AND OF THE SECOND LAW 19 



from " abnormal " conditions to the final and so-called " normal " 

 condition of thermal equilibrium and, furthermore, (b) to show that 

 each of these stages is " elementar-ungeordnet " and (c) that in 

 each one sufficient haphazard prevails to permit the legitimate 

 application of the Theory of Probabilities. 



We will first describe the unsettled (abnormal) and settled 

 (normal) states, respectively. When we consider the general 

 state of a gas " we need not think of the state of equilibrium, 

 for this is still further characterized by the condition that its 

 entropy is a maximum. Hence in the general or unsettled state 

 of the "gas an unequal distribution of density may prevail, any 

 number of arbitrarily different streams (whirls and eddies) may 

 be present, and we may in particular assume that there has taken 

 place no sort of equalization between the different velocities of the 

 molecules. We may assume beforehand, in perfectly arbitrary 

 fashion, the velocities of the molecules as well as their co-ordinates 

 of location. But there must exist (in order that we may know 

 the state in the macroscopic sense), certain mean values of density 

 and velocity, for it is through these very mean values that the 

 state is characterized from the macroscopic standpoint.' 7 The 

 differences that do exist in the successive stages of disorder of the 

 the unsettled state are mainly due to the molecular collisions 

 that are constantly taking place and which thus change the 

 locus and velocity of each molecule. 



We may now easily describe the settled state as a special case 

 of the unsettled one. In the settled state there is an equal dis- 

 tribution of density throughout all the elementary spaces, there 

 are no different streams (whirls or eddies) present, and an equal 

 partition of energy exists for all the elementary spaces. For it 

 thermal equilibrium exists, the entropy is a maximum, and tem- 

 perature of the state has now a definite meaning, because tem- 

 perature is the mean energy of the molecules for this state of 

 equilibrium. The condition is said to be a " stationary " or 

 permanent one, for the mean values of the density, velocity, and 



