III. Tables and Results. 



Star-Tables. — On the following pages are recorded the data 

 from which the final positions were obtained, together with the 

 most important part of the calculations. The tables, when taken 

 in connection with the preceding sections, require little com- 

 ment. A few points may be mentioned, however. 



The caption gives the Bonn Durchmusterung number, the 

 usual designation of a star, and Chase's number ; also the pre- 

 cession constants, together with the right ascension and declin- 

 ation for 1875, and the respective assumed proper motions 

 used in calculating the same. 



Columns i, 2, 3, 4, 5, 6 and 12 require no explanation. 

 They refer to matters treated in Sect. I of this paper. 



Columns 7 to 1 1 are discussed in Sect. II; column 7 under 

 the head " Proper Motion "; column 8 under that of " Preces- 

 sion"; and 10 under that of " Systematic Corrections." Col- 

 umn 9 is the sum of 6, 7, and 8. 1 1 is explained by the 

 heading. 



Column I 5 shows the residual of each observation, and 1 3 

 and 14 exhibit the computation by which these are derived. 

 This matter has not been treated in detail before, as I deem it 

 rather unimportant for the present purpose. The probable er- 

 ror is not made to depend on the residuals, and they are here 

 recorded merely to give an idea of the interagreement of the 

 observations ; they are nowise used in the work. The method is 

 sufficiently explained by the headings ; and it is plain that, if car- 

 ried through as shown, the desired quantities will be obtained, 

 remembering the form of the observation equations (equation 

 (i) of " Formula for Adjustment," Sect. II). 



(27) 



