STUDIES IN STELLAR Statistics. II. 7 
The first column gives the square, defined as in Meddel. Ser. II, 
N:o 8. The second column gives the number of the stars in the »Preli- 
minary Catalogue» of Boss. The third column gives u = da cos 0, 
the fourth v = 40, both taken from the Boss catalogue. The fifth 
column contains the radial velocity (expressed in Siriometers per Stel- 
lar year) of the stars, regarding which I refer to GYLLENBERGS me- 
moir (Meddel. Ser. II, N:o 13). The next column gives the magnitude 
from Harvard Annals Vol. 50. The last column gives the spectral 
subclass from the same publication. 
4. The computation of R is performed in the following way. 
Let U, V, W denote the eomponents of the velocity of a star 
in a system of right angular coordinates having its axis of Z (W) 
directed along the radius vector, the axis of X in the direction of in- 
creasing c, the axis of Y in the direction of increasing 9. 
Let further U”, V", W" denote the components of the velocity 
of the same star referred to the common astronomical equator-system. 
Denoting the direction cosines by y, we have 
U= Yu Us Va T Ya pes 
(3) V = ya U" + yu V" + y W' , 
W = ys Ur JnV--tYaW", 
where 
f = SIN 3 Yo = COS a ea) 
Mn == Si @ COS @S tn — ln Sim we He =] GO SNO) 
112 j 22 / 32 
6030 COS &) > wes 0 SM @ ; Y= Sin À. 
If uw = Aa cos 0, v = 49 denote the proper motions of the star, 
we have 
Tie o. 
or, introducing the value (1) of 7 and using the abbreviations 
(4) u' = id aom u . v! = 1 ()0: m»; , 
hence 
(5) U:—Rw 4 V=Rv. 
