(22m) 
method derived by Kapreyn from a few particular cases of proper 
motion, because it seems to me that conclusions deduced from the 
consideration of only a few proper motions, chosen quite systema- 
tically, can hardly serve as criteria of a method which, as a matter 
of course, presupposes as data a great number of proper motions 
chosen at random. Finally attention must be drawn to an important 
point. In this paper (comp. § 1), following the method of KAPTRYN 
and others, I have considered separately the equations for 7 and v. 
Also in this modified form, as I have proved, Arry’s method leads 
to the right result. In Arry’s original method however, the three 
normal equations are composed from the equations for the two com- 
ponents + and wv. In this case there is but one equation of con- 
dition, viz.: 
[m*] or [77] + I(v — = ain 1) | = minimum, 
i.e. “the direction and the amount of the parallactic motion must be 
chosen so, that the sum of the squares of the TOTAL motus peculiares 
becomes a minimum.” If this condition is applied to the instances 
given by KAPTEYN, it immediately becomes evident, that we arrive 
at the same Apex as KAPTEyYN determines by applying the con- 
dition [vy = 0]. 
Astronomy. — Reply to the criticism of Dr. J. Stem S.J. by 
J. C. KAPTEIJN. 
It appears to be very probable that Dr. SreiN has not completely 
understood my paper in the proceedings of the February meeting 
of last year. This fact, and the fear that on the other hand I may 
also have misunderstood STEIN’s reasoning (for one part at least of 
his paper this is certain) have led me to make my reply more 
circumstantial and elementary than might otherwise seem necessary. 
With a view to the importance of the application of the method 
of least squares for the whole problem, it seems desirable to recall 
to mind the following elementary points relating to that method. 
a). Let a system of equations of condition be given, thus: 
ae¢+bhy=n 
agr + bo y= ng Ay Oe OO Oa ee a (1) 
az © + bz y = ng 
