THE OUTSIDE OF A STAR 
359 
value of Tcq, i.e. k for the standard conditions T — 6000°, p G — 200 for 
comparison with (247-16). 
It will be seen that a very rough knowledge of k 0 would suffice to give 
a reasonably close value of p G for the level considered; but since estimates 
of k 0 depend on risky theoretical speculation, we prefer to proceed in the 
converse way. The discussion of the intensities of spectral lines by Fowler 
and Milne (§ 242) indicated that they are usually produced where the 
pressure is rather above 100 dynes per sq. cm. or 10 -4 atmospheres. Their 
location cannot be much below the level r = 0-25, because even at the 
centre of the disc ^ 0 f the photospheric radiation comes from above this 
level, and for the disc as a whole nearly £ is above this level. We judge 
therefore that the results for p G = 100 dynes/cm. 2 should be accepted. 
This gives in round numbers 
k 0 = 150, 
as compared with 7800 adopted by Milne and the value 2000 derived in 
(247-15). 
There is no theoretical objection to be urged against this lower value. 
Extrapolation of a theoretical formula is not the same thing as extra 
polation of a theory; and so far as we can judge the value 150 really 
corresponds better with Kramers’ theory. 
In deriving the value 2000 we assumed Z = 20; but unless the electron 
penetrates inside the ion during its encounter the actual charge influencing 
it will be Z = 1 or 2 since few atoms in the reversing layer are more than 
doubly ionised. Taking Z = 2, k 0 is thereby divided by 100. Allowing for 
various minor adjustments the value k Q = 150 is about as likely a prediction 
from Kramers’ theory as we can make. 
We verify as follows that the electron does not enter the ion deeply. 
Setting A = 5000 A, T = 5740°, Z = 2* in (155-2), we find y = 1-5 for 
o- = 1-00.10~ 7 cm. Now the main part of the emission comes from electrons 
for which y is in the neighbourhood of 1-5, and these are aimed to pass at 
the above distance o from the centre. From (153-7) we find that the 
eccentricity of these orbits is 1-09, and the closest approach to the centre 
is then calculated to be 2-1.10~ 8 cm. This will not quite clear the ion which 
has a radius 2-3.10~ 8 cm.; but the penetration is too slight to have much 
effect. 
251. Adopting the third line of Table 46 for r = 0-25, we have 
k 0 = 146-0, p G - 100, v = 9700, k = 135-9. 
If we were to solve (250-3) with this value of v and with r = 3-4, so as to 
find the conditions at the bottom of the photosphere, we should obtain 
* This is intended to apply to singly or doubly ionised calcium equally, because 
in the former case the approaching electron penetrates within the orbit of the 
valency electron. 
) 
f