326 
THE OUTSIDE OF A STAR 
If ,j v dv is the emission (per gm. per sec.) between frequencies v and 
v + dv, and k v is the absorption coefficient for frequency v, then as in 
(227-1) the emergent radiation is 
The relation between absorption and emission coefficients is by (77-15) 
where as usual I (v, T) denotes Planck’s energy distribution. Hence 
denoting the emergent radiation by H ( v , 6) dvdm/4:7T, we have from (228-4) 
The use of the equilibrium formula (228-5) is perhaps open to criticism 
considering that in the problem of spectral energy distribution we have 
to aim at rather high accuracy. The molecular velocities will correspond 
to temperature T, but the state of ionisation and excitation of the material 
will be slightly different owing to its exposure to non-equilibrium radiation. 
Thus the material may not have the normal absorbing and emitting power 
to which the equation (228-5) refers. We reserve this point (cause (c) 
above) for later consideration. 
229. We take the three causes of deviation in order— 
(a) Spread of Temperature. 
As the effect of variation of k v is not to be considered at present, we 
take k v = k, r„ = r. The formula (228-6) gives the following rule: Divide 
the range of e~ TSec6 into a large number of equal parts. Calculate the 
temperatures T x , T 2 , T 3 ... at the middle of each part. Take a cu. cm. of 
equilibrium radiation at each of these temperatures; the simple mean 
gives the constitution of the emergent radiation. 
Table 43 has been calculated in this way. The first part of it refers 
to 6 = 0, and ten equal ranges of e -T are taken so that the temperatures 
T x , T 2 ... correspond to e~ T = 0-95, 0-85, The temperatures are cal 
culated from (226-5) and (226-62) which give 
the sun’s effective temperature T e being taken as 5740°. The next three 
for three different frequencies; this represents the intensity I (v, T) for 
frequency v so far as it depends on T. 
-t„ secò 
(228-4) 
where 
I k v pdx. 
jv = ck v I ( V, T) 
(228-5), 
(228-6). 
T 4 = Tf (1 + fr) 
(229-1), 
columns give 
(g hv/RT 1)— 1 
(229-15),