77—80] 
Configurations of Equilibrium, 
85 
General Stellar Equilibrium. 
78. On introducing the value of the opacity coefficient from equation (77'1), 
the general equation of radiative equilibrium (75'6) assumes the form 
= (78-D. 
dr cFOp dr 
Let us again replace p Q by \p R , so that A, is given by 
-y _ R P 
\amp,T 3 ’ 
On inserting the value of p given by this equation, and dividing through 
out by dpjdr, equation (78‘1) becomes 
d _ ^ 1V1 12t rGyRT h 
dpn ^ + c FGam\ 
.(78-2). 
79. The case which is physically simplest and most natural occurs when 
c, F, G and p are all constant throughout the star. We shall not limit our 
discussion to this case, but shall allow for some possibility of variation in 
these quantities by assuming that 
P = T> (791), 
cFG = /3T l (79-2). 
The effective molecular weight p, does not appear at all in the equation of 
radiative equilibrium just considered, but reappears when we return to the 
dynamical equations. 
If we insert the value just assumed for cFG, and replace T by its value 
as given by p R — ^aT*, equation (78‘2) becomes 
dX VbrrGyR /3 p R \ i(i ' l) 
PR dp R 
If for brevity we put 
/3amX 
a ) 
— (A + 1) 
.(79-3). 
WirCyR ( 3p R \ i{i ~ l) _ 
/3am 
•(79-4), 
so that # is a function of p R only, and so only of T, the equation assumes 
the form 
£ (£ — l) x\ ^ = x 3 — A (A + 1) 
(79-5). 
80. The general nature of the solution is best seen by graphical methods. 
For this it will be sufficient to consider the case in which ^ — l is positive, so 
that x, as defined by equation (79 4), is small near the surface of the star, and 
increases steadily as we pass into the star s interior. 
Taking x and A as abscissa and ordinate respectively, I have found * that 
the solutions lie as shewn in Fig. 7. There is found to be an asymptotic