208 
MR. J. H. JEANS ON THE CONFIGURATIONS 
If for any reason the ratio of increase of pressure to density is about that 
corresponding to the critical value y = 2'2, the variation of density, except near the 
surface, will not be very great. An approximation which will be accurate as regards 
order of magnitude at least will be 
p„ = 4xG p‘ f \ 1 7* dr dr = -J Gp 3 B 3 , 
J 0 V J 0 3 
or, since i^pH 3 = M (the mass of the body), 
Po = iG 
Assuming the gas law 
P=Et p B.(184) 
m 
where R is the gas constant, and B a multiplying factor introduced by deviations 
from Boyle’s law, we find for the temperature at the centre 
T »=lft &=5xl0 "lUl M V(/5 /p»), 
JlIJd p 0 Xt_D 
in which p/p 0 may, in the case of equilibrium with y equal to about 2'2, be put equal 
to about 0‘6, giving 
T 0 = 3xlO- 8 ^M^.(185) 
EB 
\ i 
\~3 
5xlO- 8 M^ 5 . 
(183) 
The energy of radiation at the centre is erT 0 4 per unit volume, where or is Stefan’s 
constant of which Kurlbaum’s value is 7‘06xl0 -15 , and the pressure of radiation, 
being one-third of this, is -g-o-T 0 4 in all directions. 
Denote the pressure of radiation by p n and the gas pressure by p G . If p 0 , the pressure 
at the centre may be regarded as arising mainly from gas pressure, we have 
Pa _ WU 
Pg Po 
4x IQ" 38 
(186) 
which is independent of p. 
For a gas of molecular or atomic weight 32 the value of m/R is about 4x 10~ 7 , 
while the value of B will not differ greatly from unity until very high densities are 
reached. Thus equation (186) becomes approximately 
£s = io -63 M 2 .(187) 
Pg 
It will only be when this ratio is small that the radiation pressure will be negligible 
in comparison with gas pressure at the centre of the star, and this fixes a limit to M 
of the order of 10 31 , independently of the density of the star. 
