Physics. - ''On the Ih-oiDnlan Motion '. Hj Prof. L. S. Ornstein. 

 (Coniiiiiiiiicjiled by Prof. H. A. Lorkntz). 



(Commiinicaled in llie meeting of December i2!), J 01 7.) 



Von Smoi.uchowski ') observed (hat tlie function wliich gives the 

 probabiHij, that in tlie Pnownian Motion a ptirticle accomplishes 

 a definite way in a given time is a solntion of the eqnation 

 of diffusion. For cases in which an exterior force also acts on 

 the particles, he deduced a dilfei'ential ecpiation for the above- 

 mentioned function of probability by a phcnomenological method. 

 Some time after Mr. 11. C. Burger ') deduced this differential equation 

 following a method, which takes the essence of the function of 

 probabibty more into consideration. Both deductions do not stand 

 in direct connection with (lie mechanism of the Brownian motion; 

 my object in this paper is to demonstrate, tliat starting from a 

 relation which Mrs. dk Haas— Loricntz ') has used in her dissertation, 

 to defei-mine the average square of the distance accomplished, one 

 is able to determine the function of probability of the Brownian 

 motion. It is worth observing that tlie way in which different averages 

 depend on the time may be calculated from the results obtained 

 by Mrs. \w. Haas — Lorkntz by a slightly more careful ti-ansition of 

 the linut than was necessary for the object she had put herself 

 (viz. the determination of the stationary condition). Fii'St I want to 

 determine these averages l)y a new method, which will offer the 

 opportunity of demonstrating, that the opinion, from which Dr. A. 

 Snethlagk/) starts in the theory of the Brownian motion that Einstein's 

 theory is in conflict with statistical mechanics, is incorrect. 



Besides the function of probability for the distance I shall also 

 deduce that for the velocity. The chain of thoughts which lead to 



1) Compare e.g. M. v. Smoluchowski. Drei Vorlrage über Diffusion, BROWN'sche 

 Bewegung etc. Phys. Zeilschr. XVIf p. 557 1916. 



*) H. C. Burger, Over de theorie dev BROWN'sche beweging. Verslagen Kon. Ak. 

 XXV p. 148^, 1917. 



8) Mrs. Dr. G. L. de Haas— Lorentz. Over de theorie der BnowN'sche be- 

 weging, Diss. Leiden 1912. 



*) Miss Dr. A. Snethlage, Moleculair-kinelische verschijnselen in gassen etc. 

 Diss. Amsl. 1917. 



