RECENT ADVANCES IN SCIENCE 459 



tribution of stars in globular clusters, r being the distance 

 from the centre. This law is found to satisfy observations 

 very closely except at the centre and towards the edges of a 

 cluster, and it would seem that there must be some theoretical 

 significance underlying it. The cluster is usually compared 

 with a sphere of gas in adiabatic equilibrium under its own 

 attraction, each star representing a molecule. The density 

 law will in such a case depend upon the value of 7, the ratio 

 of the two specific heats. Plummer's law is obtained for the 

 special case in which 7 = 1*2, and von Zeipel has shown that a 

 very small deviation from this value is sufficient to spoil the 

 agreement. For four special clusters examined, the values of 

 7 determined so as to give the best agreement ranged from 

 1*194 to 1*203. 



Eddington points out objections to Plummer's explanation 

 of this result, that the cluster has developed from a nebula for 

 the constituents of which 7 had the value 1*2 ; it is hardly 

 likely that the distribution would remain unaltered as the stars 

 formed. Von Zeipel supposed that the stars behaved like 

 the molecules of a gas. The objections to this are (1) that 

 the law should in that case be that for isothermal and not for 

 adiabatic equilibrium ; (2) even if adiabatic, the value of 7 

 might be expected to be 1-67 as for monatomic molecules ; (3) 

 and even taking into consideration double stars the value 

 should not fall below 1*40. 



If (j> is the potential, Plummer's law is a particular case of 

 a more general law p = <f> n , where <y = 1 -{- i/n, obtained by 

 putting n=$. Eddington shows that from this point of 

 view it has some significance, because when n < 5, the gas is 

 in equilibrium in a globular form with a spherical boundary, 

 when n >$ the mass of the cluster is infinite, whereas only for 

 n = 5 is the mass finite, but the cluster extends to infinity. 

 This is rather an important conclusion. The problem is then 

 further examined from the dynamical point of view ; when 

 w>5 no equilibrium is possible, for n < 5, there is a quite 

 arbitrary limiting velocity, but for n = 5 the limiting velocity 

 in the cluster is the velocity of escape. 



After all, however, the law p = <j> n is itself only a very 

 particular relation, and on examining a more general law 

 than this, no reason is found why the Plummer's law should 

 be obtained. Many other distributions can be obtained which 



