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Rh error not much exceeding a minute. An important step forward as regards the accurate determination of time was made by the Arabs in the ninth century. Ibn Yunis mentions a solar eclipse observed at Bagdad on the 30th November 829 by Ahmed Ibn Abdallah, called Habash, who at the beginning of the eclipse found the altitude of the sun to be 7°, while at the end the altitude was 24°. This seems to have been the earliest though crude attempt to use observations of altitude to indicate time, but the advantage of the method was evident, and at the lunar eclipse on the 12th August 854 the altitude of Aldebaran was measured equal to 45° 30′. Ibn Yunis adds that he from this made out the hour-angle to be 44° by means of a planisphere. Ibn Yunis communicates a number of other instances from the tenth century, but the instruments used were very small, and only divided into degrees; and though Al Battani gave formulæ for the computation of the hour-angle, the Arabians generally contented themselves with the approximate graphical determination by the so-called astrolabe or planisphere.

In Europe the use of observations of altitude for determining time was introduced in 1457 by Purbach, who, at the beginning and end of the lunar eclipse on the 3rd September, measured the altitude of "penultima ex Plejadibus." Bernhard Walther was the first to introduce in observatories the use of clocks driven by weights. Thus we find among his observations one of the rising of Mercury. At the time of rising he attached the weight to a clock of which the hour-wheel had fifty-six teeth, and as one hour and thirty-five teeth passed before the sun rose, he concluded that the interval had been one hour thirty-seven minutes. Walther