i 
THE SOURCE OF STELLAR ENERGY 305 
them apart; somehow or other the assemblage of four hydrogen nuclei 
in the helium atom must be contrived, but this is too mysterious a problem 
for us to tackle. 
(1) If an electron bound to the nucleus is concerned, the law maybe 
very complex. For instance, the condition might be that the electron 
describes an ellipse which grazes the nucleus at pericentron. This involves 
excitation in a high quantum orbit and depends in a complicated manner 
on T and p according to the formulae in Chapter ni. 
(2) If a free electron is concerned the law seems to be e oc pT~^, for 
this expresses the frequency with which electrons hit the nucleus (§170)*. 
The decrease with T is due to the tracks of fast electrons being less bent 
towards the nucleus. The nature of the collision cannot be appreciably 
affected by temperature, because the kinetic energy of the electron when 
in contact with the nucleus is due almost entirely to the potential there 
of the order 3,000,000 volts; the extra 1000 volts (variable according to T) 
which represents the initial energy cannot make much difference. Hence, 
for similar nuclei, the emission will be simply proportional to the frequency 
of collision. Exhaustion effects can be provided for by supposing that in 
some nuclei the protons are better guarded from attack than in others. 
(3) If radiation is concerned it presumably acts by stimulating the 
emission as provided for in Einstein’s equation, and the stimulation is 
quite inappreciable. It must not be overlooked that there is no logical 
justification for applying Einstein’s equation to a process involving the 
annihilation of matter; for that equation implies that the converse process 
(creation of matter) can occur and that it accords with the second law of 
thermodynamics. Either of these propositions may be denied without 
striking too heavily at our sense of the fitness of things. 213 
213. Since our arguments seem to lead to a deadlock, and no sug 
gested way of escape appears very inviting, we must hold all the inferences 
under suspicion for the present. But one point seems to have emerged 
clearly. No theory will fit the astronomical facts unless it admits of 
exhaustibility of the source of energy. 
At first sight the exhaustibility of the source seems opposed to the 
hypothesis that it is due to annihilation of protons and electrons, for it 
is difficult to see why protons and electrons should ever get tired of 
destroying one another. But the argument may be turned the other way. 
If we agree that the sun’s low rate of supply is due to exhaustion, we 
are almost forced to suppose that a star changes mass considerably as it 
grows older. For suppose that the sun has always had its present mass 
and therefore practically its present rate of radiation. There must have 
been a time when its material was fresh like that of Capella, and the sun 
* A speculation which evades the law e oc pT~l has been mentioned in § 210.