Physics. — "Oil the Theorn of the Bronminti Movement. Appeiidiv." 

 Bv Piof. .). D. VAN DER Waai,s Jr. (Comninnicated by Prof. 



J. D. VAN DER WaAI.S). 



(Communicated in the meeting uf Jan. 25, 1919). 



In these Proceedings L. S. Oknstein and H. C. Burger ^) advance 

 some objections to a tlieory of the Brownian movement developed 

 by me. ') I will biiefly discnss some of them here. 



I. The first rests entirely on a misnnderstanding. It refers to a 

 calculation of x — ,/■, = L =z the measured deviation of a suspended 

 particle obtained in a certain Dieosuved time t. When determining 

 the mean value of this quantity I omit a term with the product ') 



x^wit), because this mean will be zero. 0. and B. think now that 1 

 mean that the equation: 



'x,w{t)z={i (1) 



will be valid for every value of t. They justly object to this, and 

 demonstrate that this would lead to absurd sesults. My meaning was, 

 however, that this equation would only hold for times that are 

 sufficiently great. It expresses precisely the same thing as 0. and B, 

 indicate in the graphical representation on p. 924 loc. cit., naiuely that 



w{t) *) for / large again aj)proaches zero. That the times in which 



1) L. S. Ornstkin and H. C Burger. These Proceedings, Vol. XXI. 922. 



2) J. D. VAN DER Waals Jr. These Proceedings, Vol. XX. p. 1254. 



") In this w represents the force that acts on the particle. Equation (1) some- 

 what resembles the equation : 



duit) 

 "(0^=0 . (la) 



wliich has been repeatedly used by Miss Snkthlage and me in our considerations 

 on llie Brownian movement, and is among others derived by difTerentialing the 

 equation \ u (t) \^ =: constant with respect to /. Equations 1 and 2, however, rest 

 on very different considerations, and are used in a very difterent way, so that we 

 should be very careful not to confuse them. 



*) A line over a quantity denotes a mean. When no index is given, the mean 

 has been taken over all the suspended particles. An index as here the u{0) behind 

 the line expresses that the mean lias been taken over all the particles which had 

 the definite velocity u (a) at the moment t = 0. 



