THE COEFFICIENT OF OPACITY 237 
/ 
Similarly for the L absorption, q l = 6, / = (§)~ 2 — (f)~ 2 = except 
in very light elements the result must be multiplied by 8 on account of 
the 8 L electrons in each atom. Hence 
a L = 0-0020Z 4 A 3 (163-6). 
These formulae apply to wave-lengths short enough to effect the K 
and L ionisations respectively; there are abrupt absorption edges at the 
limits where the K and L ionisations suddenly cease. 
The experimental value of the constant for a K is about 0-020, and for 
a L about 0-003, so that the agreement of the theory is entirely satisfactory. 
It will be seen that the stellar opacity can be predicted from laboratory 
data without appeal to Kramers’ theory or any other theory of absorption. 
The laws a K = -020Z 4 A 3 , a L = -003Z 4 A 3 were discovered empirically before 
any theory was suggested. To apply them to stellar absorption we have to 
discover first what proportion of the K and L electrons are retained—how 
much of the absorption indicated by these laws is still in working order in 
the stellar conditions; but that is found by the ionisation formula which 
rests on general thermodynamics and has no reference to Kramers’ or 
any other theory of the absorption processes. The small additional absorp 
tion corresponding to spectrum a can also be calculated from laboratory 
measurements of the continuous X ray spectrum. 
Evidently these experimental laws will give practically the same value 
of the stellar opacity as the theoretical laws with which they approximately 
agree. They will lead to the result k oc p/pcT but with values of k approxi 
mately j 1 ^ of those found in the stars. 164 * 
164. The question may be raised whether the material of a star may 
not have a refractive index for the radiation traversing it, which should 
be taken into account in the calculations. As the crude macroscopic con 
ceptions of refractive index and dielectric constant are liable to be mis 
leading, it may be well first to insist on two points: (1) the speed of 
propagation of radiant energy is c whatever the refractive index of the 
material; (2) the density of the radiant energy in thermodynamic equi 
librium is given by Stefan’s and Planck’s Laws whatever the dielectric 
constant of the material. The macroscopic formulae appear to contradict 
these statements, because (by a fiction which is sometimes convenient) 
they include energy of polarisation of the atoms and molecules in the 
radiant energy. 
Clearly we must not combine a macroscopic theory of wave propagation 
with a microscopic theory of absorption; and the investigation is more or 
less at a deadlock because the quantum theory of refraction, polarisation, 
etc. is scarcely far enough advanced to help us. 
It is unlikely that there can be much effect on the absorption coefficient 
from this cause. In any case, the change of refractive index will ceteris