458 KRETZ. 



A consideration of these residuals brings out several interest- 

 ing facts. In the first place it is evident that they are almost 

 entirely due to errors in the meridian places, as the residuals 

 from the different plates for any one star run very nearly alike. 

 But a more important matter is their size. On the whole 

 they are fairly large, although perhaps not more so than might 

 have been expected from the probable errors of the standard 

 stars. At least is this the case with the declinations ; the right 

 ascensions show a much greater uncertainty. This is due partly 

 to the fact that x's on the plates are more difficult to measure, 

 owing to the elongation of the images ; but the chief cause is 

 the greater inaccuracy of the catalogue right ascensions. The 

 statement regarding this matter in Part I, Sect. I, "Weights," 

 is thus fully borne out. It is important to note, that the resi- 

 duals seem to increase more rapidly than the probable errors of 

 the stars, so that the poorly determined standards show rela- 

 tively larger residuals than the others. These considerations 

 lead to the following conclusions : Unless several stars on the 

 plates can be found well determined in a considerable number 

 of reliable catalogues, it will not pay to go through the labo- 

 rious process of obtaining the positions of the standards by the 

 method which I employed. If good modern observations are 

 available, the constants determined from them will be quite 

 sufficiently accurate ; provided, of course, that the date of ob- 

 servation is not very distant from the date of exposure of the 

 plate, or otherwise, that the proper motion of the stars be accu- 

 rately known. 



To satisfy myself on this point, I deduced the constants of 

 Plate III, using values of ;/^ and //^ obtained by comparison of 

 nine of my stars with Romberg's places. The weights assigned 

 were the same as had been given to this catalogue throughout 

 the present paper. I found thus : 



/c = — 0.469 rh 0.107 



<r=r — 0.256 dz 0.107 

 / = -f- O.COO433 ± 0.000061 

 ;■= + 0.000245 ±0.000061 



(118) 



