118 
SOLUTION OF THE EQUATIONS 
85. The quantity 1 — /3 represents the ratio of radiation pressure to 
the whole pressure. We have seen in § 15 that this has probably an 
intimate connection with the aggregation of the material of the universe 
into stars of a standard mass. We there suggested that stars would be 
likely to form with radiation pressure between 15 per cent, and 50 per cent, 
of the whole—the idea being that greater radiation pressure would be 
highly dangerous to the stability of the star, whilst the aggregations would 
naturally reach a mass at which the risk began. 
With this criterion, p. = 2-2 gives a standard mass from 2 to 10 times 
the sun’s mass, and ¡i = 3-5 a mass f to 4 times the sun’s mass. The latter 
is nearer to the general average of the stars; perhaps a rather higher 
molecular weight would fit still better. We have suggested two possible 
explanations of this (1) that the critical period occurs early in the aggrega 
tion of the matter into stars when temperature and ionisation are low, so 
that ¡x is higher than in fully developed stars, (2) that stellar masses 
decrease somewhat in the course of evolution. Judging from their luminosity, 
stars in the earliest stage (K and M giants) seldom have masses below 2. 
In any case, we are scarcely in a position to attach importance to a factor 
of 2 or 3, and may well feel satisfied with the general coincidence in order 
of magnitude between stellar masses and the critical range for radiation 
pressure. 
If there were any doubt as to the existence of strong ionisation inside 
a star, the third column of Table 9 could be appealed to. For undis 
sociated atoms we should expect a molecular weight 30 or higher and the 
table shows that very intense radiation pressure would result. It would 
be difficult to accept the conclusion that in Capella 93 per cent, of the 
weight of the material is supported by pressure of the outrushing radiation; 
and it is satisfactory that the ionisation predicted by thermodynamical 
theory renders the state of the star much less precarious. 
Luminosity and Opacity. 
86 . Neglecting possible small changes of ¡x dependent on the tempera 
ture and density, 1 — /3 is a function of the mass only. Hence by (83-4)— 
For gaseous stars of the same mass the total radiation L is inversely 
proportional to the opacity k 0 . 
This fundamental result can be established on a wider basis without 
using the approximation yk = const. 
Consider two homologous stars in which corresponding regions contain 
the same mass but differ in linear scale. We shall assume (1) that the 
relative distribution of the source of energy is the same for both so that 
L r IL is the same at corresponding points, and (2) that k varies with p and 
T according to some law of the form p x T v , so that the distribution of k is 
homologous if the distribution of p and T is homologous in the two stars.