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360 observations of the comet of 1585, as we have just seen, prove conclusively that in that year the great armillæ were in excellent adjustment, so that Tycho cannot have made use of any badly placed meridian mark. I have also computed a number of observed altitudes and azimuths of stars from 1582, and from these it is evident that the zero line of the azimuth circle was within 1′ of the meridian. As Tycho never once alludes to the use of meridian marks or terrestrial azimuth marks (which he could not possibly have seen from the subterranean observatory, where stars near the horizon could only be observed with portable instruments in the open air), while he frequently states that he verified his instruments by observations, it is impossible that he can, even before 1586, have made a mistake of 14′ in azimuth in the adjustment of his numerous instruments.

The astronomical work in Tycho Brahe's observatory must have involved a considerable amount of computing, even though the great globe, no doubt, was very often used for the solution of spherical triangles. Trigonometry had made considerable advances in the fifteenth and sixteenth centuries, and Tycho could build on the labours of Purbach, Regiomontanus, Copernicus, and others, both as regards the solution of triangles and tables of sines and tangents. But