SOLUTION OF THE EQUATIONS 
143 
(103-5) the whole energy must increase as increases in order to maintain 
equilibrium. The star cannot obtain this extra energy at a moment’s 
notice; hence K + H is below the value required to maintain equilibrium. 
This means that there is too little heat and the pressures p G and p R are 
insufficient to support the weight of the material. Thus a further contrac 
tion ensues and the star deviates further and further from equilibrium. 
We have said that the star cannot at a moment’s notice secure the 
extra energy required to save it. If the star is being supplied with ex 
traneous energy it is quite possible that the changing physical conditions 
may stimulate the supply; but this effort to prevent the collapse is too 
dilatory. In a star like the sun the heat stored up represents about 
40 million years’ supply of radiation and therefore (if the radiation is 
supplied by liberation of subatomic energy) is equal to the subatomic 
energy released in 40 million years. If the rate of release is doubled when 
the collapse starts, it will take a year to increase H + K by 1 part in 
40 million; whereas the threatened collapse due to withdrawal of pressure 
support is a matter of days or hours. It is important not to confuse this 
condition of stability with another condition to be investigated later. 
We shall find in § 211 that the supply of subatomic energy must satisfy 
certain conditions in order that the star may be stable; these conditions 
are independent of, and additional to, the condition here found that 
r > I; also the threat to the star which violates them is a lingering fate 
and not the swift doom here contemplated. 
It may perhaps be suggested that some extra source of energy could 
exist which is immediately releasable as heat when the temperature and 
density change. But immediately releasable heat is not “extra”; it is 
by definition part of the specific heat and must be taken account of in 
y and, by (103-4), in K. Energy of ionisation is of this type. Energy 
which is very slowly released such as radio-active and other kinds of sub 
atomic energy is, of course, not reckoned in the total heat K + H ; it is 
treated as a non-realisable asset in the star’s balance sheet which is neg 
lected unless we are dealing with long periods of time. 
There appears to be no objection to y falling below f in a limited region 
of the star provided that the general average is above |. Circulating 
convection currents will be set up in this region (§ 70), since the convection 
process produces mechanical energy when y < f, instead of dissipating 
it. Presumably viscous forces will not allow the movement to increase 
indefinitely, and in any case the local instability can scarcely lead to 
consequences affecting the star as a whole. 
The constant y is least when the ratio of the energy of ionisation to the 
translatory energy is greatest. It is conceivable that in the course of 
evolution a star may reach a stage at which further contraction will 
involve a great deal of fresh ionisation, the stage being critical for the