This is made more probable by the existence of a specifically Islamic concentration on the astrolabe, and on its planetary companion instrument, the equatorium, as devices for mechanizing computation by use of geometrical analogues. The ordinary planispheric astrolabe, of course, was known in Islam from its first days until almost the present time. From the time of al-Biruni (_ca._ 1000)--significantly, perhaps, he is well known for his travel account of India--there is remarkable innovation. Most cogent to our purpose is a text, described for the first 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 _Farās_ 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 MUḤAMMAD B. ABĪ 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._)]