( 366 ) 
motions, viz: that these equations for groups of stars included between 
determined, arbitrary l'mits of the proper motion, howsoever nume- 
rous the stars may be, are certainly in general not true’). 
This is evident from the argument given in Astron. Nachr. N°, 3487, 
pages 100—102, to which we must refer here. The error committed 
will certainly be different in general for regions with different À even 
in the case that the proper motions are equal. 
So not only do derivations such as those of SruMPs (Astron. Nachr. 
N°. 3000) and many others, give entirely illusory determinations for 
the secular parallax of the stars (as I already tried to show in 
Astr. Nachr. N°. 3487) but neither can the determination of the 
position of the Apex be defended. It may even be anticipated with 
great probability that the error must change systematically with the 
amount of the proper motion, so that the regular change found by 
Stumps in the declination of the Apex for his various groups has 
nothing particularly surprising. 
Other writers as i. a. L. STRUVE attribute determined parallaxes 
to stars of determined magnitude. The last decisive objection dis- 
appears here, but not the first. It rans as follows: we assume that 
at least the mean parallax of the stars of determined magnitude is 
everywhere in the sky the same. For the galaxy and outside it I 
have already tried to show, some years ago, (Verslag Kon. Akad. 
Jan. 1893) that this is probably not the case. 
To sum up, according to the preceding, Arry's method comes to 
the determination of the coordinates of the Apex and the linear 
motion of the sun in such a way that the conditions (18) and (19) 
are satisfied. 
The first condition does not contain the distances but does not 
in general satisfy the conditions = +7=0 for stars in one and the 
same part of the sky, which must be considered as the principal 
condition derivable from the hypothesis H. The second condition 
contains the distances which are in general unknown. This causes 
the introduction of hypotheses which are more or less probable, 
and which may easily exercise an injurious influence on the deter- 
mination of A and D. Particularly the grouping according to proper 
motion must be absolutely objected to in the application of Arry’s 
method, because implicit suppositions are introduced which are certainly 
not realized. 
1) It is even not permissable to exclude stars with very small proper motion. 
