332 
THE OUTSIDE OF A STAR 
performed by ionised atoms *, so that if the number of ions is increased 
10 per cent. j v is increased 10 per cent. There will also be some further 
increase due to the greater abundance of free electrons. At the same time 
k v diminishes. In fact the equilibrium ionisation attains just the value 
required to bring j v and ck v I (v, T) into agreement; if greater ionisation 
occurs, then j v > ck v I ( v , T). 
The emergent intensity is seen from (228-4) to be directly proportional 
to jjk v . We can therefore see at once the excess of jjk v required to give 
the observed curve. If the excess ionisation is more or less the same at all 
depths the intensities at the centre and limb are multiplied by the same 
factor, so that the contrast-ratio is unaffected and Milne’s requirement is 
satisfied. The non-equilibrium conditions are too complicated to allow 
a prediction as to what part of the spectrum would be most affected by the 
excess ionisation but there is no reason to think that any difficulty arises 
on this point. 
I should scarcely have expected the change of ionisation to be sufficiently 
great to explain the observed curve—at least 15 per cent, seems to be 
required in order to represent the high peak. 
At present we cannot decide on a definite conclusion. The whole 
investigation leaves one with a sense not so much of puzzlement over the 
deviations of the sun from a black-body as of surprise that it should 
approach a black-body so nearly as it does. 
It should be added that the observational data to which we have 
trusted are not entirely confirmed by recent investigators, and it is possible 
that we have been laying too much stress on some of the features of Abbot’s 
curve. 
Second Approximation to the Temperature Distribution. 
230. The emergent radiation (227-2) is J (6) do>/47r for the level r = 0, 
so that 
This should now replace our original boundary condition J = 2 H which 
corresponds to the approximation in which J (6) is supposed to be 
constant over the hemisphere. Hence in place of (226-61) and (226-62) 
* Capture of electrons can be effected by neutral atoms, but their efficiency is 
likely to be much less. The negatively charged atoms H_, C_, 0_, etc. are well known 
in positive ray experiments. 
J (6) = 2 H (1 + f cos 6) for r = 0, 6 < 
For 9> ^, J (6) is zero at this level. Hence by (225-5) 
(230-1). 
we now have 
acT£ = \H , acT e 4 = 4H, 
so that 
T. = (y) 1 = i-23or 0 
(230-2).