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Rh of Ptolemy must have been familiar to him. The advantage of meridian observations for many purposes was also well known before his time, particularly for finding the declination of the sun, which gave its place in the zodiac by the tables. Hagecius had even observed the altitude and time of transit of the new star over the meridian, but nobody had erected an instrument permanently in the meridian. The great superiority as to stability which a mural quadrant possessed over the armillæ did not escape Tycho; and as he was the first thoroughly to perceive the influence of refraction in altering the apparent positions of stars, the wish naturally arose to observe the stars at their greatest altitude on the meridian, where that influence was smallest.

From the meridian quadrant to quadrants which could be placed in any azimuth the transition was simple enough, and we find accordingly among the instruments at Meragah an "instrument des quarts de circles mobiles." This consisted of an azimuth circle on which were two quadrants turning on a common vertical axis, by which two observers could find the altitudes and difference of azimuth of two objects. In Europe an azimuth instrument seems to have been first used by Landgrave Wilhelm IV., who observed altitudes and azimuths of the new star of 1572, apparently by setting the instrument to a certain whole or half degree of azimuth, and measuring the altitude when the star reached that azimuth. Quadrants capable of being turned round a vertical axis had