(231 ) 
But as in the case in hand the peculiar proper motion m is left 
out of consideration, this condition does not teach us anything about 
the position of the Apex. 
: 4 f i h 2 
20, the relation which exists between ( mien vant i) | and the 
Qg 
: h 
amount of the solar motion Bs 
0 
h ij h+dh 2° 
I(w — a sin i) | must be always smaller than I€ — ae sin i) | L 
@ 
In order that it may be so, 
di h dh / 
|— peek + ND i| or |— v sin À + ZL sin? i] must be 0, 
Q g Q 
whence follows 
h [wv sin A] 
ge [sin? A] 
Thus, after the substitution of this value, we again arrive at the 
same normal equations (B’) for the determination of dA and dD. 
8. To conclude I remark that the equations derived in this paper 
become identical with those of KAPTEYN as soon as we confine 
ourselves to stars in one direction only. But even when we apply 
our theory to a great number of stars scattered over the heavens, 
the two sets will yield little differing results. For if we resolve v, 
h 
into two parts vj + vs, where vj = ie snX = the component of the 
Q 
parallactic solar motion, and vg = the component of the peculiar 
proper motion, the coefficient of dA in the first of Kaprryn’s 
equations becomes 
[eo sin hg G4) = mn sin? Ay EN + E sin Ag (54) | : 
As according to the hypothesis there is an equal number of positive 
and negative values of vw, the second term may be neglected, by 
which the coefficient becomes identical to the corresponding one in 
our set of equations (B). The same holds for the other coefficients. 
bi is superfluous to refute at large the objections against ArRy’s 
