172 
The Evolution of the Stars 
[CH. VI 
found to coincide very closely with those parts of the diagram in which 
observation places stars. 
157. The problem of stellar evolution is now seen to be quite distinct 
from that of explaining the distribution of stars in the Russell diagram, and, 
furthermore, the problem can expect no assistance from the observed distri 
bution of stars in this diagram. The problem of the evolution of the stars 
must be attacked anew, starting from first principles. 
Fortunately these principles are perfectly clear cut. As a star ages, its mass 
decreases and its rate of generation of energy also decreases. Fig. 12 (p. 159) 
maps out the configurations possible for stars of given masses and given rates 
of generation of energy: the problem of following a star’s evolution simply 
reduces to that of calculating the path that a star will follow, in this or any 
other diagram, as its mass and rate of generation of energy change with the 
passage of time. 
It is convenient to divide the problem into two parts. In the first we 
shall consider what would be the star’s evolutionary path if the gas-laws 
were exactly obeyed throughout its whole life; in the second we examine in 
what way this evolutionary path is modified by deviation from the gas-laws. 
158. We must first find the relation between a star’s mass, luminosity 
and surface temperature when the gas-laws are supposed to be obeyed 
throughout the star’s interior. 
From equation (92'3) of Chapter III, we obtain 
where R is the radius of the star. Assuming G to be constant throughout 
the star, E — MG, so that 
In our previous discussion of the configurations of gaseous stars, T C R 
and \ c were found to depend only on M, the mass of the star, and their 
values were tabulated in Table XI. Thus the right-hand member of equation 
(158‘2) depends only on the mass of the star, and, so long as the mass of a star 
The Evolution of Gaseous Stars. 
\ c (A c +1) Ç GR* = 18-3 ( T c Rf 
(1581), 
18-3 M(T C R)* 
(158-2). 
remains unaltered, E varies as R K When the mass of the star -is allowed 
to vary, equation (158'2) gives ER^ as a function of M. Eliminating the 
star’s radius R between this equation and 
E = 47 raR^Tg, 
where T c is the star’s effective temperature, we find that 
E =f(M) TV' 8 
(158-3),