The first translation of the _Almagest_ was made by order of Al Mansur’s successor Harun al Rasid (A.D. 765 or 766-A.D. 809), the hero of the _Arabian Nights_. It seems, however, to have been found difficult to translate; fresh attempts were made by _Honein ben Ishak_ (?-873) and by his son _Ishak ben Honein_ (?-910 or 911), and a final version by _Tabit ben Korra_ (836-901) appeared towards the end of the 9th century. Ishak ben Honein translated also a number of other astronomical and mathematical books, so that by the end of the 9th century, after which translations almost ceased, most of the more important Greek books on these subjects, as well as many minor treatises, had been translated. To this activity we owe our knowledge of several books of which the Greek originals have perished. 57. During the period in which the Caliphs lived at Damascus an observatory was erected there, and another on a more magnificent scale was built at Bagdad in 829 by the Caliph Al Mamun. The instruments used were superior both in size and in workmanship to those of the Greeks, though substantially of the same type. The Arab astronomers introduced moreover the excellent practice of making regular and as far as possible nearly continuous observations of the chief heavenly bodies, as well as the custom of noting the positions of known stars at the beginning and end of an eclipse, so as to have afterwards an exact record of the times of their occurrence. So much importance was attached to correct observations that we are told that those of special interest were recorded in formal documents signed on oath by a mixed body of astronomers and lawyers. Al Mamun ordered Ptolemy’s estimate of the size of the earth to be verified by his astronomers. Two separate measurements of a portion of a meridian were made, which, however, agreed so closely with one another and with the erroneous estimate of Ptolemy that they can hardly have been independent and careful measurements, but rather rough verifications of Ptolemy’s figures. 58. The careful observations of the Arabs soon shewed the defects in the Greek astronomical tables, and new tables were from time to time issued, based on much the same principles as those in the _Almagest_, but with changes in such numerical data as the relative sizes of the various circles, the positions of the apogees, and the inclinations of the planes, etc. To Tabit ben Korra, mentioned above as the translator of the _Almagest_, belongs the doubtful honour of the discovery of a supposed variation in the amount of the precession (chapter II., §§ 42, 50). To account for this he devised a complicated mechanism which produced a certain alteration in the position of the ecliptic, thus introducing a purely imaginary complication, known as the =trepidation=, which confused and obscured most of the astronomical tables issued during the next five or six centuries.