128 
SOLUTION OF THE EQUATIONS 
failed to satisfy this. But here “vanish” must be understood in the 
ordinary physical sense, i.e. “become insignificant”; and p R and p G are 
insignificant for the present purposes when they become less than, say, 
10 8 dynes per sq. cm. Any more refined expression of the boundary con 
dition is quite superfluous. It is after all only commonsense that we shall 
not seriously disturb the internal condition of a star by applying a trivial 
radiation pressure or gas pressure of the order 100 atmospheres to its 
surface; but it is interesting to trace in the numerical calculations how 
rapidly the effects of such surface disturbances fade out as we descend. 
Variable Molecular Weight. 
94. Ionisation of the atoms is favoured by high temperature and by 
low density. In general, the influence of temperature predominates and 
we must expect the ionisation to increase as we go towards the centre of 
the star. This involves a gradual decrease of molecular weight towards the 
centre, the same atomic weight representing an increasing number of 
independently moving particles or “molecules.” 
In order to study a molecular weight decreasing inwards we consider 
laws of the form 
V = Vi T ~ s , 
and find the modification of our former results for constant p in § 84. We 
use the approximation rjk = const. 
Equation (84T) now becomes 
91 pT'+ s aT 4 
ft*i 3 (I - /3) 
(9+1), 
so that 
_ U/q/3 /773_ s 
9 391 (1 - /3) 
(94-21). 
Hence 
*0 
II 
-g 
(94-22), 
where 
r = 4/(3 - s) 
(94-23), 
a (391 (1 — /3)) y 
K 3(1-ft l a^fl j 
(94-24). 
Setting as usual 
y=l + 1 /n, 
3-5 
n = - 
1+5 
(94-3), 
and the distribution is of the polytropic type treated in Chapter iv. 
By (57-2) 
(n + l) n K n 
4:7tG 
— (n + l ) 3 
- ÆY 
■Po/