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.

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

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:

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

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 Salzburg14 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