Title: On the Origin of Clockwork, Perpetual Motion Devices, and the Compass
Author: Price, Derek J. de Solla (Derek John de Solla), 1922-1983
Language: English
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  CONTRIBUTIONS FROM

  THE MUSEUM OF HISTORY AND TECHNOLOGY:

  PAPER 6



  ON THE ORIGIN OF CLOCKWORK,

  PERPETUAL MOTION DEVICES AND THE COMPASS

  _Derek J. de Solla Price_



  POWER AND MOTION GEARING                                   83

  MECHANICAL CLOCKS                                          84

  MECHANIZED ASTRONOMICAL MODELS                             88

  PERPETUAL MOTION AND THE CLOCK BEFORE DE DONDI            108

  THE MAGNETIC COMPASS AS A FELLOW-TRAVELER FROM CHINA      110



  _ON THE ORIGIN OF CLOCKWORK,_

  _PERPETUAL MOTION DEVICES_

  _AND THE COMPASS_

  _By Derek J. de Solla Price_


_Ancestor of the mechanical clock has been thought by some to be the
sundial. Actually these devices represent two different approaches to
the problem of time-keeping. True ancestor of the clock is to be found
among the highly complex astronomical machines which man has been
building since Hellenic times to illustrate the relative motions of the
heavenly bodies._

_This study--its findings will be used in preparing the Museum's new
hall on the history of time-keeping--traces this ancestry back through
2,000 years of history on three continents._

THE AUTHOR: _Derek J. de Solla Price wrote this paper while serving as
consultant to the Museum of History and Technology of the Smithsonian
Institution's United States National Museum._

  In each successive age this construction, having become
  lost, is, by the Sun's favour, again revealed to some one
  or other at his pleasure. (_Sūrya Siddhānta_, ed.
  Burgess, xiii, 18-19.)


THE HISTORIES of the mechanical clock and the magnetic compass must be
accounted amongst the most tortured of all our efforts to understand the
origins of man's important inventions. Ignorance has too often been
replaced by conjecture, and conjecture by misquotation and the false
authority of "common knowledge" engendered by the repetition of
legendary histories from one generation of textbooks to the next. In
what follows, I can only hope that the adding of a strong new trail and
the eradication of several false and weaker ones will lead us nearer to
a balanced and integrated understanding of medieval invention and the
intercultural transmission of ideas.

For the mechanical clock, perhaps the greatest hindrance has been its
treatment within a self-contained "history of time measurement" in which
sundials, water-clocks and similar devices assume the natural role of
ancestors to the weight-driven escapement clock in the early 14th
century.[1] This view must presume that a generally sophisticated
knowledge of gearing antedates the invention of the clock and extends
back to the Classical period of Hero and Vitruvius and such authors
well-known for their mechanical ingenuities.

Furthermore, even if one admits the use of clocklike gearing before the
existence of the clock, it is still necessary to look for the
independent inventions of the weight-drive and of the mechanical
escapement. The first of these may seem comparatively trivial; anyone
familiar with the raising of heavy loads by means of ropes and pulley
could surely recognize the possibility of using such an arrangement in
reverse as a source of steady power. Nevertheless, the use of this
device is not recorded before its association with hydraulic and
perpetual motion machines in the manuscripts of Riḍwān, _ca._ 1200,
and its use in a clock using such a perpetual motion wheel (mercury
filled) as a clock escapement, in the astronomical codices of Alfonso
the Wise, King of Castile, _ca._ 1272.

The second invention, that of the mechanical escapement, has presented
one of the most tantalizing of problems. Without doubt, the crown and
foliot type of escapement appears to be the first complicated mechanical
invention known to the European Middle Ages; it heralds our whole age of
machine-making. Yet no trace has been found either of a steady evolution
of such escapements or of their invention in Europe, though the
astronomical clock powered by a water wheel and governed by an
escapement-like device had been elaborated in China for several
centuries before the first appearance of our clocks. We must now
rehearse a revised story of the origin of the clock as it has been
suggested by recent researches on the history of gearing and on Chinese
and other astronomical machines. After this we shall for the first time
present evidence to show that this story is curiously related to that of
the _Perpetuum Mobile_, one of the great chimeras of science, that came
from its medieval origin to play an important part in more recent
developments of energetics and the foundations of thermodynamics.[2] It
is a curious mixture, all the more so because, tangled inextricably in
it, we shall find the most important and earliest references to the use
of the magnetic compass in the West. It seems that in revising the
histories of clockwork and the magnetic compass, these considerations
of perpetual motion devices may provide some much needed evidence.

[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.



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