142 A Short History of Astronomy [Cn. v. 



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 HI., 68), 

 if he had lived, might probably have to a consider- 

 able 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 observa- 

 tions 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 i', 

 and in only one case as great as 2' (this error being chiefly 

 due to refraction (chapter n., 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 obser- 

 vations did not exceed i' 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 

 * By transversals. 



