88 
Gaseous Stars 
[ch. Ill 
If we suppose the variations in p to be given by our previously assumed 
relation 
or, replacing T by its value in terms of T' and X as given by equation (82 , 5), 
“L maß J * 
This equation gives the value of X in terms of T', and with this value of 
X equation (82’6) gives the value of p as a function of T'. 
83. We have seen (§ 70) that X, the ratio of gas-pressure to radiation- 
pressure, is fairly large at the centre of the sun, and for stars of different 
masses is approximately proportional to 1/M 2 . For stars of mass con 
siderably less than that of the sun, X will be quite large, so that 1/X may be 
neglected. 
In this case the left-hand member of equation (82 - 8) takes the simple 
form X 2-2 -?, so that this is proportional to throughout the star. From 
equation (82‘6) we now find that 
Thus so far as its distribution of density is concerned a star of small mass 
arranges itself like a sphere of gas, without radiation pressure, in adiabatic 
equilibrium with 
When p and cFG are uniform throughout the star, j and l are both zero, 
so that n — 3‘25. 
84. Inside an ideal star of enormously great mass, X is very small, so that, 
from equation (82‘8) 
(82-4), 
the value of T' becomes 
jv _ ^ 1 jti-j 
(82‘5), 
and the relation p G = \p R assumes the form 
3 +j 
(82-6). 
If, as in § 79, we put cFG equal to ßT l , equation (81‘3) becomes 
+ V<*-9 
Stars of Small Mass. 
p 1 ~ j oc X 1 ~ j T ' (3 +;) oc T 3 ' 25 +j ~ ¥ . 
3-25+j-# 
(831). 
Stars of Very Great Mass.