Physics. — ''The Theory of the Hrotnnlaii }fotion <in(l Stdthtical 

 Mechanics'. By Piof. L. S. Ohnstkin and Dr. V. Zkhnikk. 

 (Coirimiinicated b}- Prof. H. A. Lorkntz). 



(Communicated in the meeting of January 26, 1918). 



Prof. J. D. V. D. Waal8 Jr. and Miss. I)r, A. SNETfiT-A«K have 

 raised objections derived from statistical mechanics against the nsiial 

 deductions from Einstein's formnhi of the Hrovvnian motion. These 

 objections may be formulated as follows: 



First] ij: It is not right to introduce a resistance on an emidsion 

 particle, which is proportional to the velocity of that panicle, as 

 according to a well-known result of statistical mechanics velocities 

 and forces are independent of each other, as is appearent from 



^=0 ......... (1) 



Still more clearly this independence is visible, if one considers 

 that the above equation is not only applicable to the average over 

 a canonical ensemble, but even for any group of systems from that 

 ensemble for which the particle considered has a definite velocity ?% 

 so that for such a group /v = 0. 



Secondly: It is not right to apply to this force of resistance the 

 formula of Stokes, as it supposes that the liquid around the particle 

 has a motion dependent upon the velocity of the particle. This comes 

 into conflict with statistical mechanics, for these teach, that 



tTuV -0 . (2) 



where e.g. for v the velocity of the particle, for r, that of a molecule 

 (both e.g. in the .^-direction) in its neighbourhood may be taken. 

 And so Miss Snethlagk has assumed for the calculation of the 

 persistence of a particle in, the Brownian motion, that the surrounding 

 molecules have the usual Maxwellian distribution of velocity. 



The authors mentioned have tried to give a theory of the Brownian 

 motion which escapes these objections, by starting from (i). In what 

 follows we want to show, that the equations (1) and (2) are much 

 less far-reaching than it seems so that the objections to the usual 

 theory may be considered to have fallen away, and on the other 

 hand the leasoning given is proved not to be the right one. 



In order to deduce tbe differential ecpialion, which she wants to 



