THE OUTSIDE OF A STAR 
337 
Hence integrating 
const - - * ■- m {f+ lo «« t+t. - 2 tan " rj -< 233 ' 9 )- 
For //, we guess the value 20 since the ionisation is low; g = 2*74.10 4 on 
the sun; hence with the values of T in (232-5) 
x x — x 2 = 2-70.10 6 cm. 
To sum up—at an average point on the sun’s disc (cos 6 = |) the 
thickness of the layer furnishing 80 per cent, of the whole radiation is 
27 kilometres. In this zone the temperature increases from 5050° to 6950° 
and the density increases twelvefold. The pressure increases sixteenfold, 
and in the middle its value is about 10~ 5 atmos. 
In a giant star the thickness of the photosphere will be greatly increased 
on account of the much smaller value of g (233-9). The pressure is only 
altered to a moderate extent according to the value of /3'/(l — ft'). 
These preliminary results will be revised in § 251; but their general 
character is not much altered. 
Absorption Lines. 
234. Line absorption is caused by the excitation of an atom from one 
state to another. In this process radiation of a definite frequency v to 
v + 8v is absorbed and if the atom is free from disturbance the width 8v 
of the absorption line is small. The explanation of the appearance of 
absorption lines in stellar spectra is not quite so obvious as we might 
think at first, because absorption is closely linked with emission. 
Here are two rough (and contradictory) arguments— 
(a) Consider radiation proceeding outwards. It excites atoms and is 
accordingly absorbed; but the excited atoms subsequently relapse and 
emit radiation of the same frequency. The emission, however, occurs in 
all directions equally so that only half of it goes to reinforce the outward 
beam. Hence absorption followed by emission is equivalent to simple 
absorption with coefficient \k, and the intensity in the range v to v + 8v 
falls off exponentially giving a very dark line. 
( b ) In light of frequency v to v + 8v we can only see a very small depth 
into the star since it is highly opaque to this radiation. But the region we 
do see has a temperature not less than T 0 the boundary temperature, so 
that the intensity of the radiation in the line should not be less than that 
corresponding to T 0 . Since the surrounding spectrum has an intensity 
corresponding to T e = 1-23 T 0 the contrast is very limited. 
The first argument is nearer the truth than the second; but we have 
the uncomfortable feeling that more attention should be paid to the 
subsequent adventures of the radiation emitted backwards. I think it 
E 22