484. 
ASTRONOMY: SHARES AND SHAPLEY 
the color (second, third, and fourth columns, Table II). But the 
background stars, as well as the members of the cluster, are included, 
and it does not follow that for the cluster itself the condensation is 
variable. 
Let us assume for a moment that the ratio ni/n^ for the cluster alone 
does not vary with the color. Its value must then be approximately 
that of N1/N2 for the b and early a stars, for it is probable that all these 
belong to the cluster.^ As a round number, we may assume ni/n2 =3. 
TABLE II 
Percentage of Colors in N. G. C. 1647 and Background 
COLOR 
TOTAL NO. STARS 
N1/N2 
n 
TOTAL NO. STARS 
PERCENTAGES 
0'-15' 
15 '-30' 
Cl. 
Bkgd. 
Cl. 
Bkgd. 
Other 
Reg. 
b 
f 
g 
km 
11 
39 
36 
7 
7 
3 
25 
34 
10 
12 
3.7 
1.6 
1.1 
0.7 
0.6 
-0.25 
4.50 
8.25 
2.88 
3.62 
15 
46 
37 
55 
46 
-1 
18 
33 
IP 
146 
14 
43 
34 
5 
4 
-1 
24 
43 
15 
19 
1 
13 
47 
30 
9 
Totals 
100 
84 
19.00 
108 
76 
100 
100 
100 
The number of background stars, n, can then be calculated for each 
color by 
Ni - n 
N2 - Sn 
for which the unit of area is 225 tt sq. min. The results are in the fifth 
column of Table II. The numbers for the cluster and the background 
can now be separated ; their values are in the sixth and seventh columns. 
The percentage distribution of colors is in the two following columns. 
The last column shows the corresponding mean distribution for two other 
regions of the sky, namely, the North Pole and that of S Cygni.^ 
The background percentages were calculated on the assumption that 
the condensation within the cluster is the same for all colors; their 
agreement with the values in the last column of Table II is close enough 
to give some vahdity to that assumption. At any rate, there is no evi- 
dence for supposing that the distribution within the cluster depends upon 
the color. 
An examination of the distribution from the standpoint of distance 
and brightness suggests a relatively greater condensation of the brighter 
stars; but from 10.5 downward the distribution seems to be the same for 
all magnitudes. 
