250 The Evolution of Binary and Multiple Stars [OH. xi 



stars on the lower branch are giant stars. The six stars which occupy the 

 bottom right-hand corner must all be regarded as binary giant stars, of types 

 F, G and K and of density less than T ^. 



The densities of 40 visual binaries have been estimated by Opik*, although 

 the method does not admit of great accuracy. Of the 40 computed densities 

 32 are greater than one-tenth of the sun's density, say greater than "14, while 

 8 are less than this. The two lowest densities are O'OlT and 0*018 for the 

 brighter components of e Hydrae and Bootis. These densities are well 

 below the limit which our theory allows for fissional binaries ; moreover these 

 two stars, being of spectral types FS and Kb, must both be " giants." 



261. Thus observational material shews either that all binaries are not 

 formed by fission or else that our estimate of the critical density, below which 

 fission cannot occur, stands in need of revision. 



This estimate was based upon the study of a particular model star, namely 

 a mass of gas of uniform composition arranged in adiabatic equilibrium. Cal- 

 culations of the temperature distribution in such model stars have been 

 made by Emdenf, EddingtonJ and others. Assuming the two components of 

 fi Lyrae to consist of monatomic hydrogen in adiabatic equilibrium (7= If), 

 Emden calculates central temperatures of 6'8 x 10 6 and 4'2xl0 6 ; if the 

 matter is supposed to be diatomic hydrogen the temperatures are found to 

 be 1*8 x 10 7 and 11 x 10 7 . For a model star of mass 2'87 x 10 33 grammes and 

 mean density '002, supposed made of iron vapour of atomic weight 54 in 

 adiabatic equilibrium with <y=lj, Eddington finds a central temperature of 

 T52 x 10 8 . The essential point is that all such calculations give a central 

 temperature of the order of 10 7 . Now this temperature is so high as to be 

 quite inconsistent with the supposition that the gas is of uniform structure 

 throughout if our physical knowledge is to count for anything, it is almost 

 certain that the properties and structure of gas at a temperature of 10 7 will 

 be widely different from those at the surface temperature of a few thousand 

 degrees. 



* Astrophys. Journ. 44 (1916), p. 292. 



t Gaskugeln, p. 292. 



+ Monthly Notices R.A.S. 77 (1917), p. 22. 



