HALL, ABERRATION CONSTAM'. 



51 



Bessel, edited hy Engelmanii, I'aiid II, s. 7(1. I made an cxaiiiinatiou of 

 the errors of several of the live (l(\i>;r(*(> mailcs, iakcii a<T'ordiTig to my 

 notation, and found results so differcnl fi-oni (liosc <!f !»i-. IJiiinnow that 

 I think thoy can onl.v be oxplaiiUMl a.s aliovr. 



Discussions of the Pistor and Martins ciiclcs caii he lound also in the 

 Annals of the Leiden Observatory, the volumes of the Naval Observatory, 

 Washington, and in articles by I'rofessor Jioss, in (lonld's Astronomical 

 Journal. As I understand it. the divisions of these circles were probably 

 made by means of successive applications of dillerent standards. Thus 

 the 10° marks were first cut. Then these intervals were bisected. Then 

 the singles degrees were cut by starting from the 5° marks, and applying 

 successively a standa.rd degree, and so on. Thus, there w(uild be a cumu- 

 lative error arising from the error of the standard, to be combined with 

 the probable error of the placing of the standard in position. It would 

 hardly answer, therefore, in the case of these circles, to determine the 

 division errors of the 5° lines, and then interpolate between them. For 

 ordinary work the safest way might be to turn the circle freciuently on 

 the axis, and not a])j>ly any division errors at all. Both circles go on 

 tapering axes, and are pushed up by collars held by screws, so that the 

 circles can be revolved into any position. 



Counting the circle divisions in the manner I have adopted, the follow- 

 ing lines have been used for Polaris and the nadir in the observations pub- 

 lished in this paper, the readings being those given under microscope I 

 when the clamp is east. 



For the Nadir 71"= 

 For Polaris 



32'— 34'. 



Above pole 20i° 



Reflected Ii8 



(«'— 06' 

 00—02 



Ut io w pole :J02° 36—38' 



R- flecLt-u 120 28—30 



Since the divisions used for the Polaris observations were not changed 

 during this series, the errors would not enter into the computation of the 

 aberration constant. But for the purpose of examining the latitude as 

 found from these observations a determination was made of the. special 

 marks according to the method described by Bessel in the Abhandlungen. 

 The mean of the divisions 0°, 90°, 180°, 270° is supposed to have no error. 

 The errors as determined are the means of the errors of the four marks 

 pointed on with the microscopes. 



+0.51 



+0.06" 



-0.40 



Position 1. 

 +0.20" 

 +0.03 

 +0.03 



0.11 



+0.62 



+0.26" 



71° 32' 



+0.09 



+0.10" 



Position 2. 



+0.40' 



+0.31 



—0.39 



+0.11 



