CHAPTER Y 
LIQUID STARS 
The General Condition of Liquid Stars. 
128. In Chapter ill we investigated the internal equilibrium of the stars 
on the supposition that they were masses of gravitating gas, in which the 
gas-laws were obeyed throughout. The investigation was abandoned when it 
was found to lead to impossibly high values for the atomic weights of the 
stellar atoms. This created a suspicion that the hypothesis on which it was 
based was unfounded, and that the gas-laws are not obeyed in stellar interiors. 
The last chapter provided further evidence to the same effect. We there 
investigated the mode of generation of stellar energy, using the guiding 
principle that all modes of generation of energy which make the stars 
dynamically unstable can be ruled out of the list of practical possibilities. 
We found that when the gas-laws are supposed to be obeyed, no possibilities 
remain for stars of enormously great mass. Further the only mode of genera 
tion of energy which was both physically acceptable and consistent with the 
stability of actual stars proved to be one in which the rate of generation of 
energy is uninfluenced by changes of density and temperature, as in radio 
active substances, and this, as we shall see at once (§ 134), requires substantial 
deviations from the gas-laws in stars of all masses. 
We now rediscuss the problem of the physical constitution of the stars, 
and examine the form it assumes when the gas-laws are no longer obeyed. 
129. With Kramers’ law for the coefficient of opacity, the flow of radiant 
energy per unit area is, as in equation (98*1), 
aCfiT** dT 
H=- 
.(129*1), 
3-34x10 26 p*(N*/A)dr 
where N, A are the atomic number and weight of the stellar atoms. This 
equation is true independently of whether the gas-laws are obeyed or not. 
Let us start from a standard configuration in which the star is in equi 
librium with a specified rate of generation of energy for each element. We 
can obtain a succession of configurations suitable to stellar matter of different 
atomic weights by keeping every element of the star’s mass in its original 
position, thus maintaining the star’s distribution of density and its gravi 
tational field unaltered, but varying JV 2 /A and T throughout the star. If we 
change IP/A and T in such a way as to keep the ratio of N 2 /A to T 7,5 
unaltered throughout the star, equation (129 - 1) will still be satisfied through 
out the star with the same value of H, so that if the generation of energy is