193-196] Spherical Mass of Gas 197 



Thus equation (525) can only be satisfied if tc is of the form 



K = (a function of a) x (a function of q) ............ (526). 



This requires that as the gas contracts homologously, K shall^ change in the 

 same ratio at all points of the mass. 



In a mass of hot gas it seems highly probable that the transfer of heat is 

 effected mainly by radiation rather than by ordinary gaseous conduction*. 

 Except close to the surface of a gaseous mass it is found that, corresponding 

 to a temperature gradient dT/dx, there is a flow of radiant energy per unit 

 area of amount j~ 



( 



where cr is Stefan's constant (5'32 x 10~ 5 ) and c is the coefficient of opacity 

 of the gas, this being such that on passing a distance x through the medium 

 at density p, a beam of light is diminished in intensity in the ratio e~ cpx . 

 This flow of heat may be put in the form 



dl 



& > 



where the value of K in heat units is 



2* 



...(528). 

 cp 



This value of K is so much greater than any known coefficient of ordinary 

 -gaseous conduction, that it appears to be legitimate to assume, as an approxi- 

 mation, that the whole transfer of heat is radiative. 



As homologous contraction proceeds, T 3 and p each vary as I/a 3 , so that 

 T*/p remains constant. Thus if we assume c to be independent of the density 

 and temperature, K will be unaffected by homologous contraction, and equation 

 (526) is satisfied through K being a function of q only. 



A permanent homologous series now becomes possible ; it is defined by 

 equation (525). In this equation tc, r*dT/3r and H r /H are unaffected by 

 homologous contraction. It follows that E is unaffected by homologous con- 

 traction the emission of radiation remains always the same. 



196. It will naturally be suspected that the permanent homologous series 

 whose existence has now been demonstrated represents a stable final state in 

 the sense that a configuration not initially on this series will gradually ap- 

 proach it as contraction proceeds. A rigorous formal proof of this is not easily 

 constructed, but the general truth of the proposition can be seen as follows. 



* Eddington, Monthly Notices R.A.S. 77 (1916), p. 16. 

 t Eddington, I.e. p. 19; also Jeans, ibid. 78 (1917), p. 31. 



