132 
The Source of Stellar Energy [ch. iv 
we have already seen, the evidence of the opacity of the stars shews that 
there is no very great range in the average atomic weights of the atoms in 
different stars. Thus our statement may be put in the alternative form that 
some 99 per cent, of the atoms in Plaskett’s star and some 95 per cent, of 
the atoms in V Puppis are fated to undergo annihilation within the next 
7 x 10 12 years or so. 
We have no evidence as to whether stellar atoms are annihilated instan 
taneously or through successive stages by a gradual reduction of atomic 
weight and atomic number. But an essential feature of the process must in 
either case be the coalescence of electrons with the protons of the nucleus, 
since there is no other means of annihilating the protons. The electrons 
which fall into the nuclei might a priori either be free electrons rushing 
about through the star, or bound electrons describing orbits about the nuclei 
in question under the laws of quantum-dynamics. 
If free electrons alone were liable to annihilation, the rate of annihilation, 
and so of generation of energy, would be in some way dependent on the 
frequency of collisions or of proximity between free electrons and nuclei. The 
discussion of § 112 enables us to rule out these possibilities, and we conclude 
that the process of annihilation consists mainly or wholly of the falling of 
bound electrons into the nucleus. 
120. One conclusion appears to follow. A star whose atoms are stripped 
bare right down to their nuclei, ought to radiate little or no energy, for it 
has no bound electrons which can be annihilated, except perhaps a few in its 
surface layers. In looking for examples of such stars we naturally turn to 
the white dwarfs, the abnormally high density of these stars providing a 
positive guarantee that the majority of their atoms are stripped bare of 
electrons, since if even the AT-rings were left the densities would be less than 
those actually observed. The predictions of theory are found to be confirmed 
by observation, the white dwarfs emitting abnormally little radiation. The 
faint companion to Sirius, of mean density about 50,000, radiates only 
0*007 ergs per gramme as against the 1*9 ergs per gramme radiated by the sun. 
The faint component of o 2 Eridani, with a mean density of about 100,000, 
radiates about 0*002 ergs per gramme. The spectral type of the companion 
to Procyon is unknown. If it were of type M6 its visual luminosity would 
give it a surface only one-eightieth of that of 60 Kruger A, and so a radius 
equal to about a twenty-seventh of that of the sun, or about equal to that 
of Sirius B. A higher surface-temperature would give a still smaller radius. 
Thus, whether we call the star a white dwarf or not, its density is so great 
that we must suppose most of its atoms to be stripped bare of electrons. Its 
radiation of energy is only about 0*0005 ergs per gramme. Finally van Maanen’s 
star (0 h. 43'9 m., + 4*55), an undoubted white dwarf with a mean density of 
hundreds of thousands, radiates only about 0*001 ergs per gramme.