176 



Introduction to the Seventh Section 



counterpoises, the correction of the result of the readings of 

 the circle u arising from this cause, has the following form : 



a sin (m+1° 3?>') + b cos (w+l° 33') 

 and the comparison of the five determinations above given 

 produces a= + 1"-1636, probable error = +0"-1008 

 b = +0-2025 .... ±0-055? 



and next the altitude of the pole free from the error of flexure, 

 and therefore only affected by the errors of division and re- 

 fraction, = 54.° 42' 50"-783, with the probable error + 0"-0455. 

 The probable errors here given are founded on that of a passage 

 observed by reflexion from water = 0"'7277, as the above obser- 

 vations give it. The agreement of the values of the altitude of the 

 pole obtained by the single sets of observations, is as follows : 

 By reversing the instrument .... 54° 42' 

 ( Upper Passage East .... 



\ West 



B )' reflexlon ) Lower Passage East '. . . . 



( West. . . . 



The other method for determining flexure I have carried 

 into effect by combining the observations of a Ursa; Minoris 

 with 69 western and 55 eastern observations of 9 southern 

 stars. The distances from the pole of these 10 stars I have 

 found for the year 1820 as follow: 



50"-814 

 50 -720 

 50 -942 

 50 '744 

 50 -726 



* The observations taken by reflexion of this and the following star are 

 somewhat less accurate than the rest ; it was necessary to open the lower 

 side shutter, which remained closed when higher stars were observed, and 

 thus diminished the draught of air. The 



