336 
THE OUTSIDE OF A STAR 
Let 
Then (233-1) becomes 
(233-2). 
\a$'dT 4 = (1 - P') m (pT/n) 
(233-3). 
Suppose that jS' (and therefore k) is constant. Then by integration 
This is similar to (84-1) except that the constant of integration is no longer 
negligible. Of course jS' will not have the same value as ¡3 in the stellar 
interior. 
Owing to the constant of integration (1 — /?')//?' no longer represents 
the ratio of p R to p Q \ but it represents dp R ldp G , which is what is com 
monly meant by the ratio of radiation pressure to gas pressure, i.e. the 
ratio of the forces exerted by these pressures on a given piece of material. 
It has sometimes been thought that, since p R [po tends to infinity at 
the boundary, radiation pressure becomes of enormous importance in the 
equilibrium of the extreme layers of the star; this is a fallacy because the 
force depends on the gradient of the pressure and not on its absolute value. 
Inserting the values (232-4) and (232-5) for the limits of the photosphere 
(integrated disc) we find ^ = 12-Op 
By (233-4) and (233-5) 
According to Milne (§ 248) the value of 1 — /3' for the outer part of the 
sun is roughly 0-1. We have for the sun Hjc = 2-08. Hence for the limits 
of the solar photosphere (232-4) 
that is to say, the pressure in the solar photosphere is round about 10 -5 
atmospheres. 
T 4 - T 0 4 = 
(233-4). 
By (226-5) and (226-61) 
Hence by (233-4) 
T 4 - T ( 4 = 3 rH/ac 
Pl T l _ T 1 
(233-5). 
(233-6). 
(pa)i = 2-50, ( pg) 2 = 41-3 dynes per sq. cm., 
451 T 4 dT 
(233-8). 
pF T 4 - T 4