168 
THE MASS-LUMINOSITY RELATION 
giant and dwarf theory to finite size of the molecules. For a star of constant 
mass and molecular weight the effect is independent of the star’s density. 
It therefore affects the luminosity throughout the evolution of the star— 
in the diffuse stages as much as in the dense stages. It cannot be invoked 
to explain the turning-point from the giant to the dwarf series at a critical 
density. 
The electrical attractions and repulsions contribute a pressure which 
should be taken into account in forming the equations of equilibrium of a 
star. Naturally this pressure increases as the star condenses and the 
charges are squeezed closer together; but it increases at just the same rate 
as all the other forces in the star, so that relatively it is no more important 
in dense stars than in diffuse stars of the same mass. 
It has often been pointed out in the theory of the atom that if inverse- 
square forces alone are acting no definite scale of size can be fixed. This 
is illustrated by our results for a perfectly gaseous star, where, under 
the inverse-square force of gravitation, no scale of volume for the star is 
fixed—a giant star of given mass is equally comfortable with any radius. 
By varying the radius we have a perfectly homologous series. Thus if A 
is a star in equilibrium and B a replica of it—a precise copy of the in 
stantaneous distribution of molecules—but with all lengths altered in the 
ratio l and all speeds in the ratio l~^, then B will also be in equilibrium. 
For then p is altered in the ratio l ~ 3 and T in the ratio Z -1 so that the re 
lation p oc T 3 for stars of the same mass is satisfied. Looking into the 
details of the balance, we see that any potential energy arising from inverse- 
square forces is altered in the ratio l -1 —the same as the ratio of alteration 
of kinetic energy of all the molecules; moreover, radiant energy per unit 
volume is altered in the ratio T - 4 or Z~ 4 , and therefore radiant energy per 
unit mass is altered in the ratio Z _1 . 
To upset the homology we must have other than inverse-square forces, 
such as those which act during a collision between molecules; the potential 
energy from these forces is not altered in the ratio Z _1 , so that its importance 
will be relatively greater or less according to the radius of the star. When 
the molecule is for most of the time free from collision this energy is 
negligible, but it becomes important when the molecules are kept jammed 
in contact. According to the older theory this happened at a density 
approaching that of water, and the homologous series of giant stars stopped 
at about that point; but our present theory is that these contact forces 
do not attain the corresponding importance until enormously higher 
densities are reached. We admit that there are large forces between the 
molecules when still far apart; but these are inverse-square forces with 
potential energy varying as Z _1 , so that the homology is not disturbed. 
Therefore although the electrostatic forces will change the equilibrium 
of the stars A and B to new models A 0 and B 0 , B 0 is derived from A 0