Dreyer — On Astronomical Transit Observations. 501. 



equation in the chronograpliic method was cletermraed only once, and 

 a long time after (B. - A. == + 0^*11, January 2, 1866) in Leipzig. 

 In the determination of the difference of the longitude hetween 

 Leipzig and Gotha, the personal equation was not eliminated by 

 taking the mean between the results, found before and after the 

 observers changing stations, but in the reduction of the series of 

 observations diuing which B. observed in Leipzig, the equation found 

 at this station was used, and likewise, in the reduction of the 

 other Scries, the equation found in Gotha. According to the above- 

 mentioned experiences, it would have been impossible to use the 

 common method, which is only practicable when direct comparisons 

 show that the personal equations between the two observers had not 

 changed in the mean time. To change the stations without examin- 

 ing the equation at all (as in the determination of the difference of 

 longitude between Berlin and Leipzig) seems doubtful. 



Passing from the variation of the personal error, during longer inter- 

 vals of time, and in the different methods of observing, we shall now 

 consider a series of circumstances which, until a short time ago, were 

 rather enigmatical, and have contribiited a good deal to make many 

 astronomers look upon personal equations as a very weak point in 

 modern practical astronomy.* We allude to the changes in the personal 

 errors, which often arise from the reversal of the instrument. In itself 

 it sounds absurd that the position of the instrument should have any 

 influence upon the error of the observer ; but if we remember that a 

 great number of such observations, for which several observers are 

 wanted, and which accordingly require the determination of the 

 personal equations, are made with transit instruments, with what is 

 known as a broken telescope, the matter becomes different, because the 

 direction of the star's passage through the field in such an instrument 

 is different in its two positions. If we observe a star passing th& 

 meridian south of the zenith, it will, in both positions of the instru- 

 ment, go from left to right through the field, but the inclination of the 

 path to the horizon will be different, depending not only on the zenith 

 distance, but also on the position. When the observer is at the eastern 

 end of the axis, the star will go from the third quadrant to the first 

 one, and when he stands at the western end, it will go from the 

 second to the fourth. A star which culminates in the zenith will go 

 vertically through the field, observed from east upwards, from west 

 downwards. Between the zenith and the pole the motion will take 

 place in a similar way from right to left. 



We shall first consider the 'results obtained by artificial stars. C. 

 Wolf has taken 1 1 groups of observations with his eye-and-ear appa- 

 ratus, each group consisting of 40 transits ; and by placing a prism 



* From Brulins' Biography of Encke we learn that the latter " felt disgust at 

 personal equations" (letter to Gerling from 1855). Upon the whole Encke seems 

 to have been rather sceptical with respect to the attainable exactitude in astronomi- 

 cal observations. 



