( 285.9 
problem: “if Airy had formulated his question thus: ..”, there 
seems to be no such confusion). He says: “Kapreyn chooses the 
directions towards a point near the Antapex and the direction at 
right angles to it.” — 
The words relating to this point are however (Proceedings 1900, 
Febr. p. 362). “The direction from the star towards the Antapex 
and the great circle through the star at right angles to the former” 
while it is moreover abundantly clear from the contents of that 
paper generally, what the meaning is. 
Reading STEIN’s paper one gets the impression, that the author 
considers my decomposition either as impossible, or as identical to 
his own, if only care is taken to choose for the point z a point 
which coincides (or even approximately coincides) with the definitive 
most probable position of the Antapex. Neither of the two is true. 
It might perhaps be considered a sufficient reply to the principal 
point of STEIN’s criticism, to have pointed out this confusion. I 
think however that by going into somewhat fuller details the 
question as a whole will be more easily understood. 
3. If the total sum of the squares of the projections of the motus 
peculiares on the two directions is considered, then the methods of 
STEIN and of Kapreyn lead of course to the same result. For in 
that case, amongst all the different positions which can be given to 
the point A, that one will be (according to Airy) considered as the 
most probable position of the Antapex for which ') 
according to Kapreyn > (Da? + Sa?) minimum . . - (2) 
according to STEIN!) = (Db? 4+ Sb?) minimum . . . (3) 
or 
he. al a ef 
= jer + (v — — sin i) minimum (KAPTEYN) . . (4) 
4 
and 
h 2 eee 2 yi 
= (zo — — sin À sin (r—7)) + (vo — — sind cos (T — 7) | : (5) 
Q g 
mininum (STEIN) 
1) I have supposed that by Srern’s real” Antapex is meant what has been defined 
above as the point 4, and which might be called the variable Antapex. If this is 
not the case, then his reasoning seems to me unintelligible. 
