141 
128-130] The General Condition of Liquid Stars 
maintained unaltered, the new configuration will all be in radiative equi 
librium. Since H retains the same value throughout the star, the star’s 
luminosity remains unaltered. 
Let us suppose that the standard configuration from which we started 
was one in which the stellar matter was wholly in the gaseous state, and that 
the gas-laws were obeyed throughout the star. Let us further suppose the 
standard configuration to be one of dynamical, as well as radiative, equilibrium, 
so that equation 
dr 99 
(129-2) 
is satisfied throughout, where p is the total pressure, including pressure 
of radiation, calculated on the supposition that the gas-laws are obeyed. 
Equation (129*2) is the equation of dynamical equilibrium for all the other 
configurations also, and since we are supposing g and p to remain the same 
in all these configurations, the equation will be satisfied if p retains its original 
values throughout the star. 
When we assumed the star to be wholly gaseous we found that the values 
of N 2 /A which were necessary to give the true values of H for actual stars 
came out uniformly something like 16 times too high (§ 98). This suggested 
that the gaseous configuration is not the true configuration for actual stars, 
and we found that to obtain possible configurations we must pass along the 
series just described until we come to configurations in which T has about 
seven-tenths of its value in the gaseous state. 
For the new configuration to be in dynamical equilibrium the total pressure 
p must be equal to the total pressure p in the gaseous configuration. The 
pressure of radiation ^ctT\ having only (0*7) 4 times, or about 24 per cent, of, 
its value in the old configuration, is negligible for all except the most massive 
stars, and the new gas-pressure must shoulder the whole burden previously 
carried by gas-pressure as well as three-quarters of that previously carried 
by the pressure of radiation. 
130. Incidentally, Eddington* and myselff have investigated the relation 
between stellar masses and luminosities on the supposition that the gas-laws 
are obeyed, and the pressure of radiation played a fundamental part in both 
of our discussions. On the hypothesis of liquid stars we both assumed values 
for the pressure of radiation that were something like four times too high, so 
that both our discussions fail entirely and any apparent success achieved either 
by Eddington’s mass-luminosity law, or my mass-luminosity-temperature re 
lation, must have been fortuitous ; indeed we should have obtained far more 
accurate results by disregarding the pressure of radiation entirely. This 
probably explains why, as shewn in Table XY (p. 130), the errors in Eddington’s 
* M.N. lxxxiv. (1924), p. 308, and The Interval Constitution of the Stars. See also § 90 above, 
t Ibid, lxxxv. (1925), pp. 196 and 394.