91, 92] 
Configurations of Equilibrium 
101 
therefore (since n is given) all built on the same model, and at corresponding 
points radiation-pressure has the same importance relative to gas-pressure. 
It has also been found possible to calculate T e r, the product of the central 
temperature and the radius of the star, but it has not been found possible to 
calculate T c and r separately. Thus all stars which have given values of M 
and /x lie on a certain homologous series along which T c r is constant. 
The question arises as to what further physical conditions determine which 
particular configuration will be assumed by an actual star. The analysis of 
§ 90 supposed l and j (cf. § 79) both to be zero, and so supposed p, and cF& 
to have constant values throughout the star. We have specified the value 
of u., but have so far not found it necessary to specify any valu£ for cFG. 
At the centre of the star we have, from equation (81*3), 
In § 77 we obtained the value of cF on Kramers’ theory of absorption, in 
the form 
(7=3 x 10 10 , J R/m=8 , 26 x 10 7 , 7 = 6 66 x 10~ 8 , a = 7'64 x 10~ 15 , equation (92’1) 
All stars which have the same mass M and the same effective molecular 
series is determined jointly by the values of ( N 2 JA ) and G. 
It will be remembered that N is the atomic number and A the atomic 
weight of the atoms of which the star is formed. For a given star these will 
be fixed, and treating N 2 /A as a constant, equation (92 - 3) shews that T c varies 
star can always find a configuration of equilibrium by shrinking or expanding 
until its central temperature T c has the value appropriate to the given value 
later. Let us for the moment suppose it to be stable, then, since G is propor 
tional to the luminosity of the star, we see that: 
In gaseous stars which have the same given values for M, p and N 2 /A — 
i.e. stars whose mass and composition is fixed — T c is proportional to the square 
of the luminosity of the star. 
X c (X c + 1 ) = 
I'l-n - CRy T ^ 
cFGam 
(921). 
= 446 x 10 25 ( -j ) (92-2). 
Inserting this value for cF, and using the known numerical values 
becomes 
(92-3). 
weight p have the same values of \ e . Equation (92'3) now shews that Tf is 
( N 2 \ 
-j-J (?. As we pass along the homologous series of configura 
tions T c varies, and the actual position which a given star will assume on this 
as (G) 2 . Thus there will be one and only one configuration appropriate to a 
given value of G , and if a star’s mean generation of energy G is given, the 
of G. The question of the stability of this configuration will be considered 
J 
7