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142 speculative power or originality to be able to make much use of their observations, few of which passed into the hands of European astronomers. Regiomontanus (chapter, § 68), if he had lived, might probably have to a considerable extent anticipated Tycho, but his short life was too fully occupied with the study and interpretation of Greek astronomy for him to accomplish very much in other departments of the subject. The Landgrave and his staff, who were in constant communication with Tycho, were working in the same direction, though on the whole less effectively. Unlike the Arabs, Tycho was, however, fully impressed with the idea that observations were only a means to an end, and that mere observations without a hypothesis or theory to connect and interpret them were of little use.

The actual accuracy obtained by Tycho in his observations naturally varied considerably according to the nature of the observation, the care taken, and the period of his career at which it was made. The places which he assigned to nine stars which were fundamental in his star catalogue differ from their positions as deduced from the best modern observations by angles which are in most cases less than 1', and in only one case as great as 2' (this error being chiefly due to refraction (chapter, § 46), Tycho's knowledge of which was necessarily imperfect). Other star places were presumably less accurate, but it will not be far from the truth if we assume that in most cases the errors in Tycho's observations did not exceed 1' or 2'. Kepler in a famous passage speaks of an error of 8' in a planetary observation by Tycho as impossible. This great increase in accuracy can only be assigned in part to the size and careful construction of the instruments used, the characteristics on which the Arabs and other observers had laid such stress. Tycho certainly used good instruments, but added very much to their efficiency, partly by minor mechanical devices, such as the use of specially constructed "sights" and of a particular method of graduation, and partly by using instruments capable only of restricted motions, and therefore of much greater steadiness than instruments which were able to point to any part of the sky. Another extremely important idea