244 
THE COEFFICIENT OF OPACITY 
gold is 2-46. In Capella gold would retain at least the 10 inner electrons 
and perhaps some of the M electrons as well; this raises /x to at least 2-8. 
Changing ¡jb from 2-1 to 2-8 increases 1 — /3 from 0-28 to 0-41 and reduces 
/3/(1 — /3) 2 from 9-2 to 3-5. This precisely cancels the increase in Z 2 /A*. 
169. There is one way in which k t and k a can be reconciled by an 
assumed chemical composition of the star, namely, by mixing a consider 
able proportion of hydrogen with a heavier element, say, iron. Hydrogen 
alone would be comparatively transparent to stellar radiation, since its K 
line is of comparatively low frequency. The actual k t would be much less 
than the value given by (158-2), since the guillotine cuts off most of the 
classical radiation capable of affecting the opacity. But a mixture of 
hydrogen and iron may be more opaque than either element separately. 
Suppose that we have a mixture containing 15 hydrogen atoms 
(A = 1, Z = 1) to 1 iron atom {A = 56, Z = 26). The hydrogen atoms will 
be ionised, and the iron atom (in Capella) will have lost 24 electrons; 
hence the weight 71 corresponds to 16 ions and 39 electrons. We have 
M = U= 1-29, /=¿« = 0-41. 
In applying (158-2) A should be taken as 71 instead of 56, since the number 
of iron ions per gram is now 1/11h , and the hydrogen ions are ineffective. 
We must also recalculate T with the new value of ¡x. We find that (1 — /3) 
is now 0-100 and the central temperature of Capella is reduced in the ratio 
1-30. 
By these changes in (158-2) the absorption of the iron is increased in 
the ratio 2-38 so that 7 0 
k t = 11-8. 
The absorption by the hydrogen ions is negligible. The chief function of 
the hydrogen is to lower the molecular weight; but in addition it nearly 
pays for its own inactivity by providing more numerous electrons for the 
iron to capture. 
The astronomical coefficient is reduced in proportion to 1 — /3, and 
now becomes 7 , 0 - 
k a — 18-7 
which is in good enough agreement with k t . 
For any star of small mass such as the sun the above mixture would 
increase k t /k a 37 times, so that the original discordance would be very 
much over-corrected. About half the quantity of hydrogen (7 atoms to 
1 iron atom) is needed in order to obtain the same agreement as for Capella. 
It may be urged that this would be in keeping with the view that the stars 
* The adopted molecular weight 2-1 was not intended to correspond strictly 
to iron but to allow for some admixture of lighter elements; so that by taking 
Z 2 jA for iron we have rather minimised the discrepancy.