Chapter 2

Gaius Sulpicius Gallus ... at a time when ... he happened to be at the house of Marcus Marcellus, his colleague in the consulship [166 B.C.], ordered the celestial globe to be brought out which the grandfather of Marcellus had carried off from Syracuse, when that very rich and beautiful city was taken [212 B.C.].... Though I had heard this globe (sphaerae) mentioned quite frequently on account of the fame of Archimedes, when I saw it I did not particularly admire it; for that other celestial globe, also constructed by Archimedes, which the same Marcellus placed in the temple of Virtue, is more beautiful as well as more widely known among the people. But when Gallus began to give a very learned explanation of the device, I concluded that the famous Sicilian had been endowed with greater genius than one would imagine possible for human being to possess. For Gallus told us that the other kind of celestial globe, which was solid and contained no hollow space, was a very early invention, the first one of that kind having been constructed by Thales of Miletus, and later marked by Eudoxus of Cnidus--a disciple of Plato, it was claimed--with constellations and stars which are fixed in the sky. He also said that many years later Aratus ... had described it in verse.... But this newer kind of globe, he said, on which were delineated the motions of the sun and moon and of those five stars which are called wanderers, or, as we might say, rovers [_i. e._, the five planets], contained more than could be shown on the solid globe, and the invention of Archimedes deserved special admiration because he had thought out a way to represent accurately by a single device for turning the globe, those various and divergent movements with their different rates of speed. And when Gallus moved [_i.e._, set in motion] the globe, it was actually true that the moon was always as many revolutions behind the sun on the _bronze_ contrivance as would agree with the number of days it was behind in the sky. Thus the same eclipse of the sun happened on the globe as would actually happen, and the moon came to the point where the shadow of the earth was at the very time when the sun (appeared?) out of the region ... [several pages are missing in the manuscript; there is only one].

_De republica_, I, xiv (21-22), Keyes' translation.

When Archimedes put together in a globe the movements of the moon, sun and five wandering [planets], he brought about the same effect as that which the god of Plato did in the Timaeus when he made the world, so that one revolution produced dissimilar movements of delay and acceleration.

_Tusculanae disputationes_, I, 63.

Later descriptions from Ovid, Lactantius, Claudian, Sextus Empiricus, and Pappus, respectively, are (italics supplied):

There stands a globe suspended by a Syracusan's skill in an enclosed bronze [frame, or sphere--or perhaps, in enclosed air], a small image of the immense vault [of heaven]; and the earth is equally distant from the top and bottom; that is brought about by its [_i. e._, the outer bronze globe's] round form. The form of the temple [of Vesta] is similar....

Ovid, _Fasti_ (1st century, A.D.), VI, 277-280, Frazer's translation.

The Sicilian Archimedes, was able to make a reproduction and model of the world in concave _brass_ (concavo aere similitudinem mundi ac figuram); in it he so arranged the _sun_ and _moon_ and resembling the celestial revolutions (caelestibus similes conversionibus); and while it revolved it exhibited not only the accession and recession of the sun and the waxing and waning of the moon (incrementa deminutionesque lunae), but also the unequal _courses of the stars_, whether fixed or wandering.

Lactantius, _Institutiones divinae_ (4th century, A.D.), II, 5, 18.

Archimedes' sphere. When Jove looked down and saw the heavens figured in a sphere of _glass_, he laughed and said to the other gods: "Has the power of mortal effort gone so far? Is my handiwork now mimicked in a fragile globe?" An old man of Syracuse had imitated on earth the laws of the heavens, the order of nature, and the ordinances of the gods. Some hidden influence within the sphere directs the various courses of the _stars_ and actuates the lifelike mass with definite motions. A false _zodiac_ runs through a year of its own and a toy _moon_ waxes and wanes month by month. Now bold invention rejoices to make its own heaven revolve and sets the _stars_ [planets?] in motion by human wit....

Claudian, _Carmina minora_ (_ca._ A.D. 400), LI (LXVIII), Platnaure's translation.

The things that move by themselves are more wonderful than those which do not. At any rate, when we behold an Archimedean sphere in which the sun and the rest of the stars move, we are immensely impressed by it, not by Zeus because we are amazed at the _wood_, or at the movements of these [bodies], but by the devices and causes of the movements.

Sextus Empiricus, _Adversus mathematicos_ (3rd century, A.D.), IX, 115, Epps' translation.

Mechanics understand the making of spheres and know how to produce a model of the heavens (with the courses of the stars moving in circles?) by mean of equal and circular motions of _water_, and Archimedes the Syracusan, according to some, knows the cause and reasons for all of these.

Pappus (3rd century, A.D.), _Works_ (Hultsch edition), VIII, 2, Epps' translation.

A similar arrangement seems to be indicated in another mechanized globe, also mentioned by Cicero and said to have been made by Posidonius:

But if anyone brought to Scythia or Britain the globe (sphaeram) which our friend Posidonius [of Apameia, the Stoic philosopher] recently made, in which each revolution produced the same (movements) of the _sun_ and _moon_ and _five_ wandering stars as is produced in the sky each day and night, who would doubt that it was by exertion of reason?... Yet doubters ... think that Archimedes showed more knowledge in producing movements by revolutions of a globe than nature (does) in effecting them though the copy is so infinitely inferior to the original....

_De natura deorum_, II, xxxiv-xxxv (88), Yonge's translation.

In spite of the lack of sufficient technical details in any case, these mechanized globe models, with or without geared planetary indicators (which would make them highly complex machines), bear a striking resemblance to the earliest Chinese device described by Chang Hêng. One must not reject the possibility that transmission from Greece or Rome could have reached the East by the beginning of the 2nd century, A.D., when he was working. It is an interesting question, but even if such contact actually occurred, very soon afterwards, as we shall see, the western and eastern lines of evolution parted company and evolved so far as can be seen, quite independently until at least the 12th century.

The next Hellenistic source of which we must take note is a fragmentary and almost unintelligible chapter in the works of Hero of Alexandria. Alone and unconnected with his other chapters this describes a model which seems to be static, in direct contrast to all other devices which move by pneumatic and hydrostatic pressures; it may well be conjectured that in its original form this chapter described a mechanized rather than a static globe:

The World represented in the Centre of the Universe: The construction of a transparent globe containing air and liquid, and also of a smaller globe, in the centre, in imitation of the World. Two hemispheres of glass are made; one of them is covered with a plate of bronze, in the middle of which is a round hole. To fit this hole a light ball, of small size, is constructed, and thrown into the water contained in the other hemisphere: the covered hemisphere is next applied to this, and, a certain quantity of the liquid having been removed from the water, the intermediate space will contain the ball; thus by the application of the second hemisphere what was proposed is accomplished.

_Pneumatics_, XLVI, Woodcroft's translation.

It will be noted that these earliest literary references are concerned with pictorial, 3-dimensional models of the universe, moved perhaps by hand, perhaps by waterpower; there is no evidence that they contained complicated trains of gears, and in the absence of this we may incline to the view that in at least the earliest such models, gearing was not used.

The next developments were concerned on the one hand with increasing the mathematical sophistication of the model, on the other hand with its mechanical complexity. In both cases we are most fortunate in having archaeological evidence which far exceeds any literary sources.

The mathematical process of mapping a sphere onto a plane surface by stereographic projection was introduced by Hipparchus and had much influence on astronomical techniques and instruments thereafter. In particular, by the time of Ptolemy (_ca._ A.D. 120) it had led to the successive inventions of the anaphoric clock and of the planispheric astrolabe.[12] Both these devices consist of a pair of stereographic projections, one of the celestial sphere with its stars and ecliptic and tropics, the other of the lines of altitude and azimuth as set for an observer in a place at some particular latitude.

In the astrolabe, an openwork metal rete containing markings for the stars, etc., may be rotated by hand over a disc on which the lines of altitude and azimuth are inscribed. In the anaphoric clock a disc engraved with the stars is rotated automatically behind a fixed grille of wires marking lines of altitude and azimuth. Power for rotating the disc is provided by a float rising in a clepsydra jar and connected, by a rope or chain passing over a pulley to a counterweight or by a rack and pinion, to an axle which supported the rotating disc and communicated this motion to it.[13]

Parts of two such discs from anaphoric clocks have been found, one at Salzburg[14] and one at Grand in the Vosges,[15] both of them dating from the 2nd century A.D. Fortunately there is sufficient evidence to reconstruct the Salzburg disc and show that it must have been originally about 170 cm. in diameter, a heavy sheet of bronze to be turned by the small power provided by a float, and a large and impressive device when working (see fig. 5). Literary accounts of the anaphoric clock have been analyzed by Drachmann; there is no evidence of the representation of planets moved either by hand or by automatic gearing, only in the important case of the sun was such a feature included of necessity. A model "sun" on a pin could be plugged in to any one of 360 holes drilled in at equal intervals along the band of the ecliptic. This pin could be moved each day so that the anaphoric clock kept step with the seasonal variation of the times of sunrise and sunset and the lengths of day and night.

The anaphoric clock is not only the origin of the astrolabe and of all later planetary models, it is also the first clock dial, setting a standard for "clockwise" rotation, and leaving its mark in the rotating dial and stationary pointer found on the earliest time-keeping clocks before the change was made to a fixed dial and moving hand.

We come finally to a piece of archaeological evidence that surpasses all else. Though badly preserved and little studied it might well be the most important classical object ever found; entailing a complete re-estimation of the technical prowess of the Hellenistic Greeks. In 1901 a sunken treasure ship was discovered lying off the island of Antikythera, between Greece and Crete.[16] Many beautiful classical works of statuary were recovered from it, and these are now amongst the greatest treasures of the National Museum at Athens, Greece. Besides these obviously desirable art relics, there came to the surface some curious pieces of metal, accompanied by traces of what may have been a wooden casing. Two thousand years under the sea had reduced the metal to a mess of corroded fragments of plates, powdered verdigris, and still recognizable pieces of gear wheels.

If it were not for the established dates for other treasure from this ship, especially the minor objects found, and for traces of inscriptions on this metal device written in letters agreeing epigraphically with the other objects, one would have little doubt in supposing that such a complicated piece of machinery dated from the 18th century, at the earliest. As it is, estimates agree on _ca._ 65 B.C. ±10 years, and we can be sure that the machine is of Hellenistic origin, possibly from Rhodes or Cos.

The inscriptions, only partly legible, lead one to believe that we are dealing with an astronomical calculating mechanism of some sort. This is born out by the mechanical construction evident on the fragments. The largest one (fig. 6) contains a multiplicity of gearing involving an annular gear working epicyclic gearing on a turntable, a crown wheel, and at least four separate trains of smaller gears, as well as a 4-spoked driving wheel. One of the smaller fragments (fig. 7, bottom) contains a series of movable rings which may have served to carry movable scales on one of the three dials. The third fragment (fig. 7, top) has a pair of rings carefully engraved and graduated in degrees of the zodiac (this is, incidentally, the oldest engraved scale known, and micrometric measurements on photographs have indicated a maximum inaccuracy of about 1/2° in the 45° present).

Unfortunately, the very difficult task of cleaning the fragments is slow, and no publication has yet given sufficient detail for an adequate explanation of this object. One can only say that although the problems of restoration and mechanical analysis are peculiarly great, this must stand as the most important scientific artifact preserved from antiquity.

Some technical details can be gleaned however. The shape of the gear teeth appears to be almost exactly equilateral triangles in all cases (fig. 8), and square shanks may be seen at the centers of some of the wheels. No wheel is quite complete enough for a count of gear teeth, but a provisional reconstruction by Theophanidis (fig. 9) has shown that the appearances are consistent with the theory that the purpose of the gears was to provide the correct angular ratios to move the sun and planets at their appropriate relative speeds.

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

_Note added in proof_:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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