144 Liquid Stars [oh. v 
temperature is approximately constant throughout a large distance from the 
star’s centre. 
Thus we may regard the central regions of a star of the type we are now 
discussing as being at approximately uniform temperature and density. Out 
side these lie a region of transition in which the temperature and density fall 
rapidly, the gas-laws being partially obeyed, and outside this a further region 
in which the gas-laws are obeyed entirely. The discussion of § 86 has sug 
gested that in very massive stars this outermost region may be of very great 
extent in comparison with the two inner regions. 
Stability. 
133. With this general, and necessarily very vague, picture of a stellar 
interior before us, we may resume the discussion of stellar stability at the 
point at which we abandoned it in the last chapter. 
We had found that two conditions were necessary to ensure the stability 
of a star, the first ensuring that the star should not be liable to explosive 
vibrations, and the second that it should not be liable to continuous unchecked 
contraction or expansion. Strictly speaking, it is impossible to separate the 
parts played by dynamics and thermodynamics in determining the stability or 
instability of a star, but we may conveniently refer to the two conditions for 
stability as the thermodynamical and the dynamical conditions respectively. 
In the last chapter we hypothetically assumed the rate of generation of 
energy per gramme of the stellar matter to depend on the temperature and 
density of the gramme in question through a factor of the form p a T p . The 
condition for thermodynamical stability was then found to require that a and 
/3 should be small. To a first approximation it was possible to put them both 
equal to zero, so that the star’s generation of energy became independent of 
its conditions of temperature and pressure, and so similar to radioactive 
generation. 
We found that there is only one adequate source of stellar energy, namely, 
the annihilation of stellar matter, electrons and protons coalescing and 
destroying one another, setting free their energy in the process in the 
form of radiation. 
We found, however, that free electrons must be immune from annihilation, 
since if they were liable to annihilation the resulting values of a and /3 would 
be so large that every star would be thermodynamically unstable. Annihilation 
can only overtake electrons which are bound and are describing orbits about 
the nuclei either of complete atoms or of partial atoms from which a number of 
electrons have been stripped. In such atoms annihilation has been seen to be 
a spontaneous process, the likelihood of which cannot be affected by changes 
of density or temperature. Nevertheless an increase of temperature or a 
decrease of density, by increasing the degree of ionisation of stellar matter, 
lessens the number of electrons liable to annihilation and so indirectly lessens