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the most important instruments in use at Alexandria were the so-called spheres or armillæ. These are said to have been used in China at an early date, but the invention has doubtless been made independently by the Greek astronomers. They were probably known at the time of Timocharis and Aristillus (about 300 B.C.), and it is certain that Hipparchus employed them. In the complicated form used by him and his successors (called by Tycho "armillæ zodiacales") the instrument consisted of six circles, of which the largest represented the meridian, and was carefully placed in position on a solid stand. On the inner rim it was furnished with two pivots, representing the north and south poles, on which turned a slightly smaller circle, the solstitial colure, to which was fixed immovably and at right angles another of the same size, representing the ecliptic. The colure was furnished with pivots representing the poles of the ecliptic, and on these turned two circles, one larger than the colure, another smaller than it, while the latter enclosed a sixth circle, which could slide inside it, and was furnished with two sights diametrically opposite to each other. With this instrument the difference of longitude and latitude could be measured, the circles being divided to one-sixth degree, while half that quantity could be estimated.