STARS IN COMA BERENICES. 366 



Calculate the sums 

 Then 



J? and fi' being the remainders. Now form for each catalogue 

 position the quantities 



The computations up to this point will all be checked/ when 



S/(a„-^)=-/3, 2/(^-7;) = + ^^ 



From the expressions last obtained we easily get 

 2(Z'^) and 2(CZ)) 



which we check^ by the equations 



Z(Z>^)=2(/^ ■ C) 

 I,{CD) =2(/C2). 

 Then 



and 



fi being the previously assumed proper motion. Also 



To obtain the probable errors, I did not, however, employ 

 formulae (6) as they stand. For thereby the weight of each 

 star is placed on an independent basis, and the probable errors 

 form no means whereby to judge of the relative accuracy of 

 the final positions. For the factor r^ is not the same for all the 

 stars, depending, as it does, on the accidental error in each cat- 

 alogue as shown by the residual. We must seek a value for r^, 

 which will satisfy all the observations taken of all the stars, not 

 of one star only. Such a value is furnished by the statement 

 in Sec. I, " Weights," which reads, that the probable error of 

 an observation of unit weight was arbitrarily assumed as 0^.4 



1 As suggested in Davis, page 1 1 . 



(25) 



