|Nothing like this instrument is preserved elsewhere. Nothing comparable to it is known. from any ancient scientific text or literary allusion. On the contrary, from all that we know of science and technology in the Hellenistic Age we should have felt that such a device could not exist. Some historians have suggested that the Greeks were not interested in experiment because of a contempt-perhaps induced by the existence of the institution of slavery-for manual labor. On the other hand it has long been recognized that in abstract mathematics and in mathematical astronomy they were no beginners but rather “fellows of another college” who reached great heights of sophistication. Many of the Greek scientific devices known to us from written descriptions show much mathematical ingenuity, but in all cases the purely mechanical part of the design seems relatively crude. Gearing was clearly known to the Greeks, but it was used only in relatively simple applications. They employed pairs of gears to change angular speed or mechanical ad- vantage, or to apply power through a right angle, as in the water-driven mill.Even the most complex mechanical devices described by the ancient writers Hero of Alexandria and Vitruvius contained only simple gearing. For example, the taximeter used by the Greeks to measure the distance travelled by the wheels of a carriage employed only pairs of gears (or gears and worms) to achieve the necessary ratio of movement. It could be argued that if the Greeks knew the principle of gearing, they should have had no difficulty in constructing mechanisms as complex as epicyclic gears. We now know from the fragments in the National Museum that the Greeks did make such mechanisms, but the knowledge is so unexpected that some scholars at first thought that the fragments must belong to some more modern device.
Can we in fact be sure that the device is ancient? If we can, what was its purpose? What can it tell us of the ancient world and of the evolution of modern science? To authenticate the dating of the fragments We must. tell the story of their discovery, which involves the first (though inadvertent) adventure in underwater archaeology. Just before Easter in 1900 a party of Dodecanese sponge-divers were driven by storm to anchor near the tiny southern Greek island of Antikythera (the accent is on the “kyth,” pronounced to rhyme with pith). There, at a depth of some 200 feet, they found the wreck of an ancient ship. With the help of Greek archaeologists the wreck was explored; several fine bronze and marble statues and other objects were recovered. The finds created great excitement, but the difficulties of diving without heavy equipment were immense, and in September, 1901, the “dig’ was abandoned. Eight months later Valerios StaÎs, an archaeologist at the National Museum, was examining some calcified lumps of corroded bronze that had been set aside as possible pieces of broken statuary. Suddenly he recognized among them the fragments of a mechanism.
It is now accepted that the wreck occurred during the first century B.C. Gladys Weinberg of Athens has been kind enough to report to me the results of several recent archaeological examinations of the amphorae, pottery and minor objects from the ship. It appears from her report that one might reason-ably date the wreck more closely as 65 B.C. ±15 years. Furthermore, since the identifiable objects come from Rhodes and Cos, it seems that the ship may have. been voyaging from these islands to Rome, perhaps without calling at the Greek mainland.
The fragment that first caught the eye of StaÎs was one of the corroded, inscribed plates that is an integral part of the Antikythera mechanism, as the device later came to be called. StaÎs saw immediately that the inscription was ancient. In the opinion of the epigrapher Benjamin Dean Meritt, the forms of the letters are those of the ‘first century B.C.; they could hardly be older than 100 B.C. nor younger than the time of Christ. The dating is supported by the content of the inscriptions. The words used and their astronomical sense are all of this period. For example, the most extensive and complete piece of inscription is part of a parapegma (astronomical calendar) similar to that written by one Geminos, who is thought to have lived in Rhodes about 77 B.C. We may thus be reasonably sure that the mechanism did not find its way into the wreck at some later period. Furthermore, it cannot have been very old when it was taken aboard the ship as booty or merchandise.
As soon as the fragments had been discovered they were examined by every available archaeologist; so began the long and difficult process of identifying the mechanism and determining its function. Some things were clear from the beginning. The unique importance of the object was obvious, and the gearing was impressively complex. From the inscriptions and the dials the mechanism was correctly identified as an astronomical device. The first conjecture was that it was some kind of navigating instrument – perhaps an astrolabe (a sort of circular star-finder map also used for simple observations). Some thought that it might be a small planetarium of the kind that Archirnedes is said to have made. Unfortunately the fragments were covered by a thick curtain of calcified material and corrosion products, and these concealed so much detail that no one could be sure of his conjectures or reconstructions. There was nothing to do but wait for the slow and delicate work of the Museum technicians in cleaning away this curtain. Meantime, as the work proceeded, several scholars published accounts of all that was visible, and through their labors a general picture of the mechanism began to emerge. On the basis of new photographs made for me by the Museum in 1955 I realized that the work of cleaning had reached a point where it might at last be possible to take the work of identification to a new level. Last summer, wilt the assistance of a grant from the American Philosophical Society, I was able to visit Athens and make a minute examination of the fragments. By good fortune George Stamires, a Greek epigrapher, was there at the same time; he was able to give me invaluable help by deciphering and transcribing much more of the inscriptions than had been read before. We are now in the position of being able to “join” the fragments and to see how they fitted together in the original machine and when they were brought up from the sea [see illustration]. The success of this work has been most significant, for previously it had been supposed that the various dials and plates had been badly squashed together and distorted. It now appears that most of the pieces are very nearly in their original places, and that we have a much larger fraction of the complete device than had been thought. This work also provides a clue to the puzzle of why the fragments lay unrecognized until StaÎs saw them. When they were found, the fragments were probably held together in their original positions by the remains of the wooden frame of the case. In the Museum the waterlogged wood dried and shriveled. The fragments then fell apart, revealing the interior of the mechanism, with its gears and inscribed plates. As a result of the new examinations we shall in due course be able to publish a technical account of the fragments and of the construction of the instrument. In the meantime we can tentatively summarize some of these results and show how they help to answer the question. What is it? There are four ways of getting at the answer First, if we knew the details of the mechanism, we should know what it did. Second, if we could read the dials, we could tell what they showed. Third, if we could understand the inscriptions, they might tell us about the mechanism. Fourth, if we knew of any similar mechanism, analogies might be helpful. All these approaches must be used, for none of them is complete.
The geared wheels within the mechanism were mounted on a bronze plate. On one side of the plate we can trace all the gear wheels of the assembly and can determine, at least approximately, how many teeth each had and how they meshed together. On the other side we can do nearly as well, but we still lack vital links that would provide a complete picture of the gearing. The general pattern of the mechanism is nonetheless quite clear. An input was provided by an axle that came through the side of the casing and turned a crown-gear wheel. This moved a big, four-spoked driving-wheel that was connected with two trains of gears that respectively led up and down the plate and were connected by axles to gears on the other side of the plate. On that side the gear-trains continued, leading through an epicyclic turntable and coming eventually to a set of shafts that turned the dial pointers. When the input axle was turned, the pointers all moved at various speeds around their dials.
Certain structural features of the mechanism deserve special attention. All the metal parts of the machine seem to have been cut from a single sheet of low-tin bronze about two millimeters thick; no parts were cast or made of another metal. There are indications that the maker may have used a sheet made much earlier–uniform metal plate of good quality was probably rare and expensive. All the gear wheels have been made with teeth of just the same angle (60 degrees) and size, so that any wheel could mesh with any other. There are signs that the machine was repaired at least twice; a spoke of the driving wheel has been mended, and a broken tooth in a small wheel has been replaced. This indicates that the machine actually worked. The casing was provided with three dials, one at the front and two at the back. The fragments of all of them are still covered with pieces of the doors of the casing and with other debris. Very little can be read on the dials, but there is hope that they can be cleaned sufficiently to provide information that might be decisive. The front dial is just clean enough to say exactly what it did. It has two scales, one of which is fixed and displays the names of the signs of the zodiac; the other is on a movable slip ring and shows the months of the year. Both scales are carefully marked off in degrees. The front dial fitted exactly over the main driving-wheel, which seems to have turned the pointer by means of an eccentric drum-assembly. Clearly this dial showed the annual motion of the sun in the zodiac. By means of key letters inscribed on the zodiac scale, corresponding to other letters on the parapegma calendar plate, it also showed the main risings and settings of bright stars and constellations throughout the year.
The back dials are more complex and less legible. The lower one had three slip rings; the upper, four. Each had a little subsidiary dial resembling the “seconds” dial of a watch. Each of the large dials is inscribed with lines about every six degrees, and between the lines there are letters and numbers. On the lower dial the letters and numbers seem to record “moon, so many hours; sun, so many hours”; we therefore suggest that this scale indicates the main lunar phenomena of phases and times of rising and setting. On the upper dial the inscriptions are much more crowded and might well present information on the risings and settings, stations and retrogradations of the planets known to the Greeks (Mercury, Venus, Mars, Jupiter and Saturn).
Some of the technical details of the dials are especially interesting. The front dial provides the only known extensive specimen from antiquity of a scientifically graduated instrument. When we measure the accuracy of the graduations under the microscope, we find that their average error over the visible 45 degrees is about a quarter of a degree. The way in which the error varies suggests that the arc was first geometrically divided and then subdivided by eye only. Even more important, this dial may give a means of dating the instrument astronomically. The slip ring is necessary because the old Egyptian calendar, having no leap years, fell into error by 1/4 day every year; the month scale thus had to be adjusted by this amount. As they are preserved the two scales of the dial are out of phase by 13½ degrees. Standard tables show that this amount could only occur in the year 80 B.C. and (because we do not know the month) at all years just 120 years (i.e., 30 days divided by 1/4 day per year) before or after that date. Alternative dates are archaeologically unlikely: 200 B.C. is too early; 40 A.D. is too late. Hence, if the slip ring has not moved from its last position, it was set in. 80 B.C. Furthermore, if we are right in supposing that a fiducial mark near the month scale was put there originally to provide a means of setting that scale in case of accidental movement, we can tell more. This mark is exactly 1/2 degree away from the present position of the scale, and this implies that the mark was made two years before the setting. Thus, although the evidence is by no means conclusive, we are led to suggest that the instrument was made about 82 B.C., used for two years (just long enough for the repairs to have been needed) and then taken onto the ship within the next 30 years.
The fragments show that the original instrument carried at least four large areas of inscription: outside the front door, inside the back door, on the plate between the two back dials and on the parapegma plates near the front dial. As I have noted, there are also inscriptions around all the dials, and furthermore each part and hole would seem to have had identifying letters so that the pieces could be put together in the correct order and position. The main inscriptions are in a sorry state and only short snatches of them can be read. To provide an idea of their condition it need only be said that in some cases a plate has completely disappeared, leaving behind an impression of its letters, standing up in a mirror image, in relief on the soft corrosion products on the plate below. It is remarkable that such inscriptions can be read at all.
But even from the evidence of a few complete words one can get an idea of the subject matter. The sun is mentioned several times, and the planet Venus once; terms are used that refer to the stations and retrogradations of planets; the ecliptic is named. Pointers, apparently those of the dials, are mentioned. A line of one inscription signfficantly records “76 years, 19 years.” This refers to the well-known Calippic cycle of 76 years, which is four times the Metonic cycle of 19 years, or 235 synodic (lunar) months. The next line includes the number “223,” which refers to the eclipse cycle of 223 lunar months.
Putting together the information gathered so far, it seems reasonable to suppose that the whole purpose of the Antikythera device was to mechanize just this sort of cyclical relation, which was a strong feature of ancient astronomy. Using the cycles that have been mentioned, one could easily design gearing that would operate from one dial having a wheel that revolved annually, and turn by this gearing a series of other wheels which would move pointers indicating the sidereal, synodic and draconitic months. Similar cycles were known for the planetary phenomena; in fact, this type of arithmetical theory is the central theme of Seleucid Babylonian astronomy, which was transmitted to the Hellenistic world in the last few centuries B.C. Such arithmetical schemes are quite distinct from the geometrical theory of circles and epicycles in astronomy, which seems to have been essentially Greek. The two types of theory were unified and brought to their peak in the second century A.D. by Claudius Ptolemy, whose labors marked the triumph of the new mathematical attitude toward geometrical models that still characterizes physics today.
The Antikythera mechanism must therefore be an arithmetical counterpart of the much more familiar geometrical models of the solar system which were known to Plato and Archimedes and evolved into the orrery and the planetarium. The mechanism is like. a great astronomical clock without an escapement, or like a modern analogue computer which uses mechanical parts to save tedious calculation. It is a pity that we have no way of knowing whether the device was turned automatically or by hand. It might have been held in the hand and turned by a wheel at the side so that it would operate as a computer, possibly for astrological use. I feel it is more likely that it was permanently mounted, perhaps set in a statue, and displayed as an exhibition piece. In that case it might well have been turned by the power from a water clock or some other device. Perhaps it is just such a wondrous device that was mounted inside the famous Tower of Winds in Athens. It is certainly very similar to the great astronomical cathedral clocks that were built all over Europe during the Renaissance.
It is to the prehistory of the mechanical I clock that we must look for important analogies the Antikythera mechanism and for an assessment of its significance. Unlike other mechanical devices, the clock did not evolve from the simple to the complex. The oldest clocks of which we are well informed were the most complicated. All the evidence points to the fact that the clock started as an astronomical showpiece that happened also to indicate the time. Gradually the timekeeping functions became more important and the device that showed the marvelous clockwork of the heavens became subsidiary. Behind the astronomical clocks of the 14th century there stretches an unbroken sequence of mechanical models of astronomical theory. At the head of this sequence is the Antikythera mechanism. Following it are instruments and clocklike computers known from Islam, from China and India and from the European Middle Ages. The importance of this line is very great, because it was the tradition of clock- making that preserved most of man’s skill in scientific fine mechanics. During the Renaissance the scientific instrument-makers evolved from the clockmakers. Thus the Antikythera mechanism is, in a way, the venerable progenitor of all our present plethora of scientific hardware.
A significant passage in this story has to do with the astronomical computers of Islam. Preserved complete at the Museum of History of Science at Oxford is a 13th-century Islamic geared calendar-computer that has various periods built into it, so that it shows on dials the various cycles of the sun and moon. This design can be traced back, with slightly different periods but a similar arrangement of gears, to a manuscript written by the astronomer al-Biruni about 1000 A.D. Such instruments am much simpler than the Antikythera mechanism, but they show so many points of agreement in technical detail that it seems clear they came from a common tradition. The same 60-degree gear teeth are used; wheels are mounted on square-shanked axles; the geometrical layout of the gear assembly appears comparable. It was just at this time that Islam was drawing on Greek knowledge and rediscovering ancient Greek texts. It seems likely that the Antikythera tradition was part of a large corpus of knowledge that has since been lost to us but was known to the Arabs. It was developed and transmitted by them to medieval Europe, where it .became the foundation for the whole range of subsequent invention in the field of clockwork.
On the one hand the Islamic devices knit the whole story together, and demonstrate that it is through ancestry and not mere coincidence that the Antikythera mechanism resembles a modern clock. On the other hand they show that the Antikythera mechanism was no flash in the pan but was a part of an important current in Hellenistic civilization. History has contrived to keep that current dark to us, and only the accidental underwater preservation of fragments that would otherwise have crumbled to dust has now brought it to light. It is a bit frightening to know that just before the fall of their great civilization the ancient Greeks had come so close to our age, not only in their thought, but also in their scientific technology.
Reconstruction of the mechanism by pr. Derek de Solla Price, in collaboration
with the National Scientific Research Center Démokritos and the physicist CH Karakalos. Image source: Wikipedia
Rebuilding of the machine of Anticythère: it is the result of research of the pr. Derek de Solla Price, in collaboration with the National Scientific Research Center Démokritos and the physicist CH Karakalos who carried out the x-ray tomography of the original and the mechanism reconstituted to show their operation. Price built a rectangular box of 0.33 X 0.17 X 0.10 m with plates of information and protection, carrying Greek inscriptions of planets. The mechanism is a complex set of 32 gears of various sizes, turning at different speeds. The mechanism was offered by the pr. Price to the national Museum in 1980 and remains the reference for the study of the original despite the fact that its construction has been subject to much criticism. National archaeological museum, Athens, n°BE 109/1980.
An ancient piece of clockwork shows the deep roots
of modern technology
WHEN a Greek sponge diver called Elias Stadiatos discovered the wreck of a cargo ship off the tiny island of Antikythera in 1900, it was the statues lying on the seabed that made the greatest impression on him. He returned to the surface, removed his helmet, and gabbled that he had found a heap of dead, naked women. The ship’s cargo of luxury goods also included jewellery, pottery, fine furniture, wine and bronzes dating back to the first century BC. But the most important finds proved to be a few green, corroded lumps—the last remnants of an elaborate mechanical device.
The Antikythera mechanism, as it is now known, was originally housed in a wooden box about the size of a shoebox, with dials on the outside and a complex assembly of bronze gear wheels within. X-ray photographs of the fragments, in which around 30 separate gears can be distinguished, led the late Derek Price, a science historian at Yale University, to conclude that the device was an astronomical computer capable of predicting the positions of the sun and moon in the zodiac on any given date. A new analysis, though, suggests that the device was cleverer than Price thought, and reinforces the evidence for his theory of an ancient Greek tradition of complex mechanical technology.
Michael Wright, the curator of mechanical engineering at the Science Museum in London, has based his new analysis on detailed X-rays of the mechanism using a technique called linear tomography. This involves moving an X-ray source, the film and the object being investigated relative to one another, so that only features in a particular plane come into focus. Analysis of the resulting images, carried out in conjunction with Allan Bromley, a computer scientist at Sydney University, found the exact position of each gear, and suggested that Price was wrong in several respects.
In some cases, says Mr Wright, Price seems to have “massaged” the number of teeth on particular gears (most of which are, admittedly, incomplete) in order to arrive at significant astronomical ratios. Price’s account also, he says, displays internal contradictions, selective use of evidence and unwarranted speculation. In particular, it postulates an elaborate reversal mechanism to get some gears to turn in the right direction.
Since so little of the mechanism survives, some guesswork is unavoidable. But Mr Wright noticed a fixed boss at the centre of the mechanism’s main wheel. To his instrument-maker’s eye, this was suggestive of a fixed central gear around which other moving gears could rotate. This does away with the need for Price’s reversal mechanism and leads to the idea that the device was specifically designed to model a particular form of “epicyclic” motion.
The Greeks believed in an earth-centric universe and accounted for celestial bodies’ motions using elaborate models based on epicycles, in which each body describes a circle (the epicycle) around a point that itself moves in a circle around the earth. Mr Wright found evidence that the Antikythera mechanism would have been able to reproduce the motions of the sun and moon accurately, using an epicyclic model devised by Hipparchus, and of the planets Mercury and Venus, using an epicyclic model derived by Apollonius of Perga. (These models, which predate the mechanism, were subsequently incorporated into the work of Claudius Ptolemy in the second century AD.)
A device that just modelled the motions of the sun, moon, Mercury and Venus does not make much sense. But if an upper layer of mechanism had been built, and lost, these extra gears could have modelled the motions of the three other planets known at the time—Mars, Jupiter and Saturn. In other words, the device may have been able to predict the positions of the known celestial bodies for any given date with a respectable degree of accuracy, using bronze pointers on a circular dial with the constellations of the zodiac running round its edge.
Mr Wright devised a putative model in which the mechanisms for each celestial body stack up like layers in a sandwich, and started building it in his workshop. The completed reconstruction, details of which appeared in an article in the Horological Journal in May, went on display this week at Technopolis, a museum in Athens. By winding a knob on the side, celestial bodies can be made to advance and retreat so that their positions on any chosen date can be determined. Mr Wright says his device could have been built using ancient tools because the ancient Greeks had saws whose teeth were cut using v-shaped files—a task that is similar to the cutting of teeth on a gear wheel. He has even made several examples by hand.
How closely this reconstruction matches up to the original will never be known. The purpose of two dials on the back of the device is still unclear, although one may indicate the year. Nor is the device’s purpose obvious: it may have been an astrological computer, used to speed up the casting of horoscopes, though it might just as easily have been a luxury plaything. But Mr Wright is convinced that his epicyclic interpretation is correct, and that the original device modelled the entire known solar system.
The Greeks had a word for it
That tallies with ancient sources that refer to such devices. Cicero, writing in the first century BC, mentions an instrument “recently constructed by our friend Poseidonius, which at each revolution reproduces the same motions of the sun, the moon and the five planets.” Archimedes is also said to have made a small planetarium, and two such devices were said to have been rescued from Syracuse when it fell in 212BC. This reconstruction suggests such references can now be taken literally.
It also provides strong support for Price’s theory. He believed that the mechanism was strongly suggestive of an ancient Greek tradition of complex mechanical technology which, transmitted via the Arab world, formed the basis of European clockmaking techniques. This fits with another, smaller device that was acquired in 1983 by the Science Museum, which models the motions of the sun and moon. Dating from the sixth century AD, it provides a previously missing link between the Antikythera mechanism and later Islamic calendar computers, such as the 13th century example at the Museum of the History of Science in Oxford. That device, in turn, uses techniques described in a manuscript written by al-Biruni, an Arab astronomer, around 1000AD.
The origins of much modern technology, from railway engines to robots, can be traced back to the elaborate mechanical toys, or automata, that flourished in the 18th century. Those toys, in turn, grew out of the craft of clockmaking. And that craft, like so many other aspects of the modern world, seems to have roots that can be traced right back to ancient Greece.
More about calculator
….at the last website is the complete schematic breakdown of the device , shown in five gear colors , blue , yellow-sun gear , green , orange , purple and dark green. Thirty gear numbers are shown , each having one of the above colors. The key number constant used in all thirty gears is the modern metric to english conversion constant …( 39.3700787 inches = 1 meter )… rewritten to this form :
39.3700787 / ( 10 ^ 3 ) = m = 1/25.4
….all thirty gears are linked and can be turned all at once by the rotation of any one gear in the system . I chose the blue(50) gear as a starting point and turned this gear exactly one-revolution or 360 degrees. The gematric formula for this angle is the sacred number 72 , times one half the metric standard 254 ( 254/2 = 127 ):
72 * 127 * m = 360 degrees
….this angle is transferred to the second blue(50) gear because of its being self similar to the first blue(50) gear. This angle is also transferred to the blue(32) gear because of a shared axle. The next step is the blue(32) gear’s link to gear , blue(127) .
This link is the famous sacred Alautun time cycle number …2304…from Aztec and Mayan culture. Here is a link with the explanation of the number:
….this is very important to the explanation of the Antikythera device because both the 1152 and 2304 units are Mayan calendar constants measured in DAYS !! the same as the Antikythera mechanism !!
20 calabtun = 1 kinchiltin = a cycle of 11520000000 days
20 kinchiltin = 1 alautun = a cycle of 23040000000 days
…so I would say that 1152 ( kinchiltin ) is a thing of Mayan origin as is the 2304 (alautun ) number.
blue(127) = 2304 * m = 32 / 127 * 360 = 90.70866132 degrees
blue(24) = 2304 * m = 32 / 127 * 360 = 90.70866132 degrees
…that is when you turn the starter blue(50) gear 360 degrees, the blue(127) gear will turn 90.70866132 degrees. The blue(24) gear shares an axle with the blue(127) gear and thus shares the rotation of the blue(127) gear. Blue(24) gear then transfers this rotation to the blue(48) gear . This angle of rotation is the gematric number known as the Egyptian foot number ..1152…:
blue(38) = 1152 * m = 32/127*24/48*360 = 45.35433066 degrees
blue(48) = 1152 * m = 32/127*24/48*360 = 45.35433066 degrees
…blue(38) shares an axle with blue(48) and thus transfers this angle of rotation to the so-called Sun gear… yellow(64)..The number 19 appears here not as years of the Metonic cycle but as DAYS!! on the edge of gear wheels:
Sun gear = 36 * 19 * m = 32/127*24/48*38/64*360 = 26.92913383 degrees
….all of the green gears share the same angle of rotation as the Sun gear. The orange gears appear when the second gear with 38 cogs appears as orange(38). It has the same angle of rotation as the blue(38) gear:
orange(38) = 1152 * m = 32/127*24/48*360 = 45.3543306 degrees
orange(53) = 1152 * m = 32/127*24/48*360 = 45.3543306 degrees
…orange(53) shares an axle with orange(38) and thus transfers this angle of rotation to orange(96)
orange(96) = 25 + m = 53*12 * m = 32/127*24/48*53/96*360 = 25.0393700787 degrees
…orange(15) and orange(27) gears share axles with orange(96) and thus transfers angular rotation to the large gear purple(223):
purple(223) = 53*12*27*m/223 = 36*m+360/223 = 32/127*24/48*53/96*27/223*360 degrees
..purple(53) edges with purple(223) thus picking up an angular rotation of:
purple(53) = 54 * 6 * m = 32/127*24/48*27/96*360 = 12.7559055 degrees
purple(30) = 54 * 6 * m = 32/127*24/48*27/96*360 = 12.7559055 degrees
…purple(30) shares an axle with purple(53) and thus the same rotation. Purple(30) edges with purple(54) resulting in an angle turn of 7.086614166 degrees for purple(54):
purple(54) = 180 * m = 7.086614166 degrees
…three other gears share this angle of rotation and thus the same axle, purple(20) , dk green(53) , dk green(15). dk green(15) transfers the angle to gear dk green(60) and gear dk green(12) which shares an axle with dk green(60):
dk green(60) = 180 / 4 * m = 32/127*24/48*15/96*15/60*360 = 1.771653542 degrees
dk green(12) = 180 / 4 * m = 32/127*24/48*15/96*15/60*360 = 1.771653542 degrees
…dk green(12) transfers the angle of rotation to the last gear in the chain, dk green(60)
dk green(60) = 9 * m = 32/127*24/48*15/96*15/60*12/60*360 = .354330708 degrees
…showing the angles of rotation in spreadsheet form: cl = clockwise, c
GEAR GEMATRIA GEAR RATIO ROTATION ANGLE
blue(50) 72 * 127 * m 1 360 ccl
blue(50) 72 * 127 * m 1 360 cl
blue(32) 72 * 127 * m 1 360 cl
blue(127) 2304 * m 32/127*360 90.70866132 ccl
blue(24) 2304 * m 32/127*360 90.70855132 ccl
blue(48) 1152 * m 32/127*24/48*360 45.35433066 cl
blue(38) 1152 * m 32/127*24/48*360 45.35433066 cl
sun gear(64) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl
green(32) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl
green(32) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 ccl
green(50) 36 * 19 * m 32/127*24/48*38/64*360 26.92913383 cl
orange(38) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(53) 1152 * m 32/127*24/48*360 45.35433066 ccl
orange(96) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(15) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
orange(27) 53*12 * m = 25+m 32/127*24/48*53/96*360 25.0393700787 cl
purple(223) 53*12*27*m/223 32/127*24/48*53/96*27/223*360 3.031672609 ccl
purple(53) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(30) 54 * 6 * m 32/127*24/48*27/96*360 12.7559055 cl
purple(54) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(20) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
purple(60) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(15) 60 * m 32/127*24/48*27/96*30/54*20/60*360 2.362204722 cl
purple(60) 15 * m 32/127*24/48*27/96*30/54*20/60*15/60*360 .59055118 ccl
dk green(53) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
dk green(15) 180 * m 32/127*24/48*27/96*30/54*360 7.086614166 ccl
dk green(60) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(12) 180/4 * m 32/127*24/48*15/96*15/60*360 1.771653542 cl
dk green(60) 9 * m 32/127*24/48*15/96*15/60*12/60*36 .354330708 ccl
…how does this data relate to the earth-moon interaction? One can observe that the last gear in the chain of 360 degree rotation , blue(32)…if one makes this gear analogous to the moon lunar cycle…29.530588 days in one orbit around earth , then blue (32) and the lunar cycle share an axle that rotates 360 degrees. Transferring this 360 degree rotation of the lunar cycle to the earth cycle around the sun…365.246743 days in one tropical year , on this earth cycle axle , place the 5 sets of 47 (235) markings of the exterior dials of the device on the earth axis of rotation and multiply by the metric m :
29.530588 / 365.2467463 * 5 * 47 *m * 36 = 26.92913386 degrees = 19 * 36 * m = sun gear(64)
29.530588 / 365.2467463 * 235 / 254 = 26.92913386 degrees = 19 * 36 * m = sun gear(64)
…this is exactly the angle turned by the sun gear when the blue(50) gear is rotated once!! Checking the number constants I wanted to see if the number 37 is any where in the angles of rotation or in the gear numbers. Strangely it sits at the heart of the Earth/Moon link. When the lunar cycle 29.530588 days is rotated once (360 degrees) on the Earth cycle .365.246743 days… an angle of rotation is generated on the Earth cycle rim:
29.530588 / 365.246743 * 360 = degrees of rotation of Earth orbit disc = 29.10638332
….37 derives this angle through the 47 markings on the outside dials of the device:
(( 37 ^ 2 ) – 1 ) / 47 = 29.10638332 degrees
…which means the 37 form can generate the sun gear angle for all of the green gears:
(( 37 ^ 2 ) – 1 ) / 47 * 235 / 254 = 26.92913386 degrees = 36 * 19 * m
via World Mysteries