142 
ASTRONOMY: G. STROMBERG 
Proc. N. a. S. 
The stars of each spectral type have been divided into two groups ac- 
cording to their absolute magnitude M, and these groups, in the case of 
the later types at least, can be identified with the giant and dwarf classes. 
We see that for the giant stars the declination Do of the sun's apex shows a 
steady increase from 27° to 44° with advancing spectral type. The same 
result has been found by several investigators who have studied the dis- 
tribution of proper motions, and the effect seems to be very marked among 
the apparently faint stars studied by Dyson and Thackeray. ^ This 
indicates a larger proportion of stars belonging to the second stream among: 
the K and M stars than among those of early types. The dwarf stars 
show a much larger value of the velocity of the sun than that deduced from 
the stars in general. 
A very remarkable feature is the behavior of the stars of high velocity. 
If we group the stars according to their velocities with reference to an ori- 
gin corrected for the standard solar velocity of 20.0 km. directed toward the 
point A = 270°; D = -f 30°, we find that the velocity of the sun in- 
creases remarkably with increasing speed of the stars relative to which 
its motion is referred. 
The following table gives the result of such a computation, the stars 
being grouped according to velocity. 
V 
V KM. /sec. Ao Do km. 
Oto 60 272° -F30° 20.6 
60 to 100 295 4-43 36.3 
100 to 150 289 H-39 76 
>150 313 -F-54 209 
We see from this comparison that the stars of high speed have a syste- 
matic motion which differs from that of stars of moderate speed, and that 
they have a tendency to move in a direction opposite to the sun's motion. 
The same result was indicated by Adams and Joy^ who found from a study 
of the space-motions of 37 stars of high radial velocity that nearly all the 
apices were confined to one hemisphere. 
Distribution of Velocities. — The peculiarities in the motions of the stars 
can best be studied by determining the frequency-function according to 
which the velocity-vectors are distributed. Two different types of fre- 
quency-functions have been used hitherto, namely, those based upon the 
two-drift theory of Kapteyn^ and the ellipsoidal theory of Schwarzschild.^ 
If use is made of three-dimensional velocity-vectors it is easy to decide be- 
tween these two theories, but in order to represent the actual distribution 
of the velocity-vectors in all its aspects a more general type of frequency- 
function is necessary. In the first place the velocity-vectors were all 
corrected for a standard solar velocity of 20.0 km. in the direction Ao = 270° 
and Do = + 30°. About 100 stars which had been selected forobserva- 
