464 KRETZ. 



_ «i + A//o(^i — 1S75) + «2 + Awo(^2 — 1875) + ••• + a„ 4- ^^l^{t„,— 1875; 



— [«i4-A/i„(/i— 1875)] 



, «i + a-i + ••■ 4- ««. , A/'oCA + ^2 + ••• 4- 40 



■ «i — ^I'o ^ 



so that the two results are identical. We can therefore use the 

 formula for r^ given above, and, with the exception of the slight 

 inaccuracy mentioned, the results will be theoretically correct. 

 All the probable errors of the proper motion in the succeed- 

 ing tables were obtained in this way. 



On the following pages are recorded the separate positions 

 of all the stars on the plates. Chase's place, reduced to 1875, 

 is printed in Italics at the end of each list. The headings are 

 plain when taken in connection with the preceding discussion. 

 At the end of each table are given the final means, «, and o., 

 the date of observation, and the proper motion with its probable 

 erroi". a^ and o^, as has been stated, do not include Chase's ob- 

 servations. For the stars numbered i, 2, 4, 5, 6, 7, 8, 9, 10, 14, 

 15, 21, 22, 23, and 24, fj. and fJ-^ were computed by the method 

 detailed above. The other proper motions given in the tables 

 were obtained by subtracting the mean of my determinations 

 from Chase's position, and dividing the difference by the interval 

 in years. They are inclosed in brackets, for the sake of dis- 

 tinction. No probable error was computed for them. The 

 dates of observation are evidently the same in all cases, and are 

 as follows: Plates I-III, 1870.3, Plates IV-VIII, 1875.4, 

 Plates IX-XIV, 1876.4, and Chase 189 1.6. They are not re- 

 peated in the tables, but at the end of each is given the mean 

 date of observation (excluding Chase) corresponding to the star. 



(124) 



