On the Origin of Clockwork, Perpetual Motion Devices, and the Compass Part 2

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.

_Siddhanta Siroma?i_, xi, 50-57, L. Wilkinson's translation, revised by B?pu? deva S(h)?stri, Calcutta, 1861.

Before proceeding to an investigation of the content of these texts it is of considerable importance to establish dates for them, though there are many difficulties in establishing any chronology for Hindu astronomy. The _Surya Siddhanta_ 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 _Siddhanta Siroma?i_ is more certain for we know it was written in about 1150 by Bhaskara (born 1114). Thus both these pa.s.sages 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 pa.s.sage from the Bhaskara 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 circ.u.mference of the wheel. These seem to be the basis also, in the extract from the _Surya Siddhanta_, 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 "peac.o.c.k, man and monkey,"

cited as parts of the jackwork of astronomical clocks of Islam, a.s.sociated with the weight drive so essential to the later horology in Europe.

We have already seen that in cla.s.sical 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 quant.i.tative rather than qualitative representation. These two lines occur again in the Islamic culture area.

Nonmathematical protoclocks which are scarcely removed from the cla.s.sical forms appear continuously through the Byzantine era and in Islam as soon as it recovered from the first shocks of its formation.

Procopius (died _ca._ 535) describes a monumental water clock which was erected in Gaza _ca._ 500.[17] It contained impressive jackwork, such as a Medusa head which rolled its eyes every hour on the hour, exhibiting the time through lighted apertures and showing mythological interpretations of the cosmos. All these effects were produced by Heronic techniques, using hydraulic power and puppets moved by strings, rather than with gearing.

Again in 807 a similarly marvelous exhibition clock made of bronze was sent by Harun-al-Rashid to the Emperor Charlemagne; it seems to have been of the same type, with automata and hydraulic works. For the succeeding few centuries, Islam was in its Golden Age of development of technical astronomy (_ca._ 950-1150) and attention may have been concentrated on the more mathematical protoclocks. Towards the end of the 12th century, however, there was a revival of the old tradition, mainly at the court of the Emperor Saladin (1146-1173) when a great automaton water clock, more magnificent than any hitherto, was erected in Damascus. It was rebuilt, after 1168, by Mu?ammad b. 'Ali b.

Rustum, and repaired and improved by his son, Fakhr ad-din Ri?wan b. Mu?ammad,[18] who is most important as the author of a book which describes in considerable technical detail the construction of this and other protoclocks. Closely a.s.sociated with his book one also finds texts dealing with perpetual-motion devices, which we shall consider later.

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

In the same year [1232] the Saladin of Egypt sent by his amba.s.sadors 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.

[Ill.u.s.tration: 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 pa.s.sage; 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 a.n.a.logues. 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 _Faras_ 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.

[Ill.u.s.tration: Figure 11.--GEARED ASTROLABE BY MU?AMMAD B. ABI 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 ma.n.u.script 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.

[Ill.u.s.tration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11.

The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion of 8 has been incorrectly replaced by a more modern pinion of 10. The gear of 48 should make 13 (lunar) rotations while the double gear of 64+64 makes 6 revolutions of double months (of 29-30 days) and the gear of 60 makes a single turn in the hegiral year of 354 days. (_Photo courtesy of Science Museum, London._)]

This landmark in the history of science and technology is now preserved at the Museum of the History of Science, Oxford, England.[21] It is an astrolabe, dated 1221-22 and signed by the maker, Mu?ammad b. Abi 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.

[Ill.u.s.tration: 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 cla.s.sical 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 const.i.tute 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.

[Ill.u.s.tration: Figure 14.--ISLAMIC PERPETUAL MOTION WHEEL, after ma.n.u.script 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 ill.u.s.tration) 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 a.s.sociated with Ri?wan, which we shall next examine.

[Ill.u.s.tration: Figure 15.--ANOTHER PERPETUAL MOTION WHEEL, after the text cited in figure 14.]

It is of the greatest interest to our theme that the Islamic contributions to horology and perpetual motion seem to form a closely knit corpus. A most important series of horological texts, including those of Ri?wan and al-Jazari, 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 a.s.sociated with texts describing perpetual-motion wheels and other hydraulic devices.

Three ma.n.u.scripts 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 pa.s.sing 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.

[Ill.u.s.tration: 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, peac.o.c.ks, etc., symbolizing the pa.s.sage 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 a.s.sumption; 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 ma.n.u.script 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 n.o.body 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.

[Ill.u.s.tration: 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._)]

[Ill.u.s.tration: 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 ma.n.u.script (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 ma.n.u.script 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, circ.u.mstantial 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 ma.n.u.script 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 ill.u.s.tration (fig. 19) is from a moralized Bible written in northern France, and accompanies the pa.s.sage 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 a.s.sistants in charge of the clock.