the northwest frontier of Persia under Nasr-ed-Din as chief astronomer. Here the Ilkhanic tables were prepared. Ulugh-Beg, prince of Samarkand, a grandson of Tamerlane, founded a great observatory in 1420, on the hill of Kolik, where a hundred observers and calculators were employed. Albategnius, another Arab prince, possessed admirable instruments, as we have seen. Astronomy was in favor with princes and caliphs, and flourished accordingly. We have seen that some of the instruments of Albategnius read to one minute of arc (1') and were very likely divided to 2'. The observatory of Nisapur, in Khorassan, had in A. D. 851 a huge armilla reading to 1'. In 992 Al Chogandi set up at Bagdad a sextant of sixty feet radius. In 1260 the observatory of Meraga possessed, among many other instruments, a mural quadrant of twelve feet radius. Ulugh-Beg had a quadrant (perhaps a species of sun-dial) that had a radius of 180 feet. Colossal instruments of the sort permitted accurate readings of angles because the space corresponding to an arc of one minute was correspondingly large. Until the invention of the telescope accuracy was only to be attained by the use of large circles, and the Arabian school anticipated Tycho Brahe in the use of such instruments by several centuries. Some of the Arabian observers employed free-swinging pendulums to measure short intervals of time; and the science of gnomonics—the theory of sun-dialing—was extensively developed by them.
This is the place to describe the system by which Ptolemy explained the world. It will be sufficient to explain the two main problems that any system of astronomy was bound to consider, and to leave details to one side. These two chief problems were: (1) How to account for the rising and setting of the sun, moon, stars and planets—how to explain the general diurnal motion of all celestial bodies; (2) how to explain the motions of the planets among the stars. These motions are, in general, towards the east—but are varied by occasional westward motions, and interrupted by periods of no motion at the 'stations.' As we have seen, Ptolemy declared the earth to be a sphere fixed in the center of the heavens. The sphere of the fixed stars was at an immense distance, so that the earth was a mere point in respect of the distance of the stars and the stars revolved about the earth. All the observed phenomena of the rising and setting of the stars are satisfactorily explained in this way. Ptolemy perfectly understood that they could also be explained by the hypothesis of a rotating earth, but he concluded that it was easier to attribute motion to bodies like the stars which seem to be of the nature of fire, than to the solid earth. The sun, moon and planets share in the diurnal motion of the stars. It will be seen that no mechanical conception of the diurnal motion is attainable in this way without the assumption of crystal spheres. Ptolemy sought an analytic device by which
