4 t2 Onthe Sixth Section q/Bessel's Astronomical Observations. 



{nation, all deviations observed during a certain period, of 

 the axis from the horizon, of the middle wire from the mark, 

 and of the instrument from the pole : it supposes the inva- 

 riability of the collimation during two periods, and the suc- 

 cess has proved that this may be done : it is besides 

 apparent that a similar supposition must always be made for 

 longer or shorter spaces of time. If the eastern deviation of 

 the wire from the mark be designated by 15A, the eastern 

 azimuth of the mark by 15 Aa, we have for the southern ho- 

 rizon Aa+A = — n sec. <p -\-b tg<p + c 

 astronomical observations give p=.n-\-kc; n being eliminated 

 we obtain 



Aa—— A— p. sec <p + b t g <p + {1 + & seepje 

 where for A, p, b, the means of the values obtained for all 

 passages of the pole stars must be substituted. The values of 

 15A were registered in the last column of the Journal as often 

 as circumstances permitted ; those of b are interpolated from 

 the beginning and end of the periods. The comparison of 

 this equation with that derived from the preceding period, 

 gives the required determination of c. For the period above 

 stated (from June 12 to June 27, 1820), the equation was {for 

 example) A a= + 0"'574 -f- 2-724' c 



for the preceding one from 27th May to 10th June 



A a = — 0"-2855 + 2-7388 c 

 Hence on the supposition of the error of collimation being 

 during the two periods equal, but on different sides 

 c= — 0"-1576 and n= — 0"-0881. 

 In this manner the errors of collimation from 27th May 

 to 27th October were found as follow : 



where there is no considerable alteration. Were the cor- 

 rection above designated by /3 not = o, the value of c found 

 in this way would require the correction + (3tg %f. 



For 



