304 
THE SOURCE OF STELLAR ENERGY 
a rate comparable with the Kelvin time-scale (E = 0) and the subatomic 
energy will fail to achieve the purpose for which it was introduced. 
The danger of over-stability must again be recalled; E has to increase 
with contraction but not much faster than T 2 or the star will be set 
oscillating. It seems unlikely that a plausible law can be found between 
such narrow limits; so that we prefer *to suppose that there is a lag of a 
few months up to a thousand years in the response of E to the changed 
conditions. The response must be rapid enough to save a giant star from 
collapse. 
The second reason for denying that E is independent of p and T is 
that the assumption would make L¡M solely a function of the age of the 
material. It supposes that the material has gone on degenerating at a rate 
independent of physical conditions past and present so that its stage of 
exhaustion is determined solely by its age. The question what zero the 
age is to be reckoned from remains unanswered. We cannot fit the 
astronomical facts into so cast-iron a rule, as was shown in § 207. It is 
true that the admission of a dependence on p and T has not helped us 
far forward in reconciling the facts; but it does leave us free to explore 
further instead of coming to a blank wall of contradiction. 
The result that E increases with contraction of the star sometimes 
enables us to eliminate one of the variables p and T in a comparison. For 
example, imagine the material of Capella to be slowly compressed until 
it reaches the temperature of the sun. Then since p oz T 3 the density 
becomes | that of the sun. We have now the comparison that at the same 
temperature the material of Capella emits more than 30 times as much 
energy per gram at a density | that of the sun. 
Since the dependence on T may be very complicated, whilst the 
dependence on p is expected to be fairly simple we can get a clearer idea 
of the exhaustion of the solar material in this way. 212 
212. We shall try to classify the possible ways in which we think that 
€ (the liberation of energy per gram) might depend on p and T. 
To begin with, a nucleus must be concerned in the emission. If nothing 
else is concerned the emission by the nucleus is independent of the 
statistical state of the system and e is independent of p and T. (It is 
possible that the structure of the nucleus may be modified by temperature 
and density, that is to say, nuclei of different kinds may be evolved in 
different physical conditions; but in that case we regard the emission as 
a consequence of the event which creates the radio-active nucleus, and it 
falls under one of the succeeding alternatives.) 
If, in addition, something extraneous to the nucleus is concerned, this 
may be (1) a bound electron, (2) a free electron, (3) the field of radiation. 
Two nuclei may also be concerned although their repulsion tends to keep