THE OUTSIDE OF A STAR 
365 
) 
254. We now consider what happens as we descend in the chromo 
sphere still assuming that Ca + is the only material present. The investiga 
tion of § 226 is immediately applicable and we have 
where H', J', r refer to monochromatic radiation of frequency v 12 . The 
law of darkening towards the limb (for the residual radiation at the centre 
of the absorption line) can be worked out as before and the same result 
(227-2) is obtained as for the photospheric radiation as a whole*. This is 
believed to be confirmed by observation. 
The resultant outward force of radiation pressure is proportional to 
H and the weight to be supported is proportional to n x + n 2 . Hence, 
since H' is constant, the ratio of radiation force to gravity varies with 
depth as n x /{n x + n 2 ). A correction however is required on account of the 
momentum of the “stimulated emission.” Whilst the spontaneous emis 
sion is symmetrical in all directions, the stimulated emission is in the 
direction of the stimulating radiation ; the radiation pressure is accordingly 
reduced in corresponding proportion. It will be seen from (253-2) and 
(253-3) that the stimulated is to the spontaneous emission in the pro 
portion (e hv ™l RT < 1 — l)/|r : 1 or approximately n 2 jqn x . Hence the radiation 
pressure is reduced approximately in the ratio % — n 2 lq : %. Writing 
then 
the constant a is determined by the condition that this ratio must be 
unity at the top of the chromosphere where the gas pressure vanishes. 
Since q — 3 and n 2 Jn x for the top of the chromosphere is 3-54.10-V, this 
Now n 2 fn 1} so long as it is small, is proportional, not to H', but to J' 
and therefore to 1 + fr'. Hence 
* Not the law of darkening for the neighbouring portion of the continuous 
spectrum which introduces other considerations (§ 229). Hence the contrast or 
“blackening” will not be strictly constant over the disc. 
(254-0), 
radiation force 
gravity 
(254-1), 
gives 
e = 4-72.10-V. 
(q + 1 ) n 2 fqyi\ = (J (1 + 
By (254-1) and (254-2) 
(254-2). 
radiation force _ 1 + cr 
gravity 1 + o- + f to 
|t '<7 approximately.