257-260] The Process of Fission 249 



Since for an ordinary gas under ideal conditions, 7 is always less than If, 

 this result indicates that fission cannot begin, at any rate for a mass of gas 

 of uniform composition, until the density is so great that the ideal gas laws 

 are substantially departed from. Koch * has obtained the experimental value 

 7 = 2*21 for air at 100 atmospheres pressure and temperature 79 C., the 

 corresponding density being about 180 times that of normal air, or say *23. 

 Thus if a star were made of air in adiabatic equilibrium, the critical density 

 p would be something like J. 



More generally we have seen that the critical density p Q , for a mass of 

 uniform composition, must be one at which the gas laws are substantially 

 departed from. Now according to Russell's theory of stellar evolution, for 

 which as we have seen ( 200) there is a strong theoretical basis, a star is 

 supposed to get continually hotter until the gas laws are substantially departed 

 from, after which its temperature begins to decline. On this theory the 

 point at which the gas laws are first substantially departed from may be 

 approximately identified with the point of maximum temperature in the star's 

 evolution, and this corresponds to spectral type B for massive stars, but to a 

 later spectral type for lighter stars. 



The two estimates we have formed of the critical density p are in fair 

 agreement. Russell estimates the average density of "giant" J.-type stars 

 to be about j 1 ^, so that J is not an unreasonable estimate for the density of 

 J5-type stars. 



It would now follow, from our preliminary theory in which a star is repre- 

 sented as an adiabatic mass of air, that 



(i) no binary star which has formed by fission can have a density of 

 less than about J, 



(ii) no giant binary star can have been formed by fission, 



(iii) the temperature of a binary star which has formed by fission must 

 decrease as its evolution progresses. 



260. The densities of eclipsing binaries can be estimated with very con- 

 siderable accuracy. Shapleyf has computed the densities of 90 of these, the 

 results being given in the following table in which densities are classified 

 according to spectral type. 



At once it appears that there are binaries of very low density, 33 out of 

 the 90 having a density of less than y 1 ^, and 4 having a density of less than 

 ToW. Further, in Shapley's table the division into giant and dwarf stars 

 is quite marked, the entries in the table lying approximately thus : < ; the 



* Soc. Frang. de Physique, Recueil des Constantes, p. 321. 



f Contributions from the Princeton Univ. Observatory, 3 (1915). I have omitted from the 

 table three stars which Shapley states "should not be given much weight" and "probably 

 deserve little consideration." 



