THE OUTSIDE OF A STAR
361
allowed for the diminishing value of k between r = -25 and 0 the constant
would have been zero.) By (226-5)
i^ 4 = f (T + l).
Hence
Vo =
a/3'
(T 4 - TV 4 ) (251-6),
3(1-/8')
where T 0 ' 4 — 0-396T 0 4 .
Since (251-6) is the same as (233-4) with T 0 ' replacing T 0 , we deduce
as in (233-9)
const.
W/5' CT 0 ' 1 ~ o *2’ + y„
(251-7).
This gives for the thickness of the sun’s photosphere
#1 — x 2 = 17-0 km.,
or about half the thickness given by the former discussion.
No doubt the actual photosphere will be more extended owing to its
non-homogeneous composition. The different elements may sort themselves
out to some extent according to their atomic weights and to the force of
radiation pressure on them.
Consider next a giant star with the same effective temperature as the
sun but with a smaller value of g. Comparing the stars at corresponding
levels of t, we have k oc p Q since the temperatures are the same. Hence
by (250-1) v is proportional to q. So long as v Cr is small compared with v,
(250-4) gives Po =V№tv/c) (251-8),
so that at the reversing layer (r = 0-25)
p a cc^/vcc y/g.
For example, if g has of its value on the sun, v — 97 and, by Table
46, p Q at the reversing layer is slightly under 10.
The result p Q oc y/g for stars of the same effective temperature was
originally given by Milne as the result of the theory of § 248. By (248-3)
approximately k oc y/g, and for the same temperature k cc p G .
We can now compare the effective temperatures of giant and dwarf
stars of the same spectral type*. The result must depend on the criteria
actually used in fixing the spectral types of stars. Following Milne we
take this to correspond on the average to the state of ionisation with
regard to ionisation potentials of the order 8 volts, or ip — 1-27.10 -11 ergs.
Then by (174-2) the same spectra will appear if
rp\p- +1 rt 1 y! g -
11 —= 1 2 -—. (251-91),
(Pg) i (Pg) 2
where the suffixes 1 and 2 now refer to the reversing layers of two different
stars.
* E. A, Milne, Monthly Notices, 85, p. 782.
