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THE MASS-LUMINOSITY RELATION 
169 
by the same transformation as used in deriving B from A. The pressures 
will be transformed in the ratio l~ A and therefore in the same ratio as pT. 
The perfect gas law is obeyed, except that the constant of proportionality 
between p G and pT is modified by the electrostatic forces, so that we have 
p G = aftpT/p (115-1), 
where a is the same throughout the homologous series and depends only 
on the mass of the star. Since p only appears in the astronomical formulae 
through this equation for p G , the effect of electrostatic forces is very 
simply taken into account by substituting a fictitious molecular weight 
p/a instead of p in our formulae. 
It is true that the star B could not actually be a precise copy of A 
because at the different temperature and density the ionisation would be 
slightly altered. The ionisation depends on other than inverse-square 
forces and is therefore not purely a function of pjT 3 . Thus B 0 would not 
be strictly homologous to A 0 ; but no more is B (without electrostatic 
forces) strictly homologous to A. The differences are no greater than those 
that have previously been neglected. 
116. The investigation of the magnitude of the electrostatic forces is 
taken up in Chapter x. We shall find that they are comparatively small 
and have little effect on the mass-luminosity curve, except that they 
appear to be responsible for about half of the difference between the line 
of the observations and the theoretical curve on the left of Fig. 2. They 
make the gas superperfect; that is to say, the pressure is less than in a 
perfect gas, whereas the deviations familiar in terrestrial gases make the 
pressure greater. 
At first sight it seems absurd that we should secure greater com 
pressibility—render the atoms less able to ward off one another—by 
stripping them of their electrons and thereby exposing the large repulsive 
forces of their nuclei which were previously shielded. But the electrons 
set free by ionisation are not removed ; they wander among the ions and 
shield their repulsions very much as they did when they were bound. The 
mystery really lies in the origin of the forces corresponding to the rigidity 
of the atoms, which seem to be much greater than any electrostatic 
repulsions in the small region in which they act. 
The following calculation is intended solely to allay the idea that the 
electrostatic forces will, by creating around an ion a large region im 
penetrable to other ions, give it an effective volume sufficient to produce 
large effects. In order to take the most favourable case, consider a small 
star like Krueger 60, which at a more or less average point has a tempera 
ture 2-5.10 7 and a density 360. If the material is iron there will be 
3-9.10 24 ions per cu. cm. giving an average separation of 0-64.10“ 8 cm. 
The charge of an ion retaining 3 electrons is 23e and two such ions at