AND OF THE SECOND LAW 83 



PART IV 

 SUMMARY: 



THE CONNECTION BETWEEN PROBABILITY, IRREVERSIBILITY, 

 ENTROPY AND THE SECOND LAW 



SECTION A 



(i) Prerequisites and Conditions Necessary for the Application 

 of the Theory of Probabilities 



THESE may be briefly stated to be (a) atomic theory, (b) the 

 likeness of particles (or elements), (c) very numerous particles, 

 and (d) " elementary chaos." 



The first prerequisite is that the body (here a gas) is made up 

 of small, discrete particles. This atomic theory has long been 

 the foundation stone of chemistry, and is again coming into 

 deserved esteem in Physics pure and simple. (See simple and 

 clear article in Harper's Monthly, June, 1910). But this minute 

 subdivision must be accompanied by the particles being of the same 

 kind, or at least belonging to comparatively few groups, each con- 

 taining many particles of the same sort. This likeness is necessary ; 

 for only from this likeness results law and order in the whole 

 from disorder in the parts. If the constituents were of many 

 different kinds, the results in the aggregate would not be so simple 

 as we actually find them to be. There is an example of this sort 

 of complexity in chemistry. We have already intimated that the 

 particles of each kind must be very numerous, but special emphasis 

 must be laid on this prerequisite. If we ask how numerous these 



