178 
THE MASS-LUMINOSITY RELATION 
Finally, the type corresponding to T e according to the usual temperature 
scale is added in the sixth column. 
It should be mentioned that we have in these calculations applied to 
m 0 the correction suggested in the footnote on p. 159; that is to say, we 
have followed the line of the observational data rather than the theoretical 
curve at the left of Fig. 2, because we think that the correction is genuine*. 
Table 23. 
Results for assumed Central Temperature 40,000,000°. 
1-/3 
Mass 
Boi. Mag. 
Vis. Mag. 
Eff. Temp. 
Type 
•002 
•182 
m 
11*94 
Ill 
14*5 
2550 
< M d 
•004 
•258 
10-25 
ii-6 
3210 
K 9 
•015 
•512 
7-26 
7-6 
4540 
K 0 
•03 
•746 
5-93 
6-1 
5160 
G 4 
•05 
1-00 
4-47 
4-5 
6290 
F 8 
•10 
1-58 
2-43 
2-5 
8250 
A 8 
•18 
2-56 
0-52 
0-9 
10520 
A 0 
•30 
4-53 
- 1-38 
- 0-6 
13260 
B 7 
•50 
11-46 
- 3-86 
- 2-4 
17460 
B 2 
•70 
37-67 
- 6-44 
- 4-3 
22500 
O e 
•80 
90-63 
- 8-12 
- 6 
26200 
O 
If these magnitudes and types are plotted on a diagram similar to 
that of Seares we obtain a line which agrees as nearly as we can judge 
with the central line of the main series. The observational evidence is 
thus consistent with the assumption of a uniform central temperature of 
40 million degrees throughout the whole length. At any rate, the deviation 
from uniformity must be small. 
The question arises whether the main series is strictly a line in the 
diagram or a rather narrow band. This can scarcely be determined from 
the statistics, because the spread is largely caused by observational error. 
It is risky to appeal to particular individuals since we cannot be certain 
that these have reached the stable point; thus the fainter component of 
a Centauri is considered by Russell to be a giant of unusually small mass 
which is approaching the main series but has not reached it. I think that 
a certain amount of spread must be admitted more particularly at the hot 
* Whether the correction if genuine ought to be applied depends on its origin. 
If it is due to a decreased absorption coefficient rendering the stars more luminous 
than the law k oc p/pT? predicts, our procedure is justified. If it is due to an increase 
of molecular weight (whether actual or used as a fictitious equivalent of the electro 
static forces as in § 115) p. should be increased in determining R from (122-1). This 
would make R larger and the effective temperature smaller and to a large extent 
compensate the decrease of m 0 in (122-2). If, for this or other reasons, it is inappro 
priate to apply the correction, T c must increase a little for the smaller stars.