THE OUTSIDE OF A STAR 
339 
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line and J for the flow in the same range at practically identical frequency 
just outside the line; similarly for the other symbols. 
and in addition the absorption ( k' — k) J'pda of energy employed in 
exciting atoms. Most of the latter will be re-emitted with the same 
frequency; but a certain fraction e will be transferred to translatory energy 
by superelastic collisions and lost to that particular frequency*. Additional 
emission will be given by atoms excited by inelastic collisions; the amount 
of this is found from the condition that it balances the amount 
lost by the converse process when J' has its equilibrium value J. Its 
amount is accordingly e (k' — k) Jpds. Further, there will be the ordinary 
continuous emission kJpds for the temperature. The total emission is thus 
Multiply by dco /477 and integrate, also by da> cos 0/477- and integrate; we 
obtain 
* Transfers may also occur to or from other lines of the same spectrum, but we 
cannot very well follow this up. By ignoring it we determine the intensity of the 
spectrum rather than of one particular line in it, since these interchanges will not 
alter the sum of the intensities in the lines. 
The radiation J' will suffer the ordinary continuous absorption kJ'pds 
e (k f — k) J'pds 
pds {(1 - e) ( k ' — k) J' + e (k' — k) J + kJ }. 
Hence the equation corresponding to (225-1) is 
pdx J 
(234-2). 
By the usual first approximation we set K' = \J '. Let 
p 2 — 3 {k + e (k' — k)}/k' 
dr = — k'pdx. 
(234-3), 
(234-41), 
(234-42), 
so that 
(234-5). 
Setting k' = k in (234-5) we have 
(234-6).