( 354 ) 
vation we find that neither the method of Arry, nor that of ARGE- 
LANDER is entirely based on this hypothesis, and yet these two 
were almost without exception used in all modern determinations 
of the position of the Apex. 
Finding the distribution of the proper motions in regard to the 
great circles drawn through the position of the Apex as determined by 
these methods unsatisfactory, KoBoLp concludes that we must drop 
the hypothesis H, as not agreeing sufficiently with the facts. Such 
a conclusion however cannot be accepted until at least one compu- 
tation has been made, which is completely founded on this hypothesis. 
This has given rise to the following investigation, in which I 
have tried to develop a method satisfying this condition. After having 
explained the method I shall give a short criticism of those of 
Ary, ARGELANDER and Kosorp, which criticism however lays no 
claim whatever to being complete. 
2. Meaning of the letters and simple relations. 
P 
Antapex | 
Fig. 1. 
O the Apex; 
P the Pole of the Equator; 
S an arbitrary Star ; 
A and D the coordinates of the Apex 0; 
a and Ò the coordinates of the Star S; 
4= OS=the angular distance of the Star to the Apex; 
w= Sg the observed motion of S; 
SQ the direction towards the Antapex = direction of the paral- 
lactic proper motion ; 
