( 228 ) 
4. The reasoning which leads Kapreyn to reject the condition 
[7?]= minimum, is as follows: 
“(r?] is a minimum for 
and if we put 
ov cy or. UY 
meen op 9D 
the minimum conditions are: 
[zed] =o and [rv s4] =o. oa oa 
which differ from the right ones (C).” 
It will be seen immediately, that the set (D) corresponds to the 
solution of the equations (one for each star): 
To = — Uo (54) ve — Uo (53) ap . 2 3 EN 
It is therefore perfectly consequent to his reasoning, when KAPTEYN 
puts Airy’s relation in this form (Proceedings p. 369), differing from 
the form given by me 
En ain (GE) a — (54) 2D). 
KAPTEYN's equation (ZE) would be the right one, if Army had 
formulated his question thus: To find a point so, that if it is con- 
nected with all the stars by means of great circles, the sum of the 
squares of the components of the proper motion, perpendicular to 
those circles, is a minimum — without considering the question 
whether a parallactic solar motion exists or not. But this not being 
the principle of Arry’s method Kapreyn’s criticism of that method 
is incorrect. 
