242 
THE COEFFICIENT OF OPACITY 
so that treating e K l n ° 2RT as constant and integrating from n' = 0 to oo, we 
Comparing with (155-42), where n = a 0 V, we find the ratio of the emission 
from the bound electrons to the emission from the free electrons is 
where — ifj 0 is the energy of an n 0 quantum orbit. 
We apply this to the electrons in orbits of quantum number 4 or 
greater. Then throughout the integration n 0 is 4 or greater, and ¡/r 0 corre 
sponds to the energy of the N group or higher groups of electrons. At 
10,000,000° RT corresponds to 14-3 A, and by Table 30 the factor e' l '°l RT 
must be practically unity even for the heaviest elements. Hence it appears 
that Kramers’ absorption is increased by a very small fraction when 
we take into account the line absorption due to excitation into orbits 
beyond n = 3. It is true that we have rather diminished the result by 
substituting n' for n' + 1, but on the other hand, we have probably 
exaggerated it considerably by integrating from n' = 0 and by neglecting 
the shielding of the nucleus for the distant orbits. 
For the lighter elements up to about Z = 30 the 3-quantum orbits can 
be included without altering the conclusion. For heavier elements the 
3-quantum orbits should be examined separately, but I think it is not 
difficult to convince oneself that these do not add very much to the 
emission. 
It appears therefore that line absorption cannot be responsible for any 
large part of the observed stellar opacity. 
It is instructive to look at the problem from another point of view 
also. We found (151-5) that in Capella each free electron was responsible 
for the emission of 4-5.10 10 quanta per second. If now we propose to 
transfer the duty to bound electrons, we must recall that whereas about 
20 free electrons are allowed to each ion an allowance of 1 excited electron 
per ion is excessive. So that each excited electron must emit 10 12 quanta 
per second, or rather must emit its quantum in 10~ 12 sec. and make room 
for another to take its place in the steady average. This is between 1000 
and 10,000 times shorter life than that of electrons excited in optical 
orbits, and I believe it is contrary to the views generally held by physicists 
to admit anything like so great a speeding up at X ray levels. 
obtain by (155-32) 
The harmonic mean velocity V of the free electrons is {\tt RT/m)^, so that 
(166-8). 
1 
2 
( e K/n 0 2 RT - 1) = i (e^! RT - 1) 
(166-9)