Physics. — "On the theory of the Broionian motion.*' Bj Prof. 

 L. S. Ornstein and Dr. H. C. Burger. (Communicated by Prof. 



H. A. LORENTZ). 



(Communicated in the meeting of September 29, 1918). 



Prof. VAN ÜER Waai,s Jr. has developed in these communications ') 

 a new theory of the Brownian motion. We shall demonstrate in 

 this paper, that he has made use of various wrong suppositions and 

 theses in his reasoning. 



1. Van der Waals starts from the equation of motion of a Brow- 

 nian particle in the formula: 



XT=Lw{t) ......... (1) 



Here w{t) is the force which the particle experiences from the 

 molecules of the liquid. The force iü{t) is a magnitude depending 

 upon chance. 



In order to arrive at a theorv of the Brownian motion v. d.Waai.s 

 introduced the supposition that A\w{t) — the product of the velocity 

 at the time zero and the force at the time t — is zero "on an 

 average over all particles '). 



Now we can understand the average in two ways, viz.: 



a. at a given initial velocity ,r,, thus iu{>'J):=(). 



b. at all possible initial velocities, in which case the distribution 

 of velocity according to Maxwell must be taken into consideration. 

 Van der Waals uses the average in the way last mentioned. 

 We shall also examine to what the supposition leads if we applv 

 the tirst way of determining the average and show that the deter- 

 mination according to {a) as well as v. d. Waals uses it leads to 

 impossible consequences. 



In this purpose we take down the first integral of (1), which is 



x=x,^ Cw{i^) d» . ...... (2) 







If we determine the average according to (a) we obtain 



1) These com. Vol. XX. 1918. p. 1254. 

 ') of. p. 1258 of the paper quoted. 



