22 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



Before closing this discussion of unsettled and settled states 

 we will insert here two remarks, really at this stage, anticipatory in 

 their nature. The first is, that under the limitation imposed by our 

 supplementary hypothesis of "elementary chaos," the very sharpest 

 definition of any macro-state is the number of its possible micro- 

 states. This is evidently the number of permutations, possible with 

 the given locus and velocity elements under the restriction imposed 

 above. Later on we will find that this number of possible micro- 

 states is smaller for the unsettled state than for the settled one. 

 This gives us a clean-cut distinction between the two states con- 

 templated. The second remark is that the inevitable change in 

 the system as a whole is always from the less probable to the more 

 probable, is a passage from an unsettled state of the system to 

 its settled state and this is here synonymous with the growth of the 

 number of possible micro-states. It is this difference between the 

 initial and final states which constitutes the universal driving 

 motive in all natural events. 



SECTION B 



THE APPLICATION OF CALCULUS OF PROBABILITIES 

 IN MOLECULAR PHYSICS. 



(i) The Probability Concept, its Usefulness in the Past t its Present 

 Necessity , and its Universality. 



An indication of its essential value in this physical discussion 

 is evidenced by the fact that we have almost unwittingly been forced 

 to constantly refer to it in all of our preliminaries. But when 

 this concept is first broached to a student, he feels about it like 

 the "man in the street"; it is by the latter regarded as a matter 

 of chance and hence of uncertainty and unreliability; moreover, 

 the latter knows in a vague way that the subject has to do with 

 averages, that it is often of a statistical nature, and knows that 

 statistics in general are widely distrusted. The student is at 



