356 
THE OUTSIDE OF A STAR 
The material is taken to be calcium which is found to be singly ionised in 
these conditions so that 
Z - 20, A = 40, p = 20, / = 1. 
The result is k = 2-00.10 3 (247-15). 
Milne gives k = 7-8.10 3 , the difference being due to his neglect of Rosse- 
land’s correction. We might feel inclined to adopt a value 10 times larger 
than (247-15), since the theoretical result is only T 1 ^ of the observed value 
in the deep interior. As Milne’s value corresponds to a convenient com 
promise we shall adopt it in this section, so that 
k 0 — 7800 (247-16), 
k 0 denoting the value of k for the standard temperature and pressure 
defined above. 
Since = (247-2), 
p R a ¡xT z 
the absorption law k oc p/p,T- can be written 
At 6000°, p R = 3-30 
(247-16) 
koc^T-i (247-3). 
Vr 
dynes/cm. 2 Hence determining the constant from 
k = 129— 
Vr 
(247-4). 
248. To determine the value of k in the outer part of the sun Milne 
adopts a procedure equivalent to the following. The fundamental equation 
(233-1) gives 
dpo = 
1 )dpR (248-1). 
eg _ 
JcH L ) 
Integrating this on the assumption that k can be treated as constant and 
neglecting the constant of integration, we have 
eg 
k 
Hence by (247-4) 
Setting for the sun T 
Po== ^kH 
T 
-lj Vr (248-15). 
(uD'w/ 1 (248 ' 2 >- 
6000°, cgfH = 1-319.10 4 , we have 
k _ 13190 _ 
129 ~ k A ’ 
whence k = 1241. 
For approximate calculation the term — 1 in (248-2) is unimportant 
so that m -1 
T N“2 
,600oJ 
k* = 
129 eg 
H 
.(248-3), 
and k oc T Hence the result is consistent with the original assumption 
that k can be treated as constant for a considerable range of temperature.