98 
Gaseous Stars 
[ch. Ill 
Transforming to absolute bolometric magnitude m, by using the relation 
m = — 2*5 log E + a constant, this becomes 
m = cons — \ log log (\ + 1) — 2 log p. — 2 log T e .. .(90'5). 
appeared completely. The luminosity of a star of given mass M can be 
anything from zero to infinity, and a star can adjust its configuration to any 
surface temperature accompanies low luminosity and vice versa. 
The constant on the right of equation (90’5) admits of evaluation in terms 
of constants of nature and the coefficients in Kramers’ opacity-law. Eddington* 
average error proved to be about magnitudes, the stars having only about 
an eighth of the luminosity that Kramers’ law would require if they were 
given mass and luminosity, the average error in logT e is of the order of 1 £, 
so that the stars have some 13 times the effective temperatures and so only 
about a two-hundredth part of the radius that Eddington’s discussion would 
assign to them ; on his model, a star of the mass and luminosity of the sun 
would be as big as Betelgeux. 
Eddington accordingly treated the constant on the right of equation (90‘5) 
as adjustable f, selecting its value so that the formula gave the right absolute 
magnitude for Capella. Using this value for the constant, and taking p = 2T1, 
the formula was found to shew a fair agreement with observation which we 
shall discuss later (§ 118). 
Russell first drew attention to a general objection affecting not only 
Eddington’s model, for which l = $, but all stellar models for which l has a 
positive value. 
If l = \, as in Eddington’s model, then kG is constant, whence we readily 
Inserting Kramers’ value for k, we obtain, since p/T s is constant on this 
model, 
so that G assumes a large negative value. Thus the model demands a very 
The supposed “mass-luminosity” law mentioned in § 76 has now dis- 
given emission of radiation by selecting a suitable surface temperature. Low 
found that when the constant was evaluated in this way, the absolute magni 
tudes given by the formula did not agree with those of observed stars. The 
purely gaseous stars built on the model 1= | or kG = constant. For a star of 
find that 
In the outer regions of a star p is small and T^ decreases rapidly with r , 
M.N. lxxxiv. (1924), p. 104. 
f l.c. p. 308.