ASTRONOMY: KAPTEYN AND ADAMS 
19 
gen Publications No. S, and the absolute magnitudes were computed. 
From the resulting equations the values of b were determined by least 
squares. 
TABLE II 
Computation of the Radial Velocity as a Function of the Proper Motion 
PROPER MOTION H 
NO. STARS 
CAMPBELL 
PARALLAX TT 
GRON. NO. 8 
- 
P OBS. 
P COMP 
DIFFERENCE 
seconds (") 
seconds (') 
km. 
km. 
km. 
0.000 to 0.025 
27 
0.0064 
10.91 
12.1 
-1.2 
0.026 0.039 
37 
0.0112 
12.15 
12.5 
-0.35 
0.040 0.059 
21 
0.0148 
14.9 
12.9 
+2.0 
0.060 0.079 
24 
0.0185 
10.7 
13.3 
-2.6 
0.080 0.099 
26 
0.0218 
15.7 
13.7 
+2.0 
0.100 0.119 
12 
0.0248 
20.7 
14.3 
+6.4 
0.120 0.149 
24 
0.0283 
16.5 
14.8 
+ 1.7 
0.150 0.199 
24 
0.0332 
15.6 
15.9 
-0.3 
0.200 0.299 
18 
0.0412 
16.5 
17.7 
-1.2 
^0.300 
19 
0.108 
26.71 
24.5 
+2.2 
232 
1 These numbers have the Mount Wilson results for the corresponding proper motions included in them. 
This solution requires two corrections. The first is due to the differ- 
ence in the average value of X for the several groups. This correction 
has been appHed on the very probable assumption that the change of p 
with X is proportional to 1 + cos^ X. The second correction is due to 
the fact that while the values of fx are equal, or practically so, the values 
of TT are somewhat unequal owing to the differences in magnitude. As a 
result the average linear motions and hence the radial velocities will be 
affected. This effect is systematic in character, though small, and can 
be appHed only in the case of the K stars. 
If we combine the results for the separate groups into means for 
each spectral type we obtain 
Table III. The corrected 
value for the K stars is de- 
noted by ^2. On the assump- 
tion, which seems probable, 
that the correction in the case 
of the other spectra is the 
same as for the K stars we 
find, therefore, a change of radial velocity per unit of absolute magni- 
tude of 1.1 km. + 0.4. 
The reahty of this conclusion that the more luminous stars move more 
TABLE III, Values of the Constant b in km. 
TYPE 
bl 
b2 
PROB. ERROR 
F 
+2.1 
+0.73 
G 
+ 1.0 
0.82 
K 
+ 1.6 
+ 1.1 
0.62 
M 
+2.6 
2.5 
Mean 
+ 1.6 
+0.40 
