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322 been known long before, but as it was so much easier to graduate a straight line than an arc, the triquetrum continued to be the favourite instrument for measuring altitudes down to the end of the sixteenth century. Tycho did not think much of this instrument, which he calls "instrumentum parallacticum sive regularum," and he did not make much use of the two he had constructed, and one of which was of large dimensions, and furnished with an azimuth circle 16 feet in diameter. He preferred the "quadrans azimuthalis," and constructed four instruments of this kind, which were extensively used, though chiefly for merely observing altitudes, while the azimuths were rarely taken, especially during his later years. The largest quadrant (quadrans magnus chalibeus) was enclosed in a square (also of steel), of which the side was equal to the radius of the quadrant. Two of the sides were graduated, and the alidade pointed to these graduations as well as to those on the arc, so that the instrument was a combination of a quadrant and the "quadratum geometricum" of Purbach (which the Arabians had also known), which increased the solidity of the instrument.

An important use to which the quadrants were put at Uraniborg was the determination of time. At Alexandria the beginning, middle, or end of the hour was generally the only indication of time which accompanied the observations of planets, which was perhaps sufficient, owing to the limited accuracy of the observations. The time was found by water- or sand-clocks, which were verified by observing the culmination of some of the forty-four stars which Hipparchus had selected so well that the time could be determined with an