( 241 ) 
For brevity’s sake I will suppose that we consider a group of 
stars distributed uniformly over the whole sky. In that case we find 
h h : : . 
at once that rae and és dD are determined with the weights 
cos? Xo EAN and cos? ho el 
If the same quantities are determined from the first component 
(see STEIN’s equations B) they have, in the case here considered, 
the weights 
sin? do (2) and sin’ ho ea > 
OA Ox dA sind Ox 
am Pa ‘Ded. A 
Now 
It is thus clear at once that the weights of the two determinations 
are entirely of the same order of magnitude. 
The same thing is true of the analogous component in my 
treatment. A determination of the position of the Apex actually 
derived from this component was published by me some time ago. 
(Astr. Nachr. NO. 3721 Meth. IV). 
7. It may be urged that the objections made by me would not 
apply to Arry’s method if it were understood as is implied by the 
equation (4), i.e. if the sum of the squares of both components of 
the motus peculiares together were made minimum. 
This is quite true. I now!) go even further, and express as my 
opinion that the equations, which would be derived in this way 
for the determination of the Apex, must be considered as very 
acceptable. The confidence which they would deserve could however 
not be derived from the hypothesis (Hyp. A) of Army. For, if it 
is admitted that Srern’s criticism is erroneous, it was shown by me 
that a legitimate application of this hypothesis may lead to un- 
acceptable results. 
This confidence must therefore rest on quite another basis. For 
me this basis is the following: the equations which are derived 
1) Now, because at the time when I wrote my communication of Febr. 1900, my 
attention had not yet been drawn te Bravats’ method. 
