THE SOURCE OF STELLAR ENERGY 
315 
) 
that it had occurred. This is perhaps in favour of the hypothesis, since 
the difficulties of detailed application become of minor importance. We 
can scarcely prescribe limits to what can be performed by a process, before 
we see how the process can be possible at all. 
(7) Apart from effects depending on the presence of hydrogen in early 
stars, the theory leads to no interesting astronomical consequences. In 
particular the change of mass is insignificant ; and unless the star can gain 
or lose mass from other causes there is no evolution from bright to faint 
classes of stars. 
No. (5) may be explained a little further. We have shown that admixture 
of a large proportion of hydrogen considerably lowers the radiation 
pressure (1 — /3) and the brightness of the star. The lowered value of 1 — ¡3 
would altogether spoil the general agreement between the masses of stars 
and the critical range of radiation pressure. In fact radiation pressure 
would lose most of its importance in this subject. Further, since the 
proportion of hydrogen must on this hypothesis diminish with the age of 
the star, the luminosity would be lowered by a variable factor and we 
should not have the uniform relation of luminosity and mass which the 
observations appear to confirm. It was shown in § 168 that a proportion 
of 20 per cent, of hydrogen in Capella would bring the astronomical 
opacity into agreement with Kramers’ theory. But this is no improvement, 
since the sun and other late stars with very little hydrogen left (according 
to No. (3)) would remain outstanding. Whatever cure is suggested for the 
discrepancy of Kramers’ theory it should be one that is applicable to all 
stars alike. 
The hypothesis that the source consists of unknown elements of intense 
radio-activity requires no long discussion. Since radio-activity is inde 
pendent of density and (practically) of temperature the stars would be un 
stable. In other respects it is an arbitrary hypothesis which can be adjusted 
to fit any facts we like—assuming a sufficient variety of these provided 
sources. It seems objectionable to have to postulate an initial supply of 
complex unstable elements dating before the beginning of the star’s life 
and formed presumably in the nebula ; it is more reasonable to suppose 
that the ordinary radio-active elements are synthesised in the stars and 
are therefore a source of loss, not of gain, of available energy. 
Mode of Conversion of Subatomic Energy. 
222. If an atom of helium is formed from hydrogen at a single process 
the energy released must be a quantum. Since the energy represents 
•032 of the mass of a hydrogen atom the radiation will be of frequency v 
given by the relation 
•032 hc 2 = hv.