+--------------------------------------------------------------+
| This e-text includes characters that require UTF-8 |
| (Unicode) file encoding: |
| |
| ḍ, ā, ḥ, ȧ, ī |
| |
| If any of these characters do not display properly--in |
| particular, if the dots do not appear under the letters |
| make sure your text reader’s “character set” or “file |
| encoding” is set to Unicode (UTF-8). You may also need to |
| change the default font. Depending on available fonts, some |
| tables may not line up vertically. |
+--------------------------------------------------------------+
CONTRIBUTIONS FROM
THE MUSEUM OF HISTORY AND TECHNOLOGY:
PAPER 6
ON THE ORIGIN OF CLOCKWORK,
PERPETUAL MOTION DEVICES AND THE COMPASS
_Derek J. de Solla Price_
POWER AND MOTION GEARING 83
MECHANICAL CLOCKS 84
MECHANIZED ASTRONOMICAL MODELS 88
PERPETUAL MOTION AND THE CLOCK BEFORE DE DONDI 108
THE MAGNETIC COMPASS AS A FELLOW-TRAVELER FROM CHINA 110
_ON THE ORIGIN OF CLOCKWORK,_
_PERPETUAL MOTION DEVICES_
_AND THE COMPASS_
_By Derek J. de Solla Price_
_Ancestor of the mechanical clock has been thought by some to be the
sundial. Actually these devices represent two different approaches to
the problem of time-keeping. True ancestor of the clock is to be found
among the highly complex astronomical machines which man has been
building since Hellenic times to illustrate the relative motions of the
heavenly bodies._
_This study--its findings will be used in preparing the Museum's new
hall on the history of time-keeping--traces this ancestry back through
2,000 years of history on three continents._
THE AUTHOR: _Derek J. de Solla Price wrote this paper while serving as
consultant to the Museum of History and Technology of the Smithsonian
Institution's United States National Museum._
In each successive age this construction, having become
lost, is, by the Sun's favour, again revealed to some one
or other at his pleasure. (_Sūrya Siddhānta_, ed.
Burgess, xiii, 18-19.)
THE HISTORIES of the mechanical clock and the magnetic compass must be
accounted amongst the most tortured of all our efforts to understand the
origins of man's important inventions. Ignorance has too often been
replaced by conjecture, and conjecture by misquotation and the false
authority of "common knowledge" engendered by the repetition of
legendary histories from one generation of textbooks to the next. In
what follows, I can only hope that the adding of a strong new trail and
the eradication of several false and weaker ones will lead us nearer to
a balanced and integrated understanding of medieval invention and the
intercultural transmission of ideas.
For the mechanical clock, perhaps the greatest hindrance has been its
treatment within a self-contained "history of time measurement" in which
sundials, water-clocks and similar devices assume the natural role of
ancestors to the weight-driven escapement clock in the early 14th
century.[1] This view must presume that a generally sophisticated
knowledge of gearing antedates the invention of the clock and extends
back to the Classical period of Hero and Vitruvius and such authors
well-known for their mechanical ingenuities.
Furthermore, even if one admits the use of clocklike gearing before the
existence of the clock, it is still necessary to look for the
independent inventions of the weight-drive and of the mechanical
escapement. The first of these may seem comparatively trivial; anyone
familiar with the raising of heavy loads by means of ropes and pulley
could surely recognize the possibility of using such an arrangement in
reverse as a source of steady power. Nevertheless, the use of this
device is not recorded before its association with hydraulic and
perpetual motion machines in the manuscripts of Riḍwān, _ca._ 1200,
and its use in a clock using such a perpetual motion wheel (mercury
filled) as a clock escapement, in the astronomical codices of Alfonso
the Wise, King of Castile, _ca._ 1272.
The second invention, that of the mechanical escapement, has presented
one of the most tantalizing of problems. Without doubt, the crown and
foliot type of escapement appears to be the first complicated mechanical
invention known to the European Middle Ages; it heralds our whole age of
machine-making. Yet no trace has been found either of a steady evolution
of such escapements or of their invention in Europe, though the
astronomical clock powered by a water wheel and governed by an
escapement-like device had been elaborated in China for several
centuries before the first appearance of our clocks. We must now
rehearse a revised story of the origin of the clock as it has been
suggested by recent researches on the history of gearing and on Chinese
and other astronomical machines. After this we shall for the first time
present evidence to show that this story is curiously related to that of
the _Perpetuum Mobile_, one of the great chimeras of science, that came
from its medieval origin to play an important part in more recent
developments of energetics and the foundations of thermodynamics.[2] It
is a curious mixture, all the more so because, tangled inextricably in
it, we shall find the most important and earliest references to the use
of the magnetic compass in the West. It seems that in revising the
histories of clockwork and the magnetic compass, these considerations
of perpetual motion devices may provide some much needed evidence.
[Illustration: Figure 1.--FRAMEWORK STRUCTURE OF THE ASTRONOMICAL CLOCK
of Giovanni de Dondi of Padua, A.D. 1364.]
Power and Motion Gearing
It may be readily accepted that the use of toothed wheels to transmit
power or turn it through an angle was widespread in all cultures several
centuries before the beginning of our era. Certainly, in classical times
they were already familiar to Archimedes (born 287 B.C.),[3] and in
China actual examples of wheels and moulds for wheels dating from the
4th century B.C. have been preserved.[4] It might be remarked that
these "machine" gear wheels are characterized by having a "round number"
of teeth (examples with 16, 24 and 40 teeth are known) and a shank with
a square hole which fits without turning on a squared shaft. Another
remarkable feature in these early gears is the use of ratchet-shaped
teeth, sometimes even twisted helically so that the gears resemble worms
intermeshing on parallel axles.[5] The existence of windmills and
watermills testifies to the general familiarity, from classical times
and through the middle ages, with the use of gears to turn power through
a right angle.
[Illustration: Figure 2.--ASTRONOMICAL CLOCK of de Dondi, showing
gearing on the dial for Mercury and escapement crown wheel. Each of the
seven side walls of the structure shown in figure 1 was fitted with a
dial.]
Granted, then, this use of gears, one must guard against any conclusion
that the fine-mechanical use of gears to provide special ratios of
angular movement was similarly general and widespread. It is customary
to adduce here the evidence of the hodometer (taximeter) described by
Vitruvius (1st century B.C.) and by Hero of Alexandria (1st century
A.D.) and the ingenious automata also described by this latter author
and his Islamic followers.[6] One may also cite the use of the reduction
gear chain in power machinery as used in the geared windlass of
Archimedes and Hero.
Unfortunately, even the most complex automata described by Hero and by
such authors as Riḍwān contain gearing in no more extensive context
than as a means of transmitting action around a right angle. As for the
windlass and hodometer, they do, it is true, contain whole series of
gears used in steps as a reduction mechanism, usually for an
extraordinarily high ratio, but here the technical details are so
etherial that one must doubt whether such devices were actually realized
in practice. Thus Vitruvius writes of a wheel 4 feet in diameter and
having 400 teeth being turned by a 1-toothed pinion on a cart axle, but
it is very doubtful whether such small teeth, necessarily separated by
about 3/8 inch, would have the requisite ruggedness. Again, Hero
mentions a wheel of 30 teeth which, because of imperfections, might need
only 20 turns of a single helix worm to turn it! Such statements behove
caution and one must consider whether we have been misled by the
16th- and 17th-century editions of these authors, containing
reconstructions now often cited as authoritative but then serving as
working diagrams for practical use in that age when the clock was
already a familiar and complex mechanism. At all events, even if one
admits without substantial evidence that such gear reduction devices
were familiar from Hellenistic times onwards, they can hardly serve as
more than very distant ancestors of the earliest mechanical clocks.
Mechanical Clocks
Before proceeding to a discussion of the controversial evidence which
may be used to bridge this gap between the first use of gears and the
fully-developed mechanical clock we must examine the other side of this
gap. Recent research on the history of early mechanical clocks has
demonstrated certain peculiarities most relevant to our present
argument.
THE EUROPEAN TRADITION
If one is to establish a _terminus ante quem_ for the appearance of the
mechanical clock in Europe, it would appear that 1364 is a most
reasonable date. At that time we have the very full mechanical and
historical material concerning the horological masterpiece built by
Giovanni de Dondi of Padua,[7] and probably started as early as 1348. It
might well be possible to set a date a few decades earlier, but in
general as one proceeds backwards from this point, the evidence becomes
increasingly fragmentary and uncertain. The greatest source of doubt
arises from the confusion between sundials, water-clocks, hand-struck
time bells, and mechanical clocks, all of which are covered by the term
_horologium_ and its vernacular equivalents.
Temporarily postponing the consideration of evidence prior to _ca._
1350, we may take Giovanni de Dondi as a starting point and trace a
virtually unbroken lineage from his time to the present day. One may
follow the spread of clocks through Europe, from large towns to small
ones, from the richer cathedrals and abbeys to the less wealthy
churches.[8] There is the transition from the tower clocks--showpieces
of great institutions--to the simple chamber clock designed for domestic
use and to the smaller portable clocks and still smaller and more
portable pocket watches. In mechanical refinement a similar continuity
may be noted, so that one sees the cumulative effect of the introduction
of the spring drive (_ca._ 1475), pendulum control (_ca._ 1650), and the
anchor escapement (_ca._ 1680). The transition from de Dondi to the
modern chronometer is indeed basically continuous, and though much
research needs to be done on special topics, it has an historical unity
and seems to conform for the most part to the general pattern of steady
mechanical improvement found elsewhere in the history of technology.
[Illustration: Figure 3.--GERMAN WALL CLOCK, PROBABLY ABOUT 1450,
showing the degeneration in complexity from that of de Dondi's clock.]
Most remarkable however is the earliest period of this seemingly steady
evolution. Side by side with the advances made in the earliest period
extending for less than two centuries from the time of de Dondi one may
see a spectacular process of degeneration or devolution. Not only is de
Dondi's the earliest clock of which we have a full and trustworthy
account, it is also far more complicated than any other (see figs. 1, 2)
until comparatively modern times! Moreover, it was not an exceptional
freak. There were others like it, and one cannot therefore reject as
accidental this process of degeneration that occurs at the very
beginning of the certain history of the mechanical clock in Europe.
On the basis of such evidence I have suggested elsewhere[9] that the
clock is "nought but a fallen angel from the world of astronomy." The
first great clocks of medieval Europe were designed as astronomical
showpieces, full of complicated gearing and dials to show the motions of
the Sun, Moon and planets, to exhibit eclipses, and to carry through the
involved computations of the ecclesiastical calendar. As such they were
comparable to the orreries of the 18th century and to modern
planetariums; that they also showed the time and rang it on bells was
almost incidental to their main function. One must not neglect, too,
that it was in their glorification of the rationality of the cosmos that
they had their greatest effect. Through milleniums of civilization,
man's understanding of celestial phenomena had been the very pinnacle of
his intellect, and then as now popular exhibition of this sort was just
as necessary, as striking, and as impressive. One does not have to go
far to see how the paraphernalia of these early great astronomical
clocks had great influence on philosophers and theologians and on poets
such as Dante.
It is the thesis of this part of my argument that the ordinary
time-telling clock is no affiliate of the other simple time-telling
devices such as sundials, sand glasses and the elementary water clocks.
Rather it should be considered as a degenerate branch from the main stem
of mechanized astronomical devices (I shall call them protoclocks), a
stem which can boast a continuous history filling the gap between the
appearance of simple gearing and the complications of de Dondi. We shall
return to the discussion of this main stem after analyzing the very
recently discovered parallel stem from medieval China, which reproduced
the same evolution of mechanized astronomical devices and incidental
time telling. Of the greatest significance, this stem reveals the
crucial independent invention of a mechanical escapement, a feature not
found in the European stem in spite of centuries of intensive historical
research and effort.
THE CHINESE TRADITION
For this section I am privileged to draw upon a thrilling research
project carried out in 1956 at the University of Cambridge by a team
consisting of Dr. Joseph Needham, Dr. Wang Ling, and myself.[10] In the
course of this work we translated and commented on a series of texts
most of which had not hitherto been made available in a Western tongue
and, though well known in China, had not been recognized as important
for their horological content. The key text with which we started was
the "Hsin I Hsiang Fa Yao," or "New Design for a (mechanized) Armillary
(sphere) and (celestial) Globe," written by Su Sung in A.D. 1090. The
very full historical and technical description in this text enabled us
to establish a glossary and basic understanding of the mechanism that
later enabled us to interpret a whole series of similar, though less
extensive texts, giving a history of prior development of such devices
going back to the introduction of this type of escapement by I-Hsing and
Liang Ling-tsan, in A.D. 725, and to what seems to be the original of
all these Chinese astronomical machines, that built by Chang Hêng _ca._
A.D. 130. Filling the gaps between these landmarks are several other
similar texts, giving ample evidence that the Chinese development is
continuous and, at least from Chang Hêng onwards, largely independent of
any transmissions from the West.
So far as we can see, the beginning of the chain in China (as indeed in
the West) was the making of simple static models of the celestial
sphere. An armillary sphere was used to represent the chief imaginary
circles (_e.g._, equator, ecliptic, meridians, etc.), or a solid
celestial globe on which such circles could be drawn, together with the
constellations of the fixed stars. The whole apparatus was then mounted
so that it was free to revolve about its polar axis and another ring or
a casing was added, external and fixed, to represent the horizon that
provided a datum for the rising and setting of the Sun and the stars.
In the next stage, reached very soon after this, the rotation of the
model was arranged to proceed automatically instead of by hand. This was
done, we believe, by using a slowly revolving wheel powered by dripping
water and turning the model through a reduction mechanism, probably
involving gears or, more reasonably, a single large gear turned by a
trip lever. It did not matter much that the time-keeping properties were
poor in the long run; the model moved "by itself" and the great wonder
was that it agreed with the observed heavens "like the two halves of a
tally."
In the next, and essential, stage the turning of the water wheel was
regulated by an "escapement" mechanism consisting of a weighbridge and
trip levers so arranged that the wheel was held in check, scoop by
scoop, while each scoop was filled by the dripping water, then released
by the weighbridge and allowed to rotate until checked again by the
trip-lever arrangement. Its action was similar to that of the anchor
escapement, though its period of repose was much longer than its period
of motion and, of course, its time-keeping properties were controlled not
only by the mechanics of the device but also by the rate of flow of the
dripping water.
The Chinese escapement may justifiably be regarded as a missing link,
just halfway between the elementary clepsydra with its steady flow of
water and the mechanical escapement in which time is counted by chopping
its flow into cycles of action, repeated indefinitely and counted by a
cumulating device. With its characteristic of saving up energy for a
considerable period (about 15 minutes) before letting it go in one
powerful action, the Chinese escapement was particularly suited to the
driving of jackwork and other demonstration devices requiring much
energy but only intermittent activity.
In its final form, as built by Su Sung after many trials and
improvements, the Chinese "astronomical clock-tower" must have been a
most impressive object. It had the form of a tower about 30 feet high,
surmounted by an observation platform covered with a light roof (see
fig. 4). On the platform was an armillary sphere designed for observing
the heavens. It was turned by the clockwork so as to follow the diurnal
rotation and thus avoid the distressing computations caused by the
change of coordinates necessary when fixed alt-azimuth instruments were
used. Below the platform was an enclosed chamber containing the
automatically rotated celestial globe which so wonderfully agreed with
the heavens. Below this, on the front of the tower was a miniature
pagoda with five tiers; on each tier was a doorway through which, at due
moment, appeared jacks who rang bells, clanged gongs, beat drums, and
held tablets to announce the arrival of each hour, each quarter (they
used 100 of them to the day) and each watch of the night. Within the
tower was concealed the mechanism; it consisted mainly of a central
vertical shaft providing power for the sphere, globe, and jackwheels,
and a horizontal shaft geared to the vertical one and carrying the great
water wheel which seemed to set itself magically in motion at every
quarter. In addition to all this were the levers of the escapement
mechanism and a pair of norias by which, once each day, the water used
was pumped from a sump at the bottom to a reservoir at the top, whence
it descended to work the wheel by means of a constant level tank and
several channels.
There were many offshoots and developments of this main stem of Chinese
horology. We are told, for example, that often mercury and occasionally
sand were used to replace the water, which frequently froze in winter in
spite of the application of lighted braziers to the interior of the
machines. Then again, the astronomical models and the jackwork were
themselves subject to gradual improvement: at the time of I-Hsing, for
example, special attention was paid to the demarcation of ecliptic as
well as the normal equatorial coordinates; this was clearly an influx
from Hellenistic-Islamic astronomy, in which the relatively
sophisticated planetary mathematics had forced this change not otherwise
noted in China.
By the time of the Jesuits, this current of Chinese horology, long since
utterly destroyed by the perils of wars, storms, and governmental
reforms, had quite been forgotten. Matteo Ricci's clocks, those gifts
that aroused so much more interest than European theological teachings,
were obviously something quite new to the 16th-century Chinese scholars;
so much so that they were dubbed with a quite new name, "self-sounding
bells," a direct translation of the word "clock" (_glokke_). In view of
the fact that the medieval Chinese escapement may have been the basis of
European horology, it is a curious twist of fate that the high regard of
the Chinese for European clocks should have prompted them to open their
doors, previously so carefully and for so long kept closed against the
foreign barbarians.
[Illustration: Figure 4.--ASTRONOMICAL CLOCK TOWER OF SU SUNG in
K'ai-feng, _ca._ A.D. 1090, from an original drawing by John
Christiansen. (_Courtesy of Cambridge University Press._)]
Mechanized Astronomical Models
Now that we have seen the manner in which mechanized astronomical models
developed in China, we can detect a similar line running from
Hellenistic time, through India and Islam to the medieval Europe that
inherited their learning. There are many differences, notably because of
the especial development of that peculiar characteristic of the West,
mathematical astronomy, conditioned by the almost accidental conflux of
Babylonian arithmetical methods with those of Greek geometry. However,
the lines are surprisingly similar, with the exception only of the
crucial invention of the escapement, a feature which seems to be
replaced by the influx of ideas connected with perpetual motion wheels.
HELLENISTIC PERIOD
Most interesting and frequently cited is the bronze planetarium said to
have been made by Archimedes and described in a tantalisingly
fragmentary fashion by Cicero and by later authors. Because of its
importance as a prototype, we give the most relevant passages in
full.[11]
Cicero's descriptions of Archimedes' planetarium are (italics supplied):
Gaius Sulpicius Gallus ... at a time when ... he happened
to be at the house of Marcus Marcellus, his colleague in
the consulship [166 B.C.], ordered the celestial globe to
be brought out which the grandfather of Marcellus had
carried off from Syracuse, when that very rich and
beautiful city was taken [212 B.C.].... Though I had heard
this globe (sphaerae) mentioned quite frequently on
account of the fame of Archimedes, when I saw it I did not
particularly admire it; for that other celestial globe,
also constructed by Archimedes, which the same Marcellus
placed in the temple of Virtue, is more beautiful as well
as more widely known among the people. But when Gallus
began to give a very learned explanation of the device, I
concluded that the famous Sicilian had been endowed with
greater genius than one would imagine possible for human
being to possess. For Gallus told us that the other kind
of celestial globe, which was solid and contained no
hollow space, was a very early invention, the first one of
that kind having been constructed by Thales of Miletus,
and later marked by Eudoxus of Cnidus--a disciple of
Plato, it was claimed--with constellations and stars which
are fixed in the sky. He also said that many years later
Aratus ... had described it in verse.... But this newer
kind of globe, he said, on which were delineated the
motions of the sun and moon and of those five stars which
are called wanderers, or, as we might say, rovers
[_i. e._, the five planets], contained more than could be
shown on the solid globe, and the invention of Archimedes
deserved special admiration because he had thought out a
way to represent accurately by a single device for turning
the globe, those various and divergent movements with
their different rates of speed. And when Gallus moved
[_i.e._, set in motion] the globe, it was actually true
that the moon was always as many revolutions behind the
sun on the _bronze_ contrivance as would agree with the
number of days it was behind in the sky. Thus the same
eclipse of the sun happened on the globe as would actually
happen, and the moon came to the point where the shadow of
the earth was at the very time when the sun (appeared?)
out of the region ... [several pages are missing in the
manuscript; there is only one].
_De republica_, I, xiv (21-22), Keyes' translation.
When Archimedes put together in a globe the movements of
the moon, sun and five wandering [planets], he brought
about the same effect as that which the god of Plato did
in the Timaeus when he made the world, so that one
revolution produced dissimilar movements of delay and
acceleration.
_Tusculanae disputationes_, I, 63.
Later descriptions from Ovid, Lactantius, Claudian, Sextus Empiricus,
and Pappus, respectively, are (italics supplied):
There stands a globe suspended by a Syracusan's skill in
an enclosed bronze [frame, or sphere--or perhaps, in
enclosed air], a small image of the immense vault [of
heaven]; and the earth is equally distant from the top and
bottom; that is brought about by its [_i. e._, the outer
bronze globe's] round form. The form of the temple [of
Vesta] is similar....
Ovid, _Fasti_ (1st century, A.D.), VI, 277-280,
Frazer's translation.
The Sicilian Archimedes, was able to make a reproduction
and model of the world in concave _brass_ (concavo aere
similitudinem mundi ac figuram); in it he so arranged the
_sun_ and _moon_ and resembling the celestial revolutions
(caelestibus similes conversionibus); and while it
revolved it exhibited not only the accession and recession
of the sun and the waxing and waning of the moon
(incrementa deminutionesque lunae), but also the unequal
_courses of the stars_, whether fixed or wandering.
Lactantius, _Institutiones divinae_ (4th century, A.D.),
II, 5, 18.
Archimedes' sphere. When Jove looked down and saw the
heavens figured in a sphere of _glass_, he laughed and
said to the other gods: "Has the power of mortal effort
gone so far? Is my handiwork now mimicked in a fragile
globe?" An old man of Syracuse had imitated on earth the
laws of the heavens, the order of nature, and the
ordinances of the gods. Some hidden influence within the
sphere directs the various courses of the _stars_ and
actuates the lifelike mass with definite motions. A false
_zodiac_ runs through a year of its own and a toy _moon_
waxes and wanes month by month. Now bold invention
rejoices to make its own heaven revolve and sets the
_stars_ [planets?] in motion by human wit....
Claudian, _Carmina minora_ (_ca._ A.D. 400), LI (LXVIII),
Platnaure's translation.
The things that move by themselves are more wonderful than
those which do not. At any rate, when we behold an
Archimedean sphere in which the sun and the rest of the
stars move, we are immensely impressed by it, not by Zeus
because we are amazed at the _wood_, or at the movements
of these [bodies], but by the devices and causes of the
movements.
Sextus Empiricus, _Adversus mathematicos_ (3rd century,
A.D.), IX, 115, Epps' translation.
Mechanics understand the making of spheres and know how to
produce a model of the heavens (with the courses of the
stars moving in circles?) by mean of equal and circular
motions of _water_, and Archimedes the Syracusan,
according to some, knows the cause and reasons for all of
these.
Pappus (3rd century, A.D.), _Works_ (Hultsch edition),
VIII, 2, Epps' translation.
A similar arrangement seems to be indicated in another mechanized globe,
also mentioned by Cicero and said to have been made by Posidonius:
But if anyone brought to Scythia or Britain the globe
(sphaeram) which our friend Posidonius [of Apameia, the
Stoic philosopher] recently made, in which each revolution
produced the same (movements) of the _sun_ and _moon_ and
_five_ wandering stars as is produced in the sky each day
and night, who would doubt that it was by exertion of
reason?... Yet doubters ... think that Archimedes showed
more knowledge in producing movements by revolutions of a
globe than nature (does) in effecting them though the copy
is so infinitely inferior to the original....
_De natura deorum_, II, xxxiv-xxxv (88),
Yonge's translation.
In spite of the lack of sufficient technical details in any case, these
mechanized globe models, with or without geared planetary indicators
(which would make them highly complex machines), bear a striking
resemblance to the earliest Chinese device described by Chang Hêng. One
must not reject the possibility that transmission from Greece or Rome
could have reached the East by the beginning of the 2nd century, A.D.,
when he was working. It is an interesting question, but even if such
contact actually occurred, very soon afterwards, as we shall see, the
western and eastern lines of evolution parted company and evolved so far
as can be seen, quite independently until at least the 12th century.
The next Hellenistic source of which we must take note is a fragmentary
and almost unintelligible chapter in the works of Hero of Alexandria.
Alone and unconnected with his other chapters this describes a model
which seems to be static, in direct contrast to all other devices which
move by pneumatic and hydrostatic pressures; it may well be conjectured
that in its original form this chapter described a mechanized rather
than a static globe:
The World represented in the Centre of the Universe: The
construction of a transparent globe containing air and
liquid, and also of a smaller globe, in the centre, in
imitation of the World. Two hemispheres of glass are made;
one of them is covered with a plate of bronze, in the
middle of which is a round hole. To fit this hole a light
ball, of small size, is constructed, and thrown into the
water contained in the other hemisphere: the covered
hemisphere is next applied to this, and, a certain
quantity of the liquid having been removed from the water,
the intermediate space will contain the ball; thus by the
application of the second hemisphere what was proposed is
accomplished.
_Pneumatics_, XLVI, Woodcroft's translation.
It will be noted that these earliest literary references are concerned
with pictorial, 3-dimensional models of the universe, moved perhaps by
hand, perhaps by waterpower; there is no evidence that they contained
complicated trains of gears, and in the absence of this we may incline
to the view that in at least the earliest such models, gearing was not
used.
The next developments were concerned on the one hand with increasing the
mathematical sophistication of the model, on the other hand with its
mechanical complexity. In both cases we are most fortunate in having
archaeological evidence which far exceeds any literary sources.
The mathematical process of mapping a sphere onto a plane surface by
stereographic projection was introduced by Hipparchus and had much
influence on astronomical techniques and instruments thereafter. In
particular, by the time of Ptolemy (_ca._ A.D. 120) it had led to the
successive inventions of the anaphoric clock and of the planispheric
astrolabe.[12] Both these devices consist of a pair of stereographic
projections, one of the celestial sphere with its stars and ecliptic and
tropics, the other of the lines of altitude and azimuth as set for an
observer in a place at some particular latitude.
In the astrolabe, an openwork metal rete containing markings for the
stars, etc., may be rotated by hand over a disc on which the lines of
altitude and azimuth are inscribed. In the anaphoric clock a disc
engraved with the stars is rotated automatically behind a fixed grille
of wires marking lines of altitude and azimuth. Power for rotating the
disc is provided by a float rising in a clepsydra jar and connected, by
a rope or chain passing over a pulley to a counterweight or by a rack
and pinion, to an axle which supported the rotating disc and
communicated this motion to it.[13]
[Illustration: Figure 5. PLATE OF SALZBURG ANAPHORIC CLOCK, a
reconstruction (see footnote 14) based on a photograph of the remaining
fragment. (_Courtesy of Oxford University Press._)]
Parts of two such discs from anaphoric clocks have been found, one at
Salzburg[14] and one at Grand in the Vosges,[15] both of them dating
from the 2nd century A.D. Fortunately there is sufficient evidence to
reconstruct the Salzburg disc and show that it must have been originally
about 170 cm. in diameter, a heavy sheet of bronze to be turned by the
small power provided by a float, and a large and impressive device when
working (see fig. 5). Literary accounts of the anaphoric clock have been
analyzed by Drachmann; there is no evidence of the representation of
planets moved either by hand or by automatic gearing, only in the
important case of the sun was such a feature included of necessity. A
model "sun" on a pin could be plugged in to any one of 360 holes drilled
in at equal intervals along the band of the ecliptic. This pin could be
moved each day so that the anaphoric clock kept step with the seasonal
variation of the times of sunrise and sunset and the lengths of day and
night.
The anaphoric clock is not only the origin of the astrolabe and of all
later planetary models, it is also the first clock dial, setting a
standard for "clockwise" rotation, and leaving its mark in the rotating
dial and stationary pointer found on the earliest time-keeping clocks
before the change was made to a fixed dial and moving hand.
We come finally to a piece of archaeological evidence that surpasses all
else. Though badly preserved and little studied it might well be the
most important classical object ever found; entailing a complete
re-estimation of the technical prowess of the Hellenistic Greeks. In
1901 a sunken treasure ship was discovered lying off the island of
Antikythera, between Greece and Crete.[16] Many beautiful classical
works of statuary were recovered from it, and these are now amongst the
greatest treasures of the National Museum at Athens, Greece. Besides
these obviously desirable art relics, there came to the surface some
curious pieces of metal, accompanied by traces of what may have been a
wooden casing. Two thousand years under the sea had reduced the metal to
a mess of corroded fragments of plates, powdered verdigris, and still
recognizable pieces of gear wheels.
If it were not for the established dates for other treasure from this
ship, especially the minor objects found, and for traces of inscriptions
on this metal device written in letters agreeing epigraphically with the
other objects, one would have little doubt in supposing that such a
complicated piece of machinery dated from the 18th century, at the
earliest. As it is, estimates agree on _ca._ 65 B.C. ±10 years, and we
can be sure that the machine is of Hellenistic origin, possibly from
Rhodes or Cos.
[Illustration: Figure 6.--ANTIKYTHERA MACHINE, LARGEST FRAGMENT. (_Photo
courtesy of National Museum, Athens._)]
The inscriptions, only partly legible, lead one to believe that we are
dealing with an astronomical calculating mechanism of some sort. This is
born out by the mechanical construction evident on the fragments. The
largest one (fig. 6) contains a multiplicity of gearing involving an
annular gear working epicyclic gearing on a turntable, a crown wheel,
and at least four separate trains of smaller gears, as well as a
4-spoked driving wheel. One of the smaller fragments (fig. 7, bottom)
contains a series of movable rings which may have served to carry
movable scales on one of the three dials. The third fragment (fig. 7,
top) has a pair of rings carefully engraved and graduated in degrees of
the zodiac (this is, incidentally, the oldest engraved scale known, and
micrometric measurements on photographs have indicated a maximum
inaccuracy of about 1/2° in the 45° present).
[Illustration: Figure 7.--ANTIKYTHERA MACHINE, TWO SMALLER FRAGMENTS.
(_Photo courtesy of National Museum, Athens._)]
Unfortunately, the very difficult task of cleaning the fragments is
slow, and no publication has yet given sufficient detail for an adequate
explanation of this object. One can only say that although the problems
of restoration and mechanical analysis are peculiarly great, this must
stand as the most important scientific artifact preserved from
antiquity.
Some technical details can be gleaned however. The shape of the gear
teeth appears to be almost exactly equilateral triangles in all cases
(fig. 8), and square shanks may be seen at the centers of some of the
wheels. No wheel is quite complete enough for a count of gear teeth, but
a provisional reconstruction by Theophanidis (fig. 9) has shown that the
appearances are consistent with the theory that the purpose of the
gears was to provide the correct angular ratios to move the sun and
planets at their appropriate relative speeds.
[Illustration: Figure 8.--ANTIKYTHERA MACHINE, DETAIL FROM FIGURE 6,
showing gearing. (_Photo courtesy of National Museum, Athens._)]
Thus, if the evidence of the Antikythera machine is to be taken at its
face value, we have, already in classical times, the use of astronomical
devices as complicated as any clock. In any case, the material supplied
by the works ascribed to Archimedes, Hero, and Vitruvius, and the more
certain evidence of the anaphoric clocks is sufficient to show that
there was a strong classical tradition of such machines, a tradition
that inspired, even if it did not directly influence, later developments
in Islam and Europe on the one side, and, just possibly, China on the
other.
_Note added in proof_:
Since the above lines were written, I have been privileged
to make a full examination of the fragments in the
National Museum in Athens. As a result we can read much
more inscription and make out many more details of the
mechanism. The cleaning and disentangling of the fragments
by the museum staff has proceeded to the stage where one
can assert much more positively that the device was an
astronomical computer for sidereal, solar, lunar, and
possibly also planetary phenomena. (See my article in the
_Scientific American_, June 1959, vol. 200, No. 6, pp.
60-67.) Relevant to the present study, it must also be
noted at this point that the machine is now shown to be
strongly related to the geared astrolabe of al-Biruni and
thereby the Hellenistic, Islamic, and European
developments are drawn together even more tightly.
Let us now turn our attention to those civilizations which were
intermediaries, geographically and culturally, between Greece and
medieval Europe, and between both of these and China. From India there
are only two references, very closely related and appearing in the best
known astronomical texts in connection with descriptions of the
armillary sphere and celestial globe. These texts are both quite
garbled, but so far as one may understand them, it seems that the types
of spheres and globes mentioned are more akin to those current in China
than in the West. The relevant portions of text are as follows (italics
supplied):
The circle of the horizon is midway of the sphere. As
covered with a casing and as left uncovered, it is the
sphere surrounded by Lokāloka [the mountain range which
formed the boundary of the universe in puranic geography].
By the application of water is made ascertainment of the
revolution of time. One may construct a sphere-instrument
combined with quicksilver: this is a mystery; if plainly
described, it would be generally intelligible in the
world. Therefore let the supreme sphere be constructed
according to the instruction of the preceptor [guru]. In
each successive age this construction, having become lost,
is, by the Sun's favour, again revealed to some one or
other, at his pleasure. So also, one should construct
instruments in order to ascertain time. When quite alone,
one should apply quicksilver to the wonder-causing
instrument. By the gnomon, staff, arc, wheel, instruments
for taking the shadow of various kinds.... By
water-instruments, the vessel, by the peacock, man,
monkey, and by stringed sand-receptacles one may determine
time accurately. Quicksilver-holes, water, and cords, and
oil and water, mercury and sand are used in these: these
applications, too, are difficult.
Sūrya Siddhānta_, xiii, 15-22,
E. Burgess' translation, New Haven, 1860.
[Illustration: Figure 9.--ANTIKYTHERA MACHINE, PARTIAL RECONSTRUCTION
BY THEOPHANIDIS (see footnote 16).]
A self-revolving instrument [or swayanvaha yantra]: Make a
wheel of light wood and in its circumference put hollow
spokes all having bores of the same diameter, and let them
be placed at equal distances from each other; and let
them also be placed at an angle verging somewhat from the
perpendicular: then half fill these hollow spokes with
mercury; the wheel thus filled will, when placed on an
axis supported by two posts, revolve of itself.
Or scoop out a canal in the tire of the wheel and then
plastering leaves of the Tȧla tree over this canal with
wax, fill one half of this canal with water and the other
half with mercury, till the water begins to come out, and
then cork up the orifice left open for filling the wheel.
The wheel will then revolve of itself, drawn around by the
water.
Description of a syphon: Make up a tube of copper or other
metal, and bend it in the form of an Ankus'a or elephant
hook, fill it with water and stop up both ends. And then
putting one end into a reservoir of water let the other
end remain suspended outside. Now uncork both ends. The
water of the reservoir will be wholly sucked up and fall
outside.
Now attach to the rim of the before described
self-revolving wheel a number of water-pots, and place the
wheel and these pots like the water wheel so that the
water from the lower end of the tube flowing into them on
one side shall set the wheel in motion, impelled by the
additional weight of the pots thus filled. The water
discharge from the pots as they reach the bottom of the
revolving wheel, should be drawn off into the reservoir
before alluded to by means of a water-course or pipe.
The self-revolving machine [mentioned by _Lalla_, etc.]
which has a tube with its lower end open is a vulgar
machine on account of its being dependant, because that
which manifests an ingenious and not a rustic contrivance
is said to be a machine.
And moreover many self-revolving machines are to be met
with, but their motion is procured by a trick. They are
not connected with the subject under discussion. I have
been induced to mention the construction of these, merely
because they have been mentioned by former astronomers.
_Siddhānta Siromaṇi_, xi, 50-57, L. Wilkinson's
translation, revised by Bȧpu̇ deva S(h)ȧstri,
Calcutta, 1861.
Before proceeding to an investigation of the content of these texts it
is of considerable importance to establish dates for them, though there
are many difficulties in establishing any chronology for Hindu
astronomy. The _Sūrya Siddhānta_ is known to date, in its original
form, from the early Middle Ages, _ca._ 500. The section in question is
however quite evidently an interpolation from a later recension, most
probably that which established the complete text as it now stands; it
has been variously dated as _ca._ 1000 to _ca._ 1150 A.D. The date of
the _Siddhānta Siromaṇi_ is more certain for we know it was
written in about 1150 by Bhāskara (born 1114). Thus both these
passages must have been written within a century of the great clock-tower
made by Su Sung. The technical details will lead us to suppose there is
more than a temporal connection.
We have already noted that the armillary spheres and celestial globes
described just before these extracts are more similar in design to
Chinese than to Ptolemaic practice. The mention of mercury and of sand
as alternatives to water for the clock's fluid is another feature very
prevalent in Chinese but absent in the Greek texts. Both texts seem
conscious of the complexity of these devices and there is a hint (it is
lost and revealed) that the story has been transmitted, only half
understood, from another age or culture. It should also be noted that
the mentions of cords and strings rather than gears, and the use of
spheres rather than planispheres would suggest we are dealing with
devices similar to the earliest Greek models rather than the later
devices, or with the Chinese practice.
A quite new and important note is injected by the passage from the
Bhāskara text. Obviously intrusive in this astronomical text we have
the description of two "perpetual motion wheels" together with a third,
castigated by the author, which helps its perpetuity by letting water
flow from a reservoir by means of a syphon and drop into pots around the
circumference of the wheel. These seem to be the basis also, in the
extract from the _Sūrya Siddhānta_, of the "wonder-causing
instrument" to which mercury must be applied.
In the next sections we shall show that this idea of a perpetual motion
device occurs again in conjunction with astronomical models in Islam and
shortly afterwards in medieval Europe. At each occurrence, as here,
there are echoes of other cultures. In addition to those already
mentioned we find the otherwise mysterious "peacock, man and monkey,"
cited as parts of the jackwork of astronomical clocks of Islam,
associated with the weight drive so essential to the later horology in
Europe.
We have already seen that in classical times there were already two
different types of protoclocks; one, which may be termed
"nonmathematical," designed only to give a visual aid in the conception
of the cosmos, the other, which may be termed "mathematical" in which
stereographic projection or gearing was employed to make the device a
quantitative rather than qualitative representation. These two lines
occur again in the Islamic culture area.
Nonmathematical protoclocks which are scarcely removed from the
classical forms appear continuously through the Byzantine era and in
Islam as soon as it recovered from the first shocks of its formation.
Procopius (died _ca._ 535) describes a monumental water clock which was
erected in Gaza _ca._ 500.[17] It contained impressive jackwork, such as
a Medusa head which rolled its eyes every hour on the hour, exhibiting
the time through lighted apertures and showing mythological
interpretations of the cosmos. All these effects were produced by
Heronic techniques, using hydraulic power and puppets moved by strings,
rather than with gearing.
Again in 807 a similarly marvelous exhibition clock made of bronze was
sent by Harun-al-Rashid to the Emperor Charlemagne; it seems to have
been of the same type, with automata and hydraulic works. For the
succeeding few centuries, Islam was in its Golden Age of development of
technical astronomy (_ca._ 950-1150) and attention may have been
concentrated on the more mathematical protoclocks. Towards the end of
the 12th century, however, there was a revival of the old tradition,
mainly at the court of the Emperor Saladin (1146-1173) when a great
automaton water clock, more magnificent than any hitherto, was erected
in Damascus. It was rebuilt, after 1168, by Muḥammad b. 'Alī b.
Rustum, and repaired and improved by his son, Fakhr ad-dīn
Riḍwān b. Muḥammad,[18] who is most important as the author of
a book which describes in considerable technical detail the construction
of this and other protoclocks. Closely associated with his book one also
finds texts dealing with perpetual-motion devices, which we shall
consider later.