360 
THE OUTSIDE OF A STAR 
p G = 365, k = 497. But it is clear that the approximation has broken 
down, because the increase of k in the ratio 1 : 3-65 will be more than 
compensated by a decrease in the ratio 1 : 5-38 due to the temperature 
factor T ~ignored in the approximation. Accordingly for the stretch 
r = 0-25 to 3-4 it will be much better to pass over to Milne’s approximation 
k = const. Recomputing k by the method of § 248 with the value k 0 = 146 
now adopted we find at 6000° 
k = 177 (251-1). 
It will be seen that t = 0-25 is a very suitable place to join the two ap 
proximations since they give roughly the same value of k at the junction. 
We shall now revise the calculations of § 233 as to the solar photo 
sphere*. Using k = 177 we have 
1 - j8' = kH/cg = -0134 (251-2), 
so that (contrary to Milne’s conclusion) radiation pressure is relatively less 
important in the photosphere than in the deep interior (1 — /3 = -05). It 
should be understood however that the accuracy of our determination of 
k is not sufficient to justify any great confidence in this amendment. As 
already explained, radiation pressure, although it becomes larger in actual 
amount than gas pressure near the boundary of the star, is less important 
as a sustaining force. If any material is supported by radiation pressure 
it must be through selective line absorption and not through continuous 
absorption. 
By integrating (248-1) between the limits r = 0-25 to 3-4 
(Pg\ ~ (Pg )i = i _ p {(Pr)2 ~ (Pr) i} = Y— ft' U ( T2 — Tl ) = 483 (251-3), 
so that at the two limits of the photosphere 
(Pg)i = 100, (p 0 ) 2 = 583 (251-41). 
By (232-3) T 2 = 1-45T, (251-42). 
By (251-41) and (251-42) p 2 = 4-02p x (251-43). 
Hence by the absorption law 
¿2=1-10^ (251-44), 
showing that the assumed constancy of k is a good approximation for this 
range. 
Equation (251-3) can be written in the form 
P G = f~W^ r + O' 403 ) (251-5), 
the constant being determined from the value of (£>g')i- (If we had not 
* The calculations in this section refer to the photosphere at the centre of the 
disc whereas those in § 233 refer to the integrated disc; so they are not quite com 
parable. I have here chosen the central photosphere for the reason that it falls 
wholly in the region covered by one approximation.