143, 144] Stable and Unstable Configurations 157 
energy G on physical conditions of density, temperature and ionisation, a 
given configuration will be dynamically stable if, and only if, 
dE 
dR 
>0 
(1441), 
where E is the rate of emission of energy and R is the radius, of the star. 
If the gas-laws are obeyed throughout the star, and the coefficient of 
opacity is given by Kramers’ law, E varies as R (§ 92) and all configura 
tions are unstable, as has already been seen. We have seen that we can pass 
from a configuration in which the gas-laws are obeyed to one of the same 
mass, density and radius in which they are not obeyed, by a process of lowering 
the temperature throughout. Since the emission E for a star of given mass, 
density and radius is proportional to T 7 ' 6 , this depresses the value of E also. 
Thus the rhythmical variations which have been found to occur in (1 — x) p, 
which measures the deviations from the gas-laws, will shew themselves as 
rhythmical variations in the emission E. 
In fig. 11 let the ordinate represent \ogE and the abscissa log R, so that 
stars of low density and low temperature are to the right. If the gas-laws 
are obeyed, the relation between E and R is E oc R~^, and the graph of E 
is a straight slant line such as the one at the top of the diagram. To take 
account of variations from the gas-laws we must depress the value of T and 
so also of E. The rhythmical fluctuations in (1 — x) p which result from the 
ionisation of successive rings of electrons will shew themselves by the graph 
hanging below this line in a series of festoons. The minimum deviations 
whose positions are determined by equations (140'4) or (140'5) must coincide 
very approximately with the highest points of these festoons. As we pass to