104 
RADIATIVE EQUILIBRIUM 
The amount absorbed in the cylinder is 
E (9) - cdS . kpds 
4:77 
(73-3). 
Finally, a certain amount will be emitted by the material in the cylinder. 
This will be emitted indiscriminately in all directions so that the amount 
within doi is the fraction dayf^v of the whole. So far as ordinary thermal 
emission is concerned the amount will depend on the temperature; but 
we must here include also any sub-atomic energy liberated in the form of 
aether waves. If j is the total radiation emitted per gram per second, the 
amount from the mass pdsdS in the cylinder emitted within da> is 
Balancing the gains (73T) and (73-4) and the losses (73-2) and (73-3) 
by the cylinder in a steady state, we have 
along ds the axis of the cylinder meets successive radii at a diminishing 
angle. Hence 
74. First consider the case when r is large and the curvature of the 
stratification in the star can be neglected. Then (73-6) reduces to 
Let E be the total energy-density of the radiation, H the net outward 
flow per second across unit surface perpendicular to r, and p R ' the actual 
pressure of the radiation in the radial direction (allowing for the imperfect 
isotropy). Then 
(73-4). 
(73-5). 
When E (9) is a function of r and 9 only, as in a star, we have 
d d. sin 9 d 
The second term on the right takes account of the fact that proceeding 
cos e | E (9) (6) J±- k P E (6) 
(73-6). 
(74-1). 
\ 
(74-2). 
The proof of the last two equations follows at once from the discussions 
in §§ 31 and 22 respectively.