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Contributions from
The Museum of History and Technology:
Paper 6
On the Origin of Clockwork,
Perpetual Motion Devices, and the Compass
Derek J. de Solla Price
ON THE ORIGIN OF CLOCKWORK,
PERPETUAL MOTION DEVICES
AND THE COMPASS
By Derek J. de Solla Price
Ancestor of the mechanical clock has been thought by some to be the sundial. Actually these devices represent two different approaches to the problem of time-keeping. True ancestor of the clock is to be found among the highly complex astronomical machines which man has been building since Hellenic times to illustrate the relative motions of the heavenly bodies.
This study—its findings will be used in preparing the Museum's new hall on the history of time-keeping—traces this ancestry back through 2,000 years of history on three continents.
The Author: Derek J. de Solla Price wrote this paper while serving as consultant to the Museum of History and Technology of the Smithsonian Institution's United States National Museum.
In each successive age this construction, having become lost, is, by the Sun's favour, again revealed to some one or other at his pleasure. (Sūrya Siddhānta, ed. Burgess, xiii, 18-19.)
HE histories of the mechanical clock and the magnetic compass must be accounted amongst the most tortured of all our efforts to understand the origins of man's important inventions. Ignorance has too often been replaced by conjecture, and conjecture by misquotation and the false authority of "common knowledge" engendered by the repetition of legendary histories from one generation of textbooks to the next. In what follows, I can only hope that the adding of a strong new trail and the eradication of several false and weaker ones will lead us nearer to a balanced and integrated understanding of medieval invention and the intercultural transmission of ideas.
For the mechanical clock, perhaps the greatest hindrance has been its treatment within a self-contained "history of time measurement" in which sundials, water-clocks and similar devices assume the natural role of ancestors to the weight-driven escapement clock in the early 14th century.1 This view must presume that a generally sophisticated knowledge of gearing antedates the invention of the clock and extends back to the Classical period of Hero and Vitruvius and such authors well-known for their mechanical ingenuities.
Furthermore, even if one admits the use of clocklike gearing before the existence of the clock, it is still necessary to look for the independent inventions of the weight-drive and of the mechanical escapement. The first of these may seem comparatively trivial; anyone familiar with the raising of heavy loads by means of ropes and pulley could surely recognize the possibility of using such an arrangement in reverse as a source of steady power. Nevertheless, the use of this device is not recorded before its association with hydraulic and perpetual motion machines in the manuscripts of Riḍwān, ca. 1200, and its use in a clock using such a perpetual motion wheel (mercury filled) as a clock escapement, in the astronomical codices of Alfonso the Wise, King of Castile, ca. 1272.
The second invention, that of the mechanical escapement, has presented one of the most tantalizing of problems. Without doubt, the crown and foliot type of escapement appears to be the first complicated mechanical invention known to the European Middle Ages; it heralds our whole age of machine-making. Yet no trace has been found either of a steady evolution of such escapements or of their invention in Europe, though the astronomical clock powered by a water wheel and governed by an escapement-like device had been elaborated in China for several centuries before the first appearance of our clocks. We must now rehearse a revised story of the origin of the clock as it has been suggested by recent researches on the history of gearing and on Chinese and other astronomical machines. After this we shall for the first time present evidence to show that this story is curiously related to that of the Perpetuum Mobile, one of the great chimeras of science, that came from its medieval origin to play an important part in more recent developments of energetics and the foundations of thermodynamics.2 It is a curious mixture, all the more so because, tangled inextricably in it, we shall find the most important and earliest references to the use of the magnetic compass in the West. It seems that in revising the histories of clockwork and the magnetic compass, these considerations of perpetual motion devices may provide some much needed evidence.
Power and Motion Gearing
It may be readily accepted that the use of toothed wheels to transmit power or turn it through an angle was widespread in all cultures several centuries before the beginning of our era. Certainly, in classical times they were already familiar to Archimedes (born 287 B.C.),3 and in China actual examples of wheels and moulds for wheels dating from the 4th century
Granted, then, this use of gears, one must guard against any conclusion that the fine-mechanical use of gears to provide special ratios of angular movement was similarly general and widespread. It is customary to adduce here the evidence of the hodometer (taximeter) described by Vitruvius (1st century B.C.) and by Hero of Alexandria (1st century A.D.) and the ingenious automata also described by this latter author and his Islamic followers.6 One may also cite the use of the reduction gear chain in power machinery as used in the geared windlass of Archimedes and Hero.
Unfortunately, even the most complex automata described by Hero and by such authors as Riḍwān contain gearing in no more extensive context than as a means of transmitting action around a right angle. As for the windlass and hodometer, they do, it is true, contain whole series of gears used in steps as a reduction mechanism, usually for an extraordinarily high ratio, but here the technical details are so etherial that one must doubt whether such devices were actually realized in practice. Thus Vitruvius writes of a wheel 4 feet in diameter and having 400 teeth being turned by a 1-toothed pinion on a cart axle, but it is very doubtful whether such small teeth, necessarily separated by about 3/8 inch, would have the requisite ruggedness. Again, Hero mentions a wheel of 30 teeth which, because of imperfections, might need only 20 turns of a single helix worm to turn it! Such statements behove caution and one must consider whether we have been misled by the 16th-and 17th-century editions of these authors, containing reconstructions now often cited as authoritative but then serving as working diagrams for practical use in that age when the clock was already a familiar and complex mechanism. At all events, even if one admits without substantial evidence that such gear reduction devices were familiar from Hellenistic times onwards, they can hardly serve as more than very distant ancestors of the earliest mechanical clocks.
Mechanical Clocks
Before proceeding to a discussion of the controversial evidence which may be used to bridge this gap between the first use of gears and the fully-developed mechanical clock we must examine the other side of this gap. Recent research on the history of early mechanical clocks has demonstrated certain peculiarities most relevant to our present argument.
the european tradition
If one is to establish a terminus ante quem for the appearance of the mechanical clock in Europe, it would appear that 1364 is a most reasonable date. At that time we have the very full mechanical and historical material concerning the horological masterpiece built by Giovanni de Dondi of Padua,7 and probably started as early as 1348. It might well be possible to set a date a few decades earlier, but in general as one proceeds backwards from this point, the evidence becomes increasingly fragmentary and uncertain. The greatest source of doubt arises from the confusion between sundials, water-clocks, hand-struck time bells, and mechanical clocks, all of which are covered by the term horologium and its vernacular equivalents.
Temporarily postponing the consideration of evidence prior to ca. 1350, we may take Giovanni de Dondi as a starting point and trace a virtually unbroken lineage from his time to the present day. One may follow the spread of clocks through Europe, from large towns to small ones, from the richer cathedrals and abbeys to the less wealthy churches.8 There is the transition from the tower clocks—showpieces of great institutions—to the simple chamber clock designed for domestic use and to the smaller portable clocks and still smaller and more portable pocket watches. In mechanical refinement a similar continuity may be noted, so that one sees the cumulative effect of the introduction of the spring drive (ca. 1475), pendulum control (ca. 1650), and the anchor escapement (ca. 1680). The transition from de Dondi to the modern chronometer is indeed basically continuous, and though much research needs to be done on special topics, it has an historical unity and seems to conform for the most part to the general pattern of steady mechanical improvement found elsewhere in the history of technology.
Most remarkable however is the earliest period of this seemingly steady evolution. Side by side with the advances made in the earliest period extending for less than two centuries from the time of de Dondi one may see a spectacular process of degeneration or devolution. Not only is de Dondi's the earliest clock of which we have a full and trustworthy account, it is also far more complicated than any other (see Figs. 1, 2) until comparatively modern times! Moreover, it was not an exceptional freak. There were others like it, and one cannot therefore reject as accidental this process of degeneration that occurs at the
On the basis of such evidence I have suggested elsewhere9 that the clock is "nought but a fallen angel from the world of astronomy." The first great clocks of medieval Europe were designed as astronomical showpieces, full of complicated gearing and dials to show the motions of the Sun, Moon and planets, to exhibit eclipses, and to carry through the involved computations of the ecclesiastical calendar. As such they were comparable to the orreries of the 18th century and to modern planetariums; that they also showed the time and rang it on bells was almost incidental to their main function. One must not neglect, too, that it was in their glorification of the rationality of the cosmos that they had their greatest effect. Through milleniums of civilization, man's understanding of celestial phenomena had been the very pinnacle of his intellect, and then as now popular exhibition of this sort was just as necessary, as striking, and as impressive. One does not have to go far to see how the paraphernalia of these early great astronomical clocks had great influence on philosophers and theologians and on poets such as Dante.
It is the thesis of this part of my argument that the ordinary time-telling clock is no affiliate of the other simple time-telling devices such as sundials, sand glasses and the elementary water clocks. Rather it should be considered as a degenerate branch from the main stem of mechanized astronomical devices (I shall call them protoclocks), a stem which can boast a continuous history filling the gap between the appearance of simple gearing and the complications of de Dondi. We shall return to the discussion of this main stem after analyzing the very recently discovered parallel stem from medieval China, which reproduced and incidental time telling. Of the greatest significance, this stem reveals the crucial independent invention of a mechanical escapement, a feature not found in the European stem in spite of centuries of intensive historical research and effort.
the chinese tradition
For this section I am privileged to draw upon a thrilling research project carried out in 1956 at the University of Cambridge by a team consisting of Dr. Joseph Needham, Dr. Wang Ling, and myself.10 In the course of this work we translated and commented on a series of texts most of which had not hitherto been made available in a Western tongue and, though well known in China, had not been recognized as important for their horological content. The key text with which we started was the "Hsin I Hsiang Fa Yao," or "New Design for a (mechanized) Armillary (sphere) and (celestial) Globe," written by Su Sung in A.D. 1090. The very full historical and technical description in this text enabled us to establish a glossary and basic understanding of the mechanism that later enabled us to interpret a whole series of similar, though less extensive texts, giving a history of prior development of such devices going back to the introduction of this type of escapement by I-Hsing and Liang Ling-tsan, in A.D. 725, and to what seems to be the original of all these Chinese astronomical machines, that built by Chang Hêng ca. A.D. 130. Filling the gaps between these landmarks are several other similar texts, giving ample evidence that the Chinese development is continuous and, at least from Chang Hêng onwards, largely independent of any transmissions from the West.
So far as we can see, the beginning of the chain in China (as indeed in the West) was the making of simple static models of the celestial sphere. An armillary sphere was used to represent the chief imaginary circles (e.g., equator, ecliptic, meridians, etc.), or a solid celestial globe on which such circles could be drawn, together with the constellations of the fixed stars. The whole apparatus was then mounted so that it was free to revolve about its polar axis and another ring or a casing was added, external and fixed, to represent the horizon that provided a datum for the rising and setting of the Sun and the stars.
In the next stage, reached very soon after this, the rotation of the model was arranged to proceed automatically instead of by hand. This was done, we believe, by using a slowly revolving wheel powered by dripping water and turning the model through a reduction mechanism, probably involving gears or, more reasonably, a single large gear turned by a trip lever. It did not matter much that the time-keeping properties were poor in the long run; the model moved "by itself" and the great wonder was that it agreed with the observed heavens "like the two halves of a tally."
In the next, and essential, stage the turning of the water wheel was regulated by an "escapement" mechanism consisting of a weighbridge and trip levers so arranged that the wheel was held in check, scoop by scoop, while each scoop was filled by the dripping water, then released by the weighbridge and allowed to rotate until checked again by the trip-lever arrangement. Its action was similar to that of the anchor escapement, though its period of repose was much longer than its period of motion and, of course, its time-keeping properties were controlled not only by the mechanics of the device but also by the rate of flow of the dripping water.
The Chinese escapement may justifiably be regarded as a missing link, just halfway between the elementary clepsydra with its steady flow of water and the mechanical escapement in which time is counted by chopping its flow into cycles of action, repeated indefinitely and counted by a cumulating device. With its characteristic of saving up energy for a considerable period (about 15 minutes) before letting it go in one powerful action, the Chinese escapement was particularly suited to the driving of jackwork and other demonstration devices requiring much energy but only intermittent activity.
In its final form, as built by Su Sung after many trials and improvements, the Chinese "astronomical clocktower" must have been a most impressive object. It had the form of a tower about 30 feet high, surmounted by an observation platform covered with a light roof (see fig. 4). On the platform was an armillary sphere designed for observing the heavens. It was turned by the clockwork so as to follow the diurnal rotation and thus avoid the distressing computations caused by the change of coordinates necessary when fixed alt-azimuth instruments were used. Below the platform was an enclosed chamber containing the automatically rotated celestial globe which so wonderfully agreed with the heavens. Below this, on the front of the tower was a miniature pagoda with five tiers; on each tier was a doorway through which, at due moment, appeared jacks who rang bells, clanged gongs, beat drums, and held tablets to announce the arrival of each hour, each quarter (they used 100 of them to the day) and each watch of the night. Within the tower was concealed the mechanism; it consisted mainly of a central vertical shaft providing power for the sphere, globe, and jackwheels, and a horizontal shaft geared to the vertical one and carrying the great water wheel which seemed to set itself magically in motion at every quarter. In addition to all this were the levers of the escapement mechanism and a pair of norias by which, once each day, the water used was pumped from a sump at the bottom to a reservoir at the top, whence it descended to work the wheel by
There were many offshoots and developments of this main stem of Chinese horology. We are told, for example, that often mercury and occasionally sand were used to replace the water, which frequently froze in winter in spite of the application of lighted braziers to the interior of the machines. Then again, the astronomical models and the jackwork were themselves subject to gradual improvement: at the time of I-Hsing, for example, special attention was paid to the demarcation of ecliptic as well as the normal equatorial coordinates; this was clearly an influx from Hellenistic-Islamic astronomy, in which the relatively sophisticated planetary mathematics had forced this change not otherwise noted in China.
By the time of the Jesuits, this current of Chinese horology, long since utterly destroyed by the perils of wars, storms, and governmental reforms, had quite been forgotten. Matteo Ricci's clocks, those gifts that aroused so much more interest than European theological teachings, were obviously something quite new to the 16th-century Chinese scholars; so much so that they were dubbed with a quite new name, "self-sounding bells," a direct translation of the word "clock" (glokke). In view of the fact that the medieval Chinese escapement may have been the basis of European horology, it is a curious twist of fate that the high regard of the Chinese for European clocks should have prompted them to open their doors, previously so carefully and for so long kept closed against the foreign barbarians.
Mechanized Astronomical Models
Now that we have seen the manner in which mechanized astronomical models developed in China, we can detect a similar line running from Hellenistic time, through India and Islam to the medieval Europe that inherited their learning. There are many differences, notably because of the especial development of that peculiar characteristic of the West, mathematical astronomy, conditioned by the almost accidental conflux of Babylonian arithmetical methods with those of Greek geometry. However, the lines are surprisingly similar, with the exception only of the crucial invention of the escapement, a feature which seems to be replaced by the influx of ideas connected with perpetual motion wheels.
hellenistic period
Most interesting and frequently cited is the bronze planetarium said to have been made by Archimedes and described in a tantalisingly fragmentary fashion by Cicero and by later authors. Because of its importance as a prototype, we give the most relevant passages in full.11
Cicero's descriptions of Archimedes' planetarium are (italics supplied):
Gaius Sulpicius Gallus ... at a time when ... he happened to be at the house of Marcus Marcellus, his colleague in the consulship [166 B.C.], ordered the celestial globe to be brought out which the grandfather of Marcellus had carried off from Syracuse, when that very rich and beautiful city was taken [212 B.C.].... Though I had heard this globe (sphaerae) mentioned quite frequently on account of the fame of Archimedes, when I saw it I did not particularly admire it; for that other celestial globe, also constructed by Archimedes, which the same Marcellus placed in the temple of Virtue, is more beautiful as well as more widely known among the people. But when Gallus began to give a very learned explanation of the device, I concluded that the famous Sicilian had been endowed with greater genius than one would imagine possible for human being to possess. For Gallus told us that the other kind of celestial globe, which was solid and contained no hollow space, was a very early invention, the first one of that kind having been constructed by Thales of Miletus, and later marked by Eudoxus of Cnidus—a disciple of Plato, it was claimed—with constellations and stars which are fixed in the sky. He also said that many years later Aratus ... had described it in verse.... But this newer kind of globe, he said, on which were delineated the motions of the sun and moon and of those five stars which are called wanderers, or, as we might say, rovers [i. e., the five planets], contained more than could be shown on the solid globe, and the invention of Archimedes deserved special admiration because he had thought out a way to represent accurately by a single device for turning the globe, those various and divergent movements with their different rates of speed. And when Gallus moved [i.e., set in motion] the globe, it was actually true that the moon was always as many revolutions behind the sun on the bronze contrivance as would agree with the number of days it was behind in the sky. Thus the same eclipse of the sun happened on the globe as would actually happen, and the moon came to the point where the shadow of the earth was at the very time when the sun (appeared?) out of the region ... [several pages are missing in the manuscript; there is only one].
De republica, I, xiv (21-22), Keyes' translation.
When Archimedes put together in a globe the movements of the moon, sun and five wandering [planets], he brought about the same effect as that which the god of Plato did in the Timaeus when he made the world, so that one revolution produced dissimilar movements of delay and acceleration.
Tusculanae disputationes, I, 63.
Later descriptions from Ovid, Lactantius, Claudian, Sextus Empiricus, and Pappus, respectively, are (italics supplied):
There stands a globe suspended by a Syracusan's skill in an enclosed bronze [frame, or sphere—or perhaps, in enclosed air], a small image of the immense vault [of heaven]; and the earth is equally distant from the top and bottom; that is brought about by its [i. e., the outer bronze globe's] round form. The form of the temple [of Vesta] is similar....
Ovid, Fasti (1st century, A.D.), VI, 277-280, Frazer's translation.
The Sicilian Archimedes, was able to make a reproduction and model of the world in concave brass (concavo aere similitudinem mundi ac figuram); in it he so arranged the sun and moon and resembling the celestial revolutions (caelestibus similes conversionibus); and while it revolved it exhibited not only the accession and recession of the sun and the waxing and waning of the moon (incrementa deminutionesque lunae), but also the unequal courses of the stars, whether fixed or wandering.
Lactantius, Institutiones divinae (4th century, A.D.), II, 5, 18.
Archimedes' sphere. When Jove looked down and saw the heavens figured in a sphere of glass, he laughed and said to the other gods: "Has the power of mortal effort gone so far? Is my handiwork now mimicked in a fragile globe?" An old man of Syracuse had imitated on earth the laws of the heavens, the order of nature, and the ordinances of the gods. Some hidden influence within the sphere directs the various courses of the stars and actuates the lifelike mass
Claudian, Carmina minora (ca. A.D. 400), LI (LXVIII), Platnaure's translation.
The things that move by themselves are more wonderful than those which do not. At any rate, when we behold an Archimedean sphere in which the sun and the rest of the stars move, we are immensely impressed by it, not by Zeus because we are amazed at the wood, or at the movements of these [bodies], but by the devices and causes of the movements.
Sextus Empiricus, Adversus mathematicos (3rd century, A.D.), IX, 115, Epps' translation.
Mechanics understand the making of spheres and know how to produce a model of the heavens (with the courses of the stars moving in circles?) by mean of equal and circular motions of water, and Archimedes the Syracusan, according to some, knows the cause and reasons for all of these.
Pappus (3rd century, A.D.), Works (Hultsch edition), VIII, 2, Epps' translation.
A similar arrangement seems to be indicated in another mechanized globe, also mentioned by Cicero and said to have been made by Posidonius:
But if anyone brought to Scythia or Britain the globe (sphaeram) which our friend Posidonius [of Apameia, the Stoic philosopher] recently made, in which each revolution produced the same (movements) of the sun and moon and five wandering stars as is produced in the sky each day and night, who would doubt that it was by exertion of reason?... Yet doubters ... think that Archimedes showed more knowledge in producing movements by revolutions of a globe than nature (does) in effecting them though the copy is so infinitely inferior to the original....
De natura deorum, II, xxxiv-xxxv (88), Yonge's translation.
In spite of the lack of sufficient technical details in any case, these mechanized globe models, with or without geared planetary indicators (which would make them highly complex machines), bear a striking resemblance to the earliest Chinese device described by Chang Hêng. One must not reject the possibility that transmission from Greece or Rome could have reached the East by the beginning of the 2nd century, A.D., when he was working. It is an interesting question, but even if such contact actually occurred, very soon afterwards, as we shall see, the western and eastern lines of evolution parted company and evolved so far as can be seen, quite independently until at least the 12th century.
The next Hellenistic source of which we must take note is a fragmentary and almost unintelligible chapter in the works of Hero of Alexandria. Alone and unconnected with his other chapters this describes a model which seems to be static, in direct contrast to all other devices which move by pneumatic and hydrostatic pressures; it may well be conjectured that in its original form this chapter described a mechanized rather than a static globe:
The World represented in the Centre of the Universe: The construction of a transparent globe containing air and liquid, and also of a smaller globe, in the centre, in imitation of the World. Two hemispheres of glass are made; one of them is covered with a plate of bronze, in the middle of which is a round hole. To fit this hole a light ball, of small size, is constructed, and thrown into the water contained in the other hemisphere: the covered hemisphere is next applied to this, and, a certain quantity of the liquid having been removed from the water, the intermediate space will contain the ball; thus by the application of the second hemisphere what was proposed is accomplished.
Pneumatics, XLVI, Woodcroft's translation.
It will be noted that these earliest literary references are concerned with pictorial, 3-dimensional models of the universe, moved perhaps by hand, perhaps by waterpower; there is no evidence that they contained complicated trains of gears, and in the absence of this we may incline to the view that in at least the earliest such models, gearing was not used.
The next developments were concerned on the one hand with increasing the mathematical sophistication of the model, on the other hand with its mechanical complexity. In both cases we are most fortunate in having archaeological evidence which far exceeds any literary sources.
The mathematical process of mapping a sphere onto a plane surface by stereographic projection was introduced by Hipparchus and had much influence on astronomical techniques and instruments thereafter. In particular, by the time of Ptolemy (ca. A.D. 120) it had led to the successive inventions of the anaphoric clock and of the planispheric astrolabe.12 Both these devices consist of a pair of stereographic projections, one of the celestial sphere with its stars and ecliptic and tropics, the other of the lines of altitude and azimuth as set for an observer in a place at some particular latitude.
In the astrolabe, an openwork metal rete containing markings for the stars, etc., may be rotated by hand over a disc on which the lines of altitude and azimuth are inscribed. In the anaphoric clock a disc engraved with the stars is rotated automatically behind a fixed grille of wires marking lines of altitude and azimuth. Power for rotating the disc is provided by a float rising in a clepsydra jar and connected, by a rope or chain passing over a pulley to a counterweight or by a rack and pinion, to an axle which supported the rotating disc and communicated this motion to it.13
Parts of two such discs from anaphoric clocks have been found, one at Salzburg14 and one at Grand in the Vosges,15 both of them dating from the 2nd century A.D. Fortunately there is sufficient evidence to reconstruct the Salzburg disc and show that it must have been originally about 170 cm. in diameter, a heavy sheet of bronze to be turned by the small power provided by a float, and a large and impressive device when working (see fig. 5). Literary accounts of the anaphoric clock have been analyzed by Drachmann; there is no evidence of the representation
The anaphoric clock is not only the origin of the astrolabe and of all later planetary models, it is also the first clock dial, setting a standard for "clockwise" rotation, and leaving its mark in the rotating dial and stationary pointer found on the earliest time-keeping clocks before the change was made to a fixed dial and moving hand.
We come finally to a piece of archaeological evidence that surpasses all else. Though badly preserved and little studied it might well be the most important classical object ever found; entailing a complete re-estimation of the technical prowess of the Hellenistic Greeks. In 1901 a sunken treasure ship was discovered lying off the island of Antikythera, between Greece and Crete.16 Many beautiful classical works of statuary were recovered from it, and these are now amongst the greatest treasures of the National Museum at Athens, Greece. Besides these obviously desirable art relics, there came to the surface some curious pieces of metal, accompanied by traces of what may have been a wooden casing. Two thousand years under the sea had reduced the metal to a mess of corroded fragments of plates, powdered verdigris, and still recognizable pieces of gear wheels.
If it were not for the established dates for other treasure from this ship, especially the minor objects found, and for traces of inscriptions on this metal device written in letters agreeing epigraphically with the other objects, one would have little doubt in supposing that such a complicated piece of machinery dated from the 18th century, at the earliest. As it is, estimates agree on ca. 65 B.C. ±10 years, and we can be sure that the machine is of Hellenistic origin, possibly from Rhodes or Cos.
The inscriptions, only partly legible, lead one to believe that we are dealing with an astronomical calculating mechanism of some sort. This is born out by the mechanical construction evident on the fragments. The largest one (fig. 6) contains a multiplicity of gearing involving an annular gear working epicyclic gearing on a turntable, a crown wheel, and at least four separate trains of smaller gears, as well as a 4-spoked driving wheel. One of the smaller fragments (fig. 7, bottom) contains a series of movable rings which may have served to carry movable scales on one of the three dials. The third fragment (fig. 7, top) has a pair of rings carefully engraved and graduated in degrees of the zodiac (this is, incidentally, the oldest engraved scale known, and micrometric measurements on photographs have indicated a maximum inaccuracy of about 1/2° in the 45° present).
Unfortunately, the very difficult task of cleaning the fragments is slow, and no publication has yet given sufficient detail for an adequate explanation of this object. One can only say that although the problems of restoration and mechanical analysis are peculiarly great, this must stand as the most important scientific artifact preserved from antiquity.
Some technical details can be gleaned however. The shape of the gear teeth appears to be almost exactly equilateral triangles in all cases (fig. 8), and square shanks may be seen at the centers of some of the wheels. No wheel is quite complete enough for a count of gear teeth, but a provisional reconstruction by Theophanidis (fig. 9) has shown that the appearances are consistent with the theory that the purpose of the gears was to provide the correct angular ratios to move the sun and planets at their appropriate relative speeds.