83 
76, 77 ] The Absorption Coefficient 
In the special case of n — 3, M depends on ® only. Combining the 
general equation (65'3) with Eddington’s integral (76'2), we readily find that 
By equation (76‘3) all stars having the same mass M must have the same 
value of ® 3 , so that if equation (76‘4) were true, they would have also the 
same value of kG. Thus Eddington’s assumption that kG is constant through 
out each single star involves that kG is the same in all stars of the same mass. 
Eddington’s earlier investigations were based on the supposition that k, 
the coefficient of opacity, was also constant. The constancy of kG for stars of 
a given mass then involved the constancy of G, so that the average rate of 
generation of energy of stellar matter could depend only on the mass of the 
star of which it formed part and stars of equal mass were necessarily of equal 
luminosity. Indeed, Eddington actually announced this conclusion under the 
name of the “ mass-luminosity ” law. But it is clear that it must be a con 
sequence merely of the special assumption that kG is constant, and cannot 
have reference to actual stellar conditions; a star’s average generation of 
energy will be the average of the generations of its separate elements, and 
these will not be determined by the mass of the star, but by the substance of 
which it is made. A star made of pure uranium will necessarily generate 
100 times as much energy as one of equal mass which is only one per cent, 
uranium and the rest lead. The former star will consequently emit 100 times 
as much radiation as its fellow of equal mass, whereas on Eddington’s model 
the two stars would necessarily emit equal amounts of radiation. 
This brings out the main defect of this special model. A model which 
cannot take into account that different substances, such as lead and uranium, 
have different capacities for generating radiation, does not seem a suitable 
model to assume for stellar structure. 
After the appearance of Kramers’ theory, which we shall now discuss, 
Eddington abandoned the supposition that k was constant, although retaining 
the constancy of kG. As we shall see (§ 90), this causes the star’s luminosity 
to depend on other things than its mass, so that the supposed “mass- 
luminosity ” law disappears, and a star of given mass M can have any 1 
luminosity from 0 to oo . 
The Absorption Coefficient. 
77. In 1923 Kramers* investigated the process of absorption of X-radiation 
in matter. As the ordinary radiation inside a star has about the same wave 
length as the X-radiation of the laboratory, the investigation immediately 
Phil. Mag. xlvi. (1923), p. 836. A valuable account and critical discussion of Kramers’ 
theory will also be found in Eddington’s Internal Constitution of the Stars, Chap IX, p. 229