362 KRETZ. 



(20) Yarnall. — Corrections to this catalogue will be found in 

 both of Auwers' papers. The second set was used by me. 



Formulae for Adjustment The usual methods of least-square 



solution with artifices of computation analogous to those pub- 

 lished in Davis, pages 11 and 12, were employed. I shall de- 

 duce the formulae for right ascension only ; the discussion for 

 the other coordinate is entirely similar. 



If we let 

 i5.= the seconds of an observed right ascension reduced to 1875, 

 using an assumed value for the proper motion, and cor- 

 rected for systematic errors ; 

 A= the date of observing B^ ; 

 ttg = the seconds of the right ascension to be obtained from the 



observations, corresponding to some fixed epoch T^ ; 

 z/^^=the correction to be subtracted from the assumed proper 



motion ; 

 then evidently we should have 



or, if the weight of B^ be p^, 



Vpi Co — y 7; A/Zo i^i — ^0) — ^'Ji Bi = o. ( la) 



Writing, then, in equations of condition of the above form, one 

 for each observed B^, and solving by least squares, we get the 

 following normals, where the square brackets as usual denote 

 summation : 



By suitably selecting the epoch Z^ we can greatly facilitate the 

 succeeding work — an artifice first employed for this kind of 

 work by Professor Safford.^ For let us take T^ as the mean 

 of all the dates t, that is, let 



' See Safford, " Catalogue of 2018 Stars," Introd., p. 12. 



(22) 



