192 SYSTEMS COMPOSED OF MOLECULES. 



The constant Ii we may regard as determined by the 

 equation 



/C]\TP 

 / ^n - i - dp,... dq n , (504) 



phases J ln-'-b_ 



or 



[1/1 . . . [ 



' phases 



(505) 



where the multiple sum indicated by 2 Vl . . . 2 rft includes all 

 terms obtained by giving to each of the symbols vi . . . v h all 

 integral values from zero upward, and the multiple integral 

 (which is to be evaluated separately for each term of the 

 multiple sum) is to be extended over all the (specific) phases 

 of the system having the specified numbers of particles of the 

 various kinds. The multiple integral hi the last equation is 



JL 



what we have represented by e . See equation (92). We 

 may therefore write 



It should be observed that the summation includes a term 

 in which all the symbols v l . . . v h have the value zero. We 

 must therefore recognize in a certain sense a system consisting 

 of no particles, which, although a barren subject of study in 

 itself, cannot well be excluded as a particular case of a system 

 of a variable number of particles. In this case e is constant, 

 and there are no integrations to be performed. We have 

 therefore* 



_4 _1 

 e = e , i. e. y \j/ = e. 



* This conclusion may appear a little strained. The original definition 

 of ^ may not be regarded as fairly applying to systems of no degrees of 

 freedom. We may therefore prefer to regard these equations as defining 

 4/ in this case. 



