106 
Gaseous Stars 
[ch. Ill 
weights of the order of 1000 at least—more when we adjust for the increased 
value of /a. Thus redistribution of the generation of energy cannot solve, and 
hardly alleviates, the difficulty. 
96. Another possible line of attack is to redistribute the atomic weights. 
Instead of supposing N 2 /A to have a uniform value throughout, we imagine 
the heavier atoms to be concentrated near the centre of the star. In an 
actual star the heaviest atoms would naturally gravitate to the centre. This 
redistribution places the heaviest atoms where they are most effective in 
stopping radiation, and so, in a sense, increases the radiation-stopping 
efficiency of the stellar matter. I have examined the question in some 
detail *, and find it does not provide a solution of the problem. Redistribution 
enables us to reduce the average value of N 2 /A. throughout the star, but 
does not reduce the maximum value, which now occurs in the star’s central 
regions, and the problem remains as acute as ever. 
97. Still a third possibility is to suppose p to vary inside the star. 
Detailed calculations which I have madef, shew that this can substantially 
lessen the values of N 2 /A for stars of small mass. On the other hand, it 
makes no appreciable decrease in the values of N 2 /A necessary in the most 
massive stars, and can hardly be regarded as providing a solution. 
98. A far more drastic possibility remains. By formulae (72*3) and (77*3), 
the flow of radiant energy per unit area H is 
Near the surface of a star the value of IT is a matter of direct observation. 
Our procedure has in effect been to calculate the values of T, p, and dTjdr 
for given stars, assuming that they conform to our particular model, and to 
examine what values of N 2 /A are necessary to make the calculated value of 
H agree with the observed value. The necessary values of N 2 jA have all 
been very improbably high. 
We can reduce these values for N 2 /A, while retaining the observed value 
of H , either by increasing some factor in the denominator of the fraction on the 
right of equation (98T) or by decreasing some factor in the numerator. We 
cannot do much with p, since the mean density of the star is a matter of 
direct observation, and no possible change in p can substantially alleviate 
the discrepancy. The only remaining factor is T 6& dT/dr, or 
* M.N. lxxxvi. (1926), p. 570. The appropriate analysis is that given in the present chapter ; 
we have to assign a positive value to l. 
f L.c., p. 571. To represent this possibility, we have to assign a negative value to j in the 
analysis of the present chapter. 
4aT 3 <7 dT 
Skp dr 
aCfiT 65 dT 
3-34 xl W^\N 2 IA) dr 
.(98*1).