694 



Z X Y Z 



= O 93 h 0.21 .sm' <ƒ — + 0.03 sin'' d 1- 0.10 cos^ ö~ 



R,n R,„ Rm R,n 



These equations contain in the correction-terms only cos'' é and 

 .s'Mi' ff, so tliat they do not disappear even by integration over tlie 

 whole sphere. We see thus, that, even when the stars used are 

 spread evenly over the whole sphere, 1**' the velocity-components 

 for the mean distance, corresponding to sin"[i^=\, are not equal 

 to those which are found in the assumption of equal distances, and 

 2"'^ that the changes which A', Y, and Z undergo are not proportional 

 to the quantities themselves, so that the place deduced for the apex 

 also undergoes a change. As we have: mean value of cos^(S=^, 

 m. V. of .ym'^ff^^, we And for the entire sky: 



X Y 



0.93— - 0.08 — 



\_Rn,] 



1 — 1 = 1.06- 



X 



0.03 — 



Rm R,n 



Z X Y 



1.00 — ^ 0.07 -- + 0.01 — . 



-itjji -tti/i -^m 



Starting from the same values of the three components for the 

 BR.\DLEY-stars, as were accepted before, the corrected values for the 

 mean distance are as follows: 



Oi'iginal Corrected Correction 



X -fO".20 -f0".14 — 0".06 



Y — 2 .60 — 2 .43 +0 .17 



Z + 1 .50 +1 .51 + .01 



and the R.A. and Decl. of the apex become: 



Original Corrected Correction 



A 274° 24' 273° 20' ^J° 4' 



i) -f 30 -f 31 48 +1 48 



As we said at the beginning of this paper, this particular problem 

 appeared to have been already treated by Eudington in his Stellar 

 movements p. 81 — 83. He found, starting from practically the same 

 data, but by an entirely different method, that A in particular will 

 need a correction, viz. of about — 2.°4. The two results for A 

 agree tolerably well, and ours is also not accurate to a few minutes. 

 We find also an appreciable value for the correction of D, although 

 the Z'-c.omponent remains almost unchanged. 



The result found for the whole sky is equal to that for (f = ± 35°15'. 

 As a second example we will calculate the corrections for ff:=0. 



