Information on the specific data obtained from the fragments is detailed in the supplement to the 2006
Nature article from Freeth et al.
Operation On the front face of the mechanism, there is a fixed ring dial representing the
ecliptic, the twelve
zodiacal signs marked off with equal 30-degree sectors. This matched with the Babylonian custom of assigning one twelfth of the ecliptic to each zodiac sign equally, even though the
constellation boundaries were variable. Outside that dial is another ring which is rotatable, marked off with the months and days of the Sothic
Egyptian calendar, twelve months of 30 days plus five
intercalary days. The months are marked with the Egyptian names for the months transcribed into the
Greek alphabet. The first task is to rotate the Egyptian calendar ring to match the current zodiac points. The Egyptian calendar ignored leap days, so it advanced through a full zodiac sign in about 120 years. The mechanism was operated by turning a small hand crank (now lost) which was linked via a
crown gear to the largest gear, the four-spoked gear visible on the front of fragment A, gear b1. This moved the date pointer on the front dial, which would be set to the correct Egyptian calendar day. The year is not selectable, so it is necessary to know the year currently set, or by looking up the cycles indicated by the various calendar cycle indicators on the back in the Babylonian
ephemeris tables for the day of the year currently set, since most of the calendar cycles are not synchronous with the year. The crank moves the date pointer about 78 days per full rotation, so hitting a particular day on the dial would be easily possible if the mechanism were in good working condition. The action of turning the hand crank would also cause all interlocked gears within the mechanism to rotate, resulting in the simultaneous calculation of the position of the Sun and Moon, the
moon phase,
eclipse, and calendar cycles, and perhaps the locations of
planets. The operator also had to be aware of the position of the spiral dial pointers on the two large dials on the back. The pointer had a "follower" that tracked the spiral incisions in the metal as the dials incorporated four and five full rotations of the pointers. When a pointer reached the terminal month location at either end of the spiral, the pointer's follower had to be manually moved to the other end of the spiral before proceeding further.
Faces Front face The front dial has two concentric circular scales. The inner scale marks the Greek signs of the zodiac, with division in degrees. The outer scale, which is a movable ring that sits flush with the surface and runs in a channel, is marked off with what appear to be days and has a series of corresponding holes beneath the ring in the channel. Since the discovery of the mechanism more than a century ago, this outer ring has been presumed to represent a 365-day Egyptian solar calendar, but research (Budiselic, et al., 2020) challenged this presumption and provided direct statistical evidence there are 354 intervals, suggesting a lunar calendar. Since this initial discovery, two research teams, using different methods, independently calculated the interval count. Woan and Bayley calculate 354–355 intervals using two different methods, confirming with higher accuracy the Budiselic et al. findings and noting that "365 holes is not plausible". Malin and Dickens' best estimate is 352.3±1.5 and concluded that the number of holes (N) "has to be integral and the SE (
standard error) of 1.5 indicates that there is less than a 5% probability that N is not one of the six values in the range 350 to 355. The chances of N being as high as 365 are less than 1 in 10,000. While other contenders cannot be ruled out, of the two values that have been proposed for N on astronomical grounds, that of Budiselic et al. (354) is by far the more likely." If one supports the 365 day presumption, it is recognized the mechanism predates the
Julian calendar reform, but the
Sothic and
Callippic cycles had already pointed to a day solar year, as seen in
Ptolemy III's attempted calendar reform of 238 BC. The dials are not believed to reflect his proposed leap day (
Epag. 6), but the outer calendar dial may be moved against the inner dial to compensate for the effect of the extra quarter-day in the solar year by turning the scale backward one day every four years. If one is in favour of the 354 day evidence, the most likely interpretation is that the ring is a manifestation of a 354-day lunar calendar. Given the era of the mechanism's presumed construction and the presence of Egyptian month names, it is possibly the first example of the Egyptian civil-based
lunar calendar proposed by
Richard Anthony Parker in 1950. The lunar calendar's purpose was to serve as a day-to-day indicator of successive lunations, and would also have assisted with the interpretation of the lunar phase pointer, and the
Metonic and
Saros dials. Undiscovered gearing, synchronous with the rest of the Metonic gearing of the mechanism, is implied to drive a pointer around this scale. Movement and registration of the ring relative to the underlying holes served to facilitate both a 1-in-76-year
Callippic cycle correction, as well as convenient lunisolar intercalation. The dial also marks the position of the Sun on the ecliptic, corresponding to the current date in the year. The orbits of the Moon and the five planets known to the Greeks are close enough to the ecliptic to make it a convenient reference for defining their positions as well. The following three
Egyptian months are inscribed in
Greek letters on the surviving pieces of the outer ring: • (
Pashons) • (
Payni) • (
Epiphi) The other months have been reconstructed; some reconstructions of the mechanism omit the five days of the Egyptian intercalary month. The Zodiac dial contains Greek inscriptions of the members of the zodiac, which is believed to be adapted to the
tropical month version rather than the
sidereal: • ( [Ram], Aries) • ΤΑΥΡΟΣ (Tauros [Bull], Taurus) • ΔΙΔΥΜΟΙ (Didymoi [Twins], Gemini) • ΚΑΡΚΙΝΟΣ (Karkinos [Crab], Cancer) • ΛΕΩΝ (Leon [Lion], Leo) • ΠΑΡΘΕΝΟΣ (Parthenos [Maiden], Virgo) • ΧΗΛΑΙ (Chelai [Scorpio's Claw or Zygos], Libra) • ΣΚΟΡΠΙΟΣ (Skorpios [Scorpion], Scorpio) • ΤΟΞΟΤΗΣ (Toxotes [Archer], Sagittarius) • ΑΙΓΟΚΕΡΩΣ (Aigokeros [Goat-horned], Capricorn) • ΥΔΡΟΧΟΟΣ (Hydrokhoos [Water carrier], Aquarius) • ΙΧΘΥΕΣ (Ichthyes [Fish], Pisces) Also on the zodiac dial are single characters at specific points (see reconstruction at ref). They are keyed to a
parapegma, a precursor of the modern day
almanac inscribed on the front face above and beneath the dials. They mark the locations of longitudes on the ecliptic for specific stars. The
parapegma above the dials reads (square brackets indicate inferred text): The
parapegma beneath the dials reads: At least two pointers indicated positions of bodies upon the ecliptic. A lunar pointer indicated the position of the Moon, and a mean Sun pointer was shown, perhaps doubling as the current date pointer. The Moon position was not a simple mean Moon indicator which would indicate movement uniformly around a circular orbit; rather, it approximated the acceleration and deceleration of the Moon's elliptical orbit, through the earliest extant use of
epicyclic gearing. It also tracked the precession of the Moon's elliptical orbit around the ecliptic in an 8.88 year cycle. The mean Sun position is, by definition, the current date. It is speculated that since significant effort was taken to ensure the position of the Moon was correct, there was likely to have also been a "true sun" pointer in addition to the mean Sun pointer, to track the elliptical anomaly of the Sun (the orbit of Earth around the Sun), but there is no evidence of it among the fragments found. Similarly, neither is there the evidence of planetary orbit pointers for the five planets known to the Greeks among the fragments. But see
Proposed gear schemes below. Mechanical engineer Michael Wright demonstrated there was a mechanism to supply the lunar phase in addition to the position. The indicator was a small ball embedded in the lunar pointer, half-white and half-black, which rotated to show the phase (new, first quarter, half, third quarter, full, and back). The data to support this function is available given the Sun and Moon positions as angular rotations; essentially, it is the angle between the two, translated into the rotation of the ball. It requires a
differential gear, a gearing arrangement that sums or differences two angular inputs.
Rear face In 2008, scientists reported new findings in
Nature showing the mechanism not only tracked the
Metonic calendar and predicted
solar eclipses, but also calculated the timing of panhellenic athletic games, such as the
ancient Olympic Games. Inscriptions on the instrument closely match the names of the months that are used on calendars from
Epirus in northwestern Greece and with the island of
Corfu, which in antiquity was known as Corcyra. On the back of the mechanism, there are five dials: the two large displays, the Metonic and the
Saros, and three smaller indicators, the so-called Olympiad Dial, which has been renamed the Games dial as it did not track Olympiad years (the four-year cycle it tracks most closely is the Halieiad), the
Callippic, and the
exeligmos. The Metonic dial is the main upper dial on the rear of the mechanism. The Metonic cycle, defined in several physical units, is 235
synodic months, which is very close (to within less than 13 one-millionths) to 19 tropical years. It is therefore a convenient interval over which to convert between lunar and solar calendars. The Metonic dial covers 235 months in five rotations of the dial, following a spiral track with a follower on the pointer that keeps track of the layer of the spiral. The pointer points to the synodic month, counted from new moon to new moon, and the cell contains the
Corinthian month names. • () • ΚΡΑΝΕΙΟΣ (Kraneios) • ΛΑΝΟΤΡΟΠΙΟΣ (Lanotropios) • ΜΑΧΑΝΕΥΣ (Machaneus,
"mechanic", referring to
Zeus the inventor) • ΔΩΔΕΚΑΤΕΥΣ (Dodekateus) • ΕΥΚΛΕΙΟΣ (Eukleios) • ΑΡΤΕΜΙΣΙΟΣ (Artemisios) • ΨΥΔΡΕΥΣ (Psydreus) • ΓΑΜΕΙΛΙΟΣ (Gameilios) • ΑΓΡΙΑΝΙΟΣ (Agrianios) • ΠΑΝΑΜΟΣ (Panamos) • ΑΠΕΛΛΑΙΟΣ (Apellaios) Thus, setting the correct solar time (in days) on the front panel indicates the current lunar month on the back panel, with resolution to within a week or so. Based on the fact that the calendar month names are consistent with all the evidence of the Epirote calendar and that the Games dial mentions the very minor Naa games of Dodona (in Epirus), it has been argued that the calendar on the mechanism is likely to be the Epirote calendar, and that this calendar was probably adopted from a Corinthian colony in Epirus, possibly Ambracia. It has been argued that the first month of the calendar, Phoinikaios, was ideally the month in which the autumn equinox fell, and that the start-up date of the calendar began shortly after the astronomical new moon of 23 August 205 BC. The Games dial is the right secondary upper dial; it is the only pointer on the instrument that travels in an anticlockwise direction as time advances. The dial is divided into four sectors, each of which is inscribed with a year indicator and the name of two
Panhellenic Games: the "crown" games of
Isthmia,
Olympia,
Nemea, and
Pythia; and two lesser games: Naa (held at
Dodona) and the
Halieia of Rhodes. The inscriptions on each one of the four divisions are: The Saros dial is the main lower spiral dial on the rear of the mechanism. The Saros cycle is 18 years and days long (6585.333... days), which is very close to 223 synodic months (6585.3211 days). It is defined as the cycle of repetition of the positions required to cause solar and lunar eclipses, and therefore, it could be used to predict them—not only the month, but the day and time of day. The cycle is approximately 8 hours longer than an integer number of days. Translated into global spin, that means an eclipse occurs not only eight hours later, but one-third of a rotation farther to the west. Glyphs in 51 of the 223 synodic month cells of the dial specify the occurrence of 38 lunar and 27 solar eclipses. Some of the abbreviations in the glyphs read: • Σ = ΣΕΛΗΝΗ ("Selene", Moon) • Η = ΗΛΙΟΣ ("Helios", Sun) • H\M = ΗΜΕΡΑΣ ("Hemeras", of the day) • ω\ρ = ωρα ("hora", hour) • N\Y = ΝΥΚΤΟΣ ("Nuktos", of the night) The glyphs show whether the designated eclipse is solar or lunar, and give the day of the month and hour. Solar eclipses may not be visible at any given point, and lunar eclipses are visible only if the Moon is above the horizon at the appointed hour. In addition, the inner lines at the cardinal points of the Saros dial indicate the start of a new
full moon cycle. Based on the distribution of the times of the eclipses, it has been argued the start-up date of the Saros dial was shortly after the astronomical new moon of 28 April 205 BC. The Exeligmos dial is the secondary lower dial on the rear of the mechanism. The exeligmos cycle is a 54-year triple Saros cycle that is 19,756 days long. Since the length of the Saros cycle is to a third of a day (namely, 6,585 days plus 8 hours), a full exeligmos cycle returns the counting to an integral number of days, as reflected in the inscriptions. The labels on its three divisions are: • Blank or o ? (representing the number zero, assumed, not yet observed) • H (number 8) means add 8 hours to the time mentioned in the display • Iϛ (number 16) means add 16 hours to the time mentioned in the display Thus the dial pointer indicates how many hours must be added to the glyph times of the Saros dial in order to calculate the exact eclipse times.
Doors of 223 months, present on fragment 19. The mechanism has a wooden casing with a front and a back door, both containing inscriptions. The back door appears to be the 'instruction manual'. On fragment 19, it is written "76 years, 19 years" representing the
Callippic and
Metonic cycles. Also written is "223" for the
Saros cycle. On fragment E, it is written "on the spiral subdivisions 235" referring to the Metonic dial.
Gearing The mechanism is remarkable for the level of miniaturisation and the complexity of its parts, which is comparable to that of 14th-century
astronomical clocks. It has at least 30 gears, although mechanism expert Michael Wright has suggested the Greeks of this period were capable of implementing a system with many more gears. There is debate as to whether the mechanism had indicators for all five of the planets known to the ancient Greeks. No gearing for such a planetary display survives and all gears are accounted for—with the exception of one 63-toothed gear (r1) otherwise unaccounted for in fragment D. Fragment D is a small quasi-circular constriction that, according to Xenophon Moussas, has a gear inside a somewhat larger hollow gear. The inner gear moves inside the outer gear reproducing an epicyclical motion that, with a pointer, gives the position of planet Jupiter. The inner gear is numbered 45, "ME" in Greek, and the same number is written on two surfaces of this small cylindrical box. The purpose of the front face was to position astronomical bodies with respect to the
celestial sphere along the ecliptic, in reference to the observer's position on the Earth. That is irrelevant to the question of whether that position was computed using a heliocentric or geocentric view of the
Solar System; either computational method should, and does, result in the same position (ignoring ellipticity), within the error factors of the mechanism. The epicyclic Solar System of
Ptolemy (–)—hundreds of years after the apparent construction date of the mechanism—carried forward with more epicycles, and was more accurate predicting the positions of planets than the view of
Copernicus (1473–1543), until
Kepler (1571–1630) introduced the possibility that orbits are ellipses. Evans et al. suggest that to display the mean positions of the five
classical planets would require only 17 further gears that could be positioned in front of the large driving gear and indicated using individual circular dials on the face. Freeth and Jones modelled and published details of a version using gear trains mechanically similar to the lunar anomaly system, allowing for indication of the positions of the planets, as well as synthesis of the Sun anomaly. Their system, they claim, is more authentic than Wright's model, as it uses the known skills of the Greeks and does not add excessive complexity or internal stresses to the machine. The gear teeth were in the form of
equilateral triangles with an average circular pitch of 1.6 mm, an average wheel thickness of 1.4 mm and an average air gap between gears of 1.2 mm. The teeth were probably created from a blank bronze round using hand tools; this is evident because not all of them are even. Due to advances in imaging and
X-ray technology, it is now possible to know the precise number of teeth and size of the gears within the located fragments. Thus the basic operation of the device is no longer a mystery and has been replicated accurately. The major unknown remains the question of the presence and nature of any planet indicators. A table of the gears, their teeth, and the expected and computed rotations of important gears follows. The gear functions come from Freeth et al. (2008) and for the lower half of the table from Freeth et al. (2012). The computed values start with 1 year per revolution for the b1 gear, and the remainder are computed directly from gear teeth ratios. The gears marked with an asterisk (*) are missing, or have predecessors missing, from the known mechanism; these gears have been calculated with reasonable gear teeth counts. (Lengths in days are calculated assuming the year to be 365.2425 days.)
Table notes: There are several gear ratios for each planet that result in close matches to the correct values for synodic periods of the planets and the Sun. Those chosen above seem accurate, with reasonable tooth counts, but the specific gears actually used are unknown.
Known gear scheme It is very probable there were planetary dials, as the complicated motions and periodicities of all planets are mentioned in the manual of the mechanism. The exact position and mechanisms for the gears of the planets is unknown. There is no coaxial system except for the Moon. Fragment D that is an epicycloidal system, is considered as a planetary gear for Jupiter (Moussas, 2011, 2012, 2014) or a gear for the motion of the Sun (University of Thessaloniki group). The Sun gear is operated from the hand-operated crank (connected to gear a1, driving the large four-spoked mean Sun gear, b1) and in turn drives the rest of the gear sets. The Sun gear is b1/b2 and b2 has 64 teeth. It directly drives the date/mean sun pointer (there may have been a second, "true sun" pointer that displayed the Sun's elliptical anomaly; it is discussed below in the Freeth reconstruction). In this discussion, reference is to modelled rotational period of various pointers and indicators; they all assume the input rotation of the b1 gear of 360 degrees, corresponding with one tropical year, and are computed solely on the basis of the gear ratios of the gears named. The Moon train starts with gear b1 and proceeds through c1, c2, d1, d2, e2, e5, k1, k2, e6, e1, and b3 to the Moon pointer on the front face. The gears k1 and k2 form an
epicyclic gear system; they are an identical pair of gears that do not mesh, but rather, they operate face-to-face, with a short pin on k1 inserted into a slot in k2. The two gears have different centres of rotation, so the pin must move back and forth in the slot. That increases and decreases the radius at which k2 is driven, also necessarily varying its angular velocity (presuming the velocity of k1 is even) faster in some parts of the rotation than others. Over an entire revolution the average velocities are the same, but the fast-slow variation models the effects of the elliptical orbit of the Moon, in consequence of
Kepler's second and third laws. The modelled rotational period of the Moon pointer (averaged over a year) is 27.321 days, compared to the modern length of a lunar sidereal month of 27.321661 days. The pin/slot driving of the k1/k2 gears varies the displacement over a year's time, and the mounting of those two gears on the e3 gear supplies a precessional advancement to the ellipticity modelling with a period of 8.8826 years, compared with the current value of precession period of the moon of 8.85 years. The system also models the
phases of the Moon. The Moon pointer holds a shaft along its length, on which is mounted a small gear named r, which meshes to the Sun pointer at B0 (the connection between B0 and the rest of B is not visible in the original mechanism, so whether b0 is the current date/mean Sun pointer or a hypothetical true Sun pointer is unknown). The gear rides around the dial with the Moon, but is also geared to the Sun—the effect is to perform a
differential gear operation, so the gear turns at the synodic month period, measuring in effect, the angle of the difference between the Sun and Moon pointers. The gear drives a small ball that appears through an opening in the Moon pointer's face, painted longitudinally half white and half black, displaying the phases pictorially. It turns with a modelled rotational period of 29.53 days; the modern value for the synodic month is 29.530589 days. The Metonic train is driven by the drive train b1, b2, l1, l2, m1, m2, and n1, which is connected to the pointer. The modelled rotational period of the pointer is the length of the 6,939.5 days (over the whole five-rotation spiral), while the modern value for the
Metonic cycle is 6,939.69 days. The
Olympiad train is driven by b1, b2, l1, l2, m1, m2, n1, n2, and o1, which mounts the pointer. It has a computed modelled rotational period of exactly four years, as expected. It is the only pointer on the mechanism that rotates anticlockwise; all of the others rotate clockwise. The Callippic train is driven by b1, b2, l1, l2, m1, m2, n1, n3, p1, p2, and q1, which mounts the pointer. It has a computed modelled rotational period of 27,758 days, while the modern value is 27,758.8 days. The Saros train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, and g1, which mounts the pointer. The modelled rotational period of the Saros pointer is 1,646.3 days (in four rotations along the spiral pointer track); the modern value is 1,646.33 days. The Exeligmos train is driven by b1, b2, l1, l2, m1, m3, e3, e4, f1, f2, g1, g2, h1, h2, and i1, which mounts the pointer. The modelled rotational period of the exeligmos pointer is 19,756 days; the modern value is 19,755.96 days. It appears gears m3, n1-3, p1-2, and q1 did not survive in the wreckage. The functions of the pointers were deduced from the remains of the dials on the back face, and reasonable, appropriate gearage to fulfill the functions was proposed and is generally accepted. ==Reconstruction efforts==