48 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



PART II 

 ANALYTICAL EXPRESSIONS FOR A FEW PRIMARY RELATIONS 



AT the beginning of this presentation we disclaimed any pur- 

 pose of giving a rigorous proof for any of the many formulas 

 with which this subject bristles. We propose only to give in some 

 cases an outline of the main steps of the demonstration and 

 merely for the purpose of getting a clearer physical insight into 

 certain states and relations. Pre-eminent in importance is the 

 state of thermal equilibrium (see pp. 19, 52, 53) and we will 

 therefore consider first its main characteristic: 



SECTION A 

 MAXWELL'S LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES 



Without giving a full proof of the law we will give the main 

 steps which lead to its analytical statement, in so doing following 

 the presentation given by HANS LORENZ on pp. 526-529 of his 

 " Technische Warmelehre," and will then point out its main 

 features and consequences. 



We suppose the gas to contain in a unit of volume n molecules 

 each possessing a different velocity and direction. Let there be 

 a system of three co-ordinate axes, , 77, C A fraction f()d 

 of the total number of molecules will possess a velocity in the 

 direction, whose values lie between and +(/. The number 

 of molecules which at the same time possess velocities in the i? 

 direction, lying between y and ij+dy, will be nf()df(T))dir), 

 since no preference can be given to either the or i) direction. 

 Similarly and finally the number of molecules whose velocity 



