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.

[Illustration: 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 classical 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 constitute 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,