THE OUTSIDE OF A STAR 
367 
be valid. However, taking r 0 ' to give the base of the chromosphere and 
measuring x from the base, we have by (254-51) and (254-63) 
WTr 
.(254-7). 
liag (1 - r) 
Inserting <r/r = -00472, p = 20, 1 - r = 0-9, T = 5740°/l-23, g = 2-74 IO 4 
wefind x 0 = 1650 km. 
All the constants required in this calculation are very well determined, 
and the only uncertainty is that above-mentioned as to the conditions 
where the chromosphere merges into the photosphere. By (254-52) 
pec (x + x 0 )-\ 
so that at a height of 8200 kilometres the density is ^ the density at the 
base. The density of the emitting atoms (pn 2 /nj) is proportional to p (1 + | T '), 
which up to 8000 km. is nearly proportional to (x + # 0 ) -3 - Thus in the 
same range the emission per unit volume in the chromosphere is reduced 
to T i ïï . The problem of how the brightness of the chromosphere as seen at 
the limb of the sun will vary with the density is very complicated, and the 
solution does not seem to have been attempted. It is therefore impossible 
to say how nearly the decrease in density agrees with the observed decrease 
of brightness. 
As Milne has pointed out, the comparatively slow decrease of density 
in the chromosphere is evidence that radiation pressure supports nearly 
the whole mass. If gas pressure played more than the very subordinate 
rôle assigned to it in the above discussion the law of decrease of density 
would be exponential and p would become insignificant at a small height 
above the photosphere. It is easy to see how the balance is attained. In 
the final state of the chromosphere no more atoms can be supported at 
the top, because the screen of calcium atoms below has reduced the H 
and K radiation to an intensity too weak to give support; no more can 
be added at the bottom, the pressure of the radiation sent back from the 
chromosphere towards the interior presses them down. Until the back 
pressure attains the equilibrium amount atoms will be driven from the 
photosphere into the chromosphere by the forward pressure of the radia 
tion of H and K frequency in the photosphere. 
The monochromatic absorption coefficient for Ca + can be obtained 
from the value of t 2 (the life of an excited ion) found in (253-6); but an 
assumption must be made as to the width of the H and K lines. We 
adopt as a rough guess a combined width AA = 1 A. It-is remarkable that 
all previous results are independent of AA. Let n x and n 2 be the numbers 
of ions in the two states in a cubic centimetre in equilibrium at a low 
temperature T*. By taking a low temperature we can set (e hv l RT — 1) 
* Since ¥ and l 2 are atomic constants we find the relation (254-83) between them 
by a purely thermodynamical argument without reference to the chromospheric 
conditions. 
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