One of the most important problems which called for solution at the hands of the Moorish astronomers was that of the recession of the heavenly bodies, by which, when observed at sufficient intervals of time, they were seen to fall short of the positions they might have been expected to reach. This recession, as we have remarked already, had been very accurately studied, and computed as exactly as the methods of the time allowed; but a reason for so remarkable a phenomenon was yet to seek. Alpetrongi boldly declared that the eastward motion was apparent only and not real. He explained that the source of power lay in the _primum mobile_ or ninth sphere; that lying outside the sphere of the fixed stars. From hence the force producing circular motion was derived to the eighth, and so to the inferior spheres; each handing on a part of the impulse to that which lay beneath it. In the course of transmission, however, the prime force became gradually exhausted. Thus, said Alpetrongi, it happens that each sphere moves rather more slowly than the one above it, and so the apparent recession is accounted for in a way which shows it to be relative only and not absolute. Another matter which exercised the minds of those who studied the heavens was the difference of elevation which the heavenly bodies showed according to the seasons of summer and winter. The sun, for example, at noonday of the summer solstice stood, they saw, at his highest point in the heavens, while he sank to his lowest on the shortest day of winter. Between these extremes he held gradually every intermediate position, and as he was meanwhile supposed to be moving in a circular path round the earth, his course came to be conceived of as a spiral alternately rising and declining. How was this spiral motion to be explained? Each sphere, said Alpetrongi, has its own poles, which differ from those of the _primum mobile_, and thus each, while following the motion of the ninth sphere, accomplishes at the same time another revolution about its own proper poles. From the combination of these two movements arises one of the nature of a spiral which fully accounts for the seeming deviations of the heavenly bodies to north or south.[146] Such were the contributions of this philosopher to the astronomy of his time. They were the fruit, he assures us, of patient study of the ancients, and specially of Aristotle and his commentators. He offered them to his age as a distinct improvement on the cumbrous theories of Ptolemy, and as an advance even upon that of Azarchel, whom, in the main, he acknowledges as his master in science. Antiquated and childish as his explanations may seem to us, we cannot help feeling that he had at least grasped firmly some of the chief problems of the sky. He stood in the line of that inquiry and patient progress which have issued in the marvellous discoveries of later times.