462 KRETZ. 



of— o".44 in R. A. and + o".'j2 in Decl., indicated by direct 

 comparison with my standards, was then apphed. As date of ob- 

 servation I assumed uniformly 189 1.6. This differs in no case 

 by more than .3 of a year from the true value, and the calcula- 

 tions are greatly simplified by using the same dates throughout, 

 as then T^ and —{^CD^ remain constant. Unit weight was assigned 

 to all the observations, including those of Chase. This was 

 warranted by the probable errors, and the formulae of Part I, 

 p. 365 were greatly simplified thereby. They become 



and 



^J#)_ft r. = 5i£)-^. 





where the notation is the same as before and ;// denotes the 

 number of observations. The a^ and o^^ thus obtained include 

 Chase's position, however. As I wished to have an independent 

 determination, deduced solely from the photographic observa- 

 tions, these quantities were not used, but a value for 1875 was 

 obtamed directly by the following method : The proper mo- 

 tion having been found as explained above, the measured posi- 

 tions were corrected to 1875 by applying to them the quantity 

 /i(i875 — 0- ^^'^^ mean was then taken of the corrected places 

 excluding Chase's position, and this is the final " projected " 

 coordinate for 1875, /, e., a^ or o^, as the case may be, of the suc- 

 ceeding tables. The probable error of a single observation was 

 obtained from all the residuals by Peters' formula as given by 

 Rogers in his zone (North Decl. 50° to 55°) of the Catalog der 

 AstrononiiscJicii Geseiischaft, p. (10), which is 



.= ±0.8453 ^+''^ 



n being the total number of residuals used, and ;/' being the 

 number of stars. We find thus 



r<^ = rb o''''.0939 ^ dz ^'''.0840 in equatorial seconds, 

 .g=± 0^^0595, 



(122) 



