200 The Evolution of Gaseous Masses [CH. vm 



When ionisation is present, the value of m may decrease as we pass in- 

 wards to the more highly ionised layers, and convection currents may be set 

 up near the surface. 



The investigation of the mechanical stability of the inner layers presents 

 a more difficult problem. It can however be shewn* that in general the per- 

 manent series of homologous configurations will satisfy the conditions for 

 mechanical stability without convection currents being set up except near 

 the surface, an exception possibly arising when 7 is very close to the value 

 7-f. 



SUMMARY 



199. We may now summarise the changes which are to be expected in 

 a mass of gas in consequence of the continual emission of radiation from its 

 surface, making for the moment the somewhat illegitimate assumptions that 

 the mass obeys the laws of a perfect gas, that 7, the ratio of the specific 

 heats, has a uniform value throughout, and that the opacity c is constant 

 throughout. 



So long as the ideal gas laws are supposed to be obeyed, masses of gas 

 for which 7 < f cannot condense into spherical masses in stable equilibrium. 

 Masses for which 7 > J contract and become hotter as radiation proceeds. 

 We have seen, although by something short of strict proof, that they are 

 likely to approach to a definite series of homologous configurations, on which, 

 subject to the assumptions just mentioned, the emission of radiation E remains 

 constant as contraction proceeds. 



Our hypothetical mass has been assumed to obey the ideal gas laws 

 throughout, so that the laws we have discovered must only be expected to 

 describe the changes in a star so long as its density remains small. There 

 will be a stage later than those we have considered in which the laws are not 

 obeyed owing to the gas laws being substantially departed from. Still later 

 there will come a stage when the mass has contracted so far that further 

 contraction becomes impossible ; its temperature will now fall steadily with- 

 out contraction taking place. The emission is still given by equation (530), 

 but ?*! is now approximately constant, so that E falls as 2\ 4 . 



In fig. 40, let the temperature T^ of the photosphere be represented by the 

 abscissa and the total emission of energy by the ordinate. In the earliest 

 stages in which the ideal gas laws hold, the temperature T l goes on increasing 

 as contraction proceeds, while the emission remains constant. Thus the 

 relation between T l and E is represented by a horizontal line such as PQ 

 described in the direction of r l\ increasing. In the last stages in which con- 

 traction can proceed no further the relation between 2\ and E is that E oc Tf. 



* Monthly Notices R.A.S. 78 (1918), p. 43. 



