tical 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