220 
THE COEFFICIENT OF OPACITY 
pI/jlT 3 , since this combination of density and temperature depends only 
on the mass. Comparing with (149-1) we obtain x = 1 and 
k <x pl/xT 3 . 
We decided that owing to the uncertainties of observation an additional 
factor or T~^ was admissible, so that the variation of k is between 
p/piT' and p/fxTK This corresponds to (149-1) with values of x between 
0 and 2. 
Experiments by E. Rutherford on the capture of electrons by a 
particles have been shown by him to correspond to a probability of capture 
varying as the inverse fifth power of the velocity. The law x = 5 is far 
outside the above limits and could not be reconciled with the uniformity 
of magnitude of giant stars. We must infer that Rutherford’s experiments 
relate to a different process of capture. It has been shown by Fowler 
that they are radiationless captures analogous to the capture of comets 
by the combined efforts of the sun and a planet. Captures of this kind 
no doubt occur in the stars; but by the principle of detailed balancing 
they do not affect our study of the absorption problem, since they are not 
accompanied by radiation. 
150. It is interesting that we should be able to get so far with the 
determination of the law of opacity without having come to grips with 
the problem of the mechanism of capture or expulsion of electrons. We 
might perhaps narrow the limits a little more because it is scarcely con 
ceivable that x should be less than 1. The choice between exponents 3 and 
f, or even between § and |, does not make a great difference in practical 
calculations of the luminosities of the stars. But there are certain theoretical 
considerations which make it important to decide on which side of 3 
the exponent really falls. One illustration of this has already arisen in 
considering Cepheid pulsations; the pulsations can maintain themselves 
automatically when the exponent is a little less than 3 (§ 137). This is in 
itself an argument against an exponent as low as 2-5 for ordinary (non 
pulsating) stars; but if the normal exponent were, say, 3 there would be 
less difficulty in admitting the slightly lower value required in the Cepheids. 
Another problem for which the value 3 is critical will arise in § 211. 
Since the value x = 2 is given by what is now considered to be the best 
physical theory of electron-capture we have adopted kcc p/p,TK But the 
theory is scarcely an adequate guide and it is desirable to see whether there 
is observational support for the odd half-power of T . We obtained good 
agreement between theory and observation by using it in Fig. 2; but it is 
necessary to consider how far this agreement depends on the power of T . 
Most of the stars represented belong to the main series, which is charac 
terised by constant internal temperature (§ 122); these afford no scope