146 
THE MASS-LUMINOSITY RELATION 
We have also 
LfM = 57*8 ergs per second per gram, 
and the coefficient of absorption is calculated from (90-1) 
L _ 4t tcG (1 - §) = 25100 (1 - P) 
M ak e ak c 
which gives ak c =123. 
It has been explained that a depends on the law of distribution of the 
source of energy. We adopt the value 2*5 which is a compromise between 
the most extreme suppositions and cannot in any case be very far out. 
The choice will not affect differential comparisons between the stars; it is 
only when we compare astronomical values of k with those calculated from 
atomic physics that attention need be paid to the uncertainty. Hence 
k c = 49*1. 
Since p c and T c have been found this fixes the constant k x in the absorption 
law 
k — k x p/T : -. 
We find k x = 8-98.10 26 . 
This value will be used to predict the luminosity from the mass, or 
vice versa, in other stars. 
(2) S Cephei. 
Cepheid variable. Mean absolute visual magnitude — 2 m -19; mean type 
F 9, assumed to indicate effective temperature 5200°. 
The absolute magnitude is taken from a discussion of the distances of 
the Cepheid variables by H. Shapley*. The mass is unknown except in 
so far as it can be deduced by the present theory. 
Proceeding as before, we find absolute bolometric magnitude — 2 m -33, 
and 
L = 2-81.10 36 ergs per second, 
R = 2-32.10 12 cm. 
The mass can be easily deduced from the bolometric magnitude and 
effective temperature by interpolation in Table 14; but it will be instructive 
here to work out the result analytically. We have 
_ IttcGM (1 - /3) = 4ncGM (1 - P) T 3 T J 
ak c ak-L p c 
_ IncGM (1 - P) 39 1 (1 - P) f G_ R' p.pM\k 
ak x apP \491 M' R ) 
Astrophys. Journ. 48, p. 282.