o/*Bessel's Astronomical Observations. 107 



to appreciate the value of every addition, is it possible to de- 

 rive a real advantage from this circumstance. Each of these 

 equations gives i as accurately as the mean of so many obser- 

 vations, as there are unities in the coefficient of i : but these 

 observations have very different probable errors; they are 

 the greater, the nearer the horizon the observations have been 

 made, partly on account of the dispersion of light, which in- 

 creases in proportion of the refraction, partly on account of 

 the tremor of the stars increasing near the vicinity of the hori- 

 zon, and lastly, on account of the irregularities of the refraction 

 itself, from causes which cannot be taken into the account. 



In order to deduce these probable errors from the observa- 

 tions, i must be known ; they can, therefore, only be obtained 

 by repeated calculations. 



Calling the sum of the squares of the differences between 

 the mean of n observations and every single one, 5 ; and the 

 probable error of a single observation s ; we have 



(n-l) s 2 = (0-6745) 9 s 

 and therefore, for each star, for which an arithmetical mean 

 from n eastern, and another from n' western observations, has 

 been derived 



(»+.«'— 2) s 2 = (0-6745) 2 (s + s). 



By this formula the following probable errors have been 

 determined. 



Z.D. 





 4-6' 

 63' 

 67" 

 70- 

 73- 

 75' 

 80- 

 81- 

 83- 

 84- 

 84- 

 85" 

 85- 

 85- 

 85- 



ss- 

 sg- 



87- 



IS 



38 



19 



O 







36 



11 



88 



n 



9 



52 



8 



26 



38 



50 



59 



25 



27 



10 

 4 

 9 

 9 

 7 



10 

 6 

 3 



stars 



star 



293 



278 



265 



174 



195 



187 



100 



109 



20 



18 



19 



20 



36 



15 



15 



12 



6 



11 



15 



2 



observations 



0-7126 



0-7613 



0-794 



0-892 



0-976 



0-990 



0-907 



1*190 



1-155 



1-693 



1-127 



2-155 



1-850 



2-53 



1-87 



2-41 



2-84 



3-55 



3-79 



The 



