( 240 ) 
6. The above will be a sufficient refutation of STEIN'S criticism. 
I think I have shown: 
a. That SreiN’s equation B cannot prove anything against my con- 
tentions, because it is not to the point. 
b. That his direct criticism of my treatment of the question is 
erroneous. 
I may however be permitted to make the following remark, 
which will perhaps explain how STEIN was led to his erroneous 
views in the matter. He asserts: the second component (i.e. in his 
decomposition the component vo, in my decomposition the component 
v) “does not teach us anything about the position of the Apex”, 
or again “The two other equations” (the normal equation by which 
the position of the Antapex would be determined) “are left out of 
consideration on account of their small weight.” 
If this was really true, the determination of the position of the 
Apex would, as well for my treatment of the problem as for his, 
h 
depend solely on the components z and t% — Z sin A sin (T — 4) 
respectively and it would thus be possible, merely by a different way of 
decomposing the motus peculiares, to derive from the same equation 
(6) (for this is, as already remarked, equivalent to both (4) and (5)) 
different results for the position of the Apex, which is absurd. 
From this point of view there was thus every reason for the belief 
that either my treatment or his own was affected by some error, 
and it is explicable that the author, not finding this error in his 
own work, looked for it in mine. 
As a matter of fact however the error is neither in STEIN’s 
determination based on (8), nor in my own based on (9) but only 
in his contention about what can be derived from the second 
component. This component does actually give a determination 
of the Apex of which the weight, compared to that of the determi- 
nation from the first component, is generally not at all small. 
To show this it is sufficient to write down the neglected normal 
equations. They are: 
sin Ao cos Ag EN - + eos? do (5). |= dA + 
a. eos? Ao (5). EN le aD E cos Ay EN 
[sin hoa (3) |< ab cos? jn G ) @) Le ze 
+ [do ae: aD = [vow Go), i 
