These improved methods of calculation were soon applied to astronomy. Al Mamun, whose reign commenced in the year 813, summoned an assembly of scholars learned in that science. They met in the great Babylonian plain, having chosen that place as suitable for their observations, and measured the declination of the ecliptic, which they determined to be 23° 33ʺ. About the same time the secular motion of the heavens began to attract attention. Albategni corrected the observations of Ptolemy here, and showed that the retrograde movement amounted to one degree, not in a century as the Greek philosopher had said, but in a shorter period which is variously stated as sixty-six or seventy years. Alfargan repeated this calculation, and amended that relating to the declination of the ecliptic, which he computed at 23° 35ʺ. This was the progress and these the data which led the Moorish astronomers to abandon the earlier and simpler theories of the _sphere_ as inconsistent with ascertained facts. They were aware of motions among the heavenly bodies not to be explained by the mere supposition that round the earth as a centre moved the concentric spheres on the axes of their poles. It is true that even Ptolemy himself had felt something of this difficulty and had endeavoured to meet it by a theory of eccentrics and epicycles. As knowledge increased, however, this primitive explanation was felt to be cumbrous and unsatisfactory. Aboasar[145] and Azarchel gained fame by boldly striking out in new paths, and later Moorish astronomers eagerly followed the lead thus given them, each adding some modification of his own. Thus then we return to the preface of Alpetrongi prepared to understand his position when he declares himself obliged to depart from previous traditions. He proceeds to avow himself a scholar of Azarchel, but when we examine his work we find that the theory he proposes differs considerably even from that taught by his immediate master. It was one which, through the labours of Michael Scot, as translator of Alpetrongi, exercised no small influence on the study of astronomy among the Latins, and we may well spend a moment in considering the chief features which it presents.