( 357) 
(9) =v must be maximum. 
It is easy to see that for a group of stars as that here consi- 
dered, this condition is equivalent to the second condition of (8) 
CLO Tr) 
This latter however is not so easily extended to all parts of the sky. 
4. Influence of the different distances of the stars. For a group 
of stars at one point of the sky it is easy to derive from condition 
(9) or (10) the direction to the Antapex. We can arrive at a 
result however, at least theoretically more accurate, by modifying 
that condition (without throwing up the principle). 
It is easy to see at once that if we have stars of greatly differing 
distances to the sun, the stars whose distance is very large (and 
whose proper motion is therefore as a rule very small) will influence 
the result much less than stars at a smaller distance (and with 
as a rule greater proper motion). 
If we start from the principle that one and the same irregularity 
in the distribution of the linear, peculiar proper motions must 
have the same effect on the accuracy of the direction to the Ant- 
apex for stars at a greater distance and for those at a smaller 
distance, it is easy to show that not the condition (9) but 
(11) 2@v maximum. 
must be satisfied. 
This one would certainly be preferable to (9), if the distances 
of the stars were known. This being however the case for so very 
few objects we are forced to adhere to the theoretically less valuable 
condition (9). 
Fortunately however the objection, arising from the predominating 
influence of the stars nearest to the sun, may be met to a great extent. 
5. Grouping according to amount.of proper motion. 
This may be done by grouping the stars into classes included 
between pretty narrow, determined limits of the proper motion. The 
separate results for these groups will finally be combined into a 
single one, taking due account of their probable errors. We will 
first have to show however that for such groups of stars the condi- 
tion (9) is still satisfied, for from considerations as were given in 
Astr. Nachr. NO. 3487 Page 100 ete. (and which for the sake of 
brevity we must omit here) follows, that, for groups as are meant 
here, the distribution of the peculiar proper motions will certainly 
no longer satisfy Hypothesis H. 
