258 Introduction to the Seventh Section 



It is evident that the observations may be much improved 

 by adopting a somewhat greater refraction ; for the more ac- 

 curate determination of its increase I "have made use of all 

 stars the zenith distance of which does not exceed 85° (as far 

 as /3 Pevsei inclusive); and by solving the equations of condi- 

 tion I have obtained 



x— x' =■ — 0"-031, probable error = +0-076 

 k =+0"'004624- ..... =+0-0006063 



The stars culminating lower as far as Lyrcc agree very well 

 with this ; but I abstained from taking them into account be- 

 cause the horizontal refraction has already a sensible influence 

 on them, and for determining the horizontal refraction obser- 

 vations at the time of rising and setting of stars may be more 

 advantageously employed than meridian observations. A very 

 complete set of this kind of observations has been made by 

 Dr. Argelander, with Gary's circle, which are contained in 

 this volume; but I reserve for another place the results to be 

 deduced from them. 



The value of x — x' combined with that of x+x' gives 

 x= — 0"-033; x*= +0" - 005; they are therefore almost insen- 

 sible, and it follows that the places of the pole derived from 

 the two pole stars only very nearly agree with those deter- 

 mined from all observations. The difference is so small that 

 it is nearly indifferent which of the two determinations be 

 adopted, but the probability of the second one is greater than 

 that of the former, both from the nature of the instrument and 

 the evidence of the calculated probable errors, which are for 

 so and af only = 0''-076. I have therefore applied these small 

 corrections, as well as those arising from the increase of the 

 refraction, to the polar distances of the stars given in the 5th 

 article; these polar distances have thus been freed from all 

 those errors, the correction of which was announced in the 

 beginning as the object of this investigation. In order to per- 

 ceive, at one view, how great the agx-eement has now become, I 

 present in the following table a comparison of the four deter- 

 minations of the polar distance made for each star, with the 

 most probable one resulting from all observations in both 

 passages, on the supposition of the probable error of each of 



e Q 4 ). 



Polar 



