Chapter I: Part 1

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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_

POWER AND MOTION GEARING 83

MECHANICAL CLOCKS 84

MECHANIZED ASTRONOMICAL MODELS 88

PERPETUAL MOTION AND THE CLOCK BEFORE DE DONDI 108

THE MAGNETIC COMPASS AS A FELLOW-TRAVELER FROM CHINA 110

_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.)

THE 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 Ignorance has too often been replaced by conjecture, and conjecture by misquotation and the false authority of "common knowledge" engendered by the repetition of legendary histories from one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 B.C. have been preserved.[4] It might be remarked that these "machine" gear wheels are characterized by having a "round number" of teeth (examples with 16, 24 and 40 teeth are known) and a shank with a square hole which fits without turning on a squared shaft. Another remarkable feature in these early gears is the use of ratchet-shaped teeth, sometimes even twisted helically so that the gears resemble worms intermeshing on parallel axles.[5] The existence of windmills and watermills testifies to the general familiarity, from classical times and through the middle ages, with the use of gears to turn power through a right angle.

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 very beginning of the certain history of the mechanical clock in Europe.

On the basis of such evidence I have suggested elsewhere[9] 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 the same evolution of mechanized astronomical devices 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 clock-tower" 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 means of a constant level tank and several channels.

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 with definite motions. A false
_zodiac_ runs through a year of its own and a toy _moon_
waxes and wanes month by month. Now bold invention
rejoices to make its own heaven revolve and sets the
_stars_ [planets?] in motion by human wit....

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 Salzburg[14] 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 of planets moved either by hand or by automatic gearing, only in the important case of the sun was such a feature included of necessity. A model "sun" on a pin could be plugged in to any one of 360 holes drilled in at equal intervals along the band of the ecliptic. This pin could be moved each day so that the anaphoric clock kept step with the seasonal variation of the times of sunrise and sunset and the lengths of day and night.

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.

Thus, if the evidence of the Antikythera machine is to be taken at its face value, we have, already in classical times, the use of astronomical devices as complicated as any clock. In any case, the material supplied by the works ascribed to Archimedes, Hero, and Vitruvius, and the more certain evidence of the anaphoric clocks is sufficient to show that there was a strong classical tradition of such machines, a tradition that inspired, even if it did not directly influence, later developments in Islam and Europe on the one side, and, just possibly, China on the other.

_Note added in proof_:

Since the above lines were written, I have been privileged
to make a full examination of the fragments in the
National Museum in Athens. As a result we can read much
more inscription and make out many more details of the
mechanism. The cleaning and disentangling of the fragments
by the museum staff has proceeded to the stage where one
can assert much more positively that the device was an
astronomical computer for sidereal, solar, lunar, and
possibly also planetary phenomena. (See my article in the
_Scientific American_, June 1959, vol. 200, No. 6, pp.
60-67.) Relevant to the present study, it must also be
noted at this point that the machine is now shown to be
strongly related to the geared astrolabe of al-Biruni and
thereby the Hellenistic, Islamic, and European
developments are drawn together even more tightly.

Let us now turn our attention to those civilizations which were intermediaries, geographically and culturally, between Greece and medieval Europe, and between both of these and China. From India there are only two references, very closely related and appearing in the best known astronomical texts in connection with descriptions of the armillary sphere and celestial globe. These texts are both quite garbled, but so far as one may understand them, it seems that the types of spheres and globes mentioned are more akin to those current in China than in the West. The relevant portions of text are as follows (italics supplied):

The circle of the horizon is midway of the sphere. As
covered with a casing and as left uncovered, it is the
sphere surrounded by Lokāloka [the mountain range which
formed the boundary of the universe in puranic geography].
By the application of water is made ascertainment of the
revolution of time. One may construct a sphere-instrument
combined with quicksilver: this is a mystery; if plainly
described, it would be generally intelligible in the
world. Therefore let the supreme sphere be constructed
according to the instruction of the preceptor [guru]. 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. So also, one should construct
instruments in order to ascertain time. When quite alone,
one should apply quicksilver to the wonder-causing
instrument. By the gnomon, staff, arc, wheel, instruments
for taking the shadow of various kinds.... By
water-instruments, the vessel, by the peacock, man,
monkey, and by stringed sand-receptacles one may determine
time accurately. Quicksilver-holes, water, and cords, and
oil and water, mercury and sand are used in these: these
applications, too, are difficult.

Sūrya Siddhānta_, xiii, 15-22,
E. Burgess' translation, New Haven, 1860.

A self-revolving instrument [or swayanvaha yantra]: Make a
wheel of light wood and in its circumference put hollow
spokes all having bores of the same diameter, and let them
be placed at equal distances from each other; and let
them also be placed at an angle verging somewhat from the
perpendicular: then half fill these hollow spokes with
mercury; the wheel thus filled will, when placed on an
axis supported by two posts, revolve of itself.

Or scoop out a canal in the tire of the wheel and then
plastering leaves of the Tȧla tree over this canal with
wax, fill one half of this canal with water and the other
half with mercury, till the water begins to come out, and
then cork up the orifice left open for filling the wheel.
The wheel will then revolve of itself, drawn around by the
water.

Description of a syphon: Make up a tube of copper or other
metal, and bend it in the form of an Ankus'a or elephant
hook, fill it with water and stop up both ends. And then
putting one end into a reservoir of water let the other
end remain suspended outside. Now uncork both ends. The
water of the reservoir will be wholly sucked up and fall
outside.

Now attach to the rim of the before described
self-revolving wheel a number of water-pots, and place the
wheel and these pots like the water wheel so that the
water from the lower end of the tube flowing into them on
one side shall set the wheel in motion, impelled by the
additional weight of the pots thus filled. The water
discharge from the pots as they reach the bottom of the
revolving wheel, should be drawn off into the reservoir
before alluded to by means of a water-course or pipe.

The self-revolving machine [mentioned by _Lalla_, etc.]
which has a tube with its lower end open is a vulgar
machine on account of its being dependant, because that
which manifests an ingenious and not a rustic contrivance
is said to be a machine.

And moreover many self-revolving machines are to be met
with, but their motion is procured by a trick. They are
not connected with the subject under discussion. I have
been induced to mention the construction of these, merely
because they have been mentioned by former astronomers.

_Siddhānta Siromaṇi_, xi, 50-57, L. Wilkinson's
translation, revised by Bȧpu̇ deva S(h)ȧstri,
Calcutta, 1861.

Before proceeding to an investigation of the content of these texts it is of considerable importance to establish dates for them, though there are many difficulties in establishing any chronology for Hindu astronomy. The _Sūrya Siddhānta_ is known to date, in its original form, from the early Middle Ages, _ca._ 500. The section in question is however quite evidently an interpolation from a later recension, most probably that which established the complete text as it now stands; it has been variously dated as _ca._ 1000 to _ca._ 1150 A.D. The date of the _Siddhānta Siromaṇi_ is more certain for we know it was written in about 1150 by Bhāskara (born 1114). Thus both these passages must have been written within a century of the great clock-tower made by Su Sung. The technical details will lead us to suppose there is more than a temporal connection.

We have already noted that the armillary spheres and celestial globes described just before these extracts are more similar in design to Chinese than to Ptolemaic practice. The mention of mercury and of sand as alternatives to water for the clock's fluid is another feature very prevalent in Chinese but absent in the Greek texts. Both texts seem conscious of the complexity of these devices and there is a hint (it is lost and revealed) that the story has been transmitted, only half understood, from another age or culture. It should also be noted that the mentions of cords and strings rather than gears, and the use of spheres rather than planispheres would suggest we are dealing with devices similar to the earliest Greek models rather than the later devices, or with the Chinese practice.

A quite new and important note is injected by the passage from the Bhāskara text. Obviously intrusive in this astronomical text we have the description of two "perpetual motion wheels" together with a third, castigated by the author, which helps its perpetuity by letting water flow from a reservoir by means of a syphon and drop into pots around the circumference of the wheel. These seem to be the basis also, in the extract from the _Sūrya Siddhānta_, of the "wonder-causing instrument" to which mercury must be applied.

In the next sections we shall show that this idea of a perpetual motion device occurs again in conjunction with astronomical models in Islam and shortly afterwards in medieval Europe. At each occurrence, as here, there are echoes of other cultures. In addition to those already mentioned we find the otherwise mysterious "peacock, man and monkey," cited as parts of the jackwork of astronomical clocks of Islam, associated with the weight drive so essential to the later horology in Europe.

We have already seen that in classical times there were already two different types of protoclocks; one, which may be termed "nonmathematical," designed only to give a visual aid in the conception of the cosmos, the other, which may be termed "mathematical" in which stereographic projection or gearing was employed to make the device a quantitative rather than qualitative representation. These two lines occur again in the Islamic culture area.

Nonmathematical protoclocks which are scarcely removed from the classical forms appear continuously through the Byzantine era and in Islam as soon as it recovered from the first shocks of its formation. Procopius (died _ca._ 535) describes a monumental water clock which was erected in Gaza _ca._ 500.[17] It contained impressive jackwork, such as a Medusa head which rolled its eyes every hour on the hour, exhibiting the time through lighted apertures and showing mythological interpretations of the cosmos. All these effects were produced by Heronic techniques, using hydraulic power and puppets moved by strings, rather than with gearing.

Again in 807 a similarly marvelous exhibition clock made of bronze was sent by Harun-al-Rashid to the Emperor Charlemagne; it seems to have been of the same type, with automata and hydraulic works. For the succeeding few centuries, Islam was in its Golden Age of development of technical astronomy (_ca._ 950-1150) and attention may have been concentrated on the more mathematical protoclocks. Towards the end of the 12th century, however, there was a revival of the old tradition, mainly at the court of the Emperor Saladin (1146-1173) when a great automaton water clock, more magnificent than any hitherto, was erected in Damascus. It was rebuilt, after 1168, by Muḥammad b. 'Alī b. Rustum, and repaired and improved by his son, Fakhr ad-dīn Riḍwān b. Muḥammad,[18] who is most important as the author of a book which describes in considerable technical detail the construction of this and other protoclocks. Closely associated with his book one also finds texts dealing with perpetual-motion devices, which we shall consider later.

During the century following this horological exuberance in Damascus, the center of gravity of Islamic astronomy shifted from the East to the Hispano-Moorish West. At the same time there comes more evidence that the line of mathematical protoclocks had not been left unattended. This is suggested by a description given by Trithemius of another royal gift from East to West which seems to have been different from the automata and hydraulic devices of the tradition from Procopius to Riḍwān:[19]

In the same year [1232] the Saladin of Egypt sent by his
ambassadors as a gift to the emperor Frederic a valuable
machine of wonderful construction worth more than five
thousand ducats. For it appeared to resemble internally a
celestial globe in which figures of the sun, moon, and
other planets formed with the greatest skill moved, being
impelled by weights and wheels, so that performing their
course in certain and fixed intervals they pointed out the
hour night and day with infallible certainty; also the
twelve signs of the zodiac with certain appropriate
characters, moved with the firmament, contained within
themselves the course of the planets.

The phrase "resembled internally" is of especial interest in this passage; it may perhaps arise as a mistranslation of the technical term for stereographic projection of the sphere, and if so the device might have been an anaphoric clock or some other astrolabic device.

This is made more probable by the existence of a specifically Islamic concentration on the astrolabe, and on its planetary companion instrument, the equatorium, as devices for mechanizing computation by use of geometrical analogues. The ordinary planispheric astrolabe, of course, was known in Islam from its first days until almost the present time. From the time of al-Biruni (_ca._ 1000)--significantly, perhaps, he is well known for his travel account of India--there is remarkable innovation.

Most cogent to our purpose is a text, described for the first time by Wiedemann,[20] in which al-Biruni explains how a special train of gearing may be used to show the revolutions of the sun and moon at their relative rates and to demonstrate the changing phase of the moon, features of fundamental importance in the Islamic (lunar) calendrical system. This device necessarily uses gear wheels with an odd number of teeth (_e.g._, 7, 19, 59) as dictated by the astronomical constants involved (see fig. 10). The teeth are shaped like equilateral triangles and square shanks are used, exactly as with the Antikythera machine. Horse-headed wedges are used for fixing; a tradition borrowed from the horse-shaped _Farās_ used to fasten the traditional astrolabe. Of special interest for us is the lunar phase diagram, which is just the same in form and structure as the lunar volvelle that occurs later in horology and is still so commonly found today, especially as a decoration for the dial of grandfather clocks.

Biruni's calendrical machine is the earliest complicated geared device on record and it is therefore all the more significant that it carries a feature found in later clocks. From the manuscript description alone one could not tell whether it was designed for automatic action or merely to be turned by hand. Fortunately this point is made clear by the most happy survival of an intact specimen of this very device, without doubt the oldest geared machine in existence in a complete state.

This landmark in the history of science and technology is now preserved at the Museum of the History of Science, Oxford, England.[21] It is an astrolabe, dated 1221-22 and signed by the maker, Muḥammad b. Abī Bakr (died 1231-32) of Isfahan, Persia (see figs. 11 and 12). The very close resemblance to the design of Biruni is quite apparent, though the gearing has been simplified very cleverly so that only one wheel has an odd number of teeth (13), the rest being much easier to mark out geometrically (_e.g._, 10, 48, 60, and 64 teeth). The lunar phase volvelle can be seen through the circular opening at the back of the astrolabe. It is quite certain that no automatic action is intended; when the central pivot is turned, by hand, probably by using the astrolabe rete as a "handle," the calendrical circles and the lunar phase are moved accordingly. Using one turn for a day would be too slow for useful re-setting of the instrument, in practice a turn corresponds more nearly to an interval of one week.

In addition to this geared development of the astrolabe, the same period in Islam brought forth a new device, the equatorium, a mechanical model designed to simulate the geometrical constructions used for finding the positions of the planets in Ptolemaic astronomy. The method may have originated already in classical times, a simple device being described by Proclus Diadochus (_ca._ 450), but the first general, though crude, planetary equatorium seems to have been described by Abulcacim Abnacahm (_ca._ 1025) in Granada; it has been handed down to us in the archaic Castilian of the Alfonsine _Libros del saber_.[22] The sections of this book, dealing with the _Laminas de las VII Planetas_, describe not only this instrument but also the improved modification introduced by Azarchiel (born _ca._ 1029, died _ca._ 1087).

No Islamic examples of the equatorium have survived, but from this period onward, there appears to have been a long and active tradition of them, and ultimately they were transmitted to the West, along with the rest of the Alfonsine corpus. More important for our argument is that they were the basis for the mechanized astronomical models of Richard of Wallingford (_ca._ 1320) and probably others, and for the already mentioned great astronomical clock of de Dondi. In fact, the complicated gearwork and dials of de Dondi's clock constitute a series of equatoria, mechanized in just the same way as the calendrical device described by Biruni.

It is evident that we are coming nearer now to the beginning of the true mechanical clock, and our last step, also from the Alfonsine corpus of western Islam, provides us with an important link between the anaphoric clock, the weight drive, and a most curious perpetual-motion device, the mercury wheel, used as an escapement or regulator. The Alfonsine book on clocks contains descriptions of five devices in all, four of them being due to Isaac b. Sid (two sundials, an automaton water-clock and the present mercury clock) and one to Samuel ha-Levi Adulafia (a candle clock)--they were probably composed just before _ca._ 1276-77.

The mercury clock of Isaac b. Sid consists of an astrolabe dial, rotated as in the anaphoric clock, and fitted with 30 leaf-shaped gear teeth (see fig. 13). These are driven by a pinion of 6 leaves mounted on a horizontal axle (shown very diagrammatically in the illustration) and at the other end of this axle is a wheel on which is mounted the special mercury drum which is powered by a normal weight drive.

It is the mercury drum which forms the most novel feature of this device; the fluid, constrained in 12 chambers so as to just fill 6 of them, must slowly filter through small holes in the constraining walls. In practice, of course, the top mercury surfaces will not be level, but higher on the right so as to balance dynamically the moment of the applied weight on its driven rope. This curious arrangement shows point of resemblance to the Indian "mercury-holes," to the perpetual-motion devices found in the medieval European tradition and also in the texts associated with Riḍwān, which we shall next examine.