THE OUTSIDE OF A STAR 
357 
The ratio of radiation force to total force is determined by 
1 _ 0' = — 
eg 
1241 
13190 
0-094. 
This is the source of the value 0-1 used in § 233; and the general reason 
ableness of the results there found is considered as evidence that our 
extrapolation of the law for k has given a value of the right order of 
magnitude. 
The value of 1 — /3 in the deep interior of the sun is -05, so that ap 
parently radiation pressure becomes more important at the photosphere. 
But this conclusion lays too much stress on the accuracy of the extra 
polated value of k and the only legitimate conclusion is that 1 — /3 and 
1 — ¡3' are of the same order of magnitude. 
249. We may inquire a little further into the reason for the slowness of 
the variation of k. The absorption law (247-3) may be written 
k = Cp 0 /p B % (249-1), 
where G is a constant. Imagine that we are integrating equation (248-1) 
starting from the outside. Having reached a certain point let us continue 
the solution assuming that k remains constant. Call this solution A. 
Now takep G andp# from solution A, determine k from (249-1), and make 
a new solution B from (248-1) with this value of k. If k is decreasing (as 
usually happens), dp G ldp R is increased so that Pa/Pit gradually becomes 
larger than in solution A . The new value of k found by inserting solution 
B values in (249-1) is accordingly increased, and the next solution C will 
move back towards A, and so on. 
For example, in § 233 on the assumption of k constant we found 
(solution A ) at the limits of the photosphere 
T 2 /T ± = 1-38, p 2 f Pl = 12-0, 
whence k 2 fk x = 3-9. 
In solution B we should accordingly suppose that k increases between 
the two levels in the ratio 3-9 : 1; but this gives great over-correction, 
and the next solution moves back towards solution A. Probably a quite 
small change of k in this range would give the necessary adjustment. 
The absorption coefficient has a natural tendency to steady its own 
value. Physically the explanation is that if as we go inwards we find 
material that is specially absorbent, the increased outward force of radia 
tion pressure will support more of its weight and so check the natural 
increase of density downwards and (through the dependence of k on p) 
k falls again towards its normal value. This effect is well illustrated by 
Milne’s formula (248-3) where k varies as T^, or if anything less rapidly, 
instead of the anticipated variation as T~^. 
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