Vol. 8, 1922 
ASTRONOMY: G. STROMBERG 
143 
tion on account of their small proper motions were omitted since they would 
tend to give a ''star stream nearly parallel to the direction of the sun's 
motion. vStars recognized as members of the Taurus Group were also 
omitted, as well as fainter components of double stars. 
The frequency-function used is a three dimensional cosine-series with 
the origin in the center of the limiting planes. Such a function can be 
written 
F{xyz) == ao + aioo sin a + aoio sin (3 + clooi siny-\~a2oo cos 2a-\- auo sin a sin ^ 
+ aioi sin a sin y + amcos 2^ -f ami sin ^ sin y -f aoo2 cos 2y 
+ asoo sin ja + 0210 cos 2a sin 13 + ^201 cos 2a sin y -\- . . . . 
a = ^ 3 = ^ y = ^ 
" 2ci ^ 2C2 ^ 2cz 
In these expressions ± ci, ± C2 and ± C3, are the six limiting planes 
within which the function can be regarded as an interpolation formula in 
three dimensions. For different values of the density F we obtain a se- 
quence of equifrequential surfaces. We see then that a, /3, and 7 vary 
between the limits — \ and + \. The integration between certain 
limits as well as the determination of the coefficients in the series can be 
performed easily. All terms up to the sixth order have been computed, 
w^hile in the case of the dwarf stars, where the limits are very large, 
terms up to the 10th order have been included. The direction of the 
A;-axis is towards the intersection of the galactic plane with the equator, 
(in Aquila), the y axis is in the direction of galactic longitude 90°, 
and the z axis towards the galactic north pole. 
After the coefffcicnts in the trigonometric series had been computed, a 
synthesis was made for 2 = 0 and y = Curves of equal frequency 
were then drawn in the xy plane and the %z plane. These curves are the 
intersections of equifrequential surfaces with these two planes. The total 
number of stars including those outside the limits have in all cases been 
reduced to 1000. 
The general appearance of the frequency surfaces can be easily seen 
from the diagrams in figure 1, which give the intersections of the former 
with the xy and xz planes for the brighter stars of spectral types F to G, 
and for the dwarf stars of types GO to M. The curves for the brighter K 
and M stars are similar to those for the types Ge to Ki, although the curves 
are more nearly circular. The crosses ( + ) represent the velocities of 
stars belonging to the Taurus Group which were omitted in the analysis. 
The symbol O represents the velocity of the sun, whose velocity com- 
ponents in our system of coordinates are x = -\- 17 .0; y — ^ 7A\ 
2 = + 7.4 km. /sec. 
The general conclusions to be drawn from a study of these diagrams 
and the series on which they are based are the following : 
1. The giant stars of all types form one single "stream" with an ellip- 
