252-254] Globular Star-Clusters 245 



correspond to different values of 7 in the relation p = tcpv. The approach to 

 the final equipartition state will be represented by 7 approaching the value 

 7=1 which corresponds to isothermal equilibrium, but the lowest value of 7 

 which is possible, short of the cluster scattering to infinity, is 7= 1-|. Thus 

 with our arbitrary supposition that different laws are adequately represented 

 by different values of 7, it appears that the value of 7 cannot fall below 1J, 

 and the final law of distribution of density in a globular star-cluster would be 

 the same as that in a gas in adiabatic equilibrium with 7=1J, namely 

 Schuster's law (cf. 149) 



This is the law actually found in a number of globular star-clusters by 

 Plummer and von Zeipel ( 6). It is at best only approximate ; indeed it 

 appears that a law falling off at great distances as r~ 4 would fit the distribution 

 in many star-clusters still better*. This is hardly surprising. Our limitation 

 of the various laws to those corresponding to adiabatic equilibrium was quite 

 unjustifiable; it may lead to an approximate picture of the processes going 

 on in a globular cluster but cannot be expected to reveal the whole truth. 



* Monthly Notices R.A.S. 76 (1916), p. 567. 



