76 
Gaseous Stars 
[ch. Ill 
density 0 -fold at every point, from p to p6, keeping the dimensions of the 
star fixed. At the same time let us increase its mean molecular weight ifr 
times, from p to pyfr. 
The new star so obtained has 0 times the mass of the standard star, so 
that the value of gravity has been increased 0-fold at every point. To satisfy 
the dynamical equation 
%—np ( 70 ' 4) 
the pressure must be increased 0 2 times at each point. If this is assumed to 
be given by Boyle’s law, 
p = — pT (70*5), 
r mp 
we see that Tip must be increased 0 times, so that T must be increased 0yfr 
times. The ratio of pressure of radiation to gas-pressure, which is proportional 
- *- T > -- been increased or ff> r times. 
to 
P 
0 
As explained in § 59, we can let this star undergo any homologous con 
traction we please and so assume any radius we please. Equations (59’3) 
shew that when the radius of the star is increased a-fold, the pressure of 
radiation, which is proportional to T 4 , becomes multiplied by a factor a -4 , 
while gas-pressure is also multiplied by a factor a -4 . Thus the ratio of gas- 
pressure to pressure of radiation remains unchanged by homologous contraction. 
Hence changing the density by a factor 0, the molecular weight by a factor 
yfr and the radius of a star by any factor we please, changes the ratio of 
radiation-pressure to gas-pressure by the factor 0 2 -\|r 4 already calculated. In other 
words, in stars of different masses M and different molecular weights p, the 
ratio of pressure of radiation to gas-pressure is proportional to M 2 p*. Although 
this ratio is only of the order of £ in the sun, it becomes considerable in stars 
whose mass is several times that of the sun. We must, however, notice that 
formula (70-5) is only accurate so long as radiation-pressure is negligible in 
comparison with gas-pressure; as soon as the ratio becomes appreciable our 
calculations fail to give its exact value. Definite exact calculations will be 
given later. 
Whatever the relative importance or amount of the radiation-pressure may 
be, we get a true picture of stellar structure by thinking of the layers of 
stellar matter as held up against gravitation by the incessant impact of a 
certain number of atomic nuclei or partially stripped atoms, the “ molecular 
weight” of which is practically the same as that of the corresponding complete 
atoms, together with a far greater number of free electrons of standard 
“molecular weight” or 0-00055, and a rather small number of “molecules” 
of radiation, the molecular weight of which is negligibly small. The combined 
impacts of these three types of projectiles prevent the star from falling in 
under its own gravitational attraction.