218 
THE COEFFICIENT OF OPACITY 
moment so that this coefficient is reduced to 5-9. Thus we obtain the 
comparison 
Laboratory Capella 
Absorption coefficient due to L electrons 2950 2-5 
» „ K „ 8-3 5-9 
Total 2958 8-4 
148. In the stars the absorption is equal to the emission of radiation, 
so that we may, if we prefer, proceed by calculating the emission. The 
converse process to the expulsion of an electron is the capture of an electron, 
and the capture accordingly gives the emission corresponding to the 
absorption which we have been discussing. This cannot be studied directly 
by laboratory experiment because it is not possible in terrestrial conditions 
to obtain ions with vacant places for capture in the K and L groups ; but 
the problem can be studied theoretically. Here again we shall have two 
coefficients to consider : first, the ideal coefficient of emission when all the 
ions have their full capturing power ; second, the coefficient as reduced by 
lack of ionisation. In proportion as the places for electrons are filled up so 
the chance of capture is diminished. 
The ideal (or laboratory) absorption coefficient and the ideal emission 
coefficient (not realised in the laboratory or the stars) are each reduced, 
the one by ionisation and the other by lack of ionisation. The ionisation, 
in fact, reaches the value required to bring them to a balance; and the 
ionisation formula (47-1) was obtained from this balance as expressed by 
Einstein’s equation. 
The ideal absorption coefficient is independent of the density. Each 
complete atom is an absorbing mechanism which works independently of 
other atoms, and it makes no difference whether a given mass of material 
occupies a large thickness or a small. 
The ideal emission coefficient is approximately proportional to the 
density, or more nearly to p/p. A stripped ion emits by capturing electrons, 
and, other things being equal, the number of captures by it will be pro 
portional to the number of free electrons in given volume. The total number 
of particles per cu. cm. is equal to p/p (p being here measured in grams). 
In stellar conditions the number of ions is small compared to the number of 
free electrons so that the number of free electrons per cu. cm. is nearly 
equal to p/p. 
Thus we approach the problem of stellar opacity with the idea that it 
is likely to be (a) independent of density, (6) proportional to density, 
according as we begin with absorption or emission. Whichever line we 
follow there will be a modification when account is taken of the effect of 
density on ionisation. It is a question of expediency and not of principle 
which end we should begin from, depending on which of the two ideal 
coefficients undergoes least modification.