ASTRONOMY: SEARES AND SHAPLEY 
485 
The apparent magnitude corresponding to maximum frequency is, 
however, quite different for the different colors, as Hertzsprung has already 
pointed out^ and as appears from the results in Table III. From these 
it is seen that the magnitude at which maximum frequency occurs 
increases by about two magnitudes for an increase in the color of one 
color class. If an extrapolation of this result is to be permitted, one 
would infer that the majority of the g, k, and m stars belonging to the 
cluster are so faint that they do not fall within the limits of the available 
data. This probably accounts for the relatively small percentage of 
these colors found among the cluster stars. (See eighth column, Table 
II-) 
Inasmuch as there are no reliable data for the distribution of the 
background stars, with respect to color and magnitude, these objects 
TABLE in 
Color and Magnitude — -Number of Stars in N. G. C. 1647 
MAG. 
COLOR 
TOTAL 
h 
a 
/ 
g 
k 
m 
<9.5 
5 
0 
0 
0 
2 
0 
7 
9.5-10.5 
8 
11 
0 
1 
1 
0 
21 
10.5-11.5 
0 
13 
3 
0 
0 
1 
17 
11.5-12.5 
1 
25 
6 
1 
0 
1 
34 
12.5-13.5 
0 
8 
26 
3 
0 
2 
39 
13.5-14.5 
0 
8 
34 
12 
9 
2 
65 
> 14.5 
1 
1 
Totals 
14 
65 
69 
17 
12 
7 
184 
are necessarily included in the conclusions stated in the two preceding 
paragraphs. 
MESSIER 67 
The data consist of 231 color indices derived by Shapley with the 
60-inch reflector. The distribution for color and distance is shown in 
Table IV. The densities in the last line indicate that here the counts 
have been extended beyond the boundary of the cluster, and that from 
7 '.5 outward the tabulated stars belong to the background. 
We have, therefore, in this instance, an approximation for the con- 
stitution of the background in the direction of the cluster. After 
deducting the background stars and combining the results for the cluster 
into two zones, we find the numbers in the second and third columns of 
Table V. The totals for the cluster and the background, and the 
percentage distribution are in the remainder of the table. The percent- 
