/ 



Physics. — ''On the Theory of the Brownian Movement and the 

 Experiments of Brillouin". By H. C. Burger. (Communicated 

 by Prof. W. H. Julius.) 



(Communicated in the meeting of April 27, 1917). 



The purpose of this inquiry is of two kinds viz : 

 l**' . to give a rigorous proof of some well known formulae of 

 the Brownian movement, with and without external force. 



2"^. to trace the boundary-condition at a fixed wall and to inter- 

 pret some experimental results concerning this. 



§ 1. When a material particle is suspended in a liquid, one may 

 inquire after the probability that, in consequence of the Brownian 

 movement, it will in the time t in the direction of X cover a 

 distance between x and x -\- dx. This probability is determined by 

 V. Smoixchowski ^) by using the following image. vSnppose that this 

 particle regularly after a time t covers a distance d, with equal 

 probability to the right or to the left. Now, when one makes rfand 



T zero, but keeps ; — = /) finite, one finds for the required probability : 



f{.x, t) dx =z e ^dx. (/«) 



^ VjtDt 



From this formula we find for the mean square of the displacement, 



;c' = 21)1. 

 By entering closer into the mechanism of the phenomena, we 

 may find the last equation, in which D then proves to be : 



RT 1 

 D= , (lb\ 



where R, T and X have the usual meaning, ju is the coefficient of 

 viscosity of the liquid and a the radius of the particle. 



Now we may deduce (1«) however in a perfectly rigorous manner, 

 without making use of any image, whereby however the constant 

 D remains entirely undefined ; and at the same time we may prove, 



1) Vortrage über die Kin. Theorie der Materie p. 101, 1914 and Bull. Acad. 

 Gracovie p. 419, 1913. 



