st time by
Wiedemann,[20] in which al-Biruni explains how a special train of
gearing may be used to show the revolutions of the sun and moon at their
relative rates and to demonstrate the changing phase of the moon,
features of fundamental importance in the Islamic (lunar) calendrical
system. This device necessarily uses gear wheels with an odd number of
teeth (_e.g._, 7, 19, 59) as dictated by the astronomical constants
involved (see fig. 10). The teeth are shaped like equilateral triangles
and square shanks are used, exactly as with the Antikythera machine.
Horse-headed wedges are used for fixing; a tradition borrowed from the
horse-shaped _Far[=a]s_ used to fasten the traditional astrolabe. Of
special interest for us is the lunar phase diagram, which is just the
same in form and structure as the lunar volvelle that occurs later in
horology and is still so commonly found today, especially as a
decoration for the dial of grandfather clocks.

[Illustration: Figure 11.--GEARED ASTROLABE BY MU[H.]AMMAD B. AB[=I] BAKR
OF ISFAHAN, A.D. 1221-1222. (_Photo courtesy of Science Museum,
London._)]

Biruni's calendrical machine is the earliest complicated geared device
on record and it is therefore all the more significant that it carries a
feature found in later clocks. From the manuscript description alone one
could not tell whether it was designed for automatic action or merely to
be turned by hand. Fortunately this point is made clear by the most
happy survival of an intact specimen of this very device, without doubt
the oldest geared machine in existence in a complete state.

[Illustration: Figure 12.--GEARING FROM ASTROLABE SHOWN IN FIGURE 11.
The gear train count is as follows: 48-13+8-64+64-64+10-60. The pinion
of 8 has been incorrectly replaced by a more modern pinion of 10. The
gear of 48 should make 13 (lunar) rotations while the double gear of
64+64 makes 6 revolutions of double months (of 29-30 days) and the gear
of 60 makes a single turn in the hegiral year of 354 days. (_Photo
courtesy of Science Museum, London._)]

This landmark in the history of science and technology is now preserved
at the Museum of the History of Science, Oxford, England.[21] It is an
astrolabe, dated 1221-22 and signed by the maker, Mu[h.]ammad b. Ab[=i]
Bakr (died 1231-32) of Isfahan, Persia (see figs. 11 and 12). The very
close resemblance to the design of Biruni is quite apparent, though the
gearing has been simplified very cleverly so