of Reichenbach's Circle at Kbnigsberg. 353 



The following table contains all the errors of division suc- 

 cessively found : 



These errors, however small, present some regularity: 

 the greatest part of them might be represented by the form 

 a sin (A + 2u), and be accounted for by an elliptic form which 

 the circle may have assumed by carriage and by being screwed 

 to the axis. There is, however, no perfect regularity, nor 

 could it be expected, as in each diameter the mean of the 

 contingent errors of six divisions must considerably disturb 

 any regularity which might exist. The value of the contin- 

 gent errors of the divisions I have endeavoured to determine, 

 by comparing the mean of the three divisions employed for 

 every point with each individual division; by this means I 

 have found the probable deviation of every division from any 

 law = + 0"'3251. It follows from this number, which de- 

 pends on the examination of 288 divisions, that according to 

 the laws of probability there are among the 7200 divisions of 

 the circle, 



2352 the errors of which are between 



2192 



1295 



5SS 



205 



55 



11 



2 

 There is, therefore, only 1 division out of nearly 26, where 

 the deviation from regularity amounts to 1 second and up- 

 wards. This extraordinary accuracy in a circle of 18 inches 

 radius appears hardly credible, and I avail myself of this op- 

 Vol. 63. No. 313. May 1824. Y y portunity 



