238 
THE COEFFICIENT OF OPACITY 
paribus be proportional to the density, so that it will give rise to differences 
between dense and rarefied stars; hence the discrepant factor 10 which 
affects dense and diffuse stars alike cannot be accounted for in this way. 
Other sources of Opacity. 
165. The success of the correspondence principle as applied in Kramers’ 
theory seems to be greater than we could have expected. The general idea 
of the principle is that the results of the classical and the quantum theory 
will converge ; but, for example, in dealing with K absorption from a 1- 
quantum orbit we are as far as possible from the convergence point and it 
is fortunate that the difference is no greater. The discussion has shown 
that the use of Kramers’ theory (or of the classical theory) to calculate 
astronomical opacity is practically equivalent to using the laws ascertained 
by terrestrial experiment. Consequently, the discordance found in § 158 
is a matter of very serious concern. 
It is not as though any wide extrapolation were required in applying 
experimental results to the interior of a star. The approximate treatment 
of the electron orbits as parabolic is as satisfactory in the stars as in 
laboratory conditions*. The main point of difference is that in the stars 
the outer part of the electron system is missing and this may conceivably 
make some difference to the ease of expelling an inner electron by radia 
tion. We should also like to know more about Kulenkampff’s spectrum B. 
Does it remain at frequency y 0 when the atoms are ionised, or does it 
move on to correspond with the last occupied level ? 166 
166. We must consider whether there are any further sources of 
absorption responsible for an appreciable part of the stellar opacity. This 
brings us to the question of line absorption due to excitation of the atoms. 
Rosseland, in pointing out the distinction between opacity and absorption, 
suggested that this could be disregarded since fine absorption lines can 
have no appreciable effect on opacity. We dare not trust to this because, 
as J. Woltjerf has urged, the lines may be broadened in the stellar interior 
and effectively screen the whole spectrum. As before, we attack this 
problem by calculating emission rather than absorption. 
If we are dealing with a large number of excited electrons, a certain 
proportion will relapse and emit quanta within a given time, so that there 
will be an average rate of emission of energy per excited electron. Not 
very much is known about this emission for deep-lying electrons, since 
experimental values have only been obtained for the outermost electrons. 
But according to the general principles of the quantum theory the emission 
* Some further discussion of the applicability of Kramers’ formulae to stellar 
conditions will be found in Monthly Notices, 84, p. 115. 
f Bull. Astr. Inst. Netherlands, No. 82.