Physics. — "An. Indatermumleiu'ss in tke interpretation of the entropy 

 as log II'". By iMrs. T. Ehrknfest- A fan assjewa. (Communicated 

 bj' Prof. J. 1*. Kuenen). 



(Communicated in the meeting of March 23, 1918), 



I. A certain quantity of a gas may be given, so large that it may 

 be divided into a great number of j)ortions — great enough for the 

 purpose we -are about to discuss — without the usual statistical 

 treatment of the parts losing its value. 



Regarding the matter from a thermodynamic point of view we 

 assume : 



1. that the entropy of every system strives to attain its maximum. 



2. that the entropy of the total mass of gas is equal to the sum 

 of the entropies of the parts. 



If in accordance with the kinetic theory, we take the entropy to 

 be the logarithm of the probability of the state of the system, we 

 get the following theses as the analogues of those just given : 



1. The state of every system endeavours to approach the greatest 

 probability ; 



2. The logarithm of the pi-obability of the state of the total mass 

 of gas is equal to the sum of the logarithms of the probability of 

 the states of its parts; or in other words: the probability of the state 

 of the whole is equal to the product of the probability of the states 

 of its parts. 



At the same time it may easily be seen that the latter theses are 

 only correct provided the combinations with which we reckon in 

 the determination of the probability of the state of the whole are 

 submitted to certain limitations, which are quite arbitrary from the 

 comhinationary point of view. 



II. We will illustrate this by a simple example, which depends 

 only on the calculus of combinations. 



Let us suppose 27 tables, each provided with three holes. In each 

 of the holes a red or a black ball must come to lie. The colour 

 of the ball may be decided by a lottery, in which the chance of 

 drawing a red ball is */,, and of a black ball Vi- 



