sict. i*.] DISSERTATION SECOND. 129 



Among the improvements which he made in the art of 

 astronomical observation, was that of verifying the instru- 

 ments, or determining their errours by actual observation, 

 instead of trusting, as had been hitherto done, to the sup- 

 posed infallibility of the original construction. 



One of the first objects to which the Danish astronomer 

 applied himself was the formation of a new catalogue of the 

 fixed stars. That which was begun by Hipparchus, and 

 continued by Ptolemy, did not give the places of the 

 stars with an accuracy nearly equal to that which the new 

 instruments were capable of reaching ; and it was besides 

 desirable to know, whether the lapse of twelve centuries 

 had produced any unforeseen changes in the heavens. 



The great difficulty in the execution of this work arose 

 from the want of a direct and easy method of ascertaining 

 the distance of one heavenly body due east or west of an- 

 other. The distance north or south, either from one 

 another or from a fixed plane, that of the equator, was 

 easily determined by the common method of meridian al- 

 titudes, the equator being a plane which, for any given 

 place on the earth's surface, retains always the same posi- 

 tion. But no plane extending from north to south, or pass- 

 ing through the poles, retains a fixed position with respect 

 to an observer, and, therefore, the same way of measuring 

 distances from such a plane cannot be applied. The na- 

 tural substitute is the measure of time ; the interval 

 between the passage of two stars over the meridian, bear- 

 ing the same proportion to twenty-four hours, that the arch 

 which measures their distance perpendicular to the meri- 

 dian, or their difference of right ascension, does to four 

 right angles. 



An accurate measure of time, therefore, would answer 

 the purpose, but such a measure no more existed in the 

 age of Tycho, than it had done in the days of Hipparchus 



