$ in] Estimate of Tycho' s Work 143 



was that of systematically allowing as far as possible for 

 the inevitable mechanical imperfections of even the best 

 constructed instruments, as well as for other permanent 

 causes of error. It had been long known, for example, 

 that the refraction of light through the atmosphere had 

 the effect of slightly raising the apparent places of stars 

 in the sky. Tycho took a series of observations to ascer- 

 tain the amount of this displacement for different parts of 

 the sky, hence constructed a table of refractions (a very 

 imperfect one, it is true), and in future observations regularly 

 allowed for the effect of refraction. Again, it was known 

 that observations of the sun and planets were liable to be 

 disturbed by the effect of parallax (chapter IL, 43, 49), 

 though the amount of this correction was uncertain. In 

 cases where special accuracy was required, Tycho accord- 

 ingly observed the body in question at least twice, choosing 

 positions in which parallax was known to produce nearly 

 opposite effects, and thus by combining the observations 

 obtained a result nearly free from this particular source of 

 error. He was also one of the first to realise fully the 

 importance of repeating the same observation many times 

 under different conditions, in order that the various acci- 

 dental sources of error in the separate observations should 

 as far as possible neutralise one another. 



in. Almost every astronomical quantity of importance 

 was re-determined and generally corrected by him. The 

 annual motion of the sun's apogee relative to r , for example, 

 which Coppernicus had estimated at 24", Tycho fixed ut 

 45", the modern value being 61"; the length of the year 

 he determined with an error of less than a second ; and he 

 constructed tables of the motion of the sun which gave its 

 place to within i', previous tables being occasionally 15' or 

 20' wrong. By an unfortunate omission he made no inquiry 

 into the distance of the sun, but accepted the extremely 

 inaccurate value which had been handed down, without 

 substantial alteration, from astronomer to astronomer since 

 the time of Hipparchus (chapter n., 41). 



In the theory of the moon Tycho made several important 

 discoveries. He found that the irregularities in its move- 

 ment were not fully represented by the equation of the 

 centre and the evection (chapter n., 39, 48), but that 



