; , BOLTIIAin*'i TBHMM* ON THB AVERAGE DISTRIBUTION 



mrefttlr M their masses; eo that the average energy of motion relative to 

 the noring axes i the aame for particles of all kinds throughout the system. 



We hre already learned from equation (98) that in a free system of n 



particle* the number of cases in which the system is in a given configuration, 



( othtr wnrft. the probability of that configuration, is proportional to the 



! power of the energy of internal motion corresponding to that configuration. 



nex t to consider the manner in which this probability depends 

 oo the position of a particular particle, say of the last particle, m n . 



Let /.** denote the energy of internal motion of the complete system when 

 M. is at the centre of mass of the system and is without any velocity relative 

 to that centre. It is manifest that in this case m n contributes nothing towards 

 the energy of internal motion. 



Now let w. be carried from the centre of mass to the point (0, 0, z) and 

 left there without any velocity (that is, let u = v = w=Q). 



Let W be the work which must be done against the forces of the system 

 to eflect this transference, then since the total energy of the system and the 

 three angular momenta must be maintained constant, we shall have after this 

 displacement, for the energy of internal motion of the remaining n 1 particles, 



/.., = /.- W .............................. (102). 



But by equation (85) 



Substituting the value of /,,_, from equation (102), and remembering that 

 i = r = ir = 0, we find for the energy of internal motion in the new configuration 



/. = /."- TT+i/itl-ft/u^-'oy + liL(l-a,a?)j& ........... (104). 



The probability, therefore, of a configuration in which, the positions of all 





the other particles being given, that of m n is varied, is proportional to /"*", 

 /. being given by equation (104). 



When, as in the case of a gas, there are a great many particles similar 

 to ., we may speak of the density of the medium consisting of such particles 

 in the element dxdydz. In this case, however, for reasons already given, neglect 



