Physics. — ''The definiteness of inacroscopic processes and the 

 kinetic theory"'^). By Mrs. T. Ehrenfest — Afanassjewa. (Com- 

 municated bj' Prof. J. P. Kuenen). 



(Communicated in the meeting of December 29, 1917). 



§ 1. Let us suppose a definite quantity of gas to be a system 

 containing a very great but finite number N of molecules which 

 obey certain conservative laws of motion. Then all successive 

 states of the system are for all times perfectly determined by 

 QN "microscopic coordinates" e. g. the 3 N space-coordinates and 

 the 3 N velocity-components of alj molecules at a definite but 

 arbitrarily chosen moment t^. 



These quantities however are not directly observable. It is 

 only possible to observe certain statistical mean values of these 

 quantities : the "macroscopic coordinates", which at a definite moment 

 give by far not enough determining quantities, so that we can by 

 no means derive the microscopic quantities from the combination 

 of the macroscopic ones. 



Though therefore the microscopic state of the gas at one 

 moment perfectlj^ determines the progress of the successive "micro-" 

 and also "macroscopic" states, the macroscopic state at one moment 

 is not sufficient to determine the progress of the microscopic state, 

 nor of the successive macroscopic states. 



In this way we come to the following conclusion : though the 

 kinetic theoiy of gases involves fundamentally a well-defined deter- 

 mination of the processes in a gas, it teaches us at the same time 

 that it is practically impossible to obtain any knowledge of this 

 determination and that we cannot but treat the succession of macros- 

 copic states of a gas as the successive drawings of a lottery : after 

 a definite given state we may expect all possible different states and 

 only certain considerations on probability are at our disposal to 

 confine our expectations somewhat. 



The same is true when we want to extend the kinetic conceptions 

 to the whole world. 



') The considerations given in this paper were induced by discussions with 

 Prof. Ph. Kohnstamm and Prof. J. D. van der Waals Jr. in connexion with their 

 publications. 



