114 



to preponderate, so that we may expect that KK' is negative. The 



second derivative of v' consequently has the same sign as v, i.e. the 

 movement of the surrounding matter with the particle, which does not 

 exist at the moment of selection, arises after a short time. Accoi'ding to 

 (8) there is on the average no question of a movement of 

 the surrounding particles with the Brownian i^article in an ensemble, 

 as may be expected. 



When we want to investigate statistically the qualities of a 

 stationary system of molecules, we can make use of a statistically 

 st.itionary ensemble and identify the qualities observed with the 

 qualities of the most frequent system in this ensemble or with the 

 corresponding averages. 



The system that we consider at an investigation of the Brownian 

 motion — a liquid with a i)article suspended in it — is, it is true, not 

 stationary, but all the same it changes only slowly, the moving 

 particle changes its velocity only slightli/ by a grmt number of 

 impacts. Consequently, in order to make use of ensembles for the 

 study of the Brownian motion we must start from a "quasistationary" 

 ensemble and deduce the qualities of the real Brownian motion 

 fiom the properties of the most usual system in such an ensemble. 



The calculations given show, that the groups chosen with definite ?' 

 from a canonical ensemble do not form such quasi-stationary ensembles. 

 However it seems probable to us that such a group, when we follow 

 it a short time, will get to fulfill the requirements, though it will 

 be difficult to show this by direct calculation. The y-grou[), which 

 has become quasi-stationary at a later moment, would then conespond 

 to the ensemble selected from the canonical ensemble, by selecting 

 those systems in which the particle has already got the velocity v 

 during a short time. 



An indication with regard to the length of time required was found 

 along another method by one of us in a former paper '). 



The above quoted statistic-mechanical objections to the application 

 of the law of Stokes thus probably have no justification for a real 

 system, but only for the first moment of a v-group, i.e. at the very 

 time when it cannot yet he made use of to represent the properties 

 of a real system. 



Grojiiiigen. Ltrecht, Institute for Theoretical Physics. 



1) L. S. Ornstein. 1. c. — Tills time must iiiimely be of the order of the time 

 during which tliere is a correlation between the irreguUr impulses, i. e. 

 f(^\F(^ -|- t) differs from zero. 



