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ù the projection SC of « on SA; 
t the projection w C of « perpendicular to the former; 
The values of z and v evidently vary with the position of the 
point A, 
Let further x be an arbitrary fixed point on the celestial sphere; 
Sx the great circle joining S to that point and Sy the great circle 
perpendicular to Sz and let 
xX = the angle PSA; 
r= 
c= f— y, 
» 9 PSr. Then, according to STEIN’s notation, 
Vp, To = the projections of wu on Sz and Sy respectively. 
These projections do not vary with the position of A. 
For the present purpose we can confine ourselves to the case that 
all the stars which are considered are at the same distance from the 
eas 
sun, so that — is constant. 
Q 
We can then say that Arry’s method is based on the hypothesis 
(Hyp. A): that the projections of the motus peculiares may be treated 
as errors of observation, and that the most probable values of 
h Ry 
A, D, — are those for which the sum of the squares of the projections 
of the motus peculiares on two mutually perpendicular directions is 
a minimum. 
2. This being premised, it is easy to form a judgment about 
the value of Dr. Srein’s criticism. 
Everything depends on the choice of the directions on which 
the motus peculiares are projected. 
Airy takes the parallel and the declinationcircles ; 
STEIN takes the great circles through the fixed point « and the 
circles perpendicular thereto. He takes the point # in the 
neighbourhood of the most probable Antapex. 
KAPTEYN takes the circles through the point A and those perpen- 
dicular to them. 
In the first part of Srrin’s criticism his own decomposition and 
mine are confounded. (Further on, e.g. in the enunciation of the 
