OF ROTATING COMPRESSIBLE MASSES. 
209 
Most stars whose mass is known* have a mass comparable with that of our sun 
(M = 2 x 10 33 ), and for these the ratio (187) is far from negligible. Thus it appears 
that for stars of mass comparable with our sun, and of molecular or atomic weight 
about 32, the pressure of radiation will not be negligible in comparison with gas 
pressure ;t the equations of equilibrium must be replaced by 
av 
p a r » 
and our calculation fails from equation (184) onwards. 
57. If we had taken a molecular weight 2, instead of 32, the value of Pn/p G would 
have been reduced by a factor (16)~ 4 , and we should have had approximately 
& = 10- 68 M 2 , 
Pg 
a ratio which may be considered small when M is of the order of 10 33 . Now whether we 
consider that radiation pressure is comparable with gas pressure or not, the tempera¬ 
ture at the centre of stars such as we have considered is of the order of 10 7 degrees 
Centigrade, and at such temperatures it seems probable that matter would to a large 
extent be broken up into its constituent electrons and nuclei. For purposes of 
calculation of gas pressure each electron behaves like the molecule of a gas, and the 
effect of electronic disintegration is to reduce the effective molecular weight. It is 
readily seen that when electronic disintegration is complete, a limiting effective 
molecular weight of 2 is reached for all substances except hydrogen.| 
Further, radiation pressure when it is appreciable may be treated as arising from 
molecules of molecular weight zero, and so the effective molecular weight may be 
still further decreased. 
* The stars whose masses are known are bright binaries—binaries because there is no means of determining 
mass except by the mutual action of two bodies on one another, and bright because the fainter binaries 
escape observation. The conclusion of this paper is that bright binaries are binaries of large mass, the mass 
being of order of magnitude greater than 10 31 gm. This is borne out by the observed masses of those binaries 
which are bright enough to have attracted attention, but there is nothing to show that there are not a 
great number of less bright binaries of smaller mass. It rather appears as if the few well-determined 
masses of binaries are not likely to give a good sample of the masses of all stars. It is perhaps 
significant that Russell’s well-known diagram of absolute magnitudes (‘Nature,’ vol. 113, p. 252) shows 
a range of something like five magnitudes (ratio 100 to 1) for dwarf stars of similar spectral type, 
suggesting a range of masses enormously greater than that calculated from observations on binary stars. 
t This agrees with the result stated by Eddington (‘ M.N., Royal Ast. Soc.,’ vol. 77, p. 16), but as the 
question is of some importance for our present investigation, I have thought it worth giving a separate 
discussion freed from the special assumptions of Eddington’s paper. Eddington’s statement that 
radiation pressure is practically negligible for dwarf stars does not appear to be altogether confirmed by 
my equation (187). 
+ Cf. Eddington, ‘ M.N., Royal Ast. Soc.,’ vol. 77, p. 596. 
