116 
SOLUTION OF THE EQUATIONS 
As explained in § 67 we have not much concern with the outer regions 
of the star, and there is no need to extend the assumption (83*1) into the 
low-temperature part of the star. 
Strictly speaking* there is a small constant of integration of the order 
1 dyne per sq. cm., since radiation pressure does not vanish at the surface. 
We neglect this in comparison with the pressure of the order 10 12 dynes 
per sq. cm. in the main part of the interior. 
Introduce a constant /3, defined by 
The important equation (83-4) does not require any serious considera 
tion of the low-temperature part of the star. We have written L/M for 
the boundary value of L r /M r ; but it is not necessary that our “boundary ” 
at or near the surface is in order to have in our equation quantities deter 
mined directly by observation; but this is sufficiently provided for if our 
“boundary” is taken where the temperature is say of the central 
temperature. By the method of § 67 it is shown that the mass up to this 
point is practically the whole mass of the star. Also the radiation flowing 
through this boundary is practically the radiation which flows out of the 
star since the small mass beyond can form no appreciable sink or source 
of energy. Thus it is sufficient to develop the theory so far as to obtain 
the expression for L/M for the high-temperature part of the star; it is 
then justifiable to substitute for this in practice the observed surface 
value of L/M. 
So far the formulae are valid whether the material is a perfect gas or 
not. 
84. Now consider a star for which the material is a perfect gas so that 
it obeys the gas law 
Integrating (81-7) 
PR = ÄZ 
- 0 . p 
AttcGM 
(83-2). 
Vr = (1 - ß) p \ 
Jpo = ßP ) 
(83-3). 
Then by (83-2) 
IttcGM (1 - ß) 
(83-4). 
should coincide with the surface of the star. The only object in taking it 
Perfect Gases. 
Since also 
VR = 
we have by (83-3) 
p = KpT = aT* 
W 3 (1 - ß) 
(84-1).