diff options
| -rw-r--r-- | .gitattributes | 3 | ||||
| -rw-r--r-- | 30001-0.txt | 1964 | ||||
| -rw-r--r-- | 30001-0.zip | bin | 0 -> 47601 bytes | |||
| -rw-r--r-- | 30001-8.txt | 2353 | ||||
| -rw-r--r-- | 30001-8.zip | bin | 0 -> 47399 bytes | |||
| -rw-r--r-- | 30001-h.zip | bin | 0 -> 1195131 bytes | |||
| -rw-r--r-- | 30001-h/30001-h.htm | 2697 | ||||
| -rw-r--r-- | 30001-h/images/cap_t.png | bin | 0 -> 250 bytes | |||
| -rw-r--r-- | 30001-h/images/cover.jpg | bin | 0 -> 48770 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_1.jpg | bin | 0 -> 83952 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_10.jpg | bin | 0 -> 35760 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_11.jpg | bin | 0 -> 48971 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_12.jpg | bin | 0 -> 46922 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_13.jpg | bin | 0 -> 23733 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_14.jpg | bin | 0 -> 9901 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_15.jpg | bin | 0 -> 11944 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_16.jpg | bin | 0 -> 38405 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_17.jpg | bin | 0 -> 94699 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_18.jpg | bin | 0 -> 20688 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_19.jpg | bin | 0 -> 49200 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_2.jpg | bin | 0 -> 62512 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_20.jpg | bin | 0 -> 25199 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_21.jpg | bin | 0 -> 26384 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_22.jpg | bin | 0 -> 25530 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_3.jpg | bin | 0 -> 48159 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_4.jpg | bin | 0 -> 54649 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_4_zoom.jpg | bin | 0 -> 178507 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_5.jpg | bin | 0 -> 37357 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_6.jpg | bin | 0 -> 37516 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_7.jpg | bin | 0 -> 57444 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_8.jpg | bin | 0 -> 45758 bytes | |||
| -rw-r--r-- | 30001-h/images/fig_9.jpg | bin | 0 -> 39115 bytes | |||
| -rw-r--r-- | 30001.txt | 2353 | ||||
| -rw-r--r-- | 30001.zip | bin | 0 -> 47353 bytes | |||
| -rw-r--r-- | LICENSE.txt | 11 | ||||
| -rw-r--r-- | README.md | 2 | ||||
| -rw-r--r-- | old/30001-0.txt | 2356 | ||||
| -rw-r--r-- | old/30001-0.zip | bin | 0 -> 47601 bytes | |||
| -rw-r--r-- | old/30001-8.txt | 2353 | ||||
| -rw-r--r-- | old/30001-8.zip | bin | 0 -> 47399 bytes | |||
| -rw-r--r-- | old/30001-h.zip | bin | 0 -> 1195131 bytes | |||
| -rw-r--r-- | old/30001-h/30001-h.htm | 3117 | ||||
| -rw-r--r-- | old/30001-h/images/cap_t.png | bin | 0 -> 250 bytes | |||
| -rw-r--r-- | old/30001-h/images/cover.jpg | bin | 0 -> 48770 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_1.jpg | bin | 0 -> 83952 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_10.jpg | bin | 0 -> 35760 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_11.jpg | bin | 0 -> 48971 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_12.jpg | bin | 0 -> 46922 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_13.jpg | bin | 0 -> 23733 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_14.jpg | bin | 0 -> 9901 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_15.jpg | bin | 0 -> 11944 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_16.jpg | bin | 0 -> 38405 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_17.jpg | bin | 0 -> 94699 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_18.jpg | bin | 0 -> 20688 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_19.jpg | bin | 0 -> 49200 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_2.jpg | bin | 0 -> 62512 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_20.jpg | bin | 0 -> 25199 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_21.jpg | bin | 0 -> 26384 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_22.jpg | bin | 0 -> 25530 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_3.jpg | bin | 0 -> 48159 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_4.jpg | bin | 0 -> 54649 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_4_zoom.jpg | bin | 0 -> 178507 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_5.jpg | bin | 0 -> 37357 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_6.jpg | bin | 0 -> 37516 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_7.jpg | bin | 0 -> 57444 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_8.jpg | bin | 0 -> 45758 bytes | |||
| -rw-r--r-- | old/30001-h/images/fig_9.jpg | bin | 0 -> 39115 bytes | |||
| -rw-r--r-- | old/30001.txt | 2353 | ||||
| -rw-r--r-- | old/30001.zip | bin | 0 -> 47353 bytes |
69 files changed, 19562 insertions, 0 deletions
diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/30001-0.txt b/30001-0.txt new file mode 100644 index 0000000..4adc426 --- /dev/null +++ b/30001-0.txt @@ -0,0 +1,1964 @@ +*** START OF THE PROJECT GUTENBERG EBOOK 30001 *** + + +--------------------------------------------------------------+ + | This e-text includes characters that require UTF-8 | + | (Unicode) file encoding: | + | | + | ḍ, ā, ḥ, ȧ, ī | + | | + | If any of these characters do not display properly--in | + | particular, if the dots do not appear under the letters | + | make sure your text reader’s “character set” or “file | + | encoding” is set to Unicode (UTF-8). You may also need to | + | change the default font. Depending on available fonts, some | + | tables may not line up vertically. | + +--------------------------------------------------------------+ + + + + + 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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MUḤAMMAD B. ABĪ BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Riḍwān and al-Jazarī, have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Frémont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Frémont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Riḍwān +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfiī _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qabājaqī (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Hêng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) Sūrya Siddhānta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddhānta Siromaṇi animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Riḍwān water-clocks, perpetual motion + and weight drive + 1206 al-Jazarī clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Frühzeit der Räderuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des österreichischen archäologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Mémoires de la Société Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels Über die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "Über die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der königliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beiträge zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11ᵛ-14ᵛ = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Société Royale d'Archéologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archèologique_, 1849, vol. 6. + + [39] M. C. Frémont. _Origine de l'horloge à poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beiträge zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THE PROJECT GUTENBERG EBOOK 30001 *** diff --git a/30001-0.zip b/30001-0.zip Binary files differnew file mode 100644 index 0000000..6826c3b --- /dev/null +++ b/30001-0.zip diff --git a/30001-8.txt b/30001-8.txt new file mode 100644 index 0000000..444ae9a --- /dev/null +++ b/30001-8.txt @@ -0,0 +1,2353 @@ +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + + +-----------------------------------------------------+ + | Trancriber's note: | + | | + | Letters enclosed in square brackets represent: | + | [=x] any letter with a macron (straight line above) | + | [x.] any letter with a dot below | + | [.x] any letter with a dot above | + +-----------------------------------------------------+ + + + + + 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. (_S[=u]rya Siddh[=a]nta_, 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 Ri[d.]w[=a]n, _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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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 Ri[d.]w[=a]n 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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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 Hng _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 Hng 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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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 Hng. 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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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 Lok[=a]loka [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. + + _S[=u]rya Siddh[=a]nta_, xiii, 15-22, + E. Burgess' translation, New Haven, 1860. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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 T[.a]la 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. + + _Siddh[=a]nta Siroma[n.]i_, xi, 50-57, L. Wilkinson's + translation, revised by B[.a]p[.u] deva S(h)[.a]stri, + 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 _S[=u]rya Siddh[=a]nta_ 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 _Siddh[=a]nta Siroma[n.]i_ is more certain for we know it was +written in about 1150 by Bh[=a]skara (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 +Bh[=a]skara 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 _S[=u]rya Siddh[=a]nta_, 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 Mu[h.]ammad b. 'Al[=i] b. +Rustum, and repaired and improved by his son, Fakhr ad-d[=i]n +Ri[d.]w[=a]n b. Mu[h.]ammad,[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 + Ri[d.]w[=a]n:[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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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 _Far[=a]s_ 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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MU[H.]AMMAD B. AB[=I] BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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, Mu[h.]ammad b. Ab[=i] +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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 Ri[d.]w[=a]n, which we shall next examine. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Ri[d.]w[=a]n and al-Jazar[=i], have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Frmont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Frmont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Ri[d.]w[=a]n +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfi[=i] _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qab[=a]jaq[=i] (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Hng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) S[=u]rya Siddh[=a]nta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddh[=a]nta Siromani animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Ri[d.]w[=a]n water-clocks, perpetual motion + and weight drive + 1206 al-Jazar[=i] clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Frhzeit der Rderuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des sterreichischen archologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Mmoires de la Socit Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels ber die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "ber die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der knigliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beitrge zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11^{v}-14^{v} = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Socit Royale d'Archologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archologique_, 1849, vol. 6. + + [39] M. C. Frmont. _Origine de l'horloge poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beitrge zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001-8.txt or 30001-8.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/30001-8.zip b/30001-8.zip Binary files differnew file mode 100644 index 0000000..4b9e6bd --- /dev/null +++ b/30001-8.zip diff --git a/30001-h.zip b/30001-h.zip Binary files differnew file mode 100644 index 0000000..038c31a --- /dev/null +++ b/30001-h.zip diff --git a/30001-h/30001-h.htm b/30001-h/30001-h.htm new file mode 100644 index 0000000..cf3e159 --- /dev/null +++ b/30001-h/30001-h.htm @@ -0,0 +1,2697 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta name="generator" content="HTML Tidy, see www.w3.org" /> +<meta http-equiv="Content-Type" content= +"text/html;charset=UTF-8" /> +<title>The Project Gutenberg eBook of On the Origin of Clockwork, +Perpetual Motion Devices and the Compass by Derek J. de Solla Price</title> +<style type="text/css"> + + p { margin-top: .75em; + text-align: justify; + margin-bottom: .75em;} + + p.tb { margin-top: 1.5em; + text-align: justify; + margin-bottom: .75em;} + + p.indent { margin-top: 0em; margin-bottom: 0em; + text-align: justify; margin-left: 3.5em; text-indent: -3.5em;} + + p.title { margin-top: 1.25em; + text-align: justify; + margin-bottom: .75em;} + + + p.quotsig { margin-top: .75em; + text-align: right; + margin-bottom: .75em;} + + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; font-weight: normal; + margin-top: 1.5em; + margin-bottom: .75em; } + + + + /* sup, + sub { + height: 0em; font-size: .7em; + vertical-align: baseline; + position: relative; }*/ + + sup { bottom: .2em; font-size: .7em; margin-left: 0em;; } + + sub { top: 0em; font-size: .6em; } + + hr { width: 33%; + margin-top: 0em; + margin-bottom: 0em; + margin-left: auto; + margin-right: auto; + clear: both; + } + + + table {margin-left: auto; margin-right: auto;} + + + td.td100 {padding-right: 1em; padding-left: 0em; padding-top: 0em; padding-bottom: 0em; font-size: .9em; text-align: justify; width: 100%; vertical-align: top; } + td.td100c {padding-right: 0em; padding-left: 2.4em; padding-top: 1em; padding-bottom: .5em; font-size: 1em; text-align: left; width: 100%; vertical-align: middle;} + td.right {padding-top: .2em; padding-bottom: .2em; font-size: .8em; text-align: right; width: 10%; vertical-align: bottom;} + td.left {padding-top: .2em; padding-bottom: .2em; font-size: .8em; text-align: right; width: 90%; vertical-align: top;} + td.center {padding-top: .2em; padding-bottom: .2em; font-size: 1em; text-align: center; width: 50%; vertical-align: top;} + td.left100 {padding-right: 2em; padding-left: 2em; padding-top: .2em; padding-bottom: .2em; font-size: 1em; text-align: left; width: 100%; vertical-align: top;} + + body {margin-left: 10%; margin-right: 10%; + } + + .pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + right: 3%; font-style: normal; + font-size: .8em; + text-align: right; + } /* page numbers */ + .tn {font-size: .8em; width: 80%; background-color: #EEE; padding: 0.5em 1em 0.5em 1em; text-align: justify;} + + + .blockquot {font-size: .85em; margin-top: 1.5em; margin-bottom: 1.5em; } + + .blockquot2 {font-size: .83em; margin-top: 1.5em; margin-bottom: 1.5em; + margin-left: 20%;} + + img {text-decoration: none; border: none; margin-bottom: 0em; margin-top: 0em;} + img.floatLeft {float: left; height: 2.2em; margin-right: 0em; border: none;} + + + .smcap {font-variant: small-caps;} + .u {text-decoration: underline;} + + .caption {font-size: .85em; text-align: justify; margin-top: 1em; + margin-bottom: 2em; margin-left: 5%; margin-right: 5%; } + .caption2 {font-size: .85em; text-align: justify; margin-top: 1em; + margin-bottom: 2em; margin-left: 5%; margin-right: 5%; } + + .figcenter {margin: auto; text-align: center;} + + + .footnotes {border: none;} + .footnote {margin-left: 10%; margin-right: 5%; font-size: 0.9em;} + .footnote .label {position: absolute; right: 84%; text-align: right; font-size: .9em;} + .fnanchor {vertical-align: super; font-size: .7em; text-decoration: none;} + + +</style> +</head> +<body> +<div>*** START OF THE PROJECT GUTENBERG EBOOK 30001 ***</div> + +<h6> </h6> + +<div class="tn"> +Transcriber's note:<br /><br /> +The original three column Chronological Table +has been replaced by a single column table +with the same chronological order to make its reading easier +at all browser settings. +</div> + +<h6> </h6> + +<div class="figcenter" style="width: 500px;"><img src="images/cover.jpg" width="500" height="647" alt= +"Cover" title="Cover page" /></div> + +<p><span class='pagenum'>81</span></p> + +<p class="quotsig"><span class="smcap">Contributions from<br /> +The Museum of History and Technology:<br /> +Paper 6</span><br /><br /></p> + +<p class="quotsig"><span class="smcap">On the Origin of Clockwork,<br /> +Perpetual Motion Devices, and the Compass</span><br /> +<i>Derek J. de Solla Price</i><br /><br /></p> + +<table width="100%" summary="TOC"> + +<tr> +<td class="left">POWER AND MOTION GEARING</td> +<td class="right"><a href="#Page_83a">83</a></td> +</tr> + +<tr> +<td class="left">MECHANICAL CLOCKS</td> +<td class="right"><a href="#Page_84a">84</a></td> +</tr> + +<tr> +<td class="left">PERPETUAL MOTION AND THE CLOCK BEFORE DE DONDI</td> +<td class="right"><a href="#Page_108a">108</a></td> +</tr> + +<tr> +<td class="left">THE MAGNETIC COMPASS AS A FELLOW-TRAVELER FROM CHINA</td> +<td class="right"><a href="#Page_110a">110</a></td> +</tr> +</table> + +<p><span class='pagenum'>82</span><br /><br /></p> + +<h2><i>ON THE ORIGIN OF CLOCKWORK,<br /> +PERPETUAL MOTION DEVICES<br /> +AND THE COMPASS</i></h2> + +<h3><i>By Derek J. de Solla Price</i></h3> + +<table width="80%" summary="intro"> + +<tr> +<td><p><i>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.</i></p> + +<p><i>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.</i></p> + +<p><span class="smcap">The Author</span>: <i>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.</i></p></td> +</tr> + +</table> + +<div class="blockquot2"><p>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. (<i>Sūrya Siddhānta</i>, ed. Burgess, xiii, +18-19.)</p></div> + +<p><img src="images/cap_t.png" class="floatLeft" alt="T" />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.</p> + +<p>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.<a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">1</a> 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.</p> + +<p>Furthermore, even if one admits the use of clocklike +gearing before the existence of the clock, it is still +<span class='pagenum'>83</span>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, <i>ca.</i> 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, <i>ca.</i> 1272.</p> + +<p>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 +<i>Perpetuum Mobile</i>, 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.<a name="FNanchor_2" id="FNanchor_2"></a><a href="#Footnote_2" class="fnanchor">2</a> 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.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_1" id="fig_1" /><img src="images/fig_1.jpg" width="500" height="666" alt= +"Framework Structure of the Astronomical +Clock of Giovanni de Dondi of Padua, +A.D. 1364." title="" /> + +<div class="caption">Figure 1.—<span class="smcap">Framework Structure of the Astronomical +Clock</span> of Giovanni de Dondi of Padua, +A.D. 1364.</div></div> + + +<h3><a name="Page_83a" id="Page_83a">Power and Motion Gearing</a></h3> + +<p>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.),<a name="FNanchor_3" id="FNanchor_3"></a><a href="#Footnote_3" class="fnanchor">3</a> and in China actual examples of wheels +and moulds for wheels dating from the 4th century +<span class='pagenum'>84</span>B.C. have been preserved.<a name="FNanchor_4" id="FNanchor_4"></a><a href="#Footnote_4" class="fnanchor">4</a> 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.<a name="FNanchor_5" id="FNanchor_5"></a><a href="#Footnote_5" class="fnanchor">5</a> 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_2" id="fig_2" /><img src="images/fig_2.jpg" width="500" height="497" alt= +"Astronomical Clock of de Dondi, +showing gearing on the dial for Mercury and +escapement crown wheel. Each of the seven side +walls of the structure shown in figure 1 was fitted +with a dial." title="" /> + +<div class="caption">Figure 2.—<span class="smcap">Astronomical Clock</span> of de Dondi, +showing gearing on the dial for Mercury and +escapement crown wheel. Each of the seven side +walls of the structure shown in figure 1 was fitted +with a dial.</div></div> + + +<p>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.<a name="FNanchor_6" id="FNanchor_6"></a><a href="#Footnote_6" class="fnanchor">6</a> One may also cite +the use of the reduction gear chain in power machinery +as used in the geared windlass of Archimedes and +Hero.</p> + +<p>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.</p> + + +<h3><a name="Page_84a" id="Page_84a">Mechanical Clocks</a></h3> + +<p>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 me<span class='pagenum'>85</span>chanical clocks has demonstrated certain peculiarities +most relevant to our present argument.</p> + + +<p class="title"><span class="smcap">the european tradition</span></p> + +<p>If one is to establish a <i>terminus ante quem</i> 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,<a name="FNanchor_7" id="FNanchor_7"></a><a href="#Footnote_7" class="fnanchor">7</a> 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 <i>horologium</i> and its vernacular equivalents.</p> + +<p>Temporarily postponing the consideration of evidence +prior to <i>ca.</i> 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.<a name="FNanchor_8" id="FNanchor_8"></a><a href="#Footnote_8" class="fnanchor">8</a> 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 (<i>ca.</i> 1475), +pendulum control (<i>ca.</i> 1650), and the anchor escapement +(<i>ca.</i> 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_3.jpg" width="500" height="916" alt= +"Figure 3.—German Wall Clock, Probably About +1450, showing the degeneration in complexity from +that of de Dondi's clock." title="" /> + +<div class="caption">Figure 3.—<span class="smcap">German Wall Clock, Probably About +1450</span>, showing the degeneration in complexity from +that of de Dondi's clock.</div></div> + +<p><span class='pagenum'>86</span></p> + +<p>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. <a href="#fig_1">1,</a> <a href="#fig_2">2</a>) +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.</p> + +<p>On the basis of such evidence I have suggested elsewhere<a name="FNanchor_9" id="FNanchor_9"></a><a href="#Footnote_9" class="fnanchor">9</a> +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.</p> + +<p>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.</p> + + +<p class="title"><span class="smcap">the chinese tradition</span></p> + +<p>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.<a name="FNanchor_10" id="FNanchor_10"></a><a href="#Footnote_10" class="fnanchor">10</a> 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 H&ecirc;ng <i>ca.</i> 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 H&ecirc;ng +onwards, largely independent of any transmissions +from the West.</p> + +<p>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 (<i>e.g.</i>, equator, ecliptic, meridians, etc.), or a +solid celestial globe on which such circles could be +drawn, together with the constellations of the fixed +<span class='pagenum'>87</span>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.</p> + +<p>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."</p> + +<p>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.</p> + +<p>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.</p> + +<p>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. <a href="#fig_4">4</a>). 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.</p> + +<p>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.</p> + +<p>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" (<i>glokke</i>). 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<span class='pagenum'>88</span> +European clocks should have prompted them to +open their doors, previously so carefully and for +so long kept closed against the foreign barbarians.</p> + + +<div class="figcenter" style="width: 500px;"><a name="fig_4" id="fig_4" /><a href="images/fig_4_zoom.jpg"><img src="images/fig_4.jpg" width="500" height="516" alt= +"Astronomical Clock Tower of Su +Sung in K'ai-feng, ca. A.D. 1090." title="Click for detailed image" /></a> + +<div class="caption">Figure 4.—<span class="smcap">Astronomical Clock Tower of Su +Sung</span> in K'ai-feng, <i>ca.</i> A.D. 1090, from an original +drawing by John Christiansen. (<i>Courtesy of Cambridge +University Press.</i>)</div></div> + +<h3>Mechanized Astronomical Models</h3> + +<p>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.</p> + +<p><span class='pagenum'>89</span></p> + +<p class="title"><span class="smcap">hellenistic period</span></p> + +<p>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.<a name="FNanchor_11" id="FNanchor_11"></a><a href="#Footnote_11" class="fnanchor">11</a></p> + +<p>Cicero's descriptions of Archimedes' planetarium +are (italics supplied):</p> + +<div class="blockquot"><p>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>i. e.</i>, 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>i.e.</i>, set in motion] the globe, it was actually true +that the moon was always as many revolutions behind the +sun on the <i>bronze</i> 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].</p> + +<p class="quotsig"> +<i>De republica</i>, I, xiv (21-22), Keyes' translation. +</p> + +<p class="tb">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.</p> + +<p class="quotsig"> +<i>Tusculanae disputationes</i>, I, 63. +</p> +</div> + +<p class="tb">Later descriptions from Ovid, Lactantius, Claudian, +Sextus Empiricus, and Pappus, respectively, are +(italics supplied):</p> + +<div class="blockquot"><p>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>i. e.</i>, the outer bronze +globe's] round form. The form of the temple [of Vesta] +is similar....</p> + +<p class="quotsig"> +Ovid, <i>Fasti</i> (1st century, A.D.), VI, 277-280, +Frazer's translation. +</p> + +<p class="tb">The Sicilian Archimedes, was able to make a reproduction +and model of the world in concave <i>brass</i> (concavo aere +similitudinem mundi ac figuram); in it he so arranged +the <i>sun</i> and <i>moon</i> 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 <i>courses of +the stars</i>, whether fixed or wandering.</p> + +<p class="quotsig"> +Lactantius, <i>Institutiones divinae</i> (4th century, A.D.), II, 5, 18. +</p> + +<p class="tb">Archimedes' sphere. When Jove looked down and saw +the heavens figured in a sphere of <i>glass</i>, 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 <i>stars</i> and actuates the lifelike mass with +definite motions. A false <i>zodiac</i> runs through a year of its +own and a toy <i>moon</i> waxes and wanes month by month. +Now bold invention rejoices to make its own heaven revolve +and sets the <i>stars</i> [planets?] in motion by human wit....</p> + +<p class="quotsig"> +Claudian, <i>Carmina minora</i> (<i>ca.</i> A.D. 400), LI (LXVIII), +Platnaure's translation.<br /> +</p> + +<p class="tb">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 <i>wood</i>, or at the movements +of these [bodies], but by the devices and causes of the +movements.</p> + +<p class="quotsig"> +Sextus Empiricus, <i>Adversus mathematicos</i> (3rd century, A.D.), +IX, 115, Epps' translation. +</p></div> + +<p><span class='pagenum'>90</span></p> + +<div class="blockquot"><p> +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 <i>water</i>, and Archimedes the Syracusan, according +to some, knows the cause and reasons for all of these.</p> + +<p class="quotsig"> +Pappus (3rd century, A.D.), <i>Works</i> (Hultsch edition), +VIII, 2, Epps' translation. +</p></div> + +<p>A similar arrangement seems to be indicated in +another mechanized globe, also mentioned by Cicero +and said to have been made by Posidonius:</p> + +<div class="blockquot"><p>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 <i>sun</i> and <i>moon</i> and +<i>five</i> 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....</p> + +<p class="quotsig"> +<i>De natura deorum</i>, II, xxxiv-xxxv (88), +Yonge's translation. +</p></div> + +<p>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 H&ecirc;ng. 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.</p> + +<p class="tb">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:</p> + +<div class="blockquot"><p>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.</p> + +<p class="quotsig"> +<i>Pneumatics</i>, XLVI, Woodcroft's translation. +</p></div> + +<p>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.</p> + +<p>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.</p> + +<p>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 (<i>ca.</i> A.D. 120) +it had led to the successive inventions of the anaphoric +clock and of the planispheric astrolabe.<a name="FNanchor_12" id="FNanchor_12"></a><a href="#Footnote_12" class="fnanchor">12</a> 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.</p> + +<p>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.<a name="FNanchor_13" id="FNanchor_13"></a><a href="#Footnote_13" class="fnanchor">13</a><br /><br /></p> + +<p><span class='pagenum'>91</span></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_5" id="fig_5" /><img src="images/fig_5.jpg" width="500" height="596" alt= +"Plate of Salzburg +Anaphoric Clock," title="" /> + +<div class="caption">Figure 5. <span class="smcap">Plate of Salzburg +Anaphoric Clock</span>, a reconstruction +(see footnote <a href="#Footnote_14">14</a>) based on +a photograph of the remaining +fragment. (<i>Courtesy of Oxford +University Press.</i>)</div></div> + + +<p>Parts of two such discs from anaphoric clocks +have been found, one at Salzburg<a name="FNanchor_14" id="FNanchor_14"></a><a href="#Footnote_14" class="fnanchor">14</a> and one at +Grand in the Vosges,<a name="FNanchor_15" id="FNanchor_15"></a><a href="#Footnote_15" class="fnanchor">15</a> 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. <a href="#fig_5">5</a>). +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.</p> + +<p>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-<span class='pagenum'>92</span>keeping clocks before the change was made to a +fixed dial and moving hand.</p> + +<p>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.<a name="FNanchor_16" id="FNanchor_16"></a><a href="#Footnote_16" class="fnanchor">16</a> 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.</p> + +<p>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 <i>ca.</i> 65 B.C. &plusmn;10 years, and we can be sure +that the machine is of Hellenistic origin, possibly from +Rhodes or Cos.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_6" id="fig_6" /><img src="images/fig_6.jpg" width="500" height="301" alt= +"Antikythera Machine, Largest Fragment." title="" /> + +<div class="caption">Figure 6.—<span class="smcap">Antikythera Machine, Largest Fragment.</span> +(<i>Photo courtesy of National Museum, Athens.</i>)</div></div> + +<p>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. <a href="#fig_6">6</a>) 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. <a href="#fig_7">7</a>, 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. <a href="#fig_7">7</a>, +top) has a pair of rings carefully engraved and graduated<span class='pagenum'>93</span> +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&deg; in the 45&deg; present).</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_7" id="fig_7" /><img src="images/fig_7.jpg" width="500" height="459" alt= +"Antikythera Machine, Two Smaller +Fragments." title="" /> + +<div class="caption">Figure 7.—<span class="smcap">Antikythera Machine, Two Smaller +Fragments.</span> (<i>Photo courtesy of National Museum, +Athens.</i>)</div></div> + +<p>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.</p> + +<p>Some technical details can be gleaned however. +The shape of the gear teeth appears to be almost +exactly equilateral triangles in all cases (fig. <a href="#fig_8">8</a>), 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. <a href="#fig_9">9</a>) has shown that the appearances +are consistent with the theory that the<span class='pagenum'>94</span> +purpose of the gears was to provide the correct angular +ratios to move the sun and planets at their appropriate +relative speeds.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_8" id="fig_8" /><img src="images/fig_8.jpg" width="500" height="490" alt= +"Antikythera Machine, +Detail From Figure 6 +showing gearing." title="" /> + +<div class="caption">Figure 8.—<span class="smcap">Antikythera Machine, +Detail From Figure 6</span>, +showing gearing. (<i>Photo courtesy +of National Museum, Athens.</i>)</div></div> + +<p>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.<br /><br /></p> + +<table width="100%" summary="note" border="1"> +<tr><td class="left100"> +<div class="blockquot"><p><i>Note added in proof</i>:</p> + +<p>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 <i>Scientific American</i>, 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.</p></div> +</td></tr> +</table> + +<p class="tb">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<span class='pagenum'>95</span> +are more akin to those current in China than in the +West. The relevant portions of text are as follows +(italics supplied):</p> + +<div class="blockquot"><p>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.</p> + +<p class="quotsig"> +<i>Sūrya Siddhānta</i>, xiii, 15-22,<br /> +E. Burgess' translation, New Haven, 1860. +</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_9" id="fig_9" /><img src="images/fig_9.jpg" width="500" height="563" alt= +"Antikythera Machine, Partial Reconstruction +by Theophanidis." title="" /> + +<div class="caption">Figure 9.—<span class="smcap">Antikythera Machine, Partial Reconstruction +by Theophanidis</span> (see footnote <a href="#Footnote_16">16</a>).</div></div> + +<p>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.</p> + +<p>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 + +<span class='pagenum'>96</span> + +the orifice left open for filling the wheel. The wheel will +then revolve of itself, drawn around by the water.</p> + +<p>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.</p> + +<p>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.</p> + +<p>The self-revolving machine [mentioned by <i>Lalla</i>, 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.</p> + +<p>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.</p> + +<p class="quotsig"> +<i>Siddhānta Siromaṇi</i>, xi, 50-57, L. Wilkinson's translation,<br /> +revised by Bȧpu̇ deva S(h)ȧstri, Calcutta, 1861. +</p></div> + +<p>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 <i>Sūrya Siddhānta</i> is known to date, in +its original form, from the early Middle Ages, <i>ca.</i> 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 <i>ca.</i> 1000 to <i>ca.</i> +1150 A.D. The date of the <i>Siddhānta Siromaṇi</i> 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 +clocktower made by Su Sung. The technical details +will lead us to suppose there is more than a temporal +connection.</p> + +<p>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.</p> + +<p>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 <i>Sūrya Siddhānta</i>, of the "wonder-causing +instrument" to which mercury must be +applied.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>ca.</i> 535) describes a monumental +water clock which was erected in Gaza <i>ca.</i> 500.<a name="FNanchor_17" id="FNanchor_17"></a><a href="#Footnote_17" class="fnanchor">17</a> It +contained impressive jackwork, such as a Medusa +<span class='pagenum'>97</span> +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.</p> + +<p>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 (<i>ca.</i> 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,<a name="FNanchor_18" id="FNanchor_18"></a><a href="#Footnote_18" class="fnanchor">18</a> 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.</p> + +<p>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:<a name="FNanchor_19" id="FNanchor_19"></a><a href="#Footnote_19" class="fnanchor">19</a></p> + +<div class="blockquot"><p>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. +</p></div> + +<p>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.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_10" id="fig_10" /><img src="images/fig_10.jpg" width="500" height="518" alt= +"Calendrical Gearing Designed by +al-Biruni." title="" /> + +<div class="caption">Figure 10.—<span class="smcap">Calendrical Gearing Designed by +al-Biruni</span>, <i>ca.</i> A.D. 1000. The gear train count is +40-10+7-59+19-59+24-48. The gear of 48 therefore +makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. +The gear of 40 shows a (lunar) rotation in exactly +28 days, and the center pinions 7+10 rotate in exactly +one week. After Wiedemann (see footnote <a href="#Footnote_20">20</a>).</div></div> + +<p>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 (<i>ca.</i> 1000)—significantly, +perhaps, he is well known for his travel +account of India—there is remarkable innovation.</p> + +<p>Most cogent to our purpose is a text, described for +the first time by Wiedemann,<a name="FNanchor_20" id="FNanchor_20"></a><a href="#Footnote_20" class="fnanchor">20</a> in which al-Biruni +<span class='pagenum'>98</span>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 (<i>e.g.</i>, 7, 19, 59) as dictated by the astronomical +constants involved (see fig. <a href="#fig_10">10</a>). 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 <i>Farās</i> 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.</p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_11.jpg" width="500" height="440" alt= +"Geared Astrolabe by Muḥammad b. Abī Bakr of Isfahan, A.D. 1221-1222." title="" /> + +<div class="caption">Figure 11.—<span class="smcap">Geared Astrolabe by Muḥammad b. Abī Bakr of Isfahan</span>, A.D. 1221-1222. +(<i>Photo courtesy of Science Museum, London.</i>)</div></div> + +<p>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.</p> + +<p><span class='pagenum'>99</span></p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_12.jpg" width="500" height="517" alt= +"Gearing from Astrolabe Shown in Figure 11." title="" /> + +<div class="caption">Figure 12.—<span class="smcap">Gearing from Astrolabe Shown in Figure 11.</span> The gear train count is as +follows: 48-13+8-64+64-64+10-60. The pinion of 8 has been incorrectly replaced by a +more modern pinion of 10. The gear of 48 should make 13 (lunar) rotations while the double +gear of 64+64 makes 6 revolutions of double months (of 29-30 days) and the gear of 60 makes +a single turn in the hegiral year of 354 days. (<i>Photo courtesy of Science Museum, London.</i>)</div></div> + +<p>This landmark in the history of science and technology +is now preserved at the Museum of the +History of Science, Oxford, England.<a name="FNanchor_21" id="FNanchor_21"></a><a href="#Footnote_21" class="fnanchor">21</a> 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 +<span class='pagenum'>100</span>much easier to mark out geometrically (<i>e.g.</i>, 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_13" id="fig_13" /><img src="images/fig_13.jpg" width="500" height="351" alt= +"Astrolabe Clock, Regulated by a +Mercury Drum." title="" /> + +<div class="caption">Figure 13.—<span class="smcap">Astrolabe Clock, Regulated by a +Mercury Drum</span>, from the Alfonsine <i>Libros del saber</i> +(see footnote <a href="#Footnote_22">22</a>).</div></div> + +<p>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 (<i>ca.</i> 450), but the +first general, though crude, planetary equatorium +seems to have been described by Abulcacim Abnacahm +(<i>ca.</i> 1025) in Granada; it has been handed down +to us in the archaic Castilian of the Alfonsine <i>Libros +del saber</i>.<a name="FNanchor_22" id="FNanchor_22"></a><a href="#Footnote_22" class="fnanchor">22</a> The sections of this book, dealing with the +<i>Laminas de las VII Planetas</i>, describe not only this +instrument but also the improved modification introduced +by Azarchiel (born <i>ca.</i> 1029, died <i>ca.</i> 1087).</p> + +<p>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 (<i>ca.</i> 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.</p> + +<p>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<span class='pagenum'>101</span> 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 +<i>ca.</i> 1276-77.</p> + +<table width="100%" summary="perpetual wheels" border="0"> +<tr><td class="center"> +<div class="figcenter" style="width: 200px;"><a name="fig_14" id="fig_14" /><img src="images/fig_14.jpg" width="200" height="195" alt= +"Islamic Perpetual Motion Wheel." title="" /></div> + +<div class="caption2">Figure 14.—<span class="smcap">Islamic Perpetual Motion Wheel</span>, +after manuscript cited by Schmeller (see footnote <a href="#Footnote_26">26</a>).</div> +</td> +<td class="center"> +<div class="figcenter" style="width: 204px;"><img src="images/fig_15.jpg" width="204" height="195" alt= +"Another Perpetual Motion Wheel." title="" /></div> + +<div class="caption2">Figure 15.—<span class="smcap">Another Perpetual Motion Wheel</span>, +after the text cited in figure 14.</div> +</td></tr> +</table> + +<p>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. <a href="#fig_13">13</a>). +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.</p> + +<p>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.</p> + + +<p>It is of the greatest interest to our theme that the +Islamic contributions to horology and perpetual +motion seem to form a closely knit corpus. A most +important series of horological texts, including those +of Riḍwān and al-Jazarī, have been edited by Wiedemann +and Hauser.<a name="FNanchor_23" id="FNanchor_23"></a><a href="#Footnote_23" class="fnanchor">23</a> Other Islamic texts give versions +of the water clocks and automata of Archimedes and +of Hero and Philo of Alexandria.<a name="FNanchor_24" id="FNanchor_24"></a><a href="#Footnote_24" class="fnanchor">24</a> In at least three +cases<a name="FNanchor_25" id="FNanchor_25"></a><a href="#Footnote_25" class="fnanchor">25</a> these texts are found also associated with texts +describing perpetual-motion wheels and other hydraulic +devices. Three manuscripts of this type have +been published in German translation by Schmeller.<a name="FNanchor_26" id="FNanchor_26"></a><a href="#Footnote_26" class="fnanchor">26</a> + +<span class='pagenum'>102</span> + +The devices include a many chambered wheel (see fig. <a href="#fig_14">14</a>) similar to the Alfonsine mercury "escapement," a +wheel of slanting tubes constructed like the noria (see +fig. 15), wheels of weights swinging on arms as +described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known +example of a weight drive. This latter machine is a +pump, in which a chain of buckets is used to raise +water by passing over a pulley which is geared to a +drum powered by a falling weight (see fig. <a href="#fig_16">16</a>); +perhaps for balance, the whole arrangement is made +in duplicate with common axles for the corresponding +parts.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_16" id="fig_16" /><img src="images/fig_16.jpg" width="500" height="273" alt= +"Islamic Pump Powered by a Weight Drive." title="" /> + +<div class="caption">Figure 16.—<span class="smcap">Islamic Pump Powered by a Weight Drive</span>, after the text cited in figure 14.</div></div> + +<p>The Islamic tradition of water clocks did not involve +the use of gears, though very occasionally a pair is +used to turn power through an angle when this is +dictated by the use of a water wheel in the automata. +In the main, everything is worked by floats and +strings or by hydraulic or pneumatic forces, as in +Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing +the passage of hours.</p> + + +<p class="title"><span class="smcap">medieval europe</span></p> + +<p>Echoes from nearly all the developments already +noted from other parts of the world are found to +occur in medieval Europe, often coming through +channels of communication more precisely determinable +than those hitherto mentioned. Before +the influx of Islamic learning at the time of transmission +of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris <i>ca.</i> 1292), +there are occasional references to the most primitive +mechanized "visual aids" in astronomy.</p> + +<p>The most famous of these occurs in an historical +account by Richer of Rheims about his teacher +Gerbert (born 946, later Pope Sylvester II, 990-1003). +Several instruments made by Gerbert are described +in detail; he includes a fine celestial globe made of +wood covered with horsehide and having the stars +and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found +on Chinese instruments but never on the Ptolemaic +variety. Lastly, he cites "the construction of a +sphere, most suitable for recognizing the planets," but +unfortunately it is not clear from the description +whether or not the model planets were actually to +be animated mechanically. The text runs:<a name="FNanchor_27" id="FNanchor_27"></a><a href="#Footnote_27" class="fnanchor">27</a></p> + +<div class="blockquot"><p>Within this oblique circle (the zodiac on the ecliptic +of the globe) he hung the circles of the wandering stars (the +planets) with marvellous ingenuity, whose orbits, heights +<span class='pagenum'>103</span> +and even the distance from each other he demonstrated to +his pupils most effectually. Just how he accomplished this +it is unsuitable to enter into here because of its extent lest +we should appear to be wandering from our main theme.</p></div> + +<p>Thus, although there is a hint of mechanical complexity, +there is really no justification for such an +assumption; the description might well imply only +a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable +that Gerbert could have learned something of Islamic +and other extra-European traditions during his +period of study with the Bishop of Barcelona—a +traveling scholarship that seems to have had many +repercussions on the whole field of European +scholarship.</p> + +<p>Once the floodgates of Arabic learning were +opened, a stream of mechanized astronomical +models poured into Europe. Astrolabes and equatoria +rapidly became very popular, mainly through the +reason for which they had been first devised, the +avoidance of tedious written computation. Many +medieval astrolabes have survived, and at least +three medieval equatoria are known. Chaucer is +well known for his treatise on the astrolabe; a manuscript +in Cambridge, containing a companion treatise +on the equatorium, has been tentatively suggested +by the present author as also being the work of +Chaucer and the only piece written in his own hand.</p> + +<p>The geared astrolabe of al-Biruni is another type of +protoclock to have been transmitted. A specimen in +the Science Museum, London,<a name="FNanchor_28" id="FNanchor_28"></a><a href="#Footnote_28" class="fnanchor">28</a> though unfortunately +now incomplete, has a very sophistocated arrangement +of gears for moving pointers to indicate the +correct relative positions and movements of the sun +and moon (see figs. <a href="#fig_17">17</a> and <a href="#fig_18">18</a>). Like the earlier +Muslim example it contains wheels with odd numbers +of gear teeth (14, 27, 39); however, the teeth are no +longer equilateral in shape, but approximate a more +modern slightly rounded form. This example is +French and appears to date from <i>ca.</i> 1300. Another +Gothic astrolabe with a similar gear ring on the rete, +said to date from <i>ca.</i> 1400 (it could well be much +earlier) is now in the Billmeier collection (London).<a name="FNanchor_29" id="FNanchor_29"></a><a href="#Footnote_29" class="fnanchor">29</a></p> + +<p>Turning from the mechanized astrolabe to the +mechanized equatorium, we find the work of Richard +of Wallingford (1292?-1336) of the greatest interest +as providing an immediate precursor to that of de +Dondi. He was the son of an ingenious blacksmith, +making his way to Merton College, Oxford, then the +most active and original school of astronomy in +Europe, and winning later distinction as Abbot of St. +Albans. A text by him, dated 1326-27, described in +detail the construction of a great equatorium, more +exact and much more elaborate than any that had +gone before.<a name="FNanchor_30" id="FNanchor_30"></a><a href="#Footnote_30" class="fnanchor">30</a> Nevertheless it is evidently a normal +manually operated device like all the others. In +addition to this instrument, Richard is said to have +constructed <i>ca.</i> 1320, a fine planetary clock for his +Abbey.<a name="FNanchor_31" id="FNanchor_31"></a><a href="#Footnote_31" class="fnanchor">31</a> Bale, who seems to have seen it, regarded +it as without rival in Europe, and the greatest curiosity +of his time. Unfortunately, the issue was confused by +Leland, who identified it as the Albion (<i>i.e.</i>, all-by +one), the name Richard gives to his manual equatorium. +This clock was indeed so complex that +Edward III censured the Abbot for spending so much +money on it, but Richard replied that after his death +nobody would be able to make such a thing again. +He is said to have left a text describing the construction +of this clock, but the absence of such a work has +led many modern writers to support Leland's identification +and suppose that the device was not a mechanical +clock.<br /><br /></p> + +<p><span class='pagenum'>104</span></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_17" id="fig_17" /><img src="images/fig_17.jpg" width="500" height="668" alt= +"French Geared Astrolabe of Trefoil Gothic Design." title="" /> + +<div class="caption">Figure 17.—<span class="smcap">French Geared Astrolabe of Trefoil Gothic Design</span>, <i>ca.</i> A.D. 1300. The +gearing on the pointer is, from the center: (32)/14-45+27-39, the last meshing with a concave +annular gear of 180 teeth around the rim of the rete of the astrolabe. A second pointer, +geared to this so as to follow the Moon, seems to be lacking. (<i>Photo courtesy of Science Museum. +London.</i>)</div></div> + +<div class="figcenter" style="width: 500px;"><a name="fig_18" id="fig_18" /><img src="images/fig_18.jpg" width="500" height="221" alt= +"Gear Train Of Pointer in figure 17." title="" /> + +<div class="caption">Figure 18.—<span class="smcap">Gear Train Of +Pointer</span> in figure 17. (<i>Photo +courtesy of Science Museum, London.</i>)</div></div> + + +<p>A corrective for this view is to be had from a St. +Albans manuscript (now at Gonville and Caius College, +Cambridge) that described the methods for +setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. +Although the manuscript copy is to be dated <i>ca.</i> 1340, +it clearly indicates that a geared planetary device +was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine +made by Richard of Wallingford. Unfortunately +the text does not appear to give any relevant +information about the presence of an escapement or +any other regulatory device, nor does it mention +the source of power.<a name="FNanchor_32" id="FNanchor_32"></a><a href="#Footnote_32" class="fnanchor">32</a> Now a geared version of the + +<span class='pagenum'>105</span> + +Albion would appear to correspond very closely indeed +to the dial-work which forms the greater part of +the de Dondi clock, and for this reason we suggest +now that the two clocks were very closely related in +other ways too. This, circumstantial though it be, +is evidence for thinking that the weight drive and +some form of escapement were known to Richard of +Wallingford, <i>ca.</i> 1320. It would narrow the gap between +the clock and the protoclocks to less than half a +century, perhaps a single generation, in the interval +<i>ca.</i> 1285-1320. In this connection it may be of +interest that Richard of Wallingford knew only the +Toledo tables corpus, that of the Alfonsine school did +not arrive in England until after his death.</p> + +<p>There are, of course, many literary references to +the water-clocks in medieval literature. In fact most +of these are from quotations which have often been +produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for +that history, as noted previously in the discussion of +the horologium. There are however enough mentions +to make it certain that water clocks of some sort +were in use, especially for ecclesiastic purposes, from +the end of the 12th century onwards. Thus, Jocelin +of Brakelond tells of a fire in the Abbey Church of +Bury St. Edmunds in the year 1198.<a name="FNanchor_33" id="FNanchor_33"></a><a href="#Footnote_33" class="fnanchor">33</a> The relics +would have been destroyed during the night, but just +at the crucial moment the clock bell sounded for +matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to +get water, some to the well and others to the clock"—probably +the sole occasion on which a clock served +as a fire hydrant.</p> + +<p>It seems probable that some of these water clocks +could have been simple drip clepsydras, with perhaps +a striking arrangement added. A most fortunate +discovery by Drover has now brought to light a +manuscript illumination that shows that these water +clocks, at least by <i>ca,</i> 1285, had become more complex +and were rather similar in appearance to the Alfonsine +mercury drum.<a name="FNanchor_34" id="FNanchor_34"></a><a href="#Footnote_34" class="fnanchor">34</a> The illustration (fig. <a href="#fig_19">19</a>) is +from a moralized Bible written in northern France, +and accompanies the passage where King Hezekiah +is given a sign by the Lord, the sun being moved back +ten steps of the clock. The picture clearly shows the +central water wheel and below it a dog's head spout +gushing water into a bucket supported by chains, +with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette +which might be a fly or a model sun. The wheel +appears to have 15 compartments, each with a central +hole (perhaps similar to that in the Alfonsine +clock) and it is supported on a square axle by a +bracket, the axle being wedged in the traditional +fashion. The projections at the edge of the wheel +might be gear teeth, but more likely they are used only +for tripping the striking mechanism. If it were not for +the running water spout it would be very close to the +Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation.</p> + +<p><span class='pagenum'>106</span></p> + +<p>From the adjacent region there is +another account of a striking water +clock, the evidence being inscriptions +on slates, discovered in Villers Abbey +near Brussels;<a name="FNanchor_35" id="FNanchor_35"></a><a href="#Footnote_35" class="fnanchor">35</a> these may be closely +dated as 1267 or 1268 and provide the +remains of a memorandum for the sacrist +and his assistants in charge of the clock.</p> + +<div class="blockquot"><p>Always set the clock, however long you +may delay on [the letter "A"] afterwards +you shall pour water from the little pot +(pottulo) that is there, into the reservoir +(cacabum) until it reaches the prescribed +level, and you must do the same when you +set [the clock] after compline so that you +may sleep soundly.</p></div> + +<p>A quite different sort of evidence is to +be had from the writings of Robertus +Anglicus in 1271 where one gets the +impression that just at this time there +was active interest in the attempt to +make a weight-driven anaphoric clock +and to regulate its motion by some +unstated method so that it would keep +time with the diurnal rotation of the +heavens:<a name="FNanchor_36" id="FNanchor_36"></a><a href="#Footnote_36" class="fnanchor">36</a></p> + +<div class="blockquot"><p>Nor it is possible for any clock to follow the +judgment of astronomy with complete accuracy. +Yet clockmakers (artifices horologiorum) +are trying to make a wheel (circulum) +which will make one complete revolution for every +one of the equinoctial circle, but they cannot quite perfect +their work. But if they could, it would be a really accurate +clock (horologium verax valde) and worth more than an +astrolabe or other astronomical instrument for reckoning +the hours, if one knew how to do this according to the +method aforesaid. The method of making such a clock +would be this, that a man make a disc (circulum) of uniform +weight in every part so far as could possibly be done. +Then a lead weight should be hung from the axis of that +wheel (axi ipsius rote) and this weight would move that +wheel so that it would complete one revolution from sunrise +to sunrise, minus as much time as about one degree rises +according to an approximately correct estimate. For from +sunrise to sunrise, the whole equinoctial rises, and about +one degree more, through which degree the sun moves +against the motion of the firmament in the course of a +natural day. Moreover, this could be done more accurately +if an astrolabe were constructed with a network on which +the entire equinoctial circle was divided up.</p></div> + +<div class="figcenter" style="width: 500px;"><a name="fig_19" id="fig_19" /><img src="images/fig_19.jpg" width="500" height="559" alt= +"Manuscript Illumination of a Medieval +Waterclock." title="" /> + +<div class="caption">Figure 19.—<span class="smcap">Manuscript Illumination of a Medieval +Waterclock</span>, showing a partitioned wheel, a +weight drive, and a carillion for striking. From +Drover (see footnote <a href="#Footnote_34">34</a>).</div></div> + +<p>The text then continues with technical astronomical +details of the slight difference between the rate of +rotation of the sun and of the fixed stars (because of +the annual rotation of the sun amongst the stars) +but it gives no indication of any regulatory device. +Again it should be noted, this source comes from +France; Robertus, though of English origin, apparently +being then a lecturer either at the University +of Paris or at that of Montpellier. The date of this +passage, 1271, has been taken as a <i>terminus post quem</i> +for the invention of the mechanical clock. In the +next section we shall describe the text of Peter Peregrinus, +very close to this in place and date, which +describes just such a machine, conflating it with +accounts of an armillary sphere, perpetual motion, +and the magnetic compass—so bringing all these +threads together for the first time in Europe.</p> + +<p><span class='pagenum'>107</span></p> + +<div class="figcenter" style="width: 400px;"><a name="fig_20" id="fig_20" /><img src="images/fig_20.jpg" width="400" height="418" alt= +"Arrangement for Turning a Figure +Of an Angel." title="" /> + +<div class="caption">Figure 20.—<span class="smcap">Arrangement for Turning a Figure +Of an Angel.</span> It has been alleged that this drawing +by Villard represents an escapement. After Lassus +(see footnote <a href="#Footnote_37">37</a>).</div></div> + +<p>We have reserved to the last one section of evidence +which may or may not be misleading, the famous +notebook of Villard (Wilars) of Honnecourt, near +Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, +three of which are of special interest to our investigations.<a name="FNanchor_37" id="FNanchor_37"></a><a href="#Footnote_37" class="fnanchor">37</a> +These comprise a steeplelike structure +labeled "cest li masons don orologe" (this is the +house of a clock), a device including a rope, wheel +and axle (fig. <a href="#fig_20">20</a>), marked "par chu fait om un +angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards +the sun), and a perpetual motion wheel which we +shall reserve for later discussion.</p> + +<p>The clock tower, according to Drover, shows no +place for a dial but suggests the use of bells because +of its open structure, suitable for letting out the +sound. Moreover, he suggests that the delicacy of +the line indicates that it was not really a full-size +steeple but rather a small towerlike structure standing +only a few feet high within the church. There is, +alas, nothing to tell us about the clock it was intended +to house; most probably it was a water clock similar +to that of the illustrated Bible of <i>ca.</i> 1285.</p> + +<p>The drawing of the rope, wheel and axles, for +turning an angel to point towards the sun can have +a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal +axis acts as a windlass connected by the counterpoised +rope to the vertical shaft which it turns, thereby +moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation +was in fact suggested by M. Quicherat,<a name="FNanchor_38" id="FNanchor_38"></a><a href="#Footnote_38" class="fnanchor">38</a> who +first called attention to the Villard album and +pointed out that a leaden angel existed in Chartres +before the fire there in 1836. It is a view also supported +from another drawing in the album which +describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure +on the tail of the bird causes a similar rope mechanism +to operate.</p> + +<p>A quite different interpretation has been suggested +by Fr&eacute;mont;<a name="FNanchor_39" id="FNanchor_39"></a><a href="#Footnote_39" class="fnanchor">39</a> he believes that the wheel may have +acted as a fly-wheel and the ropes and counterpoises, +<span class='pagenum'>108</span>turning first one way then the other acted as a sort +of mechanical escapement. Such an arrangement is +however mechanically impossible without some complicated +free-wheeling device between the drive and +the escapement, and its only effect would be to +oscillate the angel rapidly rather than turn it steadily. +I believe that Fr&eacute;mont, over-anxious to provide a +protoescapement, has done too much violence to the +facts and turned away without good reason from the +more simple and reasonable explanation. It is +nevertheless still possible to adopt this simple interpretation +and yet to have the system as part of a +clock. If the left-hand counterpoise, conveniently +raised higher than that on the right, is considered as +a float fitting into a clepsydra jar, instead of as a +simple weight, one would have a very suitable +automatic system for turning the angel. On this +explanation, the purpose of the wheel would be +merely to provide the manual adjustment necessary +to set the angel from time to time, compensating +for irremediable inaccuracies of the clepsydra.</p> + +<div class="figcenter" style="width: 400px;"><a name="fig_21" id="fig_21" /><img src="images/fig_21.jpg" width="400" height="434" alt= +"Villard's Perpetual Motion Wheel." title="" /> + +<div class="caption">Figure 21.—<span class="smcap">Villard's Perpetual Motion Wheel</span>, +from Lassus (see footnote <a href="#Footnote_37">37</a>).</div></div> + +<p>Having discussed the Villard drawings which are +already cited in horological literature, we must draw +attention to the fact that this medieval architect also +gives an illustration of a perpetual motion wheel. +In this case (fig. <a href="#fig_21">21</a>) it is of the type having weights +at the end of swinging arms, a type that occurs very +frequently at later dates in Europe and is also given +in the Islamic texts. We cannot, in this case, suggest +that drawings of clocks and of perpetual motion +devices occur together by more than a coincidence, +for Villard seems to have been interested in most +sorts of mechanical device. But even this type of +coincidence becomes somewhat striking when repeated +often enough. It seems that each early +mention of "self-moving wheels" occurs in connection +with some sort of clock or mechanized astronomical +device.</p> + +<p>Having now completed a survey of the traditions +of astronomical models, we have seen that many +types of device embodying features later found in +mechanical clocks evolved through various cultures +and flowed into Europe, coming together in a burst +of multifarious activity during the second half of the +13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so +doing examine the importance of perpetual motion +devices, mechanical and magnetic, in the crucial +transition from protoclock to mechanical-escapement +clock.</p> + +<h3><a name="Page_108a" id="Page_108a">Perpetual Motion and the Clock before +de Dondi</a></h3> + +<p>We have already noted, more or less briefly, +several instances of the use of wheels "moving by +themselves" or the use of a fluid for purposes other +than as a motive power. Chronologically arranged, +these are the Indian devices of <i>ca.</i> 1150 or a little +earlier, as those of Riḍwān <i>ca.</i> 1200, that of the +Alfonsine mercury clock, <i>ca.</i> 1272, and the French +Bible illumination of <i>ca.</i> 1285. This strongly suggests +a steady transmission from East to West, and on +the basis of it, we now tentatively propose an additional +step, a transmission from China to India and +perhaps further West, <i>ca.</i> 1100, and possibly reinforced +by further transmissions at later dates.</p> + +<p>One need only assume the existence of vague +traveler's tales about the existence of the 11th-century +Chinese clocks with their astronomical +models and jackwork and with their great wheel, +apparently moving by itself but using water having +no external inlet or outlet. Such a stimulus, acting +as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low +Countries, might easily lead to the re-invention of +just such perpetual-motion wheels as we have already +noted. In many ways, once the idea has been +suggested it is natural to associate such a perpetual +motion with the incessant diurnal rotation of the +heavens. Without some such stimulus however it is +difficult to explain why this association did not occur +earlier, and why, once it comes there seems to be such +a chronological procession from culture to culture.</p> + +<p>We now turn to what is undoubtedly the most +curious part of this story, in which automatically +moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism +and the magnetic compass, another subject with +a singularly troubled historical origin. The key text +in this is the famous <i>Epistle on the magnet</i>, written by +Peter Peregrinus, a Picard, in an army camp at the +Siege of Lucera and dated August 8, 1269.<a name="FNanchor_40" id="FNanchor_40"></a><a href="#Footnote_40" class="fnanchor">40</a> In spite +of the precise dating it is certain that the work was +done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which +must have been written before <i>ca.</i> 1250.<a name="FNanchor_41" id="FNanchor_41"></a><a href="#Footnote_41" class="fnanchor">41</a></p> + +<p><span class='pagenum'>109</span></p><p>The <i>Epistle</i> contains two parts; in the +first there is a general account of magnetism +and the properties of the loadstone, +closing with a discussion "of the +inquiry whence the magnet receives the +natural virtue which it has." Peter +attributed this virtue to a sympathy +with the heavens, proposing to prove +his point by the construction of a +"terrella," a uniform sphere of loadstone +which is to be carefully balanced +and mounted in the manner of an +armillary sphere, with its axis directed +along the polar axis of the diurnal +rotation. He then continues:</p> + +<div class="blockquot"><p>Now if the stone then move according to +the motion of the heavens, rejoice that you +have arrived at a secret marvel. But if not, +let it be ascribed rather to your own want +of skill than to a defect of Nature. But in +this position, or mode of placing, I deem the +virtues of this stone to be properly conserved, +and I believe that in other positions +or parts of the sky its virtue is dulled, rather +than preserved. By means of this instrument +at all events you will be relieved from every +kind of clock (horologium), for by it you will +be able to know the Ascendant at whatever hour you will, +and all other dispositions of the heavens which Astrologers +seek after.</p></div> + +<p>It should be noted that the device is to be mounted +like an astronomical instrument and used like one, +rather than as a time teller, or as a simple demonstration +of magnetism. In the second part of the +<i>Epistle</i> Peter turns to practical instruments, describing +for the first time, the construction of a magnetic compass +consisting of a loadstone or iron needle pivoted +with a casing marked with a scale of degrees. The +third chapter of this section, concluding the <i>Epistle</i>, +then continues with the description of a perpetual +motion wheel, "elaboured with marvellous ingenuity, +in the pursuit of which invention I have seen many +people wandering about, and wearied with manifold +toil. For they did not observe that they could arrive +at the mastery of this by means of the virtue, or +power of this stone."</p> + + +<p class="tb">This tells us incidentally, that the perpetual motion +device was a subject of considerable interest at this +time.<a name="FNanchor_42" id="FNanchor_42"></a><a href="#Footnote_42" class="fnanchor">42</a> Oddly enough, Peter does not now develop +his idea of the terrella, but proceeds to something +quite new, a device (see fig. <a href="#fig_22">22</a>) in which a bar-magnet +loadstone is to be set towards the end of a pivoted +radial arm with a circle fitted on the inside with iron +"gear teeth," the teeth being there not to mesh with +others but to draw the magnet from one to the next, +a little bead providing a counterweight to help the +inertia of rotation carry the magnet from one point +of attraction to the next. It is by no means the sort +of device that one would naturally evolve as a means +of making magnetism work perpetually, and I +suggest that the toothed wheel is another instance +of some vague idea of protoclocks, perhaps that of +Su Sung, being transmitted from the East.</p> + +<div class="figcenter" style="width: 400px;"><a name="fig_22" id="fig_22" /><img src="images/fig_22.jpg" width="400" height="395" alt= +"Magnetic Perpetual Motion Wheel." title="" /> + +<div class="caption">Figure 22.—<span class="smcap">Magnetic Perpetual Motion Wheel</span> +illustrated by Peter Peregrinus; from the edition of +S. P. Thompson (see footnote <a href="#Footnote_40">40</a>).</div></div> + +<p>The work of Peter Peregrinus is cited by Roger +Bacon in his <i>De secretis</i> as well as in the <i>Opus majus</i> +<span class='pagenum'>110</span>and <i>Opus minus</i>. In the first and earliest of these +occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He +says that this cannot be made to move naturally by +any mathematical device, but "a faithful and magnificent +experimentor is straining to make one out of +such material, and by such a device, that it will +revolve naturally with the diurnal heavenly rotation." +He continues with the statement that this possibility +is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that +of the Sun and of the heavens. Only in the <i>Opus +minus</i>, where he repeats reference to this device, does +he finally reveal that it is to be made to work by +means of the loadstone.</p> + +<p>The form of Bacon's reference to Peregrinus is +strongly reminiscent of the statement by Robertus +Anglicus, already mentioned as an indication of +preoccupation with diurnally rotating wheels, at a +date (1271) remarkably close to that of the <i>Epistle</i> +(1269)—so much so that it could well be thought +that the friend to which Peter was writing was either +Robert himself or somebody associated with him, +perhaps at the University of Paris—a natural place +to which the itinerant Peter might communicate +his findings.</p> + +<p>The fundamental question here, of course, is +whether the idea of an automatic astronomical device +was transmitted from Arabic, Indian, or Chinese +sources, or whether it arose quite independently in +this case as a natural concomitant of identifying the +poles of the magnet with the poles of the heavens. +We shall now attempt to show that the history of the +magnetic compass might provide a quite independent +argument in favour of the hypothesis that there was +a 'stimulus' transmission.</p> + + +<h3><a name="Page_110a" id="Page_110a">The Magnetic Compass as a Fellow-traveler +from China</a></h3> + +<p>The elusive history of the magnetic compass has +many points in common with that of the mechanical +clock. Just as we have astronomical models from +the earliest times, so we find knowledge of the loadstone +and some of its properties. Then, parallel to +the development of protoclocks in China throughout +the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory +device and of the (nonmagnetic) south-pointing +chariot, which has been confusedly allied to the +story. Curiously, and perhaps significantly the +Chinese history comes to a head at just the same time +for compasses and clocks, and a prime authority for +the Chinese compass is Shen Kua (1030-1093) who +also appears in connection with the clock of Su Sung, +and who wrote about the mechanized armillary +spheres and other models <i>ca.</i> 1086.</p> + +<p>Another similarity occurs in connection with the +history of the compass in medieval Europe. The +treatise of Peter Peregrinus, already discussed, provides +the first complete account of the magnetic +compass with a pivoted needle and a circular scale, +and this, as we have seen, may be connected with +protoclocks and perpetual-motion devices. There +are several earlier references, however, to the use of +the directive properties of loadstone, mainly for use +in navigation, but these earliest texts have a long +history of erroneous interpretation which is only +recently being cleared away. We know now that +the famous passages in the <i>De naturis rerum</i> and <i>De +utensilibus</i> of Alexander Neckham<a name="FNanchor_43" id="FNanchor_43"></a><a href="#Footnote_43" class="fnanchor">43</a> (<i>ca.</i> 1187) and +a text by Hugues de Berze<a name="FNanchor_44" id="FNanchor_44"></a><a href="#Footnote_44" class="fnanchor">44</a> (after <i>ca.</i> 1204) refer +to nothing more than a floating magnet without +pivot or scale, but using a pointer at right angles to +the magnet, so that it pointed to the east, rather than +the north or south. A similar method is described +(<i>ca.</i> 1200) in a poem by Guyot de Provins, and in a +history of Jerusalem by Jacques de Vitry (1215).<a name="FNanchor_45" id="FNanchor_45"></a><a href="#Footnote_45" class="fnanchor">45</a> +It is of the greatest interest that, once more, all the +evidence seems to be concentrated in France (Neckham +was teaching in Paris) though at an earlier +period than that for the protoclocks.</p> + +<p>The date might suggest the time of the first great +wave of transmissal of learning from Islam, but it is +clear that in this instance, peculiar for that reason, +that Islam learned of the magnetic compass only +after it was already known in the West. In the +earliest Persian record, some anecdotes compiled by +al-'Awfiī <i>ca.</i> 1230,<a name="FNanchor_46" id="FNanchor_46"></a><a href="#Footnote_46" class="fnanchor">46</a> the instrument used by the captain +during a storm at sea has the form of a piece of +hollow iron, shaped like a fish and made to float on +the water after magnetization by rubbing with a +loadstone; the fishlike form is very significant, for +this is distinctly Chinese practice. In a second +Muslim reference, that of Bailak al-Qabājaqī (<i>ca.</i> +1282), the ordinary wet-compass is termed "al-konbas," +another indication that it was foreign to +that language and culture.<a name="FNanchor_47" id="FNanchor_47"></a><a href="#Footnote_47" class="fnanchor">47</a></p> + + +<p><span class='pagenum'>111</span></p> + +<h2>Chronological Chart</h2> + +<hr style="width: 100%; margin-top: 0em; + margin-bottom: 0em;" /> + +<table width="100%" summary="Chronological_Chart" border="0"> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">4th C., B.C. Power gearing</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Classical Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">3rd C., B.C. Archimedes planetarium</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., B.C. Hipparchus Stereographic Projection</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1st C., B.C. Vitruvius hodometer and water clocks</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">65, B.C. (<i>ca.</i>) Antikythera machine</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1st C., A.D. Hero hodometer and water clocks</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., A.D. Salzburg and Vosges anaphoric clocks</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., A.D. Chang H&ecirc;ng animated globe hodometer</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> Continuing tradition of animated astronomical models</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> 807 Harun-al-Rashid</p></td> +</tr> + + +<tr> +<td class="td100"><p class="indent"> 850 (<i>ca.</i>) Earliest extant astrolobes</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1000 Geared astrolabe of Buruni</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1000 Gerbert astronomical model</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1025 Equatorium text</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1074 Shen Kua, clocks and magnetic compass</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1080 Su Sung clock built</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1101 Su Sung clock destroyed</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">India</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1100 (<i>ca.</i>) Sūrya Siddhānta animated astronomical models and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1150 (<i>ca.</i>) Siddhānta Siromaṇi animated models and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1150 Saladin clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1187 Neckham on compass</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1198 Jocelin on water clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1200 (<i>ca.</i>) Riḍwān water-clocks, perpetual motion and weight drive</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1206 al-Jazarī clocks, etc.</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1221 Geared astrolabe</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1232 Charlemagne clock</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1243 al-Konbas (compass)</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1245 Villard clocktower, "escapement," perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1267 Villers Abbey clock</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1269 Peregrinus, compass and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1271 Robertus Anglicus, animated models and "perpetual motion" clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1272 Alfonsine corpus clock with mercury drum, equatoria</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1285 Drover's water clock with wheel and weight drive</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1300 (<i>ca.</i>) French geared astrolabe</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1320 Richard of Wallingford astronomical clock and equatorium</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1364 de Dondi's astronomical clock with mechanical escapement</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">later 14th C. Tradition of escapement clocks continues and degenerates into simple time-keepers</p></td> +</tr> + +</table> +<hr style="width: 100%; margin-top: 1em;" /> +<p><span class='pagenum'>112</span></p> + + +<p class="tb">There is therefore reasonable grounds for supporting +the medieval European tradition that the magnetic +compass had first come from China, though one +cannot well admit that the first news of it was brought, +as the legend states, by Marco Polo, when he returned +home in 1260. There might well have been +another wave of interest, giving the impetus to Peter +Peregrinus at this time, but an earlier transmission, +perhaps along the silk road or by travelers in crusades, +must be postulated to account for the evidence +in Europe, <i>ca.</i> 1200. The earlier influx does not play +any great part in our main story; it arrived in Europe +before the transmission of astronomy from Islam had +got under way sufficiently to make protoclocks a +subject of interest. For a second transmission, we +have already seen how the relevant texts seem to +cluster, in France <i>ca.</i> 1270, around a complex in which +the protoclocks seem combined with the ideas of +perpetual motion wheels and with new information +about the magnetic compass.</p> + +<p>The point of this paper is that such a complex +exists, cutting across the histories of the clock, the +various types of astronomical machines, and the +magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending +from China, through India and through Eastern and +Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various +elements make their appearances in different combinations +from place to place, sometimes one may be +dominant, sometimes another may be absent. Only +by treating it as a whole has it been possible to produce +the threads of continuity which will, I hope, +make further research possible, circumventing the +blind alleys found in the past and leading eventually +to a complete understanding of the first complicated +scientific machines.</p> + +<h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">1</span></a> This traditional view is expressed by almost every history +of horology. An ultimate source for many of these has been +the following two classic treatments: J. Beckmann, <i>A history +of inventions and discoveries</i>, 4th ed., London, 1846, vol. 1, pp. +340 ff. A. P. Usher, <i>A history of mechanical inventions</i>, 2nd ed., +Harvard University Press. 1954, pp. 191 ff., 304 ff.</p></div> + +<div class="footnote"><p><a name="Footnote_2" id="Footnote_2"></a><a href="#FNanchor_2"><span class="label">2</span></a> There is a considerable literature dealing with the later +evolution of perpetual motion devices. The most comprehensive +treatment is H. Dircks, <i>Perpetuum mobile</i>, London, 1861; +2nd ser., London, 1870. So far as I know there has not previously +been much discussion of the history of such devices +before the renaissance.</p></div> + +<div class="footnote"><p><a name="Footnote_3" id="Footnote_3"></a><a href="#FNanchor_3"><span class="label">3</span></a> For the early history of gearing in the West see C. Matschoss, +<i>Geschichte des Zahnrades</i>, Berlin, 1940. Also F. M. +Feldhaus, <i>Die geschichtliche Entwicklung des Zahnrades in Theorie +und Praxis</i>, Berlin, 1911.</p></div> + +<div class="footnote"><p><a name="Footnote_4" id="Footnote_4"></a><a href="#FNanchor_4"><span class="label">4</span></a> A general account of these important archaeological objects +will be published by J. Needham, <i>Science and civilisation in China</i>, +Cambridge, 1959(?), vol. 4. The original publications (in +Chinese) are as follows: Wang Chen-to, "Investigations and +reproduction in model form of the south-pointing carriage and +hodometer," <i>National Peiping Academy Historical Journal</i>, 1937, +vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in horological +engineering," <i>Ch'ing-Hua University Engineering Journal</i>, +1956, vol. 4, p. 1.</p></div> + +<div class="footnote"><p><a name="Footnote_5" id="Footnote_5"></a><a href="#FNanchor_5"><span class="label">5</span></a> For illustrations of intermeshing worms in Indian cotton +mills, see Matschoss, <i>op. cit.</i> (footnote <a href="#Footnote_3">3</a>), figs. 5, 6, 7, p. 7.</p></div> + +<div class="footnote"><p><a name="Footnote_6" id="Footnote_6"></a><a href="#FNanchor_6"><span class="label">6</span></a> It is interesting to note that the Chinese hodometer was contemporary +with that of Hero and Vitruvius and very similar in +design. There is no evidence whatsoever upon which to decide +whether there may have been a specific transmission of this invention +or even a "stimulus diffusion."</p></div> + +<div class="footnote"><p><a name="Footnote_7" id="Footnote_7"></a><a href="#FNanchor_7"><span class="label">7</span></a> A summary of the content of the manuscript sources, illustrated +by the original drawings, has been published by H. Alan +Lloyd, <i>Giovanni de Dondi's horological masterpiece, 1364</i>, without +date or imprint (?Lausanne, 1955), 23 pp. It should be remarked +that de Dondi declines to describe the workings of his +crown and foliot escapement (though it is well illustrated) saying +that this is of the "common" variety and if the reader does +not understand such simple things he need not hope to comprehend +the complexities of this mighty clock. But this may be +bravado to quite a large degree.</p></div> + +<div class="footnote"><p><a name="Footnote_8" id="Footnote_8"></a><a href="#FNanchor_8"><span class="label">8</span></a> See, for example, the chronological tables of the 14th +century and the later mentions of clocks in E. Zinner, <i>Aus der +Fr&uuml;hzeit der R&auml;deruhr</i>, Munich, 1954, p. 29 ff. Unfortunately +this very complete treatment tends to confuse the factual and +legendary sources prior to the clock of de Dondi; it also accepts +the very doubtful evidence of the "escapement" drawn by +Villard of Honnecourt (see p. <a href="#fig_20">107</a>). An excellent and fully +illustrated account of monumental astronomical clocks throughout +the world is given by Alfred Ungerer, <i>Les horloges astronomiques</i>, +Strasbourg, 1931, 514 pp. Available accounts of the +development of the planetarium since the middle ages are very +brief and especially weak on the early history: Helmut Werner, +<i>From the Aratus globe to the Zeiss planetarium</i>, Stuttgart, 1957; +C. A. Crommelin, "Planetaria, a historical survey," <i>Antiquarian +Horology</i>, 1955, vol. 1, pp. 70-75.</p></div> + +<div class="footnote"><p><a name="Footnote_9" id="Footnote_9"></a><a href="#FNanchor_9"><span class="label">9</span></a> Derek J. Price, "Clockwork before the clock," <i>Horological +Journal</i>, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31.</p></div> + +<div class="footnote"><p><a name="Footnote_10" id="Footnote_10"></a><a href="#FNanchor_10"><span class="label">10</span></a> For the use of this material I am indebted to my co-authors. I +must also acknowledge thanks to the Cambridge University +Press, which in the near future will be publishing our monograph, +"Heavenly Clockwork." Some of the findings of this +paper are included in shorter form as background material for +that monograph. A brief account of the discovery of this material +has been published by J. Needham, Wang Ling, and +Derek J. Price, "Chinese astronomical clockwork," <i>Nature</i>, +1956, vol. 177, pp. 600-602.</p></div> + +<div class="footnote"><p><a name="Footnote_11" id="Footnote_11"></a><a href="#FNanchor_11"><span class="label">11</span></a> For these translations from classical authors I am indebted +to Professor Loren MacKinney and Miss Harriet Lattin, who +had collected them for a history, now abandoned, of planetariums. +I am grateful for the opportunity of giving them here +the mention they deserve.</p></div> + +<div class="footnote"><p><a name="Footnote_12" id="Footnote_12"></a><a href="#FNanchor_12"><span class="label">12</span></a> A. G. Drachmann, "The plane astrolabe and the anaphoric +clock," <i>Centaurus</i>, 1954, vol. 3, pp. 183-189.</p></div> + +<div class="footnote"><p><a name="Footnote_13" id="Footnote_13"></a><a href="#FNanchor_13"><span class="label">13</span></a> A fuller description of the anaphoric clock and cognate +water-clocks is given by A. G. Drachmann, "Ktesibios, Philon +and Heron," <i>Acta Historica Scientiarum Naturalium et Medicinalium</i>, +Copenhagen, 1948, vol. 4.</p></div> + +<div class="footnote"><p><a name="Footnote_14" id="Footnote_14"></a><a href="#FNanchor_14"><span class="label">14</span></a> First published by O. Benndorf, E. Weiss, and A. Rehm, +<i>Jahreshefte des &ouml;sterreichischen arch&auml;ologischen Institut in Wien</i>, +1903, vol. 6, pp. 32-49. I have given further details of its +construction in <i>A history of technology</i>, ed. Singer, Holmyard, +and Hall, 1957, vol. 3, pp. 604-605.</p></div> + +<div class="footnote"><p><a name="Footnote_15" id="Footnote_15"></a><a href="#FNanchor_15"><span class="label">15</span></a> L. Maxe-Werly, <i>M&eacute;moires de la Soci&eacute;t&eacute; Nationale des Antiquaires +de France</i>, 1887, vol. 48, pp. 170-178.</p></div> + +<div class="footnote"><p><a name="Footnote_16" id="Footnote_16"></a><a href="#FNanchor_16"><span class="label">16</span></a> The first definitive account of the Antikythera machine +was given by Perikles Rediadis in J. Svoronos, <i>Das Athener +Nationalmuseum</i>, Athens, 1908, Textband I, pp. 43-51. +Since then, other photographs (mostly very poor) have appeared, +and an attempt at a reconstruction has been made +by Rear Admiral Jean Theophanidis, <i>Praktika tes Akademias +Athenon</i>, Athens, 1934, vol. 9, pp. 140-149 (in French). I am +deeply grateful to the Director of the Athens National Museum, +M. Karouzos, for providing me with an excellent new set of +photos, from which figures 6-8 are now taken.</p></div> + +<div class="footnote"><p><a name="Footnote_17" id="Footnote_17"></a><a href="#FNanchor_17"><span class="label">17</span></a> H. Diels &Uuml;ber die von Prokop beschriebene Kunstuhr von +Gaza, <i>Abhandlungen, Akademie der Wissenschaften</i>, Berlin, Philos.-Hist. +Klasse, 1917, No. 7.</p></div> + +<div class="footnote"><p><a name="Footnote_18" id="Footnote_18"></a><a href="#FNanchor_18"><span class="label">18</span></a> L. A. Mayer, <i>Islamic astrolabists and their works</i>, Geneva, +1956, p. 62.</p></div> + +<div class="footnote"><p><a name="Footnote_19" id="Footnote_19"></a><a href="#FNanchor_19"><span class="label">19</span></a> The translation which follows is quoted from J. Beckmann, +<i>op. cit.</i> (footnote <a href="#Footnote_1">1</a>), p. 349.</p></div> + +<div class="footnote"><p><a name="Footnote_20" id="Footnote_20"></a><a href="#FNanchor_20"><span class="label">20</span></a> E. Wiedemann, "Ein Instrument das die Bewegung von +Sonne und Mond darstellt, nach al Biruni," <i>Der Islam</i>, 1913, +vol. 4, p. 5.</p></div> + +<div class="footnote"><p><a name="Footnote_21" id="Footnote_21"></a><a href="#FNanchor_21"><span class="label">21</span></a> I acknowledge with thanks to the Curator of that museum +the permission to reproduce photographs of this instrument. It +is item 5 in R. T. Gunther, <i>Astrolabes of the world</i>, Oxford, 1932.</p></div> + +<div class="footnote"><p><a name="Footnote_22" id="Footnote_22"></a><a href="#FNanchor_22"><span class="label">22</span></a> Abulcacim Abnacahm, <i>Libros del saber</i>, edition by Rico y +Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of +the instrument has been very fully discussed by A. Wegener, +"Die astronomischen Werke Alfons X," <i>Bibliotheca Mathematica</i>, +1905, pp. 129-189. A more complete discussion of the +historical evolution of the equatorium is given in Derek J. Price, +<i>The equatorie of the planetis</i>, Cambridge (Eng.), 1955, pp. 119-133.</p></div> + +<div class="footnote"><p><a name="Footnote_23" id="Footnote_23"></a><a href="#FNanchor_23"><span class="label">23</span></a> E. Wiedemann, and F. Hauser, "Uber die Uhren im +Bereich d. islamischen Kultur," <i>Nova Acta; Abhandlungen der +k&ouml;nigliche Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher +zu Halle</i>, 1915, vol. 100, no. 5.</p></div> + +<div class="footnote"><p><a name="Footnote_24" id="Footnote_24"></a><a href="#FNanchor_24"><span class="label">24</span></a> E. Wiedemann, and F. Hauser, <i>Die Uhr des Archimedes und +zwei andere Vorrichtungen</i>, Halle, 1918.</p></div> + +<div class="footnote"><p><a name="Footnote_25" id="Footnote_25"></a><a href="#FNanchor_25"><span class="label">25</span></a> The manuscripts in question are as follows: Gotha, Kat. v. +Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, 288, +no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, no. +1415, Cod. 93 Gol.</p></div> + +<div class="footnote"><p><a name="Footnote_26" id="Footnote_26"></a><a href="#FNanchor_26"><span class="label">26</span></a> H. Schmeller, Beitr&auml;ge zur Geschichte der Technik in der +Antike und bei den Arabern, Erlangen, 1922 (<i>Abhandlungen zur +Geschichte der Naturwissenschaften und der Medizin</i> no. 6).</p></div> + +<div class="footnote"><p><a name="Footnote_27" id="Footnote_27"></a><a href="#FNanchor_27"><span class="label">27</span></a> Once more I am indebted to Professor Loren MacKinney +and Miss Harriet Lattin (see footnote <a href="#Footnote_11">11</a>) for making their +collections on Gerbert available to me.</p></div> + +<div class="footnote"><p><a name="Footnote_28" id="Footnote_28"></a><a href="#FNanchor_28"><span class="label">28</span></a> Item 198 in Gunther, <i>op. cit.</i> (footnote <a href="#Footnote_21">21</a>). I am grateful to +the authorities of that museum for permission to reproduce +photographs of this instrument.</p></div> + +<div class="footnote"><p><a name="Footnote_29" id="Footnote_29"></a><a href="#FNanchor_29"><span class="label">29</span></a> Sotheby and Co., London, sale of March 14, 1957, lot 154. +The outer rim of the rete has 120 teeth.</p></div> + +<div class="footnote"><p><a name="Footnote_30" id="Footnote_30"></a><a href="#FNanchor_30"><span class="label">30</span></a> The Latin text of the treatise on the Albion, has been +transcribed by Rev. H. Salter and published in R. T. Gunther, +<i>Early science in Oxford</i>, Oxford, 1923, vol. 2, pp. 349-370. An +analysis of its design is given in Price, <i>op. cit.</i> (footnote <a href="#Footnote_22">22</a>), pp. +127-130.</p></div> + +<div class="footnote"><p><a name="Footnote_31" id="Footnote_31"></a><a href="#FNanchor_31"><span class="label">31</span></a> Such evidence as there is for the existence and form of the +clock is collected by Gunther, <i>op. cit.</i> (footnote <a href="#Footnote_30">30</a>), p. 49.</p></div> + +<div class="footnote"><p><a name="Footnote_32" id="Footnote_32"></a><a href="#FNanchor_32"><span class="label">32</span></a> I have discussed this new manuscript source in "Two +medieval texts on astronomical clocks," <i>Antiquarian Horology</i>, +1956, vol. 1, no. 10, p. 156. The manuscript in question is +ms. 230/116, Gonville and Caius College, Cambridge, folios +11<sup>v</sup>-14<sup>v</sup> = pp. 31-36.</p></div> + +<div class="footnote"><p><a name="Footnote_33" id="Footnote_33"></a><a href="#FNanchor_33"><span class="label">33</span></a> <i>The Chronicle of Jocelin of Brakelond</i> ..., H. E. Butler (ed.), +London, 1949, p. 106.</p></div> + +<div class="footnote"><p><a name="Footnote_34" id="Footnote_34"></a><a href="#FNanchor_34"><span class="label">34</span></a> C. B. Drover, "A medieval monastic water-clock," <i>Antiquarian +Horology</i>, 1954, vol. 1, no. 5, pp. 54-58, 63. Because +this water clock uses wheels and strikes bells one must reject +the evidence of literary reference, such as by Dante, from +which the mention of wheels and bells have been taken as +positive proof of the existence of mechanical clocks with +mechanical escapements. The to-and-fro motion of the +mechanical clock escapement is quite an impressive feature, +but there seems to be no literary reference to it before the +time of de Dondi.</p></div> + +<div class="footnote"><p><a name="Footnote_35" id="Footnote_35"></a><a href="#FNanchor_35"><span class="label">35</span></a> <i>Annales de la Soci&eacute;t&eacute; Royale d'Arch&eacute;ologie de Bruxelles</i>, 1896, +vol. 1/8, pp. 203-215, 404-451. The translation here is cited +from Drover, <i>op. cit.</i>, (footnote <a href="#Footnote_34">34</a>), p. 56.</p></div> + +<div class="footnote"><p><a name="Footnote_36" id="Footnote_36"></a><a href="#FNanchor_36"><span class="label">36</span></a> L. Thorndike, <i>The sphere of Sacrobosco and its commentators</i>, +Chicago, 1949, pp. 180, 230.</p></div> + +<div class="footnote"><p><a name="Footnote_37" id="Footnote_37"></a><a href="#FNanchor_37"><span class="label">37</span></a> The album was published with facsimiles by J. B. A. +Lassus, 1858. An English edition with facsimiles of 33 of the +41 folios was published by Rev. Robert Willis, Oxford, 1859. +An extensive summary of this section is given, with illustrations, +by J. Drummond Robertson, <i>The evolution of clockwork</i>, London, +1931, pp. 11-15.</p></div> + +<div class="footnote"><p><a name="Footnote_38" id="Footnote_38"></a><a href="#FNanchor_38"><span class="label">38</span></a> M. Jules Quicherat, <i>Revue Arch&egrave;ologique</i>, 1849, vol. 6.</p></div> + +<div class="footnote"><p><a name="Footnote_39" id="Footnote_39"></a><a href="#FNanchor_39"><span class="label">39</span></a> M. C. Fr&eacute;mont. <i>Origine de l'horloge &agrave; poids</i>, Paris, 1915.</p></div> + +<div class="footnote"><p><a name="Footnote_40" id="Footnote_40"></a><a href="#FNanchor_40"><span class="label">40</span></a> For this, I have used and quoted from the very beautiful +edition in English, prepared by Silvanus P. Thompson, London, +Chiswick Press, 1902.</p></div> + +<div class="footnote"><p><a name="Footnote_41" id="Footnote_41"></a><a href="#FNanchor_41"><span class="label">41</span></a> See E. G. R. Taylor, "The South-pointing needle," +<i>Imago Mundi</i>, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2).</p></div> + +<div class="footnote"><p><a name="Footnote_42" id="Footnote_42"></a><a href="#FNanchor_42"><span class="label">42</span></a> I have wondered whether the medieval interest in perpetual +motion could be connected with the use of the "Wheel of +Fortune" in churches as a substitute for bell-ringing on Good +Friday. Unfortunately I can find no evidence for or against +the conjecture.</p></div> + +<div class="footnote"><p><a name="Footnote_43" id="Footnote_43"></a><a href="#FNanchor_43"><span class="label">43</span></a> W. E. May, "Alexander Neckham and the pivoted compass +needle," <i>Journal of the Institute of Navigation</i>, 1955, vol. 8, +no. 3, pp. 283-284.</p></div> + +<div class="footnote"><p><a name="Footnote_44" id="Footnote_44"></a><a href="#FNanchor_44"><span class="label">44</span></a> W. E. May, "Hugues de Berze and the mariner's compass," +<i>The Mariner's Mirror</i>, 1953, vol. 39, no. 2, pp. 103-106.</p></div> + +<div class="footnote"><p><a name="Footnote_45" id="Footnote_45"></a><a href="#FNanchor_45"><span class="label">45</span></a> H. Balmer, <i>Beitr&auml;ge zur Geschichte der Erkenntnis des Erdmagnetismus</i>, +Aarau, 1956, p. 52.</p></div> + +<div class="footnote"><p><a name="Footnote_46" id="Footnote_46"></a><a href="#FNanchor_46"><span class="label">46</span></a> The collection is the <i>Gami 'al Hikajat</i>; the relevant passage +being given in German translation in Balmer. <i>op. cit.</i> (footnote +<a href="#Footnote_45">45</a>), p. 54.</p></div> + +<div class="footnote"><p><a name="Footnote_47" id="Footnote_47"></a><a href="#FNanchor_47"><span class="label">47</span></a> Balmer, op. <i>cit.</i> (footnote <a href="#Footnote_45">45</a>), p. 53.</p></div> + + +<h4>U.S. GOVERNMENT PRINTING OFFICE: 1959</h4> + +<div>*** END OF THE PROJECT GUTENBERG EBOOK 30001 ***</div> +</body> +</html> diff --git a/30001-h/images/cap_t.png b/30001-h/images/cap_t.png Binary files differnew file mode 100644 index 0000000..347a6f0 --- /dev/null +++ b/30001-h/images/cap_t.png diff --git a/30001-h/images/cover.jpg b/30001-h/images/cover.jpg Binary files differnew file mode 100644 index 0000000..91137b2 --- /dev/null +++ b/30001-h/images/cover.jpg diff --git a/30001-h/images/fig_1.jpg b/30001-h/images/fig_1.jpg Binary files differnew file mode 100644 index 0000000..bffd014 --- /dev/null +++ b/30001-h/images/fig_1.jpg diff --git a/30001-h/images/fig_10.jpg b/30001-h/images/fig_10.jpg Binary files differnew file mode 100644 index 0000000..ca2c0ee --- /dev/null +++ b/30001-h/images/fig_10.jpg diff --git a/30001-h/images/fig_11.jpg b/30001-h/images/fig_11.jpg Binary files differnew file mode 100644 index 0000000..6544929 --- /dev/null +++ b/30001-h/images/fig_11.jpg diff --git a/30001-h/images/fig_12.jpg b/30001-h/images/fig_12.jpg Binary files differnew file mode 100644 index 0000000..a4926bf --- /dev/null +++ b/30001-h/images/fig_12.jpg diff --git a/30001-h/images/fig_13.jpg b/30001-h/images/fig_13.jpg Binary files differnew file mode 100644 index 0000000..86d83c1 --- /dev/null +++ b/30001-h/images/fig_13.jpg diff --git a/30001-h/images/fig_14.jpg b/30001-h/images/fig_14.jpg Binary files differnew file mode 100644 index 0000000..8de12ee --- /dev/null +++ b/30001-h/images/fig_14.jpg diff --git a/30001-h/images/fig_15.jpg b/30001-h/images/fig_15.jpg Binary files differnew file mode 100644 index 0000000..d063890 --- /dev/null +++ b/30001-h/images/fig_15.jpg diff --git a/30001-h/images/fig_16.jpg b/30001-h/images/fig_16.jpg Binary files differnew file mode 100644 index 0000000..7764787 --- /dev/null +++ b/30001-h/images/fig_16.jpg diff --git a/30001-h/images/fig_17.jpg b/30001-h/images/fig_17.jpg Binary files differnew file mode 100644 index 0000000..cd30918 --- /dev/null +++ b/30001-h/images/fig_17.jpg diff --git a/30001-h/images/fig_18.jpg b/30001-h/images/fig_18.jpg Binary files differnew file mode 100644 index 0000000..3a2c00f --- /dev/null +++ b/30001-h/images/fig_18.jpg diff --git a/30001-h/images/fig_19.jpg b/30001-h/images/fig_19.jpg Binary files differnew file mode 100644 index 0000000..96939ff --- /dev/null +++ b/30001-h/images/fig_19.jpg diff --git a/30001-h/images/fig_2.jpg b/30001-h/images/fig_2.jpg Binary files differnew file mode 100644 index 0000000..e4aad78 --- /dev/null +++ b/30001-h/images/fig_2.jpg diff --git a/30001-h/images/fig_20.jpg b/30001-h/images/fig_20.jpg Binary files differnew file mode 100644 index 0000000..11caacf --- /dev/null +++ b/30001-h/images/fig_20.jpg diff --git a/30001-h/images/fig_21.jpg b/30001-h/images/fig_21.jpg Binary files differnew file mode 100644 index 0000000..35b6725 --- /dev/null +++ b/30001-h/images/fig_21.jpg diff --git a/30001-h/images/fig_22.jpg b/30001-h/images/fig_22.jpg Binary files differnew file mode 100644 index 0000000..390672a --- /dev/null +++ b/30001-h/images/fig_22.jpg diff --git a/30001-h/images/fig_3.jpg b/30001-h/images/fig_3.jpg Binary files differnew file mode 100644 index 0000000..ea1677b --- /dev/null +++ b/30001-h/images/fig_3.jpg diff --git a/30001-h/images/fig_4.jpg b/30001-h/images/fig_4.jpg Binary files differnew file mode 100644 index 0000000..24a3696 --- /dev/null +++ b/30001-h/images/fig_4.jpg diff --git a/30001-h/images/fig_4_zoom.jpg b/30001-h/images/fig_4_zoom.jpg Binary files differnew file mode 100644 index 0000000..3c4c311 --- /dev/null +++ b/30001-h/images/fig_4_zoom.jpg diff --git a/30001-h/images/fig_5.jpg b/30001-h/images/fig_5.jpg Binary files differnew file mode 100644 index 0000000..e0d4791 --- /dev/null +++ b/30001-h/images/fig_5.jpg diff --git a/30001-h/images/fig_6.jpg b/30001-h/images/fig_6.jpg Binary files differnew file mode 100644 index 0000000..43276ea --- /dev/null +++ b/30001-h/images/fig_6.jpg diff --git a/30001-h/images/fig_7.jpg b/30001-h/images/fig_7.jpg Binary files differnew file mode 100644 index 0000000..5935d35 --- /dev/null +++ b/30001-h/images/fig_7.jpg diff --git a/30001-h/images/fig_8.jpg b/30001-h/images/fig_8.jpg Binary files differnew file mode 100644 index 0000000..3c5110d --- /dev/null +++ b/30001-h/images/fig_8.jpg diff --git a/30001-h/images/fig_9.jpg b/30001-h/images/fig_9.jpg Binary files differnew file mode 100644 index 0000000..fc5b91b --- /dev/null +++ b/30001-h/images/fig_9.jpg diff --git a/30001.txt b/30001.txt new file mode 100644 index 0000000..6cb0421 --- /dev/null +++ b/30001.txt @@ -0,0 +1,2353 @@ +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + + +-----------------------------------------------------+ + | Trancriber's note: | + | | + | Letters enclosed in square brackets represent: | + | [=x] any letter with a macron (straight line above) | + | [x.] any letter with a dot below | + | [.x] any letter with a dot above | + +-----------------------------------------------------+ + + + + + 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. (_S[=u]rya Siddh[=a]nta_, 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 Ri[d.]w[=a]n, _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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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 Ri[d.]w[=a]n 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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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 Heng _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 Heng 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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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 Heng. 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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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 deg. in the 45 deg. present). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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 Lok[=a]loka [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. + + _S[=u]rya Siddh[=a]nta_, xiii, 15-22, + E. Burgess' translation, New Haven, 1860. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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 T[.a]la 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. + + _Siddh[=a]nta Siroma[n.]i_, xi, 50-57, L. Wilkinson's + translation, revised by B[.a]p[.u] deva S(h)[.a]stri, + 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 _S[=u]rya Siddh[=a]nta_ 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 _Siddh[=a]nta Siroma[n.]i_ is more certain for we know it was +written in about 1150 by Bh[=a]skara (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 +Bh[=a]skara 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 _S[=u]rya Siddh[=a]nta_, 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 Mu[h.]ammad b. 'Al[=i] b. +Rustum, and repaired and improved by his son, Fakhr ad-d[=i]n +Ri[d.]w[=a]n b. Mu[h.]ammad,[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 + Ri[d.]w[=a]n:[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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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 _Far[=a]s_ 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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MU[H.]AMMAD B. AB[=I] BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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, Mu[h.]ammad b. Ab[=i] +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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 Ri[d.]w[=a]n, which we shall next examine. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Ri[d.]w[=a]n and al-Jazar[=i], have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Fremont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Fremont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Ri[d.]w[=a]n +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfi[=i] _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qab[=a]jaq[=i] (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Heng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) S[=u]rya Siddh[=a]nta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddh[=a]nta Siromani animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Ri[d.]w[=a]n water-clocks, perpetual motion + and weight drive + 1206 al-Jazar[=i] clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Fruehzeit der Raederuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des oesterreichischen archaeologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Memoires de la Societe Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels Ueber die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "Ueber die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der koenigliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beitraege zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11^{v}-14^{v} = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Societe Royale d'Archeologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archeologique_, 1849, vol. 6. + + [39] M. C. Fremont. _Origine de l'horloge a poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beitraege zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001.txt or 30001.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/30001.zip b/30001.zip Binary files differnew file mode 100644 index 0000000..2c6c38b --- /dev/null +++ b/30001.zip diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..720d091 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #30001 (https://www.gutenberg.org/ebooks/30001) diff --git a/old/30001-0.txt b/old/30001-0.txt new file mode 100644 index 0000000..c9c6e58 --- /dev/null +++ b/old/30001-0.txt @@ -0,0 +1,2356 @@ +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + + +--------------------------------------------------------------+ + | This e-text includes characters that require UTF-8 | + | (Unicode) file encoding: | + | | + | ḍ, ā, ḥ, ȧ, ī | + | | + | If any of these characters do not display properly--in | + | particular, if the dots do not appear under the letters | + | make sure your text reader’s “character set” or “file | + | encoding” is set to Unicode (UTF-8). You may also need to | + | change the default font. Depending on available fonts, some | + | tables may not line up vertically. | + +--------------------------------------------------------------+ + + + + + 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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MUḤAMMAD B. ABĪ BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Riḍwān and al-Jazarī, have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Frémont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Frémont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Riḍwān +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfiī _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qabājaqī (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Hêng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) Sūrya Siddhānta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddhānta Siromaṇi animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Riḍwān water-clocks, perpetual motion + and weight drive + 1206 al-Jazarī clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Frühzeit der Räderuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des österreichischen archäologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Mémoires de la Société Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels Über die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "Über die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der königliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beiträge zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11ᵛ-14ᵛ = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Société Royale d'Archéologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archèologique_, 1849, vol. 6. + + [39] M. C. Frémont. _Origine de l'horloge à poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beiträge zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001-0.txt or 30001-0.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/old/30001-0.zip b/old/30001-0.zip Binary files differnew file mode 100644 index 0000000..6826c3b --- /dev/null +++ b/old/30001-0.zip diff --git a/old/30001-8.txt b/old/30001-8.txt new file mode 100644 index 0000000..444ae9a --- /dev/null +++ b/old/30001-8.txt @@ -0,0 +1,2353 @@ +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + + +-----------------------------------------------------+ + | Trancriber's note: | + | | + | Letters enclosed in square brackets represent: | + | [=x] any letter with a macron (straight line above) | + | [x.] any letter with a dot below | + | [.x] any letter with a dot above | + +-----------------------------------------------------+ + + + + + 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. (_S[=u]rya Siddh[=a]nta_, 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 Ri[d.]w[=a]n, _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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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 Ri[d.]w[=a]n 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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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 Hng _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 Hng 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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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 Hng. 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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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 Lok[=a]loka [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. + + _S[=u]rya Siddh[=a]nta_, xiii, 15-22, + E. Burgess' translation, New Haven, 1860. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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 T[.a]la 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. + + _Siddh[=a]nta Siroma[n.]i_, xi, 50-57, L. Wilkinson's + translation, revised by B[.a]p[.u] deva S(h)[.a]stri, + 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 _S[=u]rya Siddh[=a]nta_ 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 _Siddh[=a]nta Siroma[n.]i_ is more certain for we know it was +written in about 1150 by Bh[=a]skara (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 +Bh[=a]skara 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 _S[=u]rya Siddh[=a]nta_, 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 Mu[h.]ammad b. 'Al[=i] b. +Rustum, and repaired and improved by his son, Fakhr ad-d[=i]n +Ri[d.]w[=a]n b. Mu[h.]ammad,[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 + Ri[d.]w[=a]n:[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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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 _Far[=a]s_ 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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MU[H.]AMMAD B. AB[=I] BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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, Mu[h.]ammad b. Ab[=i] +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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 Ri[d.]w[=a]n, which we shall next examine. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Ri[d.]w[=a]n and al-Jazar[=i], have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Frmont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Frmont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Ri[d.]w[=a]n +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfi[=i] _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qab[=a]jaq[=i] (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Hng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) S[=u]rya Siddh[=a]nta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddh[=a]nta Siromani animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Ri[d.]w[=a]n water-clocks, perpetual motion + and weight drive + 1206 al-Jazar[=i] clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Frhzeit der Rderuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des sterreichischen archologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Mmoires de la Socit Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels ber die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "ber die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der knigliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beitrge zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11^{v}-14^{v} = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Socit Royale d'Archologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archologique_, 1849, vol. 6. + + [39] M. C. Frmont. _Origine de l'horloge poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beitrge zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001-8.txt or 30001-8.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/old/30001-8.zip b/old/30001-8.zip Binary files differnew file mode 100644 index 0000000..4b9e6bd --- /dev/null +++ b/old/30001-8.zip diff --git a/old/30001-h.zip b/old/30001-h.zip Binary files differnew file mode 100644 index 0000000..038c31a --- /dev/null +++ b/old/30001-h.zip diff --git a/old/30001-h/30001-h.htm b/old/30001-h/30001-h.htm new file mode 100644 index 0000000..f055a45 --- /dev/null +++ b/old/30001-h/30001-h.htm @@ -0,0 +1,3117 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta name="generator" content="HTML Tidy, see www.w3.org" /> +<meta http-equiv="Content-Type" content= +"text/html;charset=utf-8" /> +<title>The Project Gutenberg eBook of On the Origin of Clockwork, +Perpetual Motion Devices and the Compass by Derek J. de Solla Price</title> +<style type="text/css"> + + p { margin-top: .75em; + text-align: justify; + margin-bottom: .75em;} + + p.tb { margin-top: 1.5em; + text-align: justify; + margin-bottom: .75em;} + + p.indent { margin-top: 0em; margin-bottom: 0em; + text-align: justify; margin-left: 3.5em; text-indent: -3.5em;} + + p.title { margin-top: 1.25em; + text-align: justify; + margin-bottom: .75em;} + + + p.quotsig { margin-top: .75em; + text-align: right; + margin-bottom: .75em;} + + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; font-weight: normal; + margin-top: 1.5em; + margin-bottom: .75em; } + + + + /* sup, + sub { + height: 0em; font-size: .7em; + vertical-align: baseline; + position: relative; }*/ + + sup { bottom: .2em; font-size: .7em; margin-left: 0em;; } + + sub { top: 0em; font-size: .6em; } + + hr { width: 33%; + margin-top: 0em; + margin-bottom: 0em; + margin-left: auto; + margin-right: auto; + clear: both; + } + + + table {margin-left: auto; margin-right: auto;} + + + td.td100 {padding-right: 1em; padding-left: 0em; padding-top: 0em; padding-bottom: 0em; font-size: .9em; text-align: justify; width: 100%; vertical-align: top; } + td.td100c {padding-right: 0em; padding-left: 2.4em; padding-top: 1em; padding-bottom: .5em; font-size: 1em; text-align: left; width: 100%; vertical-align: middle;} + td.right {padding-top: .2em; padding-bottom: .2em; font-size: .8em; text-align: right; width: 10%; vertical-align: bottom;} + td.left {padding-top: .2em; padding-bottom: .2em; font-size: .8em; text-align: right; width: 90%; vertical-align: top;} + td.center {padding-top: .2em; padding-bottom: .2em; font-size: 1em; text-align: center; width: 50%; vertical-align: top;} + td.left100 {padding-right: 2em; padding-left: 2em; padding-top: .2em; padding-bottom: .2em; font-size: 1em; text-align: left; width: 100%; vertical-align: top;} + + body {margin-left: 10%; margin-right: 10%; + } + + .pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + right: 3%; font-style: normal; + font-size: .8em; + text-align: right; + } /* page numbers */ + .tn {font-size: .8em; width: 80%; background-color: #EEE; padding: 0.5em 1em 0.5em 1em; text-align: justify;} + + + .blockquot {font-size: .85em; margin-top: 1.5em; margin-bottom: 1.5em; } + + .blockquot2 {font-size: .83em; margin-top: 1.5em; margin-bottom: 1.5em; + margin-left: 20%;} + + img {text-decoration: none; border: none; margin-bottom: 0em; margin-top: 0em;} + img.floatLeft {float: left; height: 2.2em; margin-right: 0em; border: none;} + + + .smcap {font-variant: small-caps;} + .u {text-decoration: underline;} + + .caption {font-size: .85em; text-align: justify; margin-top: 1em; + margin-bottom: 2em; margin-left: 5%; margin-right: 5%; } + .caption2 {font-size: .85em; text-align: justify; margin-top: 1em; + margin-bottom: 2em; margin-left: 5%; margin-right: 5%; } + + .figcenter {margin: auto; text-align: center;} + + + .footnotes {border: none;} + .footnote {margin-left: 10%; margin-right: 5%; font-size: 0.9em;} + .footnote .label {position: absolute; right: 84%; text-align: right; font-size: .9em;} + .fnanchor {vertical-align: super; font-size: .7em; text-decoration: none;} + + +</style> +</head> +<body> + + +<pre> + +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] +[Last updated: August 25, 2014] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + +</pre> + + +<h6> </h6> + +<div class="tn"> +Transcriber's note:<br /><br /> +The original three column Chronological Table +has been replaced by a single column table +with the same chronological order to make its reading easier +at all browser settings. +</div> + +<h6> </h6> + +<div class="figcenter" style="width: 500px;"><img src="images/cover.jpg" width="500" height="647" alt= +"Cover" title="Cover page" /></div> + +<p><span class='pagenum'>81</span></p> + +<p class="quotsig"><span class="smcap">Contributions from<br /> +The Museum of History and Technology:<br /> +Paper 6</span><br /><br /></p> + +<p class="quotsig"><span class="smcap">On the Origin of Clockwork,<br /> +Perpetual Motion Devices, and the Compass</span><br /> +<i>Derek J. de Solla Price</i><br /><br /></p> + +<table width="100%" summary="TOC"> + +<tr> +<td class="left">POWER AND MOTION GEARING</td> +<td class="right"><a href="#Page_83a">83</a></td> +</tr> + +<tr> +<td class="left">MECHANICAL CLOCKS</td> +<td class="right"><a href="#Page_84a">84</a></td> +</tr> + +<tr> +<td class="left">PERPETUAL MOTION AND THE CLOCK BEFORE DE DONDI</td> +<td class="right"><a href="#Page_108a">108</a></td> +</tr> + +<tr> +<td class="left">THE MAGNETIC COMPASS AS A FELLOW-TRAVELER FROM CHINA</td> +<td class="right"><a href="#Page_110a">110</a></td> +</tr> +</table> + +<p><span class='pagenum'>82</span><br /><br /></p> + +<h2><i>ON THE ORIGIN OF CLOCKWORK,<br /> +PERPETUAL MOTION DEVICES<br /> +AND THE COMPASS</i></h2> + +<h3><i>By Derek J. de Solla Price</i></h3> + +<table width="80%" summary="intro"> + +<tr> +<td><p><i>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.</i></p> + +<p><i>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.</i></p> + +<p><span class="smcap">The Author</span>: <i>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.</i></p></td> +</tr> + +</table> + +<div class="blockquot2"><p>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. (<i>Sūrya Siddhānta</i>, ed. Burgess, xiii, +18-19.)</p></div> + +<p><img src="images/cap_t.png" class="floatLeft" alt="T" />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.</p> + +<p>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.<a name="FNanchor_1" id="FNanchor_1"></a><a href="#Footnote_1" class="fnanchor">1</a> 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.</p> + +<p>Furthermore, even if one admits the use of clocklike +gearing before the existence of the clock, it is still +<span class='pagenum'>83</span>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, <i>ca.</i> 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, <i>ca.</i> 1272.</p> + +<p>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 +<i>Perpetuum Mobile</i>, 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.<a name="FNanchor_2" id="FNanchor_2"></a><a href="#Footnote_2" class="fnanchor">2</a> 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.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_1" id="fig_1" /><img src="images/fig_1.jpg" width="500" height="666" alt= +"Framework Structure of the Astronomical +Clock of Giovanni de Dondi of Padua, +A.D. 1364." title="" /> + +<div class="caption">Figure 1.—<span class="smcap">Framework Structure of the Astronomical +Clock</span> of Giovanni de Dondi of Padua, +A.D. 1364.</div></div> + + +<h3><a name="Page_83a" id="Page_83a">Power and Motion Gearing</a></h3> + +<p>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.),<a name="FNanchor_3" id="FNanchor_3"></a><a href="#Footnote_3" class="fnanchor">3</a> and in China actual examples of wheels +and moulds for wheels dating from the 4th century +<span class='pagenum'>84</span>B.C. have been preserved.<a name="FNanchor_4" id="FNanchor_4"></a><a href="#Footnote_4" class="fnanchor">4</a> 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.<a name="FNanchor_5" id="FNanchor_5"></a><a href="#Footnote_5" class="fnanchor">5</a> 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_2" id="fig_2" /><img src="images/fig_2.jpg" width="500" height="497" alt= +"Astronomical Clock of de Dondi, +showing gearing on the dial for Mercury and +escapement crown wheel. Each of the seven side +walls of the structure shown in figure 1 was fitted +with a dial." title="" /> + +<div class="caption">Figure 2.—<span class="smcap">Astronomical Clock</span> of de Dondi, +showing gearing on the dial for Mercury and +escapement crown wheel. Each of the seven side +walls of the structure shown in figure 1 was fitted +with a dial.</div></div> + + +<p>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.<a name="FNanchor_6" id="FNanchor_6"></a><a href="#Footnote_6" class="fnanchor">6</a> One may also cite +the use of the reduction gear chain in power machinery +as used in the geared windlass of Archimedes and +Hero.</p> + +<p>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.</p> + + +<h3><a name="Page_84a" id="Page_84a">Mechanical Clocks</a></h3> + +<p>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 me<span class='pagenum'>85</span>chanical clocks has demonstrated certain peculiarities +most relevant to our present argument.</p> + + +<p class="title"><span class="smcap">the european tradition</span></p> + +<p>If one is to establish a <i>terminus ante quem</i> 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,<a name="FNanchor_7" id="FNanchor_7"></a><a href="#Footnote_7" class="fnanchor">7</a> 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 <i>horologium</i> and its vernacular equivalents.</p> + +<p>Temporarily postponing the consideration of evidence +prior to <i>ca.</i> 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.<a name="FNanchor_8" id="FNanchor_8"></a><a href="#Footnote_8" class="fnanchor">8</a> 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 (<i>ca.</i> 1475), +pendulum control (<i>ca.</i> 1650), and the anchor escapement +(<i>ca.</i> 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_3.jpg" width="500" height="916" alt= +"Figure 3.—German Wall Clock, Probably About +1450, showing the degeneration in complexity from +that of de Dondi's clock." title="" /> + +<div class="caption">Figure 3.—<span class="smcap">German Wall Clock, Probably About +1450</span>, showing the degeneration in complexity from +that of de Dondi's clock.</div></div> + +<p><span class='pagenum'>86</span></p> + +<p>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. <a href="#fig_1">1,</a> <a href="#fig_2">2</a>) +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.</p> + +<p>On the basis of such evidence I have suggested elsewhere<a name="FNanchor_9" id="FNanchor_9"></a><a href="#Footnote_9" class="fnanchor">9</a> +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.</p> + +<p>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.</p> + + +<p class="title"><span class="smcap">the chinese tradition</span></p> + +<p>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.<a name="FNanchor_10" id="FNanchor_10"></a><a href="#Footnote_10" class="fnanchor">10</a> 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 H&ecirc;ng <i>ca.</i> 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 H&ecirc;ng +onwards, largely independent of any transmissions +from the West.</p> + +<p>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 (<i>e.g.</i>, equator, ecliptic, meridians, etc.), or a +solid celestial globe on which such circles could be +drawn, together with the constellations of the fixed +<span class='pagenum'>87</span>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.</p> + +<p>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."</p> + +<p>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.</p> + +<p>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.</p> + +<p>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. <a href="#fig_4">4</a>). 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.</p> + +<p>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.</p> + +<p>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" (<i>glokke</i>). 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<span class='pagenum'>88</span> +European clocks should have prompted them to +open their doors, previously so carefully and for +so long kept closed against the foreign barbarians.</p> + + +<div class="figcenter" style="width: 500px;"><a name="fig_4" id="fig_4" /><a href="images/fig_4_zoom.jpg"><img src="images/fig_4.jpg" width="500" height="516" alt= +"Astronomical Clock Tower of Su +Sung in K'ai-feng, ca. A.D. 1090." title="Click for detailed image" /></a> + +<div class="caption">Figure 4.—<span class="smcap">Astronomical Clock Tower of Su +Sung</span> in K'ai-feng, <i>ca.</i> A.D. 1090, from an original +drawing by John Christiansen. (<i>Courtesy of Cambridge +University Press.</i>)</div></div> + +<h3>Mechanized Astronomical Models</h3> + +<p>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.</p> + +<p><span class='pagenum'>89</span></p> + +<p class="title"><span class="smcap">hellenistic period</span></p> + +<p>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.<a name="FNanchor_11" id="FNanchor_11"></a><a href="#Footnote_11" class="fnanchor">11</a></p> + +<p>Cicero's descriptions of Archimedes' planetarium +are (italics supplied):</p> + +<div class="blockquot"><p>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>i. e.</i>, 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>i.e.</i>, set in motion] the globe, it was actually true +that the moon was always as many revolutions behind the +sun on the <i>bronze</i> 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].</p> + +<p class="quotsig"> +<i>De republica</i>, I, xiv (21-22), Keyes' translation. +</p> + +<p class="tb">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.</p> + +<p class="quotsig"> +<i>Tusculanae disputationes</i>, I, 63. +</p> +</div> + +<p class="tb">Later descriptions from Ovid, Lactantius, Claudian, +Sextus Empiricus, and Pappus, respectively, are +(italics supplied):</p> + +<div class="blockquot"><p>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>i. e.</i>, the outer bronze +globe's] round form. The form of the temple [of Vesta] +is similar....</p> + +<p class="quotsig"> +Ovid, <i>Fasti</i> (1st century, A.D.), VI, 277-280, +Frazer's translation. +</p> + +<p class="tb">The Sicilian Archimedes, was able to make a reproduction +and model of the world in concave <i>brass</i> (concavo aere +similitudinem mundi ac figuram); in it he so arranged +the <i>sun</i> and <i>moon</i> 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 <i>courses of +the stars</i>, whether fixed or wandering.</p> + +<p class="quotsig"> +Lactantius, <i>Institutiones divinae</i> (4th century, A.D.), II, 5, 18. +</p> + +<p class="tb">Archimedes' sphere. When Jove looked down and saw +the heavens figured in a sphere of <i>glass</i>, 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 <i>stars</i> and actuates the lifelike mass with +definite motions. A false <i>zodiac</i> runs through a year of its +own and a toy <i>moon</i> waxes and wanes month by month. +Now bold invention rejoices to make its own heaven revolve +and sets the <i>stars</i> [planets?] in motion by human wit....</p> + +<p class="quotsig"> +Claudian, <i>Carmina minora</i> (<i>ca.</i> A.D. 400), LI (LXVIII), +Platnaure's translation.<br /> +</p> + +<p class="tb">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 <i>wood</i>, or at the movements +of these [bodies], but by the devices and causes of the +movements.</p> + +<p class="quotsig"> +Sextus Empiricus, <i>Adversus mathematicos</i> (3rd century, A.D.), +IX, 115, Epps' translation. +</p></div> + +<p><span class='pagenum'>90</span></p> + +<div class="blockquot"><p> +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 <i>water</i>, and Archimedes the Syracusan, according +to some, knows the cause and reasons for all of these.</p> + +<p class="quotsig"> +Pappus (3rd century, A.D.), <i>Works</i> (Hultsch edition), +VIII, 2, Epps' translation. +</p></div> + +<p>A similar arrangement seems to be indicated in +another mechanized globe, also mentioned by Cicero +and said to have been made by Posidonius:</p> + +<div class="blockquot"><p>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 <i>sun</i> and <i>moon</i> and +<i>five</i> 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....</p> + +<p class="quotsig"> +<i>De natura deorum</i>, II, xxxiv-xxxv (88), +Yonge's translation. +</p></div> + +<p>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 H&ecirc;ng. 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.</p> + +<p class="tb">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:</p> + +<div class="blockquot"><p>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.</p> + +<p class="quotsig"> +<i>Pneumatics</i>, XLVI, Woodcroft's translation. +</p></div> + +<p>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.</p> + +<p>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.</p> + +<p>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 (<i>ca.</i> A.D. 120) +it had led to the successive inventions of the anaphoric +clock and of the planispheric astrolabe.<a name="FNanchor_12" id="FNanchor_12"></a><a href="#Footnote_12" class="fnanchor">12</a> 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.</p> + +<p>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.<a name="FNanchor_13" id="FNanchor_13"></a><a href="#Footnote_13" class="fnanchor">13</a><br /><br /></p> + +<p><span class='pagenum'>91</span></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_5" id="fig_5" /><img src="images/fig_5.jpg" width="500" height="596" alt= +"Plate of Salzburg +Anaphoric Clock," title="" /> + +<div class="caption">Figure 5. <span class="smcap">Plate of Salzburg +Anaphoric Clock</span>, a reconstruction +(see footnote <a href="#Footnote_14">14</a>) based on +a photograph of the remaining +fragment. (<i>Courtesy of Oxford +University Press.</i>)</div></div> + + +<p>Parts of two such discs from anaphoric clocks +have been found, one at Salzburg<a name="FNanchor_14" id="FNanchor_14"></a><a href="#Footnote_14" class="fnanchor">14</a> and one at +Grand in the Vosges,<a name="FNanchor_15" id="FNanchor_15"></a><a href="#Footnote_15" class="fnanchor">15</a> 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. <a href="#fig_5">5</a>). +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.</p> + +<p>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-<span class='pagenum'>92</span>keeping clocks before the change was made to a +fixed dial and moving hand.</p> + +<p>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.<a name="FNanchor_16" id="FNanchor_16"></a><a href="#Footnote_16" class="fnanchor">16</a> 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.</p> + +<p>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 <i>ca.</i> 65 B.C. &plusmn;10 years, and we can be sure +that the machine is of Hellenistic origin, possibly from +Rhodes or Cos.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_6" id="fig_6" /><img src="images/fig_6.jpg" width="500" height="301" alt= +"Antikythera Machine, Largest Fragment." title="" /> + +<div class="caption">Figure 6.—<span class="smcap">Antikythera Machine, Largest Fragment.</span> +(<i>Photo courtesy of National Museum, Athens.</i>)</div></div> + +<p>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. <a href="#fig_6">6</a>) 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. <a href="#fig_7">7</a>, 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. <a href="#fig_7">7</a>, +top) has a pair of rings carefully engraved and graduated<span class='pagenum'>93</span> +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&deg; in the 45&deg; present).</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_7" id="fig_7" /><img src="images/fig_7.jpg" width="500" height="459" alt= +"Antikythera Machine, Two Smaller +Fragments." title="" /> + +<div class="caption">Figure 7.—<span class="smcap">Antikythera Machine, Two Smaller +Fragments.</span> (<i>Photo courtesy of National Museum, +Athens.</i>)</div></div> + +<p>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.</p> + +<p>Some technical details can be gleaned however. +The shape of the gear teeth appears to be almost +exactly equilateral triangles in all cases (fig. <a href="#fig_8">8</a>), 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. <a href="#fig_9">9</a>) has shown that the appearances +are consistent with the theory that the<span class='pagenum'>94</span> +purpose of the gears was to provide the correct angular +ratios to move the sun and planets at their appropriate +relative speeds.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_8" id="fig_8" /><img src="images/fig_8.jpg" width="500" height="490" alt= +"Antikythera Machine, +Detail From Figure 6 +showing gearing." title="" /> + +<div class="caption">Figure 8.—<span class="smcap">Antikythera Machine, +Detail From Figure 6</span>, +showing gearing. (<i>Photo courtesy +of National Museum, Athens.</i>)</div></div> + +<p>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.<br /><br /></p> + +<table width="100%" summary="note" border="1"> +<tr><td class="left100"> +<div class="blockquot"><p><i>Note added in proof</i>:</p> + +<p>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 <i>Scientific American</i>, 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.</p></div> +</td></tr> +</table> + +<p class="tb">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<span class='pagenum'>95</span> +are more akin to those current in China than in the +West. The relevant portions of text are as follows +(italics supplied):</p> + +<div class="blockquot"><p>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.</p> + +<p class="quotsig"> +<i>Sūrya Siddhānta</i>, xiii, 15-22,<br /> +E. Burgess' translation, New Haven, 1860. +</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_9" id="fig_9" /><img src="images/fig_9.jpg" width="500" height="563" alt= +"Antikythera Machine, Partial Reconstruction +by Theophanidis." title="" /> + +<div class="caption">Figure 9.—<span class="smcap">Antikythera Machine, Partial Reconstruction +by Theophanidis</span> (see footnote <a href="#Footnote_16">16</a>).</div></div> + +<p>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.</p> + +<p>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 + +<span class='pagenum'>96</span> + +the orifice left open for filling the wheel. The wheel will +then revolve of itself, drawn around by the water.</p> + +<p>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.</p> + +<p>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.</p> + +<p>The self-revolving machine [mentioned by <i>Lalla</i>, 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.</p> + +<p>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.</p> + +<p class="quotsig"> +<i>Siddhānta Siromaṇi</i>, xi, 50-57, L. Wilkinson's translation,<br /> +revised by Bȧpu̇ deva S(h)ȧstri, Calcutta, 1861. +</p></div> + +<p>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 <i>Sūrya Siddhānta</i> is known to date, in +its original form, from the early Middle Ages, <i>ca.</i> 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 <i>ca.</i> 1000 to <i>ca.</i> +1150 A.D. The date of the <i>Siddhānta Siromaṇi</i> 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 +clocktower made by Su Sung. The technical details +will lead us to suppose there is more than a temporal +connection.</p> + +<p>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.</p> + +<p>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 <i>Sūrya Siddhānta</i>, of the "wonder-causing +instrument" to which mercury must be +applied.</p> + +<p>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.</p> + +<p>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.</p> + +<p>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 <i>ca.</i> 535) describes a monumental +water clock which was erected in Gaza <i>ca.</i> 500.<a name="FNanchor_17" id="FNanchor_17"></a><a href="#Footnote_17" class="fnanchor">17</a> It +contained impressive jackwork, such as a Medusa +<span class='pagenum'>97</span> +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.</p> + +<p>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 (<i>ca.</i> 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,<a name="FNanchor_18" id="FNanchor_18"></a><a href="#Footnote_18" class="fnanchor">18</a> 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.</p> + +<p>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:<a name="FNanchor_19" id="FNanchor_19"></a><a href="#Footnote_19" class="fnanchor">19</a></p> + +<div class="blockquot"><p>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. +</p></div> + +<p>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.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_10" id="fig_10" /><img src="images/fig_10.jpg" width="500" height="518" alt= +"Calendrical Gearing Designed by +al-Biruni." title="" /> + +<div class="caption">Figure 10.—<span class="smcap">Calendrical Gearing Designed by +al-Biruni</span>, <i>ca.</i> A.D. 1000. The gear train count is +40-10+7-59+19-59+24-48. The gear of 48 therefore +makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. +The gear of 40 shows a (lunar) rotation in exactly +28 days, and the center pinions 7+10 rotate in exactly +one week. After Wiedemann (see footnote <a href="#Footnote_20">20</a>).</div></div> + +<p>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 (<i>ca.</i> 1000)—significantly, +perhaps, he is well known for his travel +account of India—there is remarkable innovation.</p> + +<p>Most cogent to our purpose is a text, described for +the first time by Wiedemann,<a name="FNanchor_20" id="FNanchor_20"></a><a href="#Footnote_20" class="fnanchor">20</a> in which al-Biruni +<span class='pagenum'>98</span>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 (<i>e.g.</i>, 7, 19, 59) as dictated by the astronomical +constants involved (see fig. <a href="#fig_10">10</a>). 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 <i>Farās</i> 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.</p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_11.jpg" width="500" height="440" alt= +"Geared Astrolabe by Muḥammad b. Abī Bakr of Isfahan, A.D. 1221-1222." title="" /> + +<div class="caption">Figure 11.—<span class="smcap">Geared Astrolabe by Muḥammad b. Abī Bakr of Isfahan</span>, A.D. 1221-1222. +(<i>Photo courtesy of Science Museum, London.</i>)</div></div> + +<p>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.</p> + +<p><span class='pagenum'>99</span></p> + +<div class="figcenter" style="width: 500px;"><img src="images/fig_12.jpg" width="500" height="517" alt= +"Gearing from Astrolabe Shown in Figure 11." title="" /> + +<div class="caption">Figure 12.—<span class="smcap">Gearing from Astrolabe Shown in Figure 11.</span> The gear train count is as +follows: 48-13+8-64+64-64+10-60. The pinion of 8 has been incorrectly replaced by a +more modern pinion of 10. The gear of 48 should make 13 (lunar) rotations while the double +gear of 64+64 makes 6 revolutions of double months (of 29-30 days) and the gear of 60 makes +a single turn in the hegiral year of 354 days. (<i>Photo courtesy of Science Museum, London.</i>)</div></div> + +<p>This landmark in the history of science and technology +is now preserved at the Museum of the +History of Science, Oxford, England.<a name="FNanchor_21" id="FNanchor_21"></a><a href="#Footnote_21" class="fnanchor">21</a> 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 +<span class='pagenum'>100</span>much easier to mark out geometrically (<i>e.g.</i>, 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.<br /><br /></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_13" id="fig_13" /><img src="images/fig_13.jpg" width="500" height="351" alt= +"Astrolabe Clock, Regulated by a +Mercury Drum." title="" /> + +<div class="caption">Figure 13.—<span class="smcap">Astrolabe Clock, Regulated by a +Mercury Drum</span>, from the Alfonsine <i>Libros del saber</i> +(see footnote <a href="#Footnote_22">22</a>).</div></div> + +<p>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 (<i>ca.</i> 450), but the +first general, though crude, planetary equatorium +seems to have been described by Abulcacim Abnacahm +(<i>ca.</i> 1025) in Granada; it has been handed down +to us in the archaic Castilian of the Alfonsine <i>Libros +del saber</i>.<a name="FNanchor_22" id="FNanchor_22"></a><a href="#Footnote_22" class="fnanchor">22</a> The sections of this book, dealing with the +<i>Laminas de las VII Planetas</i>, describe not only this +instrument but also the improved modification introduced +by Azarchiel (born <i>ca.</i> 1029, died <i>ca.</i> 1087).</p> + +<p>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 (<i>ca.</i> 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.</p> + +<p>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<span class='pagenum'>101</span> 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 +<i>ca.</i> 1276-77.</p> + +<table width="100%" summary="perpetual wheels" border="0"> +<tr><td class="center"> +<div class="figcenter" style="width: 200px;"><a name="fig_14" id="fig_14" /><img src="images/fig_14.jpg" width="200" height="195" alt= +"Islamic Perpetual Motion Wheel." title="" /></div> + +<div class="caption2">Figure 14.—<span class="smcap">Islamic Perpetual Motion Wheel</span>, +after manuscript cited by Schmeller (see footnote <a href="#Footnote_26">26</a>).</div> +</td> +<td class="center"> +<div class="figcenter" style="width: 204px;"><img src="images/fig_15.jpg" width="204" height="195" alt= +"Another Perpetual Motion Wheel." title="" /></div> + +<div class="caption2">Figure 15.—<span class="smcap">Another Perpetual Motion Wheel</span>, +after the text cited in figure 14.</div> +</td></tr> +</table> + +<p>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. <a href="#fig_13">13</a>). +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.</p> + +<p>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.</p> + + +<p>It is of the greatest interest to our theme that the +Islamic contributions to horology and perpetual +motion seem to form a closely knit corpus. A most +important series of horological texts, including those +of Riḍwān and al-Jazarī, have been edited by Wiedemann +and Hauser.<a name="FNanchor_23" id="FNanchor_23"></a><a href="#Footnote_23" class="fnanchor">23</a> Other Islamic texts give versions +of the water clocks and automata of Archimedes and +of Hero and Philo of Alexandria.<a name="FNanchor_24" id="FNanchor_24"></a><a href="#Footnote_24" class="fnanchor">24</a> In at least three +cases<a name="FNanchor_25" id="FNanchor_25"></a><a href="#Footnote_25" class="fnanchor">25</a> these texts are found also associated with texts +describing perpetual-motion wheels and other hydraulic +devices. Three manuscripts of this type have +been published in German translation by Schmeller.<a name="FNanchor_26" id="FNanchor_26"></a><a href="#Footnote_26" class="fnanchor">26</a> + +<span class='pagenum'>102</span> + +The devices include a many chambered wheel (see fig. <a href="#fig_14">14</a>) similar to the Alfonsine mercury "escapement," a +wheel of slanting tubes constructed like the noria (see +fig. 15), wheels of weights swinging on arms as +described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known +example of a weight drive. This latter machine is a +pump, in which a chain of buckets is used to raise +water by passing over a pulley which is geared to a +drum powered by a falling weight (see fig. <a href="#fig_16">16</a>); +perhaps for balance, the whole arrangement is made +in duplicate with common axles for the corresponding +parts.</p> + +<div class="figcenter" style="width: 500px;"><a name="fig_16" id="fig_16" /><img src="images/fig_16.jpg" width="500" height="273" alt= +"Islamic Pump Powered by a Weight Drive." title="" /> + +<div class="caption">Figure 16.—<span class="smcap">Islamic Pump Powered by a Weight Drive</span>, after the text cited in figure 14.</div></div> + +<p>The Islamic tradition of water clocks did not involve +the use of gears, though very occasionally a pair is +used to turn power through an angle when this is +dictated by the use of a water wheel in the automata. +In the main, everything is worked by floats and +strings or by hydraulic or pneumatic forces, as in +Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing +the passage of hours.</p> + + +<p class="title"><span class="smcap">medieval europe</span></p> + +<p>Echoes from nearly all the developments already +noted from other parts of the world are found to +occur in medieval Europe, often coming through +channels of communication more precisely determinable +than those hitherto mentioned. Before +the influx of Islamic learning at the time of transmission +of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris <i>ca.</i> 1292), +there are occasional references to the most primitive +mechanized "visual aids" in astronomy.</p> + +<p>The most famous of these occurs in an historical +account by Richer of Rheims about his teacher +Gerbert (born 946, later Pope Sylvester II, 990-1003). +Several instruments made by Gerbert are described +in detail; he includes a fine celestial globe made of +wood covered with horsehide and having the stars +and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found +on Chinese instruments but never on the Ptolemaic +variety. Lastly, he cites "the construction of a +sphere, most suitable for recognizing the planets," but +unfortunately it is not clear from the description +whether or not the model planets were actually to +be animated mechanically. The text runs:<a name="FNanchor_27" id="FNanchor_27"></a><a href="#Footnote_27" class="fnanchor">27</a></p> + +<div class="blockquot"><p>Within this oblique circle (the zodiac on the ecliptic +of the globe) he hung the circles of the wandering stars (the +planets) with marvellous ingenuity, whose orbits, heights +<span class='pagenum'>103</span> +and even the distance from each other he demonstrated to +his pupils most effectually. Just how he accomplished this +it is unsuitable to enter into here because of its extent lest +we should appear to be wandering from our main theme.</p></div> + +<p>Thus, although there is a hint of mechanical complexity, +there is really no justification for such an +assumption; the description might well imply only +a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable +that Gerbert could have learned something of Islamic +and other extra-European traditions during his +period of study with the Bishop of Barcelona—a +traveling scholarship that seems to have had many +repercussions on the whole field of European +scholarship.</p> + +<p>Once the floodgates of Arabic learning were +opened, a stream of mechanized astronomical +models poured into Europe. Astrolabes and equatoria +rapidly became very popular, mainly through the +reason for which they had been first devised, the +avoidance of tedious written computation. Many +medieval astrolabes have survived, and at least +three medieval equatoria are known. Chaucer is +well known for his treatise on the astrolabe; a manuscript +in Cambridge, containing a companion treatise +on the equatorium, has been tentatively suggested +by the present author as also being the work of +Chaucer and the only piece written in his own hand.</p> + +<p>The geared astrolabe of al-Biruni is another type of +protoclock to have been transmitted. A specimen in +the Science Museum, London,<a name="FNanchor_28" id="FNanchor_28"></a><a href="#Footnote_28" class="fnanchor">28</a> though unfortunately +now incomplete, has a very sophistocated arrangement +of gears for moving pointers to indicate the +correct relative positions and movements of the sun +and moon (see figs. <a href="#fig_17">17</a> and <a href="#fig_18">18</a>). Like the earlier +Muslim example it contains wheels with odd numbers +of gear teeth (14, 27, 39); however, the teeth are no +longer equilateral in shape, but approximate a more +modern slightly rounded form. This example is +French and appears to date from <i>ca.</i> 1300. Another +Gothic astrolabe with a similar gear ring on the rete, +said to date from <i>ca.</i> 1400 (it could well be much +earlier) is now in the Billmeier collection (London).<a name="FNanchor_29" id="FNanchor_29"></a><a href="#Footnote_29" class="fnanchor">29</a></p> + +<p>Turning from the mechanized astrolabe to the +mechanized equatorium, we find the work of Richard +of Wallingford (1292?-1336) of the greatest interest +as providing an immediate precursor to that of de +Dondi. He was the son of an ingenious blacksmith, +making his way to Merton College, Oxford, then the +most active and original school of astronomy in +Europe, and winning later distinction as Abbot of St. +Albans. A text by him, dated 1326-27, described in +detail the construction of a great equatorium, more +exact and much more elaborate than any that had +gone before.<a name="FNanchor_30" id="FNanchor_30"></a><a href="#Footnote_30" class="fnanchor">30</a> Nevertheless it is evidently a normal +manually operated device like all the others. In +addition to this instrument, Richard is said to have +constructed <i>ca.</i> 1320, a fine planetary clock for his +Abbey.<a name="FNanchor_31" id="FNanchor_31"></a><a href="#Footnote_31" class="fnanchor">31</a> Bale, who seems to have seen it, regarded +it as without rival in Europe, and the greatest curiosity +of his time. Unfortunately, the issue was confused by +Leland, who identified it as the Albion (<i>i.e.</i>, all-by +one), the name Richard gives to his manual equatorium. +This clock was indeed so complex that +Edward III censured the Abbot for spending so much +money on it, but Richard replied that after his death +nobody would be able to make such a thing again. +He is said to have left a text describing the construction +of this clock, but the absence of such a work has +led many modern writers to support Leland's identification +and suppose that the device was not a mechanical +clock.<br /><br /></p> + +<p><span class='pagenum'>104</span></p> + +<div class="figcenter" style="width: 500px;"><a name="fig_17" id="fig_17" /><img src="images/fig_17.jpg" width="500" height="668" alt= +"French Geared Astrolabe of Trefoil Gothic Design." title="" /> + +<div class="caption">Figure 17.—<span class="smcap">French Geared Astrolabe of Trefoil Gothic Design</span>, <i>ca.</i> A.D. 1300. The +gearing on the pointer is, from the center: (32)/14-45+27-39, the last meshing with a concave +annular gear of 180 teeth around the rim of the rete of the astrolabe. A second pointer, +geared to this so as to follow the Moon, seems to be lacking. (<i>Photo courtesy of Science Museum. +London.</i>)</div></div> + +<div class="figcenter" style="width: 500px;"><a name="fig_18" id="fig_18" /><img src="images/fig_18.jpg" width="500" height="221" alt= +"Gear Train Of Pointer in figure 17." title="" /> + +<div class="caption">Figure 18.—<span class="smcap">Gear Train Of +Pointer</span> in figure 17. (<i>Photo +courtesy of Science Museum, London.</i>)</div></div> + + +<p>A corrective for this view is to be had from a St. +Albans manuscript (now at Gonville and Caius College, +Cambridge) that described the methods for +setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. +Although the manuscript copy is to be dated <i>ca.</i> 1340, +it clearly indicates that a geared planetary device +was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine +made by Richard of Wallingford. Unfortunately +the text does not appear to give any relevant +information about the presence of an escapement or +any other regulatory device, nor does it mention +the source of power.<a name="FNanchor_32" id="FNanchor_32"></a><a href="#Footnote_32" class="fnanchor">32</a> Now a geared version of the + +<span class='pagenum'>105</span> + +Albion would appear to correspond very closely indeed +to the dial-work which forms the greater part of +the de Dondi clock, and for this reason we suggest +now that the two clocks were very closely related in +other ways too. This, circumstantial though it be, +is evidence for thinking that the weight drive and +some form of escapement were known to Richard of +Wallingford, <i>ca.</i> 1320. It would narrow the gap between +the clock and the protoclocks to less than half a +century, perhaps a single generation, in the interval +<i>ca.</i> 1285-1320. In this connection it may be of +interest that Richard of Wallingford knew only the +Toledo tables corpus, that of the Alfonsine school did +not arrive in England until after his death.</p> + +<p>There are, of course, many literary references to +the water-clocks in medieval literature. In fact most +of these are from quotations which have often been +produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for +that history, as noted previously in the discussion of +the horologium. There are however enough mentions +to make it certain that water clocks of some sort +were in use, especially for ecclesiastic purposes, from +the end of the 12th century onwards. Thus, Jocelin +of Brakelond tells of a fire in the Abbey Church of +Bury St. Edmunds in the year 1198.<a name="FNanchor_33" id="FNanchor_33"></a><a href="#Footnote_33" class="fnanchor">33</a> The relics +would have been destroyed during the night, but just +at the crucial moment the clock bell sounded for +matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to +get water, some to the well and others to the clock"—probably +the sole occasion on which a clock served +as a fire hydrant.</p> + +<p>It seems probable that some of these water clocks +could have been simple drip clepsydras, with perhaps +a striking arrangement added. A most fortunate +discovery by Drover has now brought to light a +manuscript illumination that shows that these water +clocks, at least by <i>ca,</i> 1285, had become more complex +and were rather similar in appearance to the Alfonsine +mercury drum.<a name="FNanchor_34" id="FNanchor_34"></a><a href="#Footnote_34" class="fnanchor">34</a> The illustration (fig. <a href="#fig_19">19</a>) is +from a moralized Bible written in northern France, +and accompanies the passage where King Hezekiah +is given a sign by the Lord, the sun being moved back +ten steps of the clock. The picture clearly shows the +central water wheel and below it a dog's head spout +gushing water into a bucket supported by chains, +with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette +which might be a fly or a model sun. The wheel +appears to have 15 compartments, each with a central +hole (perhaps similar to that in the Alfonsine +clock) and it is supported on a square axle by a +bracket, the axle being wedged in the traditional +fashion. The projections at the edge of the wheel +might be gear teeth, but more likely they are used only +for tripping the striking mechanism. If it were not for +the running water spout it would be very close to the +Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation.</p> + +<p><span class='pagenum'>106</span></p> + +<p>From the adjacent region there is +another account of a striking water +clock, the evidence being inscriptions +on slates, discovered in Villers Abbey +near Brussels;<a name="FNanchor_35" id="FNanchor_35"></a><a href="#Footnote_35" class="fnanchor">35</a> these may be closely +dated as 1267 or 1268 and provide the +remains of a memorandum for the sacrist +and his assistants in charge of the clock.</p> + +<div class="blockquot"><p>Always set the clock, however long you +may delay on [the letter "A"] afterwards +you shall pour water from the little pot +(pottulo) that is there, into the reservoir +(cacabum) until it reaches the prescribed +level, and you must do the same when you +set [the clock] after compline so that you +may sleep soundly.</p></div> + +<p>A quite different sort of evidence is to +be had from the writings of Robertus +Anglicus in 1271 where one gets the +impression that just at this time there +was active interest in the attempt to +make a weight-driven anaphoric clock +and to regulate its motion by some +unstated method so that it would keep +time with the diurnal rotation of the +heavens:<a name="FNanchor_36" id="FNanchor_36"></a><a href="#Footnote_36" class="fnanchor">36</a></p> + +<div class="blockquot"><p>Nor it is possible for any clock to follow the +judgment of astronomy with complete accuracy. +Yet clockmakers (artifices horologiorum) +are trying to make a wheel (circulum) +which will make one complete revolution for every +one of the equinoctial circle, but they cannot quite perfect +their work. But if they could, it would be a really accurate +clock (horologium verax valde) and worth more than an +astrolabe or other astronomical instrument for reckoning +the hours, if one knew how to do this according to the +method aforesaid. The method of making such a clock +would be this, that a man make a disc (circulum) of uniform +weight in every part so far as could possibly be done. +Then a lead weight should be hung from the axis of that +wheel (axi ipsius rote) and this weight would move that +wheel so that it would complete one revolution from sunrise +to sunrise, minus as much time as about one degree rises +according to an approximately correct estimate. For from +sunrise to sunrise, the whole equinoctial rises, and about +one degree more, through which degree the sun moves +against the motion of the firmament in the course of a +natural day. Moreover, this could be done more accurately +if an astrolabe were constructed with a network on which +the entire equinoctial circle was divided up.</p></div> + +<div class="figcenter" style="width: 500px;"><a name="fig_19" id="fig_19" /><img src="images/fig_19.jpg" width="500" height="559" alt= +"Manuscript Illumination of a Medieval +Waterclock." title="" /> + +<div class="caption">Figure 19.—<span class="smcap">Manuscript Illumination of a Medieval +Waterclock</span>, showing a partitioned wheel, a +weight drive, and a carillion for striking. From +Drover (see footnote <a href="#Footnote_34">34</a>).</div></div> + +<p>The text then continues with technical astronomical +details of the slight difference between the rate of +rotation of the sun and of the fixed stars (because of +the annual rotation of the sun amongst the stars) +but it gives no indication of any regulatory device. +Again it should be noted, this source comes from +France; Robertus, though of English origin, apparently +being then a lecturer either at the University +of Paris or at that of Montpellier. The date of this +passage, 1271, has been taken as a <i>terminus post quem</i> +for the invention of the mechanical clock. In the +next section we shall describe the text of Peter Peregrinus, +very close to this in place and date, which +describes just such a machine, conflating it with +accounts of an armillary sphere, perpetual motion, +and the magnetic compass—so bringing all these +threads together for the first time in Europe.</p> + +<p><span class='pagenum'>107</span></p> + +<div class="figcenter" style="width: 400px;"><a name="fig_20" id="fig_20" /><img src="images/fig_20.jpg" width="400" height="418" alt= +"Arrangement for Turning a Figure +Of an Angel." title="" /> + +<div class="caption">Figure 20.—<span class="smcap">Arrangement for Turning a Figure +Of an Angel.</span> It has been alleged that this drawing +by Villard represents an escapement. After Lassus +(see footnote <a href="#Footnote_37">37</a>).</div></div> + +<p>We have reserved to the last one section of evidence +which may or may not be misleading, the famous +notebook of Villard (Wilars) of Honnecourt, near +Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, +three of which are of special interest to our investigations.<a name="FNanchor_37" id="FNanchor_37"></a><a href="#Footnote_37" class="fnanchor">37</a> +These comprise a steeplelike structure +labeled "cest li masons don orologe" (this is the +house of a clock), a device including a rope, wheel +and axle (fig. <a href="#fig_20">20</a>), marked "par chu fait om un +angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards +the sun), and a perpetual motion wheel which we +shall reserve for later discussion.</p> + +<p>The clock tower, according to Drover, shows no +place for a dial but suggests the use of bells because +of its open structure, suitable for letting out the +sound. Moreover, he suggests that the delicacy of +the line indicates that it was not really a full-size +steeple but rather a small towerlike structure standing +only a few feet high within the church. There is, +alas, nothing to tell us about the clock it was intended +to house; most probably it was a water clock similar +to that of the illustrated Bible of <i>ca.</i> 1285.</p> + +<p>The drawing of the rope, wheel and axles, for +turning an angel to point towards the sun can have +a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal +axis acts as a windlass connected by the counterpoised +rope to the vertical shaft which it turns, thereby +moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation +was in fact suggested by M. Quicherat,<a name="FNanchor_38" id="FNanchor_38"></a><a href="#Footnote_38" class="fnanchor">38</a> who +first called attention to the Villard album and +pointed out that a leaden angel existed in Chartres +before the fire there in 1836. It is a view also supported +from another drawing in the album which +describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure +on the tail of the bird causes a similar rope mechanism +to operate.</p> + +<p>A quite different interpretation has been suggested +by Fr&eacute;mont;<a name="FNanchor_39" id="FNanchor_39"></a><a href="#Footnote_39" class="fnanchor">39</a> he believes that the wheel may have +acted as a fly-wheel and the ropes and counterpoises, +<span class='pagenum'>108</span>turning first one way then the other acted as a sort +of mechanical escapement. Such an arrangement is +however mechanically impossible without some complicated +free-wheeling device between the drive and +the escapement, and its only effect would be to +oscillate the angel rapidly rather than turn it steadily. +I believe that Fr&eacute;mont, over-anxious to provide a +protoescapement, has done too much violence to the +facts and turned away without good reason from the +more simple and reasonable explanation. It is +nevertheless still possible to adopt this simple interpretation +and yet to have the system as part of a +clock. If the left-hand counterpoise, conveniently +raised higher than that on the right, is considered as +a float fitting into a clepsydra jar, instead of as a +simple weight, one would have a very suitable +automatic system for turning the angel. On this +explanation, the purpose of the wheel would be +merely to provide the manual adjustment necessary +to set the angel from time to time, compensating +for irremediable inaccuracies of the clepsydra.</p> + +<div class="figcenter" style="width: 400px;"><a name="fig_21" id="fig_21" /><img src="images/fig_21.jpg" width="400" height="434" alt= +"Villard's Perpetual Motion Wheel." title="" /> + +<div class="caption">Figure 21.—<span class="smcap">Villard's Perpetual Motion Wheel</span>, +from Lassus (see footnote <a href="#Footnote_37">37</a>).</div></div> + +<p>Having discussed the Villard drawings which are +already cited in horological literature, we must draw +attention to the fact that this medieval architect also +gives an illustration of a perpetual motion wheel. +In this case (fig. <a href="#fig_21">21</a>) it is of the type having weights +at the end of swinging arms, a type that occurs very +frequently at later dates in Europe and is also given +in the Islamic texts. We cannot, in this case, suggest +that drawings of clocks and of perpetual motion +devices occur together by more than a coincidence, +for Villard seems to have been interested in most +sorts of mechanical device. But even this type of +coincidence becomes somewhat striking when repeated +often enough. It seems that each early +mention of "self-moving wheels" occurs in connection +with some sort of clock or mechanized astronomical +device.</p> + +<p>Having now completed a survey of the traditions +of astronomical models, we have seen that many +types of device embodying features later found in +mechanical clocks evolved through various cultures +and flowed into Europe, coming together in a burst +of multifarious activity during the second half of the +13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so +doing examine the importance of perpetual motion +devices, mechanical and magnetic, in the crucial +transition from protoclock to mechanical-escapement +clock.</p> + +<h3><a name="Page_108a" id="Page_108a">Perpetual Motion and the Clock before +de Dondi</a></h3> + +<p>We have already noted, more or less briefly, +several instances of the use of wheels "moving by +themselves" or the use of a fluid for purposes other +than as a motive power. Chronologically arranged, +these are the Indian devices of <i>ca.</i> 1150 or a little +earlier, as those of Riḍwān <i>ca.</i> 1200, that of the +Alfonsine mercury clock, <i>ca.</i> 1272, and the French +Bible illumination of <i>ca.</i> 1285. This strongly suggests +a steady transmission from East to West, and on +the basis of it, we now tentatively propose an additional +step, a transmission from China to India and +perhaps further West, <i>ca.</i> 1100, and possibly reinforced +by further transmissions at later dates.</p> + +<p>One need only assume the existence of vague +traveler's tales about the existence of the 11th-century +Chinese clocks with their astronomical +models and jackwork and with their great wheel, +apparently moving by itself but using water having +no external inlet or outlet. Such a stimulus, acting +as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low +Countries, might easily lead to the re-invention of +just such perpetual-motion wheels as we have already +noted. In many ways, once the idea has been +suggested it is natural to associate such a perpetual +motion with the incessant diurnal rotation of the +heavens. Without some such stimulus however it is +difficult to explain why this association did not occur +earlier, and why, once it comes there seems to be such +a chronological procession from culture to culture.</p> + +<p>We now turn to what is undoubtedly the most +curious part of this story, in which automatically +moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism +and the magnetic compass, another subject with +a singularly troubled historical origin. The key text +in this is the famous <i>Epistle on the magnet</i>, written by +Peter Peregrinus, a Picard, in an army camp at the +Siege of Lucera and dated August 8, 1269.<a name="FNanchor_40" id="FNanchor_40"></a><a href="#Footnote_40" class="fnanchor">40</a> In spite +of the precise dating it is certain that the work was +done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which +must have been written before <i>ca.</i> 1250.<a name="FNanchor_41" id="FNanchor_41"></a><a href="#Footnote_41" class="fnanchor">41</a></p> + +<p><span class='pagenum'>109</span></p><p>The <i>Epistle</i> contains two parts; in the +first there is a general account of magnetism +and the properties of the loadstone, +closing with a discussion "of the +inquiry whence the magnet receives the +natural virtue which it has." Peter +attributed this virtue to a sympathy +with the heavens, proposing to prove +his point by the construction of a +"terrella," a uniform sphere of loadstone +which is to be carefully balanced +and mounted in the manner of an +armillary sphere, with its axis directed +along the polar axis of the diurnal +rotation. He then continues:</p> + +<div class="blockquot"><p>Now if the stone then move according to +the motion of the heavens, rejoice that you +have arrived at a secret marvel. But if not, +let it be ascribed rather to your own want +of skill than to a defect of Nature. But in +this position, or mode of placing, I deem the +virtues of this stone to be properly conserved, +and I believe that in other positions +or parts of the sky its virtue is dulled, rather +than preserved. By means of this instrument +at all events you will be relieved from every +kind of clock (horologium), for by it you will +be able to know the Ascendant at whatever hour you will, +and all other dispositions of the heavens which Astrologers +seek after.</p></div> + +<p>It should be noted that the device is to be mounted +like an astronomical instrument and used like one, +rather than as a time teller, or as a simple demonstration +of magnetism. In the second part of the +<i>Epistle</i> Peter turns to practical instruments, describing +for the first time, the construction of a magnetic compass +consisting of a loadstone or iron needle pivoted +with a casing marked with a scale of degrees. The +third chapter of this section, concluding the <i>Epistle</i>, +then continues with the description of a perpetual +motion wheel, "elaboured with marvellous ingenuity, +in the pursuit of which invention I have seen many +people wandering about, and wearied with manifold +toil. For they did not observe that they could arrive +at the mastery of this by means of the virtue, or +power of this stone."</p> + + +<p class="tb">This tells us incidentally, that the perpetual motion +device was a subject of considerable interest at this +time.<a name="FNanchor_42" id="FNanchor_42"></a><a href="#Footnote_42" class="fnanchor">42</a> Oddly enough, Peter does not now develop +his idea of the terrella, but proceeds to something +quite new, a device (see fig. <a href="#fig_22">22</a>) in which a bar-magnet +loadstone is to be set towards the end of a pivoted +radial arm with a circle fitted on the inside with iron +"gear teeth," the teeth being there not to mesh with +others but to draw the magnet from one to the next, +a little bead providing a counterweight to help the +inertia of rotation carry the magnet from one point +of attraction to the next. It is by no means the sort +of device that one would naturally evolve as a means +of making magnetism work perpetually, and I +suggest that the toothed wheel is another instance +of some vague idea of protoclocks, perhaps that of +Su Sung, being transmitted from the East.</p> + +<div class="figcenter" style="width: 400px;"><a name="fig_22" id="fig_22" /><img src="images/fig_22.jpg" width="400" height="395" alt= +"Magnetic Perpetual Motion Wheel." title="" /> + +<div class="caption">Figure 22.—<span class="smcap">Magnetic Perpetual Motion Wheel</span> +illustrated by Peter Peregrinus; from the edition of +S. P. Thompson (see footnote <a href="#Footnote_40">40</a>).</div></div> + +<p>The work of Peter Peregrinus is cited by Roger +Bacon in his <i>De secretis</i> as well as in the <i>Opus majus</i> +<span class='pagenum'>110</span>and <i>Opus minus</i>. In the first and earliest of these +occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He +says that this cannot be made to move naturally by +any mathematical device, but "a faithful and magnificent +experimentor is straining to make one out of +such material, and by such a device, that it will +revolve naturally with the diurnal heavenly rotation." +He continues with the statement that this possibility +is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that +of the Sun and of the heavens. Only in the <i>Opus +minus</i>, where he repeats reference to this device, does +he finally reveal that it is to be made to work by +means of the loadstone.</p> + +<p>The form of Bacon's reference to Peregrinus is +strongly reminiscent of the statement by Robertus +Anglicus, already mentioned as an indication of +preoccupation with diurnally rotating wheels, at a +date (1271) remarkably close to that of the <i>Epistle</i> +(1269)—so much so that it could well be thought +that the friend to which Peter was writing was either +Robert himself or somebody associated with him, +perhaps at the University of Paris—a natural place +to which the itinerant Peter might communicate +his findings.</p> + +<p>The fundamental question here, of course, is +whether the idea of an automatic astronomical device +was transmitted from Arabic, Indian, or Chinese +sources, or whether it arose quite independently in +this case as a natural concomitant of identifying the +poles of the magnet with the poles of the heavens. +We shall now attempt to show that the history of the +magnetic compass might provide a quite independent +argument in favour of the hypothesis that there was +a 'stimulus' transmission.</p> + + +<h3><a name="Page_110a" id="Page_110a">The Magnetic Compass as a Fellow-traveler +from China</a></h3> + +<p>The elusive history of the magnetic compass has +many points in common with that of the mechanical +clock. Just as we have astronomical models from +the earliest times, so we find knowledge of the loadstone +and some of its properties. Then, parallel to +the development of protoclocks in China throughout +the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory +device and of the (nonmagnetic) south-pointing +chariot, which has been confusedly allied to the +story. Curiously, and perhaps significantly the +Chinese history comes to a head at just the same time +for compasses and clocks, and a prime authority for +the Chinese compass is Shen Kua (1030-1093) who +also appears in connection with the clock of Su Sung, +and who wrote about the mechanized armillary +spheres and other models <i>ca.</i> 1086.</p> + +<p>Another similarity occurs in connection with the +history of the compass in medieval Europe. The +treatise of Peter Peregrinus, already discussed, provides +the first complete account of the magnetic +compass with a pivoted needle and a circular scale, +and this, as we have seen, may be connected with +protoclocks and perpetual-motion devices. There +are several earlier references, however, to the use of +the directive properties of loadstone, mainly for use +in navigation, but these earliest texts have a long +history of erroneous interpretation which is only +recently being cleared away. We know now that +the famous passages in the <i>De naturis rerum</i> and <i>De +utensilibus</i> of Alexander Neckham<a name="FNanchor_43" id="FNanchor_43"></a><a href="#Footnote_43" class="fnanchor">43</a> (<i>ca.</i> 1187) and +a text by Hugues de Berze<a name="FNanchor_44" id="FNanchor_44"></a><a href="#Footnote_44" class="fnanchor">44</a> (after <i>ca.</i> 1204) refer +to nothing more than a floating magnet without +pivot or scale, but using a pointer at right angles to +the magnet, so that it pointed to the east, rather than +the north or south. A similar method is described +(<i>ca.</i> 1200) in a poem by Guyot de Provins, and in a +history of Jerusalem by Jacques de Vitry (1215).<a name="FNanchor_45" id="FNanchor_45"></a><a href="#Footnote_45" class="fnanchor">45</a> +It is of the greatest interest that, once more, all the +evidence seems to be concentrated in France (Neckham +was teaching in Paris) though at an earlier +period than that for the protoclocks.</p> + +<p>The date might suggest the time of the first great +wave of transmissal of learning from Islam, but it is +clear that in this instance, peculiar for that reason, +that Islam learned of the magnetic compass only +after it was already known in the West. In the +earliest Persian record, some anecdotes compiled by +al-'Awfiī <i>ca.</i> 1230,<a name="FNanchor_46" id="FNanchor_46"></a><a href="#Footnote_46" class="fnanchor">46</a> the instrument used by the captain +during a storm at sea has the form of a piece of +hollow iron, shaped like a fish and made to float on +the water after magnetization by rubbing with a +loadstone; the fishlike form is very significant, for +this is distinctly Chinese practice. In a second +Muslim reference, that of Bailak al-Qabājaqī (<i>ca.</i> +1282), the ordinary wet-compass is termed "al-konbas," +another indication that it was foreign to +that language and culture.<a name="FNanchor_47" id="FNanchor_47"></a><a href="#Footnote_47" class="fnanchor">47</a></p> + + +<p><span class='pagenum'>111</span></p> + +<h2>Chronological Chart</h2> + +<hr style="width: 100%; margin-top: 0em; + margin-bottom: 0em;" /> + +<table width="100%" summary="Chronological_Chart" border="0"> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">4th C., B.C. Power gearing</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Classical Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">3rd C., B.C. Archimedes planetarium</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., B.C. Hipparchus Stereographic Projection</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1st C., B.C. Vitruvius hodometer and water clocks</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">65, B.C. (<i>ca.</i>) Antikythera machine</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1st C., A.D. Hero hodometer and water clocks</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., A.D. Salzburg and Vosges anaphoric clocks</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">2nd C., A.D. Chang H&ecirc;ng animated globe hodometer</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> Continuing tradition of animated astronomical models</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent"> 807 Harun-al-Rashid</p></td> +</tr> + + +<tr> +<td class="td100"><p class="indent"> 850 (<i>ca.</i>) Earliest extant astrolobes</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1000 Geared astrolabe of Buruni</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1000 Gerbert astronomical model</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1025 Equatorium text</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">China</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1074 Shen Kua, clocks and magnetic compass</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1080 Su Sung clock built</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1101 Su Sung clock destroyed</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">India</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1100 (<i>ca.</i>) Sūrya Siddhānta animated astronomical models and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1150 (<i>ca.</i>) Siddhānta Siromaṇi animated models and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1150 Saladin clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1187 Neckham on compass</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1198 Jocelin on water clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1200 (<i>ca.</i>) Riḍwān water-clocks, perpetual motion and weight drive</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1206 al-Jazarī clocks, etc.</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1221 Geared astrolabe</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1232 Charlemagne clock</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1243 al-Konbas (compass)</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1245 Villard clocktower, "escapement," perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1267 Villers Abbey clock</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1269 Peregrinus, compass and perpetual motion</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1271 Robertus Anglicus, animated models and "perpetual motion" clock</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Islam</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1272 Alfonsine corpus clock with mercury drum, equatoria</p></td> +</tr> + +<tr> +<td class="td100c"><span class="smcap">Europe</span></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1285 Drover's water clock with wheel and weight drive</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1300 (<i>ca.</i>) French geared astrolabe</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1320 Richard of Wallingford astronomical clock and equatorium</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">1364 de Dondi's astronomical clock with mechanical escapement</p></td> +</tr> + +<tr> +<td class="td100"><p class="indent">later 14th C. Tradition of escapement clocks continues and degenerates into simple time-keepers</p></td> +</tr> + +</table> +<hr style="width: 100%; margin-top: 1em;" /> +<p><span class='pagenum'>112</span></p> + + +<p class="tb">There is therefore reasonable grounds for supporting +the medieval European tradition that the magnetic +compass had first come from China, though one +cannot well admit that the first news of it was brought, +as the legend states, by Marco Polo, when he returned +home in 1260. There might well have been +another wave of interest, giving the impetus to Peter +Peregrinus at this time, but an earlier transmission, +perhaps along the silk road or by travelers in crusades, +must be postulated to account for the evidence +in Europe, <i>ca.</i> 1200. The earlier influx does not play +any great part in our main story; it arrived in Europe +before the transmission of astronomy from Islam had +got under way sufficiently to make protoclocks a +subject of interest. For a second transmission, we +have already seen how the relevant texts seem to +cluster, in France <i>ca.</i> 1270, around a complex in which +the protoclocks seem combined with the ideas of +perpetual motion wheels and with new information +about the magnetic compass.</p> + +<p>The point of this paper is that such a complex +exists, cutting across the histories of the clock, the +various types of astronomical machines, and the +magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending +from China, through India and through Eastern and +Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various +elements make their appearances in different combinations +from place to place, sometimes one may be +dominant, sometimes another may be absent. Only +by treating it as a whole has it been possible to produce +the threads of continuity which will, I hope, +make further research possible, circumventing the +blind alleys found in the past and leading eventually +to a complete understanding of the first complicated +scientific machines.</p> + +<h3>FOOTNOTES:</h3> + +<div class="footnote"><p><a name="Footnote_1" id="Footnote_1"></a><a href="#FNanchor_1"><span class="label">1</span></a> This traditional view is expressed by almost every history +of horology. An ultimate source for many of these has been +the following two classic treatments: J. Beckmann, <i>A history +of inventions and discoveries</i>, 4th ed., London, 1846, vol. 1, pp. +340 ff. A. P. Usher, <i>A history of mechanical inventions</i>, 2nd ed., +Harvard University Press. 1954, pp. 191 ff., 304 ff.</p></div> + +<div class="footnote"><p><a name="Footnote_2" id="Footnote_2"></a><a href="#FNanchor_2"><span class="label">2</span></a> There is a considerable literature dealing with the later +evolution of perpetual motion devices. The most comprehensive +treatment is H. Dircks, <i>Perpetuum mobile</i>, London, 1861; +2nd ser., London, 1870. So far as I know there has not previously +been much discussion of the history of such devices +before the renaissance.</p></div> + +<div class="footnote"><p><a name="Footnote_3" id="Footnote_3"></a><a href="#FNanchor_3"><span class="label">3</span></a> For the early history of gearing in the West see C. Matschoss, +<i>Geschichte des Zahnrades</i>, Berlin, 1940. Also F. M. +Feldhaus, <i>Die geschichtliche Entwicklung des Zahnrades in Theorie +und Praxis</i>, Berlin, 1911.</p></div> + +<div class="footnote"><p><a name="Footnote_4" id="Footnote_4"></a><a href="#FNanchor_4"><span class="label">4</span></a> A general account of these important archaeological objects +will be published by J. Needham, <i>Science and civilisation in China</i>, +Cambridge, 1959(?), vol. 4. The original publications (in +Chinese) are as follows: Wang Chen-to, "Investigations and +reproduction in model form of the south-pointing carriage and +hodometer," <i>National Peiping Academy Historical Journal</i>, 1937, +vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in horological +engineering," <i>Ch'ing-Hua University Engineering Journal</i>, +1956, vol. 4, p. 1.</p></div> + +<div class="footnote"><p><a name="Footnote_5" id="Footnote_5"></a><a href="#FNanchor_5"><span class="label">5</span></a> For illustrations of intermeshing worms in Indian cotton +mills, see Matschoss, <i>op. cit.</i> (footnote <a href="#Footnote_3">3</a>), figs. 5, 6, 7, p. 7.</p></div> + +<div class="footnote"><p><a name="Footnote_6" id="Footnote_6"></a><a href="#FNanchor_6"><span class="label">6</span></a> It is interesting to note that the Chinese hodometer was contemporary +with that of Hero and Vitruvius and very similar in +design. There is no evidence whatsoever upon which to decide +whether there may have been a specific transmission of this invention +or even a "stimulus diffusion."</p></div> + +<div class="footnote"><p><a name="Footnote_7" id="Footnote_7"></a><a href="#FNanchor_7"><span class="label">7</span></a> A summary of the content of the manuscript sources, illustrated +by the original drawings, has been published by H. Alan +Lloyd, <i>Giovanni de Dondi's horological masterpiece, 1364</i>, without +date or imprint (?Lausanne, 1955), 23 pp. It should be remarked +that de Dondi declines to describe the workings of his +crown and foliot escapement (though it is well illustrated) saying +that this is of the "common" variety and if the reader does +not understand such simple things he need not hope to comprehend +the complexities of this mighty clock. But this may be +bravado to quite a large degree.</p></div> + +<div class="footnote"><p><a name="Footnote_8" id="Footnote_8"></a><a href="#FNanchor_8"><span class="label">8</span></a> See, for example, the chronological tables of the 14th +century and the later mentions of clocks in E. Zinner, <i>Aus der +Fr&uuml;hzeit der R&auml;deruhr</i>, Munich, 1954, p. 29 ff. Unfortunately +this very complete treatment tends to confuse the factual and +legendary sources prior to the clock of de Dondi; it also accepts +the very doubtful evidence of the "escapement" drawn by +Villard of Honnecourt (see p. <a href="#fig_20">107</a>). An excellent and fully +illustrated account of monumental astronomical clocks throughout +the world is given by Alfred Ungerer, <i>Les horloges astronomiques</i>, +Strasbourg, 1931, 514 pp. Available accounts of the +development of the planetarium since the middle ages are very +brief and especially weak on the early history: Helmut Werner, +<i>From the Aratus globe to the Zeiss planetarium</i>, Stuttgart, 1957; +C. A. Crommelin, "Planetaria, a historical survey," <i>Antiquarian +Horology</i>, 1955, vol. 1, pp. 70-75.</p></div> + +<div class="footnote"><p><a name="Footnote_9" id="Footnote_9"></a><a href="#FNanchor_9"><span class="label">9</span></a> Derek J. Price, "Clockwork before the clock," <i>Horological +Journal</i>, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31.</p></div> + +<div class="footnote"><p><a name="Footnote_10" id="Footnote_10"></a><a href="#FNanchor_10"><span class="label">10</span></a> For the use of this material I am indebted to my co-authors. I +must also acknowledge thanks to the Cambridge University +Press, which in the near future will be publishing our monograph, +"Heavenly Clockwork." Some of the findings of this +paper are included in shorter form as background material for +that monograph. A brief account of the discovery of this material +has been published by J. Needham, Wang Ling, and +Derek J. Price, "Chinese astronomical clockwork," <i>Nature</i>, +1956, vol. 177, pp. 600-602.</p></div> + +<div class="footnote"><p><a name="Footnote_11" id="Footnote_11"></a><a href="#FNanchor_11"><span class="label">11</span></a> For these translations from classical authors I am indebted +to Professor Loren MacKinney and Miss Harriet Lattin, who +had collected them for a history, now abandoned, of planetariums. +I am grateful for the opportunity of giving them here +the mention they deserve.</p></div> + +<div class="footnote"><p><a name="Footnote_12" id="Footnote_12"></a><a href="#FNanchor_12"><span class="label">12</span></a> A. G. Drachmann, "The plane astrolabe and the anaphoric +clock," <i>Centaurus</i>, 1954, vol. 3, pp. 183-189.</p></div> + +<div class="footnote"><p><a name="Footnote_13" id="Footnote_13"></a><a href="#FNanchor_13"><span class="label">13</span></a> A fuller description of the anaphoric clock and cognate +water-clocks is given by A. G. Drachmann, "Ktesibios, Philon +and Heron," <i>Acta Historica Scientiarum Naturalium et Medicinalium</i>, +Copenhagen, 1948, vol. 4.</p></div> + +<div class="footnote"><p><a name="Footnote_14" id="Footnote_14"></a><a href="#FNanchor_14"><span class="label">14</span></a> First published by O. Benndorf, E. Weiss, and A. Rehm, +<i>Jahreshefte des &ouml;sterreichischen arch&auml;ologischen Institut in Wien</i>, +1903, vol. 6, pp. 32-49. I have given further details of its +construction in <i>A history of technology</i>, ed. Singer, Holmyard, +and Hall, 1957, vol. 3, pp. 604-605.</p></div> + +<div class="footnote"><p><a name="Footnote_15" id="Footnote_15"></a><a href="#FNanchor_15"><span class="label">15</span></a> L. Maxe-Werly, <i>M&eacute;moires de la Soci&eacute;t&eacute; Nationale des Antiquaires +de France</i>, 1887, vol. 48, pp. 170-178.</p></div> + +<div class="footnote"><p><a name="Footnote_16" id="Footnote_16"></a><a href="#FNanchor_16"><span class="label">16</span></a> The first definitive account of the Antikythera machine +was given by Perikles Rediadis in J. Svoronos, <i>Das Athener +Nationalmuseum</i>, Athens, 1908, Textband I, pp. 43-51. +Since then, other photographs (mostly very poor) have appeared, +and an attempt at a reconstruction has been made +by Rear Admiral Jean Theophanidis, <i>Praktika tes Akademias +Athenon</i>, Athens, 1934, vol. 9, pp. 140-149 (in French). I am +deeply grateful to the Director of the Athens National Museum, +M. Karouzos, for providing me with an excellent new set of +photos, from which figures 6-8 are now taken.</p></div> + +<div class="footnote"><p><a name="Footnote_17" id="Footnote_17"></a><a href="#FNanchor_17"><span class="label">17</span></a> H. Diels &Uuml;ber die von Prokop beschriebene Kunstuhr von +Gaza, <i>Abhandlungen, Akademie der Wissenschaften</i>, Berlin, Philos.-Hist. +Klasse, 1917, No. 7.</p></div> + +<div class="footnote"><p><a name="Footnote_18" id="Footnote_18"></a><a href="#FNanchor_18"><span class="label">18</span></a> L. A. Mayer, <i>Islamic astrolabists and their works</i>, Geneva, +1956, p. 62.</p></div> + +<div class="footnote"><p><a name="Footnote_19" id="Footnote_19"></a><a href="#FNanchor_19"><span class="label">19</span></a> The translation which follows is quoted from J. Beckmann, +<i>op. cit.</i> (footnote <a href="#Footnote_1">1</a>), p. 349.</p></div> + +<div class="footnote"><p><a name="Footnote_20" id="Footnote_20"></a><a href="#FNanchor_20"><span class="label">20</span></a> E. Wiedemann, "Ein Instrument das die Bewegung von +Sonne und Mond darstellt, nach al Biruni," <i>Der Islam</i>, 1913, +vol. 4, p. 5.</p></div> + +<div class="footnote"><p><a name="Footnote_21" id="Footnote_21"></a><a href="#FNanchor_21"><span class="label">21</span></a> I acknowledge with thanks to the Curator of that museum +the permission to reproduce photographs of this instrument. It +is item 5 in R. T. Gunther, <i>Astrolabes of the world</i>, Oxford, 1932.</p></div> + +<div class="footnote"><p><a name="Footnote_22" id="Footnote_22"></a><a href="#FNanchor_22"><span class="label">22</span></a> Abulcacim Abnacahm, <i>Libros del saber</i>, edition by Rico y +Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of +the instrument has been very fully discussed by A. Wegener, +"Die astronomischen Werke Alfons X," <i>Bibliotheca Mathematica</i>, +1905, pp. 129-189. A more complete discussion of the +historical evolution of the equatorium is given in Derek J. Price, +<i>The equatorie of the planetis</i>, Cambridge (Eng.), 1955, pp. 119-133.</p></div> + +<div class="footnote"><p><a name="Footnote_23" id="Footnote_23"></a><a href="#FNanchor_23"><span class="label">23</span></a> E. Wiedemann, and F. Hauser, "Uber die Uhren im +Bereich d. islamischen Kultur," <i>Nova Acta; Abhandlungen der +k&ouml;nigliche Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher +zu Halle</i>, 1915, vol. 100, no. 5.</p></div> + +<div class="footnote"><p><a name="Footnote_24" id="Footnote_24"></a><a href="#FNanchor_24"><span class="label">24</span></a> E. Wiedemann, and F. Hauser, <i>Die Uhr des Archimedes und +zwei andere Vorrichtungen</i>, Halle, 1918.</p></div> + +<div class="footnote"><p><a name="Footnote_25" id="Footnote_25"></a><a href="#FNanchor_25"><span class="label">25</span></a> The manuscripts in question are as follows: Gotha, Kat. v. +Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, 288, +no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, no. +1415, Cod. 93 Gol.</p></div> + +<div class="footnote"><p><a name="Footnote_26" id="Footnote_26"></a><a href="#FNanchor_26"><span class="label">26</span></a> H. Schmeller, Beitr&auml;ge zur Geschichte der Technik in der +Antike und bei den Arabern, Erlangen, 1922 (<i>Abhandlungen zur +Geschichte der Naturwissenschaften und der Medizin</i> no. 6).</p></div> + +<div class="footnote"><p><a name="Footnote_27" id="Footnote_27"></a><a href="#FNanchor_27"><span class="label">27</span></a> Once more I am indebted to Professor Loren MacKinney +and Miss Harriet Lattin (see footnote <a href="#Footnote_11">11</a>) for making their +collections on Gerbert available to me.</p></div> + +<div class="footnote"><p><a name="Footnote_28" id="Footnote_28"></a><a href="#FNanchor_28"><span class="label">28</span></a> Item 198 in Gunther, <i>op. cit.</i> (footnote <a href="#Footnote_21">21</a>). I am grateful to +the authorities of that museum for permission to reproduce +photographs of this instrument.</p></div> + +<div class="footnote"><p><a name="Footnote_29" id="Footnote_29"></a><a href="#FNanchor_29"><span class="label">29</span></a> Sotheby and Co., London, sale of March 14, 1957, lot 154. +The outer rim of the rete has 120 teeth.</p></div> + +<div class="footnote"><p><a name="Footnote_30" id="Footnote_30"></a><a href="#FNanchor_30"><span class="label">30</span></a> The Latin text of the treatise on the Albion, has been +transcribed by Rev. H. Salter and published in R. T. Gunther, +<i>Early science in Oxford</i>, Oxford, 1923, vol. 2, pp. 349-370. An +analysis of its design is given in Price, <i>op. cit.</i> (footnote <a href="#Footnote_22">22</a>), pp. +127-130.</p></div> + +<div class="footnote"><p><a name="Footnote_31" id="Footnote_31"></a><a href="#FNanchor_31"><span class="label">31</span></a> Such evidence as there is for the existence and form of the +clock is collected by Gunther, <i>op. cit.</i> (footnote <a href="#Footnote_30">30</a>), p. 49.</p></div> + +<div class="footnote"><p><a name="Footnote_32" id="Footnote_32"></a><a href="#FNanchor_32"><span class="label">32</span></a> I have discussed this new manuscript source in "Two +medieval texts on astronomical clocks," <i>Antiquarian Horology</i>, +1956, vol. 1, no. 10, p. 156. The manuscript in question is +ms. 230/116, Gonville and Caius College, Cambridge, folios +11<sup>v</sup>-14<sup>v</sup> = pp. 31-36.</p></div> + +<div class="footnote"><p><a name="Footnote_33" id="Footnote_33"></a><a href="#FNanchor_33"><span class="label">33</span></a> <i>The Chronicle of Jocelin of Brakelond</i> ..., H. E. Butler (ed.), +London, 1949, p. 106.</p></div> + +<div class="footnote"><p><a name="Footnote_34" id="Footnote_34"></a><a href="#FNanchor_34"><span class="label">34</span></a> C. B. Drover, "A medieval monastic water-clock," <i>Antiquarian +Horology</i>, 1954, vol. 1, no. 5, pp. 54-58, 63. Because +this water clock uses wheels and strikes bells one must reject +the evidence of literary reference, such as by Dante, from +which the mention of wheels and bells have been taken as +positive proof of the existence of mechanical clocks with +mechanical escapements. The to-and-fro motion of the +mechanical clock escapement is quite an impressive feature, +but there seems to be no literary reference to it before the +time of de Dondi.</p></div> + +<div class="footnote"><p><a name="Footnote_35" id="Footnote_35"></a><a href="#FNanchor_35"><span class="label">35</span></a> <i>Annales de la Soci&eacute;t&eacute; Royale d'Arch&eacute;ologie de Bruxelles</i>, 1896, +vol. 1/8, pp. 203-215, 404-451. The translation here is cited +from Drover, <i>op. cit.</i>, (footnote <a href="#Footnote_34">34</a>), p. 56.</p></div> + +<div class="footnote"><p><a name="Footnote_36" id="Footnote_36"></a><a href="#FNanchor_36"><span class="label">36</span></a> L. Thorndike, <i>The sphere of Sacrobosco and its commentators</i>, +Chicago, 1949, pp. 180, 230.</p></div> + +<div class="footnote"><p><a name="Footnote_37" id="Footnote_37"></a><a href="#FNanchor_37"><span class="label">37</span></a> The album was published with facsimiles by J. B. A. +Lassus, 1858. An English edition with facsimiles of 33 of the +41 folios was published by Rev. Robert Willis, Oxford, 1859. +An extensive summary of this section is given, with illustrations, +by J. Drummond Robertson, <i>The evolution of clockwork</i>, London, +1931, pp. 11-15.</p></div> + +<div class="footnote"><p><a name="Footnote_38" id="Footnote_38"></a><a href="#FNanchor_38"><span class="label">38</span></a> M. Jules Quicherat, <i>Revue Arch&egrave;ologique</i>, 1849, vol. 6.</p></div> + +<div class="footnote"><p><a name="Footnote_39" id="Footnote_39"></a><a href="#FNanchor_39"><span class="label">39</span></a> M. C. Fr&eacute;mont. <i>Origine de l'horloge &agrave; poids</i>, Paris, 1915.</p></div> + +<div class="footnote"><p><a name="Footnote_40" id="Footnote_40"></a><a href="#FNanchor_40"><span class="label">40</span></a> For this, I have used and quoted from the very beautiful +edition in English, prepared by Silvanus P. Thompson, London, +Chiswick Press, 1902.</p></div> + +<div class="footnote"><p><a name="Footnote_41" id="Footnote_41"></a><a href="#FNanchor_41"><span class="label">41</span></a> See E. G. R. Taylor, "The South-pointing needle," +<i>Imago Mundi</i>, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2).</p></div> + +<div class="footnote"><p><a name="Footnote_42" id="Footnote_42"></a><a href="#FNanchor_42"><span class="label">42</span></a> I have wondered whether the medieval interest in perpetual +motion could be connected with the use of the "Wheel of +Fortune" in churches as a substitute for bell-ringing on Good +Friday. Unfortunately I can find no evidence for or against +the conjecture.</p></div> + +<div class="footnote"><p><a name="Footnote_43" id="Footnote_43"></a><a href="#FNanchor_43"><span class="label">43</span></a> W. E. May, "Alexander Neckham and the pivoted compass +needle," <i>Journal of the Institute of Navigation</i>, 1955, vol. 8, +no. 3, pp. 283-284.</p></div> + +<div class="footnote"><p><a name="Footnote_44" id="Footnote_44"></a><a href="#FNanchor_44"><span class="label">44</span></a> W. E. May, "Hugues de Berze and the mariner's compass," +<i>The Mariner's Mirror</i>, 1953, vol. 39, no. 2, pp. 103-106.</p></div> + +<div class="footnote"><p><a name="Footnote_45" id="Footnote_45"></a><a href="#FNanchor_45"><span class="label">45</span></a> H. Balmer, <i>Beitr&auml;ge zur Geschichte der Erkenntnis des Erdmagnetismus</i>, +Aarau, 1956, p. 52.</p></div> + +<div class="footnote"><p><a name="Footnote_46" id="Footnote_46"></a><a href="#FNanchor_46"><span class="label">46</span></a> The collection is the <i>Gami 'al Hikajat</i>; the relevant passage +being given in German translation in Balmer. <i>op. cit.</i> (footnote +<a href="#Footnote_45">45</a>), p. 54.</p></div> + +<div class="footnote"><p><a name="Footnote_47" id="Footnote_47"></a><a href="#FNanchor_47"><span class="label">47</span></a> Balmer, op. <i>cit.</i> (footnote <a href="#Footnote_45">45</a>), p. 53.</p></div> + + +<h4>U.S. GOVERNMENT PRINTING OFFICE: 1959</h4> + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001-h.htm or 30001-h.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. + + +</pre> + +</body> +</html> diff --git a/old/30001-h/images/cap_t.png b/old/30001-h/images/cap_t.png Binary files differnew file mode 100644 index 0000000..347a6f0 --- /dev/null +++ b/old/30001-h/images/cap_t.png diff --git a/old/30001-h/images/cover.jpg b/old/30001-h/images/cover.jpg Binary files differnew file mode 100644 index 0000000..91137b2 --- /dev/null +++ b/old/30001-h/images/cover.jpg diff --git a/old/30001-h/images/fig_1.jpg b/old/30001-h/images/fig_1.jpg Binary files differnew file mode 100644 index 0000000..bffd014 --- /dev/null +++ b/old/30001-h/images/fig_1.jpg diff --git a/old/30001-h/images/fig_10.jpg b/old/30001-h/images/fig_10.jpg Binary files differnew file mode 100644 index 0000000..ca2c0ee --- /dev/null +++ b/old/30001-h/images/fig_10.jpg diff --git a/old/30001-h/images/fig_11.jpg b/old/30001-h/images/fig_11.jpg Binary files differnew file mode 100644 index 0000000..6544929 --- /dev/null +++ b/old/30001-h/images/fig_11.jpg diff --git a/old/30001-h/images/fig_12.jpg b/old/30001-h/images/fig_12.jpg Binary files differnew file mode 100644 index 0000000..a4926bf --- /dev/null +++ b/old/30001-h/images/fig_12.jpg diff --git a/old/30001-h/images/fig_13.jpg b/old/30001-h/images/fig_13.jpg Binary files differnew file mode 100644 index 0000000..86d83c1 --- /dev/null +++ b/old/30001-h/images/fig_13.jpg diff --git a/old/30001-h/images/fig_14.jpg b/old/30001-h/images/fig_14.jpg Binary files differnew file mode 100644 index 0000000..8de12ee --- /dev/null +++ b/old/30001-h/images/fig_14.jpg diff --git a/old/30001-h/images/fig_15.jpg b/old/30001-h/images/fig_15.jpg Binary files differnew file mode 100644 index 0000000..d063890 --- /dev/null +++ b/old/30001-h/images/fig_15.jpg diff --git a/old/30001-h/images/fig_16.jpg b/old/30001-h/images/fig_16.jpg Binary files differnew file mode 100644 index 0000000..7764787 --- /dev/null +++ b/old/30001-h/images/fig_16.jpg diff --git a/old/30001-h/images/fig_17.jpg b/old/30001-h/images/fig_17.jpg Binary files differnew file mode 100644 index 0000000..cd30918 --- /dev/null +++ b/old/30001-h/images/fig_17.jpg diff --git a/old/30001-h/images/fig_18.jpg b/old/30001-h/images/fig_18.jpg Binary files differnew file mode 100644 index 0000000..3a2c00f --- /dev/null +++ b/old/30001-h/images/fig_18.jpg diff --git a/old/30001-h/images/fig_19.jpg b/old/30001-h/images/fig_19.jpg Binary files differnew file mode 100644 index 0000000..96939ff --- /dev/null +++ b/old/30001-h/images/fig_19.jpg diff --git a/old/30001-h/images/fig_2.jpg b/old/30001-h/images/fig_2.jpg Binary files differnew file mode 100644 index 0000000..e4aad78 --- /dev/null +++ b/old/30001-h/images/fig_2.jpg diff --git a/old/30001-h/images/fig_20.jpg b/old/30001-h/images/fig_20.jpg Binary files differnew file mode 100644 index 0000000..11caacf --- /dev/null +++ b/old/30001-h/images/fig_20.jpg diff --git a/old/30001-h/images/fig_21.jpg b/old/30001-h/images/fig_21.jpg Binary files differnew file mode 100644 index 0000000..35b6725 --- /dev/null +++ b/old/30001-h/images/fig_21.jpg diff --git a/old/30001-h/images/fig_22.jpg b/old/30001-h/images/fig_22.jpg Binary files differnew file mode 100644 index 0000000..390672a --- /dev/null +++ b/old/30001-h/images/fig_22.jpg diff --git a/old/30001-h/images/fig_3.jpg b/old/30001-h/images/fig_3.jpg Binary files differnew file mode 100644 index 0000000..ea1677b --- /dev/null +++ b/old/30001-h/images/fig_3.jpg diff --git a/old/30001-h/images/fig_4.jpg b/old/30001-h/images/fig_4.jpg Binary files differnew file mode 100644 index 0000000..24a3696 --- /dev/null +++ b/old/30001-h/images/fig_4.jpg diff --git a/old/30001-h/images/fig_4_zoom.jpg b/old/30001-h/images/fig_4_zoom.jpg Binary files differnew file mode 100644 index 0000000..3c4c311 --- /dev/null +++ b/old/30001-h/images/fig_4_zoom.jpg diff --git a/old/30001-h/images/fig_5.jpg b/old/30001-h/images/fig_5.jpg Binary files differnew file mode 100644 index 0000000..e0d4791 --- /dev/null +++ b/old/30001-h/images/fig_5.jpg diff --git a/old/30001-h/images/fig_6.jpg b/old/30001-h/images/fig_6.jpg Binary files differnew file mode 100644 index 0000000..43276ea --- /dev/null +++ b/old/30001-h/images/fig_6.jpg diff --git a/old/30001-h/images/fig_7.jpg b/old/30001-h/images/fig_7.jpg Binary files differnew file mode 100644 index 0000000..5935d35 --- /dev/null +++ b/old/30001-h/images/fig_7.jpg diff --git a/old/30001-h/images/fig_8.jpg b/old/30001-h/images/fig_8.jpg Binary files differnew file mode 100644 index 0000000..3c5110d --- /dev/null +++ b/old/30001-h/images/fig_8.jpg diff --git a/old/30001-h/images/fig_9.jpg b/old/30001-h/images/fig_9.jpg Binary files differnew file mode 100644 index 0000000..fc5b91b --- /dev/null +++ b/old/30001-h/images/fig_9.jpg diff --git a/old/30001.txt b/old/30001.txt new file mode 100644 index 0000000..6cb0421 --- /dev/null +++ b/old/30001.txt @@ -0,0 +1,2353 @@ +The Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass + +Author: Derek J. de Solla Price + +Release Date: September 16, 2009 [EBook #30001] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + + + + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + + + + + + +-----------------------------------------------------+ + | Trancriber's note: | + | | + | Letters enclosed in square brackets represent: | + | [=x] any letter with a macron (straight line above) | + | [x.] any letter with a dot below | + | [.x] any letter with a dot above | + +-----------------------------------------------------+ + + + + + 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. (_S[=u]rya Siddh[=a]nta_, 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 Ri[d.]w[=a]n, _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. + +[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK +of Giovanni de Dondi of Padua, A.D. 1364.] + + + + +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. + +[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing +gearing on the dial for Mercury and escapement crown wheel. Each of the +seven side walls of the structure shown in figure 1 was fitted with a +dial.] + +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 Ri[d.]w[=a]n 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. + +[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450, +showing the degeneration in complexity from that of de Dondi's clock.] + +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 Heng _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 Heng 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. + +[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in +K'ai-feng, _ca._ A.D. 1090, from an original drawing by John +Christiansen. (_Courtesy of Cambridge University Press._)] + + + + +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 Heng. 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] + +[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a +reconstruction (see footnote 14) based on a photograph of the remaining +fragment. (_Courtesy of Oxford University Press._)] + +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. + +[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo +courtesy of National Museum, Athens._)] + +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 deg. in the 45 deg. present). + +[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS. +(_Photo courtesy of National Museum, Athens._)] + +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. + +[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6, +showing gearing. (_Photo courtesy of National Museum, Athens._)] + +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 Lok[=a]loka [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. + + _S[=u]rya Siddh[=a]nta_, xiii, 15-22, + E. Burgess' translation, New Haven, 1860. + +[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION +BY THEOPHANIDIS (see footnote 16).] + + 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 T[.a]la 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. + + _Siddh[=a]nta Siroma[n.]i_, xi, 50-57, L. Wilkinson's + translation, revised by B[.a]p[.u] deva S(h)[.a]stri, + 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 _S[=u]rya Siddh[=a]nta_ 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 _Siddh[=a]nta Siroma[n.]i_ is more certain for we know it was +written in about 1150 by Bh[=a]skara (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 +Bh[=a]skara 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 _S[=u]rya Siddh[=a]nta_, 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 Mu[h.]ammad b. 'Al[=i] b. +Rustum, and repaired and improved by his son, Fakhr ad-d[=i]n +Ri[d.]w[=a]n b. Mu[h.]ammad,[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 + Ri[d.]w[=a]n:[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. + +[Illustration: Figure 10.--CALENDRICAL GEARING DESIGNED BY AL-BIRUNI, +_ca._ A.D. 1000. The gear train count is 40-10+7-59+19-59+24-48. The +gear of 48 therefore makes 19 (annual) rotations while that of 19-59 +shows 118 double lunations of 29+30=59 days. The gear of 40 shows a +(lunar) rotation in exactly 28 days, and the center pinions 7+10 rotate +in exactly one week. After Wiedemann (see footnote 20).] + +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 _Far[=a]s_ 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. + +[Illustration: Figure 11.--GEARED ASTROLABE BY MU[H.]AMMAD B. AB[=I] BAKR +OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum, +London._)] + +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. + +[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11. +The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion +of 8 has been incorrectly replaced by a more modern pinion of 10. The +gear of 48 should make 13 (lunar) rotations while the double gear of +64+64 makes 6 revolutions of double months (of 29-30 days) and the gear +of 60 makes a single turn in the hegiral year of 354 days. (_Photo +courtesy of Science Museum, London._)] + +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, Mu[h.]ammad b. Ab[=i] +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. + +[Illustration: Figure 13.--ASTROLABE CLOCK, REGULATED BY A MERCURY DRUM, +from the Alfonsine _Libros del saber_ (see footnote 22).] + +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. + +[Illustration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after +manuscript cited by Schmeller (see footnote 26).] + +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 Ri[d.]w[=a]n, which we shall next examine. + +[Illustration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the +text cited in figure 14.] + +It is of the greatest interest to our theme that the Islamic +contributions to horology and perpetual motion seem to form a closely +knit corpus. A most important series of horological texts, including +those of Ri[d.]w[=a]n and al-Jazar[=i], have been edited by Wiedemann +and Hauser.[23] Other Islamic texts give versions of the water clocks +and automata of Archimedes and of Hero and Philo of Alexandria.[24] In +at least three cases[25] these texts are found also associated with +texts describing perpetual-motion wheels and other hydraulic devices. +Three manuscripts of this type have been published in German translation +by Schmeller.[26] The devices include a many chambered wheel (see fig. +14) similar to the Alfonsine mercury "escapement," a wheel of slanting +tubes constructed like the noria (see fig. 15), wheels of weights +swinging on arms as described by Villard of Honnecourt, and a remarkable +device which seems to be the earliest known example of a weight drive. +This latter machine is a pump, in which a chain of buckets is used to +raise water by passing over a pulley which is geared to a drum powered +by a falling weight (see fig. 16); perhaps for balance, the whole +arrangement is made in duplicate with common axles for the corresponding +parts. + +[Illustration: Figure 16.--ISLAMIC PUMP POWERED BY A WEIGHT DRIVE, +after the text cited in figure 14.] + +The Islamic tradition of water clocks did not involve the use of gears, +though very occasionally a pair is used to turn power through an angle +when this is dictated by the use of a water wheel in the automata. In +the main, everything is worked by floats and strings or by hydraulic or +pneumatic forces, as in Heros devices. The automata are very elaborate, +with figures of men, monkeys, peacocks, etc., symbolizing the passage of +hours. + + +MEDIEVAL EUROPE + +Echoes from nearly all the developments already noted from other parts +of the world are found to occur in medieval Europe, often coming +through channels of communication more precisely determinable than +those hitherto mentioned. Before the influx of Islamic learning at the +time of transmission of the Toledo Tables (12th century) and the +Alfonsine Tables (which reached Paris _ca._ 1292), there are occasional +references to the most primitive mechanized "visual aids" in astronomy. + +The most famous of these occurs in an historical account by Richer of +Rheims about his teacher Gerbert (born 946, later Pope Sylvester II, +990-1003). Several instruments made by Gerbert are described in detail; +he includes a fine celestial globe made of wood covered with horsehide +and having the stars and lines painted in color, and an armillary sphere +having sighting tubes similar to those always found on Chinese +instruments but never on the Ptolemaic variety. Lastly, he cites "the +construction of a sphere, most suitable for recognizing the planets," +but unfortunately it is not clear from the description whether or not +the model planets were actually to be animated mechanically. The text +runs:[27] + + Within this oblique circle (the zodiac on the ecliptic of + the globe) he hung the circles of the wandering stars (the + planets) with marvellous ingenuity, whose orbits, heights + and even the distance from each other he demonstrated to + his pupils most effectually. Just how he accomplished this + it is unsuitable to enter into here because of its extent + lest we should appear to be wandering from our main theme. + +Thus, although there is a hint of mechanical complexity, there is really +no justification for such an assumption; the description might well +imply only a zodiac band on which the orbits of the planets were +painted. On the other hand it is not inconceivable that Gerbert could +have learned something of Islamic and other extra-European traditions +during his period of study with the Bishop of Barcelona--a traveling +scholarship that seems to have had many repercussions on the whole field +of European scholarship. + +Once the floodgates of Arabic learning were opened, a stream of +mechanized astronomical models poured into Europe. Astrolabes and +equatoria rapidly became very popular, mainly through the reason for +which they had been first devised, the avoidance of tedious written +computation. Many medieval astrolabes have survived, and at least three +medieval equatoria are known. Chaucer is well known for his treatise on +the astrolabe; a manuscript in Cambridge, containing a companion +treatise on the equatorium, has been tentatively suggested by the +present author as also being the work of Chaucer and the only piece +written in his own hand. + +The geared astrolabe of al-Biruni is another type of protoclock to have +been transmitted. A specimen in the Science Museum, London,[28] though +unfortunately now incomplete, has a very sophistocated arrangement of +gears for moving pointers to indicate the correct relative positions and +movements of the sun and moon (see figs. 17 and 18). Like the earlier +Muslim example it contains wheels with odd numbers of gear teeth (14, +27, 39); however, the teeth are no longer equilateral in shape, but +approximate a more modern slightly rounded form. This example is French +and appears to date from _ca._ 1300. Another Gothic astrolabe with a +similar gear ring on the rete, said to date from _ca._ 1400 (it could +well be much earlier) is now in the Billmeier collection (London).[29] + +Turning from the mechanized astrolabe to the mechanized equatorium, we +find the work of Richard of Wallingford (1292?-1336) of the greatest +interest as providing an immediate precursor to that of de Dondi. He +was the son of an ingenious blacksmith, making his way to Merton +College, Oxford, then the most active and original school of astronomy +in Europe, and winning later distinction as Abbot of St. Albans. A text +by him, dated 1326-27, described in detail the construction of a great +equatorium, more exact and much more elaborate than any that had gone +before.[30] Nevertheless it is evidently a normal manually operated +device like all the others. In addition to this instrument, Richard is +said to have constructed _ca._ 1320, a fine planetary clock for his +Abbey.[31] Bale, who seems to have seen it, regarded it as without rival +in Europe, and the greatest curiosity of his time. Unfortunately, the +issue was confused by Leland, who identified it as the Albion (_i.e._, +all-by one), the name Richard gives to his manual equatorium. This clock +was indeed so complex that Edward III censured the Abbot for spending so +much money on it, but Richard replied that after his death nobody would +be able to make such a thing again. He is said to have left a text +describing the construction of this clock, but the absence of such a +work has led many modern writers to support Leland's identification and +suppose that the device was not a mechanical clock. + +[Illustration: Figure 17.--FRENCH GEARED ASTROLABE OF TREFOIL GOTHIC +DESIGN, _ca._ A.D. 1300. The gearing on the pointer is, from the +center: (32)/14-45+27-39, the last meshing with a concave annular gear +of 180 teeth around the rim of the rete of the astrolabe. A second +pointer, geared to this so as to follow the Moon, seems to be lacking. +(_Photo courtesy of Science Museum. London._)] + +[Illustration: Figure 18.--GEAR TRAIN OF POINTER in figure 17. (_Photo +courtesy of Science Museum, London._)] + +A corrective for this view is to be had from a St. Albans manuscript +(now at Gonville and Caius College, Cambridge) that described the +methods for setting out toothed wheels for an astronomical horologium +designed to show the motions of the planets. Although the manuscript +copy is to be dated _ca._ 1340, it clearly indicates that a geared +planetary device was known in St. Albans at an early date, and it is +reasonable to suppose that this was in fact the machine made by Richard +of Wallingford. Unfortunately the text does not appear to give any +relevant information about the presence of an escapement or any other +regulatory device, nor does it mention the source of power.[32] Now a +geared version of the Albion would appear to correspond very closely +indeed to the dial-work which forms the greater part of the de Dondi +clock, and for this reason we suggest now that the two clocks were very +closely related in other ways too. This, circumstantial though it be, is +evidence for thinking that the weight drive and some form of escapement +were known to Richard of Wallingford, _ca._ 1320. It would narrow the +gap between the clock and the protoclocks to less than half a century, +perhaps a single generation, in the interval _ca._ 1285-1320. In this +connection it may be of interest that Richard of Wallingford knew only +the Toledo tables corpus, that of the Alfonsine school did not arrive in +England until after his death. + +There are, of course, many literary references to the water-clocks in +medieval literature. In fact most of these are from quotations which +have often been produced erroneously in the history of the mechanical +clock, thereby providing many misleading starts for that history, as +noted previously in the discussion of the horologium. There are however +enough mentions to make it certain that water clocks of some sort were +in use, especially for ecclesiastic purposes, from the end of the 12th +century onwards. Thus, Jocelin of Brakelond tells of a fire in the Abbey +Church of Bury St. Edmunds in the year 1198.[33] The relics would have +been destroyed during the night, but just at the crucial moment the +clock bell sounded for matins and the master of the vestry sounded the +alarm. On this "the young men amongst us ran to get water, some to the +well and others to the clock"--probably the sole occasion on which a +clock served as a fire hydrant. + +It seems probable that some of these water clocks could have been simple +drip clepsydras, with perhaps a striking arrangement added. A most +fortunate discovery by Drover has now brought to light a manuscript +illumination that shows that these water clocks, at least by _ca,_ 1285, +had become more complex and were rather similar in appearance to the +Alfonsine mercury drum.[34] The illustration (fig. 19) is from a +moralized Bible written in northern France, and accompanies the passage +where King Hezekiah is given a sign by the Lord, the sun being moved +back ten steps of the clock. The picture clearly shows the central water +wheel and below it a dog's head spout gushing water into a bucket +supported by chains, with a (weight?) cord running behind. Above the +wheel is a carillon of bells, and to one side a rosette which might be a +fly or a model sun. The wheel appears to have 15 compartments, each with +a central hole (perhaps similar to that in the Alfonsine clock) and it +is supported on a square axle by a bracket, the axle being wedged in the +traditional fashion. The projections at the edge of the wheel might be +gear teeth, but more likely they are used only for tripping the striking +mechanism. If it were not for the running water spout it would be very +close to the Alfonsine model; but with this evidence it seems impossible +to arrive at a clear mechanical interpretation. + +From the adjacent region there is another account of a striking water +clock, the evidence being inscriptions on slates, discovered in Villers +Abbey near Brussels;[35] these may be closely dated as 1267 or 1268 and +provide the remains of a memorandum for the sacrist and his assistants +in charge of the clock. + + Always set the clock, however long you may delay on [the + letter "A"] afterwards you shall pour water from the + little pot (pottulo) that is there, into the reservoir + (cacabum) until it reaches the prescribed level, and you + must do the same when you set [the clock] after compline + so that you may sleep soundly. + +A quite different sort of evidence is to be had from the writings of +Robertus Anglicus in 1271 where one gets the impression that just at +this time there was active interest in the attempt to make a +weight-driven anaphoric clock and to regulate its motion by some +unstated method so that it would keep time with the diurnal rotation of +the heavens:[36] + + Nor it is possible for any clock to follow the judgment of + astronomy with complete accuracy. Yet clockmakers + (artifices horologiorum) are trying to make a wheel + (circulum) which will make one complete revolution for + every one of the equinoctial circle, but they cannot quite + perfect their work. But if they could, it would be a + really accurate clock (horologium verax valde) and worth + more than an astrolabe or other astronomical instrument + for reckoning the hours, if one knew how to do this + according to the method aforesaid. The method of making + such a clock would be this, that a man make a disc + (circulum) of uniform weight in every part so far as could + possibly be done. Then a lead weight should be hung from + the axis of that wheel (axi ipsius rote) and this weight + would move that wheel so that it would complete one + revolution from sunrise to sunrise, minus as much time as + about one degree rises according to an approximately + correct estimate. For from sunrise to sunrise, the whole + equinoctial rises, and about one degree more, through + which degree the sun moves against the motion of the + firmament in the course of a natural day. Moreover, this + could be done more accurately if an astrolabe were + constructed with a network on which the entire equinoctial + circle was divided up. + +[Illustration: Figure 19.--MANUSCRIPT ILLUMINATION OF A MEDIEVAL +WATERCLOCK, showing a partitioned wheel, a weight drive, and a carillion +for striking. From Drover (see footnote 34).] + +The text then continues with technical astronomical details of the +slight difference between the rate of rotation of the sun and of the +fixed stars (because of the annual rotation of the sun amongst the +stars) but it gives no indication of any regulatory device. Again it +should be noted, this source comes from France; Robertus, though of +English origin, apparently being then a lecturer either at the +University of Paris or at that of Montpellier. The date of this passage, +1271, has been taken as a _terminus post quem_ for the invention of the +mechanical clock. In the next section we shall describe the text of +Peter Peregrinus, very close to this in place and date, which describes +just such a machine, conflating it with accounts of an armillary sphere, +perpetual motion, and the magnetic compass--so bringing all these +threads together for the first time in Europe. + +[Illustration: Figure 20.--ARRANGEMENT FOR TURNING A FIGURE OF AN ANGEL. +It has been alleged that this drawing by Villard represents an +escapement. After Lassus (see footnote 37).] + +We have reserved to the last one section of evidence which may or may +not be misleading, the famous notebook of Villard (Wilars) of +Honnecourt, near Cambrai. The album, attributed to the period 1240-1251, +contains many drawings with short annotations, three of which are of +special interest to our investigations.[37] These comprise a steeplelike +structure labeled "cest li masons don orologe" (this is the house of a +clock), a device including a rope, wheel and axle (fig. 20), marked "par +chu fait om un angle tenir son doit ades vers le solel" (by this means +an angel is made to keep his finger directed towards the sun), and a +perpetual motion wheel which we shall reserve for later discussion. + +The clock tower, according to Drover, shows no place for a dial but +suggests the use of bells because of its open structure, suitable for +letting out the sound. Moreover, he suggests that the delicacy of the +line indicates that it was not really a full-size steeple but rather a +small towerlike structure standing only a few feet high within the +church. There is, alas, nothing to tell us about the clock it was +intended to house; most probably it was a water clock similar to that of +the illustrated Bible of _ca._ 1285. + +The drawing of the rope, wheel and axles, for turning an angel to point +towards the sun can have a simple explanation or a more complicated one. +If taken at its face value the wheel on its horizontal axis acts as a +windlass connected by the counterpoised rope to the vertical shaft which +it turns, thereby moving (by hand) the figure of an angel (not shown) +fixed to the top of this latter shaft. Such an explanation was in fact +suggested by M. Quicherat,[38] who first called attention to the Villard +album and pointed out that a leaden angel existed in Chartres before the +fire there in 1836. It is a view also supported from another drawing in +the album which describes an eagle whose head is made to turn towards +the deacon when he reads the Gospel. Slight pressure on the tail of the +bird causes a similar rope mechanism to operate. + +A quite different interpretation has been suggested by Fremont;[39] he +believes that the wheel may have acted as a fly-wheel and the ropes and +counterpoises, turning first one way then the other acted as a sort of +mechanical escapement. Such an arrangement is however mechanically +impossible without some complicated free-wheeling device between the +drive and the escapement, and its only effect would be to oscillate the +angel rapidly rather than turn it steadily. I believe that Fremont, +over-anxious to provide a protoescapement, has done too much violence to +the facts and turned away without good reason from the more simple and +reasonable explanation. It is nevertheless still possible to adopt this +simple interpretation and yet to have the system as part of a clock. If +the left-hand counterpoise, conveniently raised higher than that on the +right, is considered as a float fitting into a clepsydra jar, instead of +as a simple weight, one would have a very suitable automatic system for +turning the angel. On this explanation, the purpose of the wheel would +be merely to provide the manual adjustment necessary to set the angel +from time to time, compensating for irremediable inaccuracies of the +clepsydra. + +[Illustration: Figure 21.--VILLARD'S PERPETUAL MOTION WHEEL, from Lassus +(see footnote 37).] + +Having discussed the Villard drawings which are already cited in +horological literature, we must draw attention to the fact that this +medieval architect also gives an illustration of a perpetual motion +wheel. In this case (fig. 21) it is of the type having weights at the +end of swinging arms, a type that occurs very frequently at later dates +in Europe and is also given in the Islamic texts. We cannot, in this +case, suggest that drawings of clocks and of perpetual motion devices +occur together by more than a coincidence, for Villard seems to have +been interested in most sorts of mechanical device. But even this type +of coincidence becomes somewhat striking when repeated often enough. It +seems that each early mention of "self-moving wheels" occurs in +connection with some sort of clock or mechanized astronomical device. + +Having now completed a survey of the traditions of astronomical models, +we have seen that many types of device embodying features later found in +mechanical clocks evolved through various cultures and flowed into +Europe, coming together in a burst of multifarious activity during the +second half of the 13th century, notably in the region of France. We +must now attempt to fill the residual gap, and in so doing examine the +importance of perpetual motion devices, mechanical and magnetic, in the +crucial transition from protoclock to mechanical-escapement clock. + + + + +Perpetual Motion and the Clock before de Dondi + +We have already noted, more or less briefly, several instances of the +use of wheels "moving by themselves" or the use of a fluid for purposes +other than as a motive power. Chronologically arranged, these are the +Indian devices of _ca._ 1150 or a little earlier, as those of Ri[d.]w[=a]n +_ca._ 1200, that of the Alfonsine mercury clock, _ca._ 1272, and the +French Bible illumination of _ca._ 1285. This strongly suggests a steady +transmission from East to West, and on the basis of it, we now +tentatively propose an additional step, a transmission from China to +India and perhaps further West, _ca._ 1100, and possibly reinforced by +further transmissions at later dates. + +One need only assume the existence of vague traveler's tales about the +existence of the 11th-century Chinese clocks with their astronomical +models and jackwork and with their great wheel, apparently moving by +itself but using water having no external inlet or outlet. Such a +stimulus, acting as it did on a later occasion when Galileo received +word of the invention of the telescope in the Low Countries, might +easily lead to the re-invention of just such perpetual-motion wheels as +we have already noted. In many ways, once the idea has been suggested it +is natural to associate such a perpetual motion with the incessant +diurnal rotation of the heavens. Without some such stimulus however it +is difficult to explain why this association did not occur earlier, and +why, once it comes there seems to be such a chronological procession +from culture to culture. + +We now turn to what is undoubtedly the most curious part of this story, +in which automatically moving astronomical models and perpetual motion +wheels are linked with the earliest texts on magnetism and the magnetic +compass, another subject with a singularly troubled historical origin. +The key text in this is the famous _Epistle on the magnet_, written by +Peter Peregrinus, a Picard, in an army camp at the Siege of Lucera and +dated August 8, 1269.[40] In spite of the precise dating it is certain +that the work was done long before, for it is quoted unmistakably by +Roger Bacon in at least three places, one of which must have been +written before _ca._ 1250.[41] + +The _Epistle_ contains two parts; in the first there is a general +account of magnetism and the properties of the loadstone, closing with a +discussion "of the inquiry whence the magnet receives the natural virtue +which it has." Peter attributed this virtue to a sympathy with the +heavens, proposing to prove his point by the construction of a +"terrella," a uniform sphere of loadstone which is to be carefully +balanced and mounted in the manner of an armillary sphere, with its axis +directed along the polar axis of the diurnal rotation. He then +continues: + + Now if the stone then move according to the motion of the + heavens, rejoice that you have arrived at a secret marvel. + But if not, let it be ascribed rather to your own want of + skill than to a defect of Nature. But in this position, or + mode of placing, I deem the virtues of this stone to be + properly conserved, and I believe that in other positions + or parts of the sky its virtue is dulled, rather than + preserved. By means of this instrument at all events you + will be relieved from every kind of clock (horologium), + for by it you will be able to know the Ascendant at + whatever hour you will, and all other dispositions of the + heavens which Astrologers seek after. + +It should be noted that the device is to be mounted like an astronomical +instrument and used like one, rather than as a time teller, or as a +simple demonstration of magnetism. In the second part of the _Epistle_ +Peter turns to practical instruments, describing for the first time, the +construction of a magnetic compass consisting of a loadstone or iron +needle pivoted with a casing marked with a scale of degrees. The third +chapter of this section, concluding the _Epistle_, then continues with +the description of a perpetual motion wheel, "elaboured with marvellous +ingenuity, in the pursuit of which invention I have seen many people +wandering about, and wearied with manifold toil. For they did not +observe that they could arrive at the mastery of this by means of the +virtue, or power of this stone." + +This tells us incidentally, that the perpetual motion device was a +subject of considerable interest at this time.[42] Oddly enough, Peter +does not now develop his idea of the terrella, but proceeds to something +quite new, a device (see fig. 22) in which a bar-magnet loadstone is to +be set towards the end of a pivoted radial arm with a circle fitted on +the inside with iron "gear teeth," the teeth being there not to mesh +with others but to draw the magnet from one to the next, a little bead +providing a counterweight to help the inertia of rotation carry the +magnet from one point of attraction to the next. It is by no means the +sort of device that one would naturally evolve as a means of making +magnetism work perpetually, and I suggest that the toothed wheel is +another instance of some vague idea of protoclocks, perhaps that of Su +Sung, being transmitted from the East. + +[Illustration: Figure 22.--MAGNETIC PERPETUAL MOTION WHEEL illustrated +by Peter Peregrinus; from the edition of S. P. Thompson (see footnote +40).] + +The work of Peter Peregrinus is cited by Roger Bacon in his _De +secretis_ as well as in the _Opus majus_ and _Opus minus_. In the first +and earliest of these occurs a description, taken from Ptolemy, of the +construction of the (observing) armillary sphere. He says that this +cannot be made to move naturally by any mathematical device, but "a +faithful and magnificent experimentor is straining to make one out of +such material, and by such a device, that it will revolve naturally with +the diurnal heavenly rotation." He continues with the statement that +this possibility is also suggested by the fact that the motions of +comets, of tides, and of certain planets also follow that of the Sun and +of the heavens. Only in the _Opus minus_, where he repeats reference to +this device, does he finally reveal that it is to be made to work by +means of the loadstone. + +The form of Bacon's reference to Peregrinus is strongly reminiscent of +the statement by Robertus Anglicus, already mentioned as an indication +of preoccupation with diurnally rotating wheels, at a date (1271) +remarkably close to that of the _Epistle_ (1269)--so much so that it +could well be thought that the friend to which Peter was writing was +either Robert himself or somebody associated with him, perhaps at the +University of Paris--a natural place to which the itinerant Peter might +communicate his findings. + +The fundamental question here, of course, is whether the idea of an +automatic astronomical device was transmitted from Arabic, Indian, or +Chinese sources, or whether it arose quite independently in this case as +a natural concomitant of identifying the poles of the magnet with the +poles of the heavens. We shall now attempt to show that the history of +the magnetic compass might provide a quite independent argument in +favour of the hypothesis that there was a 'stimulus' transmission. + + + + +The Magnetic Compass as a Fellow-traveler from China + +The elusive history of the magnetic compass has many points in common +with that of the mechanical clock. Just as we have astronomical models +from the earliest times, so we find knowledge of the loadstone and some +of its properties. Then, parallel to the development of protoclocks in +China throughout the middle ages, we have the evidence analyzed by +Needham, showing the use of the magnet as a divinatory device and of the +(nonmagnetic) south-pointing chariot, which has been confusedly allied +to the story. Curiously, and perhaps significantly the Chinese history +comes to a head at just the same time for compasses and clocks, and a +prime authority for the Chinese compass is Shen Kua (1030-1093) who also +appears in connection with the clock of Su Sung, and who wrote about the +mechanized armillary spheres and other models _ca._ 1086. + +Another similarity occurs in connection with the history of the compass +in medieval Europe. The treatise of Peter Peregrinus, already discussed, +provides the first complete account of the magnetic compass with a +pivoted needle and a circular scale, and this, as we have seen, may be +connected with protoclocks and perpetual-motion devices. There are +several earlier references, however, to the use of the directive +properties of loadstone, mainly for use in navigation, but these +earliest texts have a long history of erroneous interpretation which is +only recently being cleared away. We know now that the famous passages +in the _De naturis rerum_ and _De utensilibus_ of Alexander Neckham[43] +(_ca._ 1187) and a text by Hugues de Berze[44] (after _ca._ 1204) refer +to nothing more than a floating magnet without pivot or scale, but using +a pointer at right angles to the magnet, so that it pointed to the east, +rather than the north or south. A similar method is described (_ca._ +1200) in a poem by Guyot de Provins, and in a history of Jerusalem by +Jacques de Vitry (1215).[45] It is of the greatest interest that, once +more, all the evidence seems to be concentrated in France (Neckham was +teaching in Paris) though at an earlier period than that for the +protoclocks. + +The date might suggest the time of the first great wave of transmissal +of learning from Islam, but it is clear that in this instance, peculiar +for that reason, that Islam learned of the magnetic compass only after +it was already known in the West. In the earliest Persian record, some +anecdotes compiled by al-'Awfi[=i] _ca._ 1230,[46] the instrument used +by the captain during a storm at sea has the form of a piece of hollow +iron, shaped like a fish and made to float on the water after +magnetization by rubbing with a loadstone; the fishlike form is very +significant, for this is distinctly Chinese practice. In a second Muslim +reference, that of Bailak al-Qab[=a]jaq[=i] (_ca._ 1282), the ordinary +wet-compass is termed "al-konbas," another indication that it was +foreign to that language and culture.[47] + + +Chronological Chart + +------------------------------------------------------------------------ + + CHINA + + 4th C., B.C. Power gearing + + CLASSICAL EUROPE + + 3rd C., B.C. Archimedes planetarium + 2nd C., B.C. Hipparchus Stereographic Projection + 1st C., B.C. Vitruvius hodometer and water clocks + 65, B.C. (_ca._) Antikythera machine + 1st C., A.D. Hero hodometer and water clocks + 2nd C., A.D. Salzburg and Vosges anaphoric clocks + + CHINA + + 2nd C., A.D. Chang Heng animated globe hodometer + Continuing tradition of animated astronomical models + 725 Invention of Chinese escapement by I-Hsing and Liang Ling-tsan + + ISLAM + + 807 Harun-al-Rashid + 850 (_ca._) Earliest extant astrolabes + 1000 Geared astrolabe of al-Biruni + + EUROPE + + 1000 Gerbert astronomical model + + ISLAM + + 1025 Equatorium text + + CHINA + + 1074 Shen Kua, clocks and magnetic compass + 1080 Su Sung clock built + 1101 Su Sung clock destroyed + + INDIA + + 1100 (_ca._) S[=u]rya Siddh[=a]nta animated astronomical models + and perpetual motion + 1150 (_ca._) Siddh[=a]nta Siromani animated models and perpetual + motion + + ISLAM + + 1150 Saladin clock + + EUROPE + + 1187 Neckham on compass + 1198 Jocelin on water clock + + ISLAM + + 1200 (_ca._) Ri[d.]w[=a]n water-clocks, perpetual motion + and weight drive + 1206 al-Jazar[=i] clocks, etc. + 1221 Geared astrolabe + 1232 Charlemagne clock + 1243 al-Konbas (compass) + + EUROPE + + 1245 Villard clocktower, "escapement," perpetual motion + 1267 Villers Abbey clock + 1269 Peregrinus, compass and perpetual motion + 1271 Robertus Anglicus, animated models and "perpetual motion" clock + + ISLAM + + 1272 Alfonsine corpus clock with mercury drum, equatoria + + EUROPE + + 1285 Drover's water clock with wheel and weight drive + 1300 (_ca._) French geared astrolabe + 1320 Richard of Wallingford astronomical clock and equatorium + 1364 de Dondi's astronomical clock with mechanical escapement + later 14th C. Tradition of escapement clocks continues + and degenerates into simple time-keepers +------------------------------------------------------------------------ + +There is therefore reasonable grounds for supporting the medieval +European tradition that the magnetic compass had first come from China, +though one cannot well admit that the first news of it was brought, as +the legend states, by Marco Polo, when he returned home in 1260. There +might well have been another wave of interest, giving the impetus to +Peter Peregrinus at this time, but an earlier transmission, perhaps +along the silk road or by travelers in crusades, must be postulated to +account for the evidence in Europe, _ca._ 1200. The earlier influx does +not play any great part in our main story; it arrived in Europe before +the transmission of astronomy from Islam had got under way sufficiently +to make protoclocks a subject of interest. For a second transmission, we +have already seen how the relevant texts seem to cluster, in France +_ca._ 1270, around a complex in which the protoclocks seem combined with +the ideas of perpetual motion wheels and with new information about the +magnetic compass. + +The point of this paper is that such a complex exists, cutting across +the histories of the clock, the various types of astronomical machines, +and the magnetic compass, and including the origin of "self-moving +wheels." It seems to trace a path extending from China, through India +and through Eastern and Western Islam, ending in Europe in the Middle +Ages. This path is not a simple one, for the various elements make their +appearances in different combinations from place to place, sometimes one +may be dominant, sometimes another may be absent. Only by treating it as +a whole has it been possible to produce the threads of continuity which +will, I hope, make further research possible, circumventing the blind +alleys found in the past and leading eventually to a complete +understanding of the first complicated scientific machines. + + + FOOTNOTES: + + [1] This traditional view is expressed by almost every history + of horology. An ultimate source for many of these has been the + following two classic treatments: J. Beckmann, _A history of + inventions and discoveries_, 4th ed., London, 1846, vol. 1, pp. + 340 ff. A. P. Usher, _A history of mechanical inventions_, 2nd + ed., Harvard University Press. 1954, pp. 191 ff., 304 ff. + + [2] There is a considerable literature dealing with the later + evolution of perpetual motion devices. The most comprehensive + treatment is H. Dircks, _Perpetuum mobile_, London, 1861; 2nd + ser., London, 1870. So far as I know there has not previously + been much discussion of the history of such devices before the + renaissance. + + [3] For the early history of gearing in the West see C. + Matschoss, _Geschichte des Zahnrades_, Berlin, 1940. Also F. M. + Feldhaus, _Die geschichtliche Entwicklung des Zahnrades in + Theorie und Praxis_, Berlin, 1911. + + [4] A general account of these important archaeological objects + will be published by J. Needham, _Science and civilisation in + China_, Cambridge, 1959(?), vol. 4. The original publications + (in Chinese) are as follows: Wang Chen-to, "Investigations and + reproduction in model form of the south-pointing carriage and + hodometer," _National Peiping Academy Historical Journal_, + 1937, vol. 3, p. 1. Liu Hsien-chou, "Chinese inventions in + horological engineering," _Ch'ing-Hua University Engineering + Journal_, 1956, vol. 4, p. 1. + + [5] For illustrations of intermeshing worms in Indian cotton + mills, see Matschoss, _op. cit._ (footnote 3), figs. 5, 6, 7, + p. 7. + + [6] It is interesting to note that the Chinese hodometer was + contemporary with that of Hero and Vitruvius and very similar + in design. There is no evidence whatsoever upon which to decide + whether there may have been a specific transmission of this + invention or even a "stimulus diffusion." + + [7] A summary of the content of the manuscript sources, + illustrated by the original drawings, has been published by H. + Alan Lloyd, _Giovanni de Dondi's horological masterpiece, + 1364_, without date or imprint (?Lausanne, 1955), 23 pp. It + should be remarked that de Dondi declines to describe the + workings of his crown and foliot escapement (though it is well + illustrated) saying that this is of the "common" variety and if + the reader does not understand such simple things he need not + hope to comprehend the complexities of this mighty clock. But + this may be bravado to quite a large degree. + + [8] See, for example, the chronological tables of the 14th + century and the later mentions of clocks in E. Zinner, _Aus der + Fruehzeit der Raederuhr_, Munich, 1954, p. 29 ff. Unfortunately + this very complete treatment tends to confuse the factual and + legendary sources prior to the clock of de Dondi; it also + accepts the very doubtful evidence of the "escapement" drawn by + Villard of Honnecourt (see p. 107). An excellent and fully + illustrated account of monumental astronomical clocks + throughout the world is given by Alfred Ungerer, _Les horloges + astronomiques_, Strasbourg, 1931, 514 pp. Available accounts of + the development of the planetarium since the middle ages are + very brief and especially weak on the early history: Helmut + Werner, _From the Aratus globe to the Zeiss planetarium_, + Stuttgart, 1957; C. A. Crommelin, "Planetaria, a historical + survey," _Antiquarian Horology_, 1955, vol. 1, pp. 70-75. + + [9] Derek J. Price, "Clockwork before the clock," _Horological + Journal_, 1955, vol. 97, p. 810, and 1956, vol. 98, p. 31. + + [10] For the use of this material I am indebted to my + co-authors. I must also acknowledge thanks to the Cambridge + University Press, which in the near future will be publishing + our monograph, "Heavenly Clockwork." Some of the findings of + this paper are included in shorter form as background material + for that monograph. A brief account of the discovery of this + material has been published by J. Needham, Wang Ling, and Derek + J. Price, "Chinese astronomical clockwork," _Nature_, 1956, + vol. 177, pp. 600-602. + + [11] For these translations from classical authors I am + indebted to Professor Loren MacKinney and Miss Harriet Lattin, + who had collected them for a history, now abandoned, of + planetariums. I am grateful for the opportunity of giving them + here the mention they deserve. + + [12] A. G. Drachmann, "The plane astrolabe and the anaphoric + clock," _Centaurus_, 1954, vol. 3, pp. 183-189. + + [13] A fuller description of the anaphoric clock and cognate + water-clocks is given by A. G. Drachmann, "Ktesibios, Philon + and Heron," _Acta Historica Scientiarum Naturalium et + Medicinalium_, Copenhagen, 1948, vol. 4. + + [14] First published by O. Benndorf, E. Weiss, and A. Rehm, + _Jahreshefte des oesterreichischen archaeologischen Institut in + Wien_, 1903, vol. 6, pp. 32-49. I have given further details of + its construction in _A history of technology_, ed. Singer, + Holmyard, and Hall, 1957, vol. 3, pp. 604-605. + + [15] L. Maxe-Werly, _Memoires de la Societe Nationale des + Antiquaires de France_, 1887, vol. 48, pp. 170-178. + + [16] The first definitive account of the Antikythera machine + was given by Perikles Rediadis in J. Svoronos, _Das Athener + Nationalmuseum_, Athens, 1908, Textband I, pp. 43-51. Since + then, other photographs (mostly very poor) have appeared, and + an attempt at a reconstruction has been made by Rear Admiral + Jean Theophanidis, _Praktika tes Akademias Athenon_, Athens, + 1934, vol. 9, pp. 140-149 (in French). I am deeply grateful to + the Director of the Athens National Museum, M. Karouzos, for + providing me with an excellent new set of photos, from which + figures 6-8 are now taken. + + [17] H. Diels Ueber die von Prokop beschriebene Kunstuhr von + Gaza, _Abhandlungen, Akademie der Wissenschaften_, Berlin, + Philos.-Hist. Klasse, 1917, No. 7. + + [18] L. A. Mayer, _Islamic astrolabists and their works_, + Geneva, 1956, p. 62. + + [19] The translation which follows is quoted from J. Beckmann, + _op. cit._ (footnote 1), p. 349. + + [20] E. Wiedemann, "Ein Instrument das die Bewegung von Sonne + und Mond darstellt, nach al Biruni," _Der Islam_, 1913, vol. 4, + p. 5. + + [21] I acknowledge with thanks to the Curator of that museum + the permission to reproduce photographs of this instrument. It + is item 5 in R. T. Gunther, _Astrolabes of the world_, Oxford, + 1932. + + [22] Abulcacim Abnacahm, _Libros del saber_, edition by Rico y + Sinobas, Madrid, 1866, vol. 3, pp. 241-271. The design of the + instrument has been very fully discussed by A. Wegener, "Die + astronomischen Werke Alfons X," _Bibliotheca Mathematica_, + 1905, pp. 129-189. A more complete discussion of the historical + evolution of the equatorium is given in Derek J. Price, _The + equatorie of the planetis_, Cambridge (Eng.), 1955, pp. + 119-133. + + [23] E. Wiedemann, and F. Hauser, "Ueber die Uhren im Bereich d. + islamischen Kultur," _Nova Acta; Abhandlungen der koenigliche + Leopoldinisch-Carolinische Deutsche Akademie der Naturforscher + zu Halle_, 1915, vol. 100, no. 5. + + [24] E. Wiedemann, and F. Hauser, _Die Uhr des Archimedes und + zwei andere Vorrichtungen_, Halle, 1918. + + [25] The manuscripts in question are as follows: Gotha, Kat. v. + Pertsch. 3, 18, no. 1348; Oxford, Cod. 954; Leiden, Kat. 3, + 288, no. 1414, Cod. 499 Warn; and another similar, Kat. 3, 291, + no. 1415, Cod. 93 Gol. + + [26] H. Schmeller, Beitraege zur Geschichte der Technik in der + Antike und bei den Arabern, Erlangen, 1922 (_Abhandlungen zur + Geschichte der Naturwissenschaften und der Medizin_ no. 6). + + [27] Once more I am indebted to Professor Loren MacKinney and + Miss Harriet Lattin (see footnote 11) for making their + collections on Gerbert available to me. + + [28] Item 198 in Gunther, _op. cit._ (footnote 21). I am + grateful to the authorities of that museum for permission to + reproduce photographs of this instrument. + + [29] Sotheby and Co., London, sale of March 14, 1957, lot 154. + The outer rim of the rete has 120 teeth. + + [30] The Latin text of the treatise on the Albion, has been + transcribed by Rev. H. Salter and published in R. T. Gunther, + _Early science in Oxford_, Oxford, 1923, vol. 2, pp. 349-370. + An analysis of its design is given in Price, _op. cit._ + (footnote 22), pp. 127-130. + + [31] Such evidence as there is for the existence and form of + the clock is collected by Gunther, _op. cit._ (footnote 30), p. + 49. + + [32] I have discussed this new manuscript source in "Two + medieval texts on astronomical clocks," _Antiquarian Horology_, + 1956, vol. 1, no. 10, p. 156. The manuscript in question is ms. + 230/116, Gonville and Caius College, Cambridge, folios + 11^{v}-14^{v} = pp. 31-36. + + [33] _The Chronicle of Jocelin of Brakelond_ ..., H. E. Butler + (ed.), London, 1949, p. 106. + + [34] C. B. Drover, "A medieval monastic water-clock," + _Antiquarian Horology_, 1954, vol. 1, no. 5, pp. 54-58, 63. + Because this water clock uses wheels and strikes bells one must + reject the evidence of literary reference, such as by Dante, + from which the mention of wheels and bells have been taken as + positive proof of the existence of mechanical clocks with + mechanical escapements. The to-and-fro motion of the mechanical + clock escapement is quite an impressive feature, but there + seems to be no literary reference to it before the time of de + Dondi. + + [35] _Annales de la Societe Royale d'Archeologie de Bruxelles_, + 1896, vol. 1/8, pp. 203-215, 404-451. The translation here is + cited from Drover, _op. cit._, (footnote 34), p. 56. + + [36] L. Thorndike, _The sphere of Sacrobosco and its + commentators_, Chicago, 1949, pp. 180, 230. + + [37] The album was published with facsimiles by J. B. A. + Lassus, 1858. An English edition with facsimiles of 33 of the + 41 folios was published by Rev. Robert Willis, Oxford, 1859. An + extensive summary of this section is given, with illustrations, + by J. Drummond Robertson, _The evolution of clockwork_, London, + 1931, pp. 11-15. + + [38] M. Jules Quicherat, _Revue Archeologique_, 1849, vol. 6. + + [39] M. C. Fremont. _Origine de l'horloge a poids_, Paris, + 1915. + + [40] For this, I have used and quoted from the very beautiful + edition in English, prepared by Silvanus P. Thompson, London, + Chiswick Press, 1902. + + [41] See E. G. R. Taylor, "The South-pointing needle," _Imago + Mundi_, Leiden, 1951, vol. 8, pp. 1-7 (especially pp. 1, 2). + + [42] I have wondered whether the medieval interest in perpetual + motion could be connected with the use of the "Wheel of + Fortune" in churches as a substitute for bell-ringing on Good + Friday. Unfortunately I can find no evidence for or against the + conjecture. + + [43] W. E. May, "Alexander Neckham and the pivoted compass + needle," _Journal of the Institute of Navigation_, 1955, vol. + 8, no. 3, pp. 283-284. + + [44] W. E. May, "Hugues de Berze and the mariner's compass," + _The Mariner's Mirror_, 1953, vol. 39, no. 2, pp. 103-106. + + [45] H. Balmer, _Beitraege zur Geschichte der Erkenntnis des + Erdmagnetismus_, Aarau, 1956, p. 52. + + [46] The collection is the _Gami 'al Hikajat_; the relevant + passage being given in German translation in Balmer. _op. cit._ + (footnote 45), p. 54. + + [47] Balmer, op. _cit._ (footnote 45), p. 53. + + + +U.S. GOVERNMENT PRINTING OFFICE: 1959 + + + + + +End of the Project Gutenberg EBook of On the Origin of Clockwork, Perpetual +Motion Devices, and the Compass, by Derek J. de Solla Price + +*** END OF THIS PROJECT GUTENBERG EBOOK ON THE ORIGIN OF CLOCKWORK *** + +***** This file should be named 30001.txt or 30001.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/0/0/30001/ + +Produced by Chris Curnow, Turgut Dincer, Joseph Cooper and +the Online Distributed Proofreading Team at +https://www.pgdp.net. + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +https://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at https://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +https://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at https://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit https://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including including checks, online payments and credit card +donations. To donate, please visit: https://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart was the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + https://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/old/30001.zip b/old/30001.zip Binary files differnew file mode 100644 index 0000000..2c6c38b --- /dev/null +++ b/old/30001.zip |
