t/'Bessel's Astronomical Observations. 105 



If, instead of 0-0020779, we put 0-0020779 (1 + the calcu- 

 lated refraction is thereby changed by 



-fo (t-48 75) Q-0020779-j _ m j 



[l + ( r - 50) 0-0020779] [1 - 1° 25- 0-0020779] 



and the polar distance of a star calculated from the obser- 

 vations suffers the change 



— ( m + m i)i for the upper passage south of zenith 



+ { m — n /}j north of zenith 



—\m — m')i lower 

 where m' is the same for the pole as m for the star. 



In order to determine i by observation, I have calculated 

 by this formula all stars observed up to the end of the year 

 1821, the zenith distance of which exceeds 60°; I have taken 

 the mean of all observations made in every position of the in- 

 strument, and compared the single ones with this mean, and 

 thence, agreeably to the method of least squares, I have formed 

 the following 56 equations of condition. 



Urwe 



