STARS IN COMA BERENICES. 463 



as the probable error of a single observation. The probable 

 error of a catalogue position depending on fourteen plates is 

 therefore 



ra = ±0^^.025, rg = =b 0^^.016, 



the r^ being in seconds of arc of a parallel of declination 

 through the center of the plate. It should be mentioned, that 

 the residuals as used are assumed to be all of equal weight. 

 This, while not theoretically correct (since some of the positions 

 include, besides errors of direct observation, the uncertainty 

 of the proper motion) is sufficiently accurate, owing to the 

 small value of the probable errors of the proper motions, and 

 the fact that (1875 — t) is in no case larger than 4.7. 



The probable errors of the proper motions were obtained by 

 the usual formulae (cf. Part 1, Sect. II, '' Formulae for Ad- 

 justment") 



:± 0.6745 Ji!^, '>=V^- 



The v''-, used here were the same as before, including, how- 

 ever, the residuals obtained from Chase's position reduced to 

 1875 and corrected for proper motion. Neglecting the fact 

 that the mean a.^ or 0^ does not include Chase's observations, 

 which can be done without appreciable effect on the result, it 

 is easy to show that the residuals obtained as explained above 

 have the same value as they would have if computed by the 

 method described in Part I, Sect. Ill, " Star Tables." For by 

 the latter method 



^1 4-^2 -f ••• -\-^m 



— I Oi + ^H 



mt^—{t^-\-t,_^---\-t„,) 



\ + «2+ ■■■ -^ am . A/^o(^i-f-^2 + ••• + fm) 



for the case of equal weights of all the a's. But by the first 

 method 



(123) 



