o/"Reichenbach's Circle at the Observatory at Konigsberg. 343 



no microscopes, but verniers ; and instead of one additional 

 microscope, two must be applied. But these microscopes can- 

 not be fixed any where but on the alhidade circle; and 

 from this circumstance a change of the angle between them 

 may arise, for the alhidade circle is attached to the principal 

 axis of the instrument ; and as there must always be a little play 

 between this axis and its collar, their centres will not always 

 coincide: and this accidental eccentricity will be mingled with 

 the errors of division which are the objects of investigation, 

 and destroy the accuracy of their determination. In order to 

 avoid the effect of this eccentricity, it is necessary to deter- 

 mine the means of the errors of points diametrically opposite, 

 which may be done by means of four microscopes so placed 

 that two diameters determined by them inclose the angle 

 which is to be examined. An apparatus of this description, 

 made by M. Pistor, has been used on this occasion ; the mi- 

 croscopes are so constructed that by proper solid clamps they 

 may be fastened to any point of the alhidade. I have in the 

 first place determined the angles from 15° to 15° ; next I have 

 bisected these angles ; and lastly, again bisected the angles of 

 22°*30, and thereby determined all the errors of the divisions 

 of those diameters which belong to multiples of 3f° ; for every 

 diameter I have taken the mean of the two divisions which be- 

 long to it and likewise the preceding and following ones, so 

 that each diameter is determined by the mean of six divisions. 

 In order to obtain the angles of the form n. 15° with the 

 greatest accuracy, and free from all accumulation of error, I 

 have changed the position of the microsopes four times, mak- 

 ing the angle between them successively 60°, 45°, 30° and 1 5°. 

 In all these positions the first microscope was placed on the 

 points 0°, 15°, 30°,. ..330°, 345°, and the other three micro- 

 scopes read off; each of these four sets of observations was 

 repeated on three different days in such a manner, that the 

 angles were brought under the microscope, not in any regular 

 succession, but entirely without any order, by which means 

 I intended to destroy the effect of a change of temperature of 

 the instrument. I denote the error of division of the point u 

 of the circle with the sign with which it is to be added to the 

 reading of the circle by $u and £[<pw-f-$(180 -f w)] by \{/w; 

 agreeably to this notation the single sets of observations have 

 given the following results. 



The 



