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.