the Zodiac Dial Ring into 365 Equal Subdivisions/Days The Egyptian and the zodiac dial rings have equal design, were concentric and their common centers coincided with the bin/bout axis (which was also the center of the Mechanism’s lunar disk), which was where the Earth was located. ~ 263 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 7: A close-up on the central front area of the authors’ bronze reconstructed functioning model of the Antikythera Mechanism (here only the relevant parts are assembled): the lunar disc—ΔΙΣΚΟΣ ΣΕΛΗΝΗΣ (the ideal and proper input to the device; Voulgaris et al., 2018b; 2022; 2024; Roumeliotis, 2018); its lunar pointer— ΠΡΟΕΧΟΝ ΑΥΤΟΥ ΓΝΩΜΟΝΙΟΝ Σ[ΕΛΗΝΗΣ; the golden sphere–Sun—ΧΡΥΣΟΥΝ ΣΦΑΙΡΙΟΝ; its solar pointer Sun ray—ΗΛΙΟΥ ΑΚΤΙΝ (Bitsakis and Jones, 2016a); the zodiac month ring—ΚΥΚΛΟΣ ΕΓΛΕΙΠΤΙΚΟΣ; and the Egyptian dial ring—ΚΥΚΛΟΣ ΑΙΓΥΠΤΙΑΚΟΣ (as defined by the authors). If the two rings (which in this photograph are randomly placed) are divided into days, then any date on the zodiac month ring can correspond to a date in the Egyptian calendar (and vice versa). In the photograph (by the authors), the lunar pointer points at the golden sphere–Sun, New Moon phase and therefore the lunar phases sphere is totally black. The solar pointer points at the zodiac day subdivision of 22 Cancer, which corresponds to the 16th day of Thoth. The position of the two rings changes by one subdivision every four rotations of the golden sphere. The lost cover of the b1-gear is also presented, in which six circles are engraved, presenting the orbit of each of the five planets and the Sun, according to the preserved phrase on the back cover Inscription (Bitsakis and Jones, 2016b). ΚΡΟΝΟΥ ΦΑ[ΙΝΟΝΤΟΣ ΚΥΚΛΟΣ—orbit of Kronos–Phainon–Saturn; ΠΕΡΙΦΕΡΕΙΑ—(circumference) for Mercury, Venus and the Sun; ΚΥΚΛΟΣ—(circle) for Mars, Jupiter and Saturn (see the Appendix at the end of this paper). The scale of the Egyptian dial ring represents the duration of the Egyptian year: 12 months of 30 days plus 5 days named ΕΠΑΓΟΜΕΝΑΙ epagomenal, in total 365.0 days. ery four solar tropical years, as Geminus also mentions. This procedure can be mechanically represented on the Mechanism by turning the Egyptian dial ring by one sub-division-day counterclockwise every four full turns of the golden sphere. The second dial scale with a common center to the Egyptian dial ring, the zodiac dial ring could also be a time-measuring scale, which represents the solar tropical year. Under this assumption, the two concentric and successive Egyptian and zodiac scales have equal design and represent the concept of the year’s duration in units of time for these two different systems. Both systems are directly related to the timed motion of the Sun (while the lunar year has no relation to this operation). The time difference between the Egyptian year (= 365.0d) and one full turn of the golden sphere–Sun (= 365.25d), becomes one day ev- The division of the two rings into 365 days creates a visualization of this time difference between the two calendars. For a specific year, the user can match any date between the two rings e.g. which Egyptian date corresponds to the Summer Solstice (1st Cancer) or to a specific star event, or which zodiac date corresponds to the 17th day of Hathyr, which is the starting date of the Isia Feast (Jones 2000; Voulgaris et al., 2023a; 2023c); see Figure 7. Additionally, the parapegma events occur on specific dates (not in degrees of Ecliptic long~ 264 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Table 2: The duration of the astronomical seasons according to Democritus; Meton (observations in 432 BC); Euctemon (collaborated with Meton); Callippus (c. 370 BC – 300 BC); Geminus, work and parapegma collection (1st cent. BC); and Cleomedes (between the mid-1st century BC and 400 AD). The preserved numbers are in red. Spring has the maximum number of days, as the aphelion day occurs a little before the end of Spring. The Earth is located at perihelion close to the end of Autumn. Eudoxus’ season durations are not in agreement with the solar anomaly. Astronomical Season/ Period Winter Solstice up to 1 day before the Vernal Equinox According to: Meton Euctemon Callippus Eudoxus Democritus Summer Solstice up to 1 day before the Autumn Equinox 90⅛ Vernal Equinox up to 1 day before Summer Solstice (includes the aphelion day) 93 93 <94> <91> [91] or [92] or [93] or [90] 94½ 89 95 90¼ 94½ 92 92 90 91 91 Geminus (Elem. Astron.) Geminus (Par. collection) Cleomedes 90 90 92 91 [92] or [91] or [90] or [93] 92½ Autumn Equinox up to 1 day before Winter Solstice (includes the perihelion day) 90 90 89 92 Duration of the Year 365d 365d 365d 365d 365d 91 88⅛ 365.25d 92 89 365d 92½ 88 365.25d itude), and the parapegma units-days would be in better agreement if the zodiac subdivisions were in days, since the index letters of the events are engraved on some of the zodiac subdivisions (Anastasiou et al., 2013; Bitsakis and Jones, 2016a). Sun around the perihelion needs fewer days to travel across a zodiac sign of 30° (higher angular velocity) and more days when it is around the aphelion (lower angular velocity). This means that the four seasons do not have the same duration. The 365 subdivisions of the zodiac dial ring correspond to the days for the solar tropical cycle, and at the same time they cannot be considered as ‘days’ for the lunar pointer: the number of days for one full turn of the lunar disc/pointer should be 27.321 subdivisions, as one full turn of the lunar pointer corresponds to one sidereal cycle14 i.e. the lunar pointer after its rotation, returns to the same position in the same zodiac constellation15 (the gearing of the Antikythera Mechanism agrees with this condition). The duration of the four seasons is mentioned by Democritus, Meton, Euctemon, Callippus, Eudoxus, Geminus and Cleomedes (see Blass, 1887; Bowen and Goldstein, 1988; Goldstein and Bowen, 1983; Hannah, 2002; Huxley, 1963; Lehoux, 2007; Manitius, 1880; Neugebauer, 1975; Rehm, 1913, 1941; 1949; van der Waerden, 1960; 1984a). Geminus and Cleomedes (Bowen and Todd, 2004; Manitius, 1898; Spandagos, 2002; Ziegler, 1891) state the duration of each astronomical season with an accuracy up to ⅛ of a day (Table 2). Probably they had measuring instruments with higher resolution than the older astronomers and a larger number of observations. 2.4 Four Scenarios for the Zodiac Ring Division 2.4.1 Scenario 1 For practical measuring reasons, rounding the day fraction to an integer number of days is needed. This means that the rounding can be to the next or to the current day (e.g. 94½ can be rounded to 94 or to 95, as also 90⅛ is rounded to 90 or 91). Only about 20% of the zodiac dial ring is preserved, so we do not know the exact durations of the four seasons, nor the day distribution per zodiac month, except for the months ΧΗΛΑΙ and ΣΚΟΡΠΙΟΣ, which have 30 subdivisions/days (Bitsakis and Jones, 2016a). The zodiac dial ring was a time-measuring scale, just like the Egyptian dial calendar ring. The zodiac ring was divided into 365 equal subdivisions representing the rounded value of 365.25 days per one solar tropical year (Voulgaris et al., 2018a). The 365 equal distance subdivisions correspond to the 12 zodiac months and each zodiac month has an unequal number of days: the number of days per zodiac month depends on the number of days the Sun is found within the boundaries of the corresponding zodiac sign spanning 30° (see Table 2). The day distribution for each zodiac month can be calculated taking into account the number of days per astronomical season (Table 2). The two opposite zodiac months, which include Zodiac months do not all have an equal number of days, due to the solar anomaly: the ~ 265 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Table 3: Analysis of the seasons and the durations of the zodiac months. The first row presents the duration of each season mentioned by Geminus. Following are five best rounding allocations to an integer number of days per zodiac month. For the calculations it was taken into account that the perihelion date belongs to the zodiac month of Sagittarius (with the shortest number of days) and the aphelion date belongs to the zodiac month of Gemini (with the largest number of days—see Voulgaris et al., 2018a). Note that five out of six options of the best rounding present Libra and Scorpio with 30 subdivisions-days, as are also preserved for Libra and Scorpio in Fragment C. Further below, the duration of the seasons mentioned by Cleomedes and the two best roundings in integer numbers are presented. The calendar of Dionysios is presented at the end, which was divided into 12 zodiac months: 11 months  30 days + 1 month  35 days or 36 days every four years (ΔΙΔΥΜΩΝΟΣ—Gemini; see Boeckh, 1863; van der Waerden, 1984b). Number of days per Zodiac month (distribution) Best rounding 1 Seasons duration 1 Best rounding 2 Seasons duration 2 Best rounding 3 Seasons duration 3 Best rounding 4 Seasons duration 4 Best rounding 5 Seasons duration 5 Best rounding 6 Seasons duration 6 Lib 30 30 30 30 30 30 30 Seasons’ Durations Best rounding A Best rounding B Best rounding C Days/zodiac month Days per Season 30 Astronomical Season Duration According to Geminus Autumn 881/8 Winter 901/8 Spring 941/2 Sco Sgr Cap Aqr Psc Ari Tau Gem Perihelion Aphelion 31 31 31 311/2 32 30 31 31 31 32 89 90 94 30 29 29 30 31 31 31 32 89 90 94 30 29 29 30 30 31 31 32 89 89 94 30 28 30 30 30 31 31 32 88 90 94 30 28 29 30 31 31 31 32 90 94 29 29 29 30 31 31 31 32 88 90 94 Astronomical Season Duration According to Cleomedes Autumn 88 Winter 90¼ Spring 94½ 88 90 94 88 91 94 88 90 95 Zodiac Month Duration of Dionysios’ Calendar 30 30 30 30 30 30 30 35/(36) 90 90 95/(96) 30 30 281/8 29 281/8 29 Summer 921/2 Cnc Leo Vir 32 32 31 32 31 31 31 301/2 30 92 31 92 31 93 31 93 31 93 31 93 30 30 30 30 31 31 31 Summer 92½ 93 92 92 30 30 90 30 aphelion (Gemini) and perihelion (Sagittarius), should have the maximum and the minimum number of days respectively. The distribution of days for the remaining zodiac months can be determined by adding a ‘uniform’ increment for every month when moving from Sagittarius towards Gemini, and a ‘uniform’ decrement for the months moving from Gemini towards Sagittarius (Neugebauer, 1975: 628, 1352, Figures 3 and 4; see also Voulgaris et al., 2018a: Figure 12). ed in Figures 8 and 9. By selecting the ‘Best rounding 1’ in Table 3, the 12 zodiac months were divided into days/subdivisions ranging from 29 to 32. The distribution of the number of days per zodiac month is symmetrical with respect to the line of Solstices. By applying the ‘Best rounding 1’ for the initial calibration date of the Antikythera Mechanism (23 December 178 BC—Winter Solstice—1st Day of Capricorn; Voulgaris et al., 2023a; 2023c), the dates for each zodiac month can be deduced (Table 4). Since there is a strong correlation between Geminus’ astronomy and the Antikythera Mechanism (parapegma events on the plates, the information engraved on the Metonic spiral, intercalary months, excluded days and Saros spirals, the Exeligmos pointer, and the initial starting date of the Mechanism based on Geminus’ definition for Exeligmos), the season duration mentioned by Geminus (Manitius, 1880: Chapter 1) was selected for the analysis in Table 3. That said, it is not clear if the season durations mentioned by Geminus were based on his own observations or on the work of earlier astronomers. The phrase ΔΙΔΥΜΟΙ ΑΡΧΟΝΤΑΙ ΕΠΙΤΕΛΛΕΙΝ (Gemini begins to rise) engraved by the ancient craftsman on parapegma plate 1 (Bitsakis and Jones, 2016a), means that the Sun crosses the first boundary/entry of the Gemini sign and rises at the same time with it on this specific date. For seven zodiac signs there is no prominent star in the sky on/near the first entry/ boundary of the respective sign. Therefore, the position of these signs in the sky can only be found if the first entries have been predefined on specific dates, or if the first entries of these signs are prepositioned in the sky and therefore their corresponding dates can be calculated. An exception is the first entry in the Leo Based on Table 3, two out of the six rounded distributions are reconstructed and present~ 266 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Figure 8 (left): An option for the zodiac dial ring divided into twelve zodiac months and a total of 365 equal subdivisions (days). The 12 zodiac months do not have the same numbers of days. For the zodiac ring reconstruction, the ‘Best Rounding 1’ of Table 4 was selected. Insert: the center of the zodiac ring. In magenta the line of Solstices connects the 1st of Capricorn and the 1st of Cancer. The line of Solstices does not cross the center of the zodiac dial ring due to the unequal lengths of the seasons. Note that no two ‘opposite’ radii form a real diameter. (About the headline: for the letter ‘Z’ the ancient craftsman used an ‘I’ with long serifs). Figure 9 (right): A second option for the zodiac dial ring, divided into twelve zodiac months and a total of 365 equal subdivisions (days). The zodiac months do not have the same numbers of days. For the zodiac dial ring reconstruction, the ‘Best Rounding 2’ in Table 4 was selected. This option is also in agreement with the preserved 30 subdivisions of Claws (Libra) and Scorpion (after Bitsakis and Jones, 2016a). Table 4: The duration of each zodiac month, based on Geminus’ seasonal durations, using the ‘Best Rounding 1’ from Table 3. The calculated corresponding dates of the zodiac months start from 23 December 178 BC (1st day of Capricorn), which is the initial calibration date of the Antikythera Mechanism (Voulgaris et al., 2023a). The dates of perihelion and aphelion were calculated using the Starry Night Pro planetarium software. Zodiac Month Capricorn/Winter Solstice/ ΑΙΓΟΚΕΡΩΣ/ΤΡΟΠΑΙ ΧΕΙΜΕΡΙΝΑΙ Aquarius/ΥΔΡΟΧΟΟΣ Pisces/ΙΧΘΥΕΣ Aries/Spring Equinox ΚΡΙΟΣ/ΙΣΗΜΕΡΙΑ ΕΑΡΙΝΗ Taurus/ΤΑΥΡΟΣ Gemini/ΔΙΔΥΜΟΙ Cancer/Summer Solstice ΚΑΡΚΙΝΟΣ/ΤΡΟΠΑΙ ΘΕΡΙΝΑΙ Leo/ΛΕΩΝ Virgo/ΠΑΡΘΕΝΟΣ Claws/Libra/Autumnal Equinox ΧΗΛΑΙ/ΙΣΗΜΕΡΙΑ ΦΘΙΝΟΠΩΡΙΝΗ Scorpius/ΣΚΟΡΠΙΟΣ Sagittarius/ΤΟΞΟΤΗΣ Zodiac Month Duration (Best rounding 1) 29 Winter Season Period: 90 days 30 31 31 Spring Season Period: 94 days 31 32 32 Summer Season Period: 92 days 30 30 30 Autumn Season Period: 89 days Dates of Zodiac Months for 178 BC 23 December–20 January 21 January–19 February 20 February–22 March 23 March–22 April 23 April–23 May 24 May–24 June (aphelion ~30 May) 25 June–26 July 27 July (α Leonis/Regulus rises with the Sun on this date)–25 August 26 August–24 September 25 September–24 October 30 29 25 October–23 November 24 November–22 December (perihelion ~29 November) sign, which presents a peculiarity: α Leonis/ Regulus (Basiliscus = ‘The Little King’ or ‘The Lion Heart’, named in the Almagest—see Heiberg, 1898–1903; see, also, Allen, 1963; Plakidis, 1992) is too close to the Ecliptic (see Voulgaris et al., 2023b: Figure 12), only ~21 arc min apart and rises with the Sun on 27 July in the era 180 BC (calculated with Starry Night Pro software) and this also applies for more than 150 years before and after 180 BC. There- fore, the zodiac sign of Leo could have a predefined rising date. The division of the Ecliptic into 12 sectors of 30° each can be easily achieved with high accuracy by starting the Ecliptic circle division with Regulus, using an astrolabe and an astronomical map. 2.4.2 Scenario 2 In the Eudoxus papyrus (Blass, 1887: Column I, 10 – 20) it is mentioned that the Sun travels ~ 267 ~ The Antikythera Mechanism’s Zodiac Dial Ring A. Voulgaris, C. Mouratidis and A. Vossinakis Table 5: According to Column I, 10–20 in the Eudoxus papyrus (Blass, 1887), the duration of each zodiac month is 30 days, but there are two extra days for the Summer solstice (before the 1st day of Cancer) and three extra days for the Winter solstice (before the 1st day of Capricorn). However, the specific ordinance of the extra days contradicts the solar anomaly effect. The present reference could be erroneous, since the opposite arrangement (here in red) of the extra days matches very well the solar anomaly/dates of perihelion and aphelion (the 3rd column in the table). The extra days could be considered as independent days (3 rd column) or they could be included in the zodiac months of Cancer (33 days) and Capricorn (32 days) (the 4thcolumn). Zodiac Month Number of Days per Zodiac Month Aries/Kριός Taurus/Ταύρος Gemini/Δίδυμοι Summer Solstice/ΤΡΟΠΑΙ ΘΕΡΙΝΑΙ Cancer/Καρκίνος Leo/Λέων Virgo/Παρθένος Libra/Claws/Χηλαί Scorpion/Σκορπιός Sagittarius/Τοξότης Winter Solstice/ΤΡΟΠΑΙ ΧΕΙΜΕΡΙΝΑΙ Capricorn/Αιγόκερως Aquarius/Υδροχόος Pisces/Ιχθείς Tropical Year duration 30 30 30 2(!) 30 30 30 30 30 30 3(!) 30 30 30 Correction Based on the Solar Anomaly (Scenario 2A in Figure 10) 30 30 30 3 (engraved letters ΤΘ) 30 3