358 
THE OUTSIDE OF A STAR 
250. If the method of § 248 is applied to the conditions in the reversing 
layer the neglect of the constant of integration will introduce inaccuracy 
which seems likely to be serious. Near the bottom of the photosphere 
this “end correction” will have practically disappeared, and k and 1 — /3 
will have settled down to Milne’s values; but we are chiefly interested in 
regions where they can scarcely have begun to recover from the boundary 
disturbance. 
The following method should give a good approximation for the outer 
layers down to about t x = 0-25, which we have taken as the top of the 
photosphere for the centre of the disc (§ 232)*. In this region T lies 
between 0-84 T e and 0-91T e so that we shall treat it as an isothermal 
region so far as k and p G are concerned. 
Introduce a quantity v defined by 
kH _ po 
eg v 
(250-1). 
Since in the isothermal region k and p Q are both proportional to p, we have 
v constant. Then (248-1) becomes 
dpa = l) dp R , 
\Po ) 
or l~ = d P- < 250 ' 2 >- 
Integrating we obtain 
- v log (1 - p 0 /v) - p G = Sp R = \a ( T 4 - Tf) 
= HtIc (250-3) 
by (226-5). In most cases pg/v is small and the equation 
1 Pa 2 Ipa 3 
2 v 3 v 2 c 
.(250-4). 
In Table 46 the first column gives an assumed gas pressure at the 
conventional upper limit of the photosphere r = 0-25. The second column 
gives v deduced from (250-3). The third column gives the value of k at 
this point deduced from (250-1). The last column gives the corresponding 
Table 46. 
Absorption Coefficient for Sun’s Reversing Layer. 
Va 
V 
lc 
k 0 
1 
1-69 
7820 
840000 
10 
102-5 
1286 
13810 
100 
9700 
135-9 
146-0 
1000 
963000 
13-7 
1-47 
* An alternative treatment is given by Milne, loc. cit. § 9.