438 Introduction to the Sixth Section 



The y contained in the last column of these tables are cal- 

 culated from the formula — -s> where a and a' denote the num- 



a + a 



ber of wires observed by direct vision and by reflexion. The 

 probable error for y = 1 is found = 0" # 453 ; and hence that of the 

 first mean = 0"-1205, that of the second = 0"094; so that the 

 small value of /3 thus found, may without great improbability be 

 attributed to the contingent errors of observation. The mean 

 of both determinations is +0"'\\2, and its probable error 

 = 0" , 0742. This investigation rests on the supposition that the 

 deviation of the instrument from the meridian is dependent on 

 the sine and cosine of the single zenith distance, which is indeed 

 not improbable, but is not proved to be true ; without this sup- 

 position we should have obtained in place of /3, two differ- 

 ences of the deviations for the direct and reflected place of the 

 pole. But other deviations may yet exist which do not com- 

 port with a great circle, and the complete destruction of which 

 is not necessarily obtained by the construction of the instru- 

 ment, by which observations in nearly equal numbers are ob- 

 tained in the two contrary positions of the axis. The errors, 

 however, if existing, would become apparent in the right as- 

 cension of fixed stars, if observed above and below the pole in 

 both positions of the instrument; it may be required of every 

 transit, that either immediately, or after applying the proper 

 corrections, it should constantly give the same right-ascension, 

 whether the star be compared to the fundamental stars above 

 or below the pole in one or the other position of the axis ; a 

 constant difference of these four determinations would indicate 

 an error of the instrument, which would require further inves- 

 tigation. 



This subject being of the highest importance for practical 

 astronomy, I have thought necessary to undertake this inves- 

 tigation, which I have founded on 58 circumpolar stars almost 

 down to the horizon. But before I communicate the results 

 thereby obtained, I must explain my method of adjusting the 

 instrument. 



5. Corrections of the Times of Transit over the middle Wire. 

 The position of the transit has hitherto been adjusted in the 

 Konigsberg observatory by determining the distance of the 

 line of collimation from the pole, by means of observations of 

 the pole star, the line of collimation by reversing, and the devia- 

 tion from the meridian in the equator by the level or the me- 

 ridian mark. The first of these determinations lias in certain 

 seasons some difficulty, from the inconvenience of the moment 

 of one of the passages, which, owing to that circumstance, is 

 commonly not observed. In that case one must be satisfied 



with 



