CHAPTER XV. 



SYSTEMS COMPOSED OF MOLECULES. 



THE nature of material bodies is such, that especial interest 

 attaches to the dynamics of systems composed of a great 

 number of entirely similar particles, or, it may be, of a great 

 number of particles of several kinds, all of each kind being 

 entirely similar to each other. We shall therefore proceed to 

 consider systems composed of such particles, whether in great 

 numbers or otherwise, and especially to consider the statistical 

 equilibrium of ensembles of such systems. One of the varia- 

 tions to be considered in regard to such systems is a variation 

 in the numbers of the particles of the various kinds which it 

 contains, and the question of statistical equilibrium between 

 two ensembles of such systems relates in part to the tendencies 

 of the various kinds of particles to pass from the one to the 

 other. 



First of all, we must define precisely what is meant by 

 statistical equilibrium of such an ensemble of systems. The 

 essence of statistical equilibrium is the permanence of the 

 number of systems which fall within any given limits with 

 respect to phase. We have therefore to define how the term 

 " phase " is to be understood in such cases. If two phases differ 

 only in that certain entirely similar particles have changed 

 places with one another, are they to be regarded as identical 

 or different phases? If the particles are regarded as indis- 

 tinguishable, it seems in accordance with the spirit of the 

 statistical method to regard the phases as identical. In fact, 

 it might be urged that in such an ensemble of systems as we 

 are considering no identity is possible between the particles 

 of different systems except that of qualities, and if v particles 

 of one system are described as entirely similar to one another 

 and to v of another system, nothing remains on which to base 



