o^Bessel's Astronomical Observations. 171 



likewise in all other investigations which are founded on ob- 

 servations with the circle, is the pole as determined by the 

 mean of the upper and lower passages of « and 8 Ursce 

 Minoris. This fixed point I have always endeavoured to ob- 

 tain with such a degree of accuracy that I never reversed the 

 instrument before its determination had the weight of 30 ob- 

 servations, five of which were usually made at each passage. 

 I have thought such a large number requisite, in order that 

 the uncertainty which they leave might not too unequally in- 

 crease the uncertainty of every single observation of a star in 

 the different periods between two reversions, even when there 

 are considerably more than 30 observations in one period. This 

 arrangement of the observations allows, indeed, to assign an 

 equal value to every measured distance of a star from the fixed 

 point, as the inequality, which strictly taken still remains, 

 thereby becomes inconsiderable ; it would besides not be easy 

 correctly to estimate it, as it undoubtedly does not depend on 

 the number of observations only. I have therefore used the 

 two polar stars only as the means of ensuring the same point 

 of comparison, not caring whether that point be the true pole 

 or not : the admission of other more distant stars would have 

 created the difficulty of drawing into the investigation other 

 points of the division possibly affected with different errors; 

 an inequality of this kind was not to be apprehended with re- 

 gard to the two above-mentioned stars, as the verniers of the 

 circle cover spaces of 4° 30', which are greater than the di- 

 stance of these stars. 



The places of the pole were determined from the beginning 

 of the observations to the end of 1821, by applying the above 

 determined thermometrical correction of refraction as follows : 



Y2 



Period 



