1048 
Physics. — “Entropy and Probability” By O. Postma. (Com- 
municated by Prof. H. A. Lorentz). 
(Communicated in the meeting of November 27, 1915). i 
§ 1. In the kinetic definition of the entropy it is necessary to 
fecha foe . dQ 
determine a function S which 1. satisfies the equation dS a 
on transition from a state of equilibrium to a neighbouring one, and 
2. increases in an isolated system which is not in equilibrium. Many 
such definitions have been given, in which now special attention 
was paid to one, now to the other property. The S that satisfies the 
second demand, must then also satisfy the first in the particular case 
that there is equilibrium. Additional constants evidently have no 
influence (by constant we understand here for |: independent of 
energy and volume; for 2: independent of distribution of place and 
velocity). 
In connection with the theory of quanta, however, these constants 
have come more into the foreground, specially for so far as they 
depend on the elementary region g of the extension in phase of the 
molecules and the number of molecules .V. Of late attention has 
also been drawn to other properties which the entropy-function should 
satisfy, and more particularly: 8. the entropy of a quantity of 
substance is equal to the sum of the entropies of its parts. Further 
the dimension of the entropy has also become of more importance. 
When following PranNcK’s example we calculate the entropy in the 
state of equilibrium for a perfect gas by the aid of the definition 
S=k log P(P = probability), and make use of the condition that 
property (3) must be fulfilled, we come to the conclusion that the 
above mentiened elementary region g must be proportional to NV. 
Important objections are, however, adduced against this result by 
Lorentz in his article: “Observations on the theory of the mon- 
atomic gases.” *) 
This result, hence also these objections are obviated by TrrropE 
by dividing the expression found for the entropy by N/. In the 
cited article Lorentz observes, however, in reference to this that 
there is no physical reason to be found for this division. 
The purpose of this article is chiefly to subject the existing diffi- 
culties to a closer examination. 
§ 2. If we define the entropy by means of S=k log P, the 
1) Verslagen Kon. Ak. v. Wet. Amsterdam, Deel XXIII (1914) p. 515. 
