142 
Liquid Stars 
[ch. y 
law become large for stars of great mass, where the pressure of radiation in 
gaseous stars is large, and no doubt my own mass-luminosity-temperature 
relation would shew similar errors*. 
This estimate of the importance of radiation-pressure can hardly be much 
affected by errors of observation, since all stars agree in telling practically 
the same story. The estimate depends directly on the numerical coefficient F 
by which we multiplied Kramers’ opacity formula in § 77. Probably our 
estimate of F= 20 was, if anything, on the high side, but lowering the value 
of F would depress the importance of radiation-pressure still lower. 
131. In place of the vanished or insignificant pressure of radiation a new 
pressure assumes importance. In the actual configuration of equilibrium, the 
free electrons and bare atomic nuclei probably, on account of their smallness, 
still exert pressure in accordance with Boyle’s law. Thus the deficiency of 
about 30 per cent, in the gas-pressure and of about 76 per cent, in the 
pressure of radiation must be made good by the deviations from the gas-laws, 
which arise from the finite sizes of the atoms. To make good this deficiency, 
we have seen that each atom must exert about 40 times the pressure which 
it would exert if Boyle’s law were actually obeyed. This requires the atoms to 
be so closely jammed together that the condition of the stellar material may 
properly be described as liquid or semi-liquid. 
When the atoms are jammed as closely as they can be packed, a limiting 
density p is reached (cf. § 144 below), and we can obtain a general idea of the 
conditions in the central parts of a star by studying the ideal case in which 
all the matter in the central regions of the star is compressed to this limiting 
density. This of course represents an extreme case, and the actual truth will 
lie somewhere intermediate between this extreme and the other extreme of a 
purely gaseous star already discussed in Chapter ill. 
132. In general the flux of energy across a sphere of radius r drawn round 
the centre of a star is 47 rr 2 H, where H is given by equation (129T). It is also 
|7 Tr*pG where pG denotes the mean value of pG, estimated by volume, inside 
the sphere of radius r. Hence 
where B is a constant. On integration from r = 0 outwards, this gives 
H — %rpG 
(1321) 
or, by reference to (129*1) 
^<TT‘) = -Bp>rpG 
T 7 - 5 = TJ* - B f r p 2 pGrdr 
(132-2), 
o 
For a comparison between the two relations, see Ohlsson, Charlier Festschrift (Lund, 1927),