Physics. — "(hl the Tlipory of the Brornnian Mopeiuent". By Prof. 

 J. D. VAN DER Waals Jr. (Communicated by Prof. J. D. van 

 DER Waals.) 



(Communicated in the meeling of February 23, 1918). 



Pretty numerous are tlie methods by which it has been tried to 

 calculate the mean path to be expected of a "Brownian" particle 

 suspended in a liquid or gas. Most of the methods of calculation 

 start from the supposition that such a pai'ticle will experience a 

 friction in its movement. This means that it is assumed that from 

 the force acting on such a particle, a term may be separated oppo- 

 site to and proportional to its velocity, and that the remaining part 

 of the force will be independent of the velocity. Both forces are a 

 consequence of the collisions of the surrounding molecules of the 

 substance in which the particle is suspended. The methods of cal- 

 culation based on this supposition arrive at a result which 

 Einstein was the first to communicate, namely that: 



— RT 1 



A' = — ^ t (la) 



In this R = the absolute gas constant 



iV=the number of molecules per gramme-molecule 

 ^ = the coefficient of viscosity of the medium 

 a = the radius of the particle 

 t ^ the time 



A = the deviation in the time t in a definite^ direction, 

 e.g. in the direction of the .Y-axis. I shall call L briefly the devia- 

 tion in what follows. I shall further speak of the force, when I 

 mean the A'-component of the force. The dash over A" denotes that 

 the mean value has been taken for all the suspended particles (a 

 great number). 



In the derivation of this formida it has been assumed that the 

 force of friction may be represented by the formula gi\en for it 

 by Stokes : 



^l =z 6 n H a a; (2) 



Let us examine the way in which e.g. Langevin arrives at the 

 formula for A'. He starts from : 



m j; = — 6 .T C a .V -f- A (3) 



