Physics. — "()n friction in connexion loitli Brownian movement" . 

 Bj Dr. 0. PosTMA. (Communicated bj Prof. H. A. Lorentz). 



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



§ 1. The dittereiit de(iiKMioiis of the mean displacement of a 

 suspended particle caused bv the Brownian movement in a certain 

 time, can be divided into two groups. In the deductions of the first 

 kind the forces acting on the particle are divided into accelerating 

 and retarding forces, in those of the second kind this difference is 

 not made. 



To the deductions of the tlrst group belongs that of Einstkin, the 

 second one of von Smoluchowski, that of Langevin and that of dk 

 Haas — Lorentz (bv the method of Einstein and Hopf). To those of 

 the second group belongs the first deduction of von Smoluchowski, 

 that of Van uek Waals and Snethlagk and that of Snkthlage (given 

 in her dissertation) 'j "•'). 



In the theories first mentioned a retarding force (friction) has been 

 assumed proportional to the radius of the particle, which is consi- 

 dei-ed as a sphere and has the velocity v. The applied formula 

 W ^ i^ T^av is (ieduced in hydrodynamics on the supposition that 

 at the surface of the [)article the fluid has the same velocity 

 as this. All theories of the first kind come to the result that the 

 mean square of the displacement (A-) is inversely proportional to 

 i and proportional to a. 



The theories of the second kind give the result: A* proportional 

 to t and inversely proportional to «' and to the density q *). 



It is however not to the resolution of the forces into accelerating 



') See: G. L. de Haas - Lorentz "Die Brownsche Bewegung", die Wissenschaft 

 1913, J. D. VAN DER Waals Jr. and Miss A. Snethlage: "The theory of tlie 

 Brownian movement". These Proceedings Vol. XVIII, p. 1322 and A. Snethlage: 

 ' Molecular-kinetic phenomena in gases, especially the Brownian movement". 

 Amsterdam 1917. 



*) Kecently Van der Waals Jr. gave still a theory in which, though in a some- 

 what different form, the two kinds of forces are found back. (These Proc. XX 

 p. 1254. 



^) The first result gives the best agreement with the investigations of Snethlage. 



