CHAPTER IX 
THE COEFFICIENT OF OPACITY 
146. Results reached in the present Chapter have been used in an 
ticipation from § 89 onwards. We must therefore return and take up the 
problem of the absorption coefficient as it presented itself in § 88. At that 
stage we were occupied with our first astronomical result of importance, 
viz. that for the series of giant stars from type M to type A the opacity 
is nearly constant although the internal temperature increases twelvefold 
between the beginning and end of the series. This suggested (but, as we 
now see, wrongly) that the opacity might tend to a constant value at high 
temperatures and so be the same for all stars. Actually, however, the 
constancy of the opacity was a statistical result applying to groups of 
stars presumed to be of the same average mass, and there was no test 
whether the constancy continued for stars of a different mass. 
The radiation in the main interior of a star consists of X rays, and 
comparison is invited with measurements of absorption of X rays made 
in the laboratory. In § 105 we have found the absorption coefficient at 
the centre of Capella to be 49 c.G.s. units. This is of the general order of 
magnitude of the measured coefficients of most elements for hard X rays ; 
for example, it agrees with the coefficient for iron for wave-length about 
0*8 A. It must, however, be noted that the radiation at the centre of 
Capella is of much greater wave-length, the maximum intensity being at 
3-2 A. 
According to laboratory determinations k increases very rapidly with 
the wave-length. Subject to certain discontinuities it varies as À 3 . This 
brings about a double discrepancy with astronomical observation ; firstly, 
it makes the laboratory coefficients much greater than the astronomical 
coefficient for the same wave-length* ; secondly, it is at variance with the 
astronomical result that stars differing widely in temperature show little 
change of k. 
It is clear that there is something which invalidates the direct com 
parison of astronomical and terrestrial determinations. That which stands 
in the way of the comparison is ionisation, strong in the stars, but almost 
absent in terrestrial experiments. 
* The difference is even wider than would at first appear; for the comparison 
would more fairly be made at an average temperature of Capella (to which the 
astronomical coefficient must be supposed to refer) instead of with values extra 
polated for the central temperature.