AND OF THE SECOND LAW 7 



magnitudes. For the micro-observer, the state and the sequence 

 of the event would not be determined until all these many mag- 

 nitudes had been separately given. The state thus defined we 

 will call the "micro-state." The macroscopic-observer on the 

 other hand gets along with much fewer data; he will say that the 

 state of the contemplated homogeneous gas is already determined 

 by the density, the visible velocity and the temperature at each 

 place of the gas and he will expect, when these magnitudes are 

 given, that the course of the physical events will be completely 

 determined, namely, will occur in obedience to the two laws of 

 thermodynamics and therefore be bound to show an increase in 

 entropy. The state thus defined we will call the "macro-state." 

 The difference in the two observers is that one sees only the atomic 

 events and the other the occurences in the aggregate. The former 

 would have the absolute mechanical idea of state and the latter 

 the statistical idea. Before attempting to reconcile their apparently 

 conflicting conclusions, we will here call attention to some neces- 

 sary relations between the micro-state and the macro-state. 

 In the first place we must remember that all a priori possible 

 micro-states are not realized in nature; they are conceivable 

 but never attain fruition. How shall we select what may be 

 called these natural micro-states? The principles of general 

 dynamics furnish no guide for such selection and so recourse 

 may be had to any dynamic hypothesis whose selection will be 

 fully justified by experience. 



Now PLANCK says: " In order to traverse this path of investi- 

 gation, we must evidently first of all keep in mind all the con- 

 ceivable positions and velocities of the individual atoms, which 

 are compatible with particular values of the density, the velocity 

 and the temperature of the gas, or, in other words, we must con- 

 sider all the micro-states which belong to a particular macro- 

 state and must examine all the different events which follow 

 from the different micro-states according to the fixed laws of 

 dynamics. Now up to this time, the closer calculation and com- 



