the results given below shows great similarity to the deductions 

 which Lord Kayleigh ^) gave utterance to alreadj- years ago. Kindred 

 ways of regarding the stationary condition are also found in the 

 work of Dr. Fokkek') and M. Planck"). 



§ 1. In the dissertation Mrs, dk Haas — Lorentz starts from the 



equation of motion for a emidsion parlicle, which she brings in 



the formula 



du 

 m — = — loH -\- mF (1) 



(It 



Here u is the velocity of the particle, ?/; =: 6 nr ft nf the resistance 



which according to Stokes' formula the spherical particle (radius a) 



would experience in a liquid with internal coeflicient of friclion /i. 



The force expended by the shocks of the molecules is divided into 



two parts, of which one is that according to Stokes, I he second is 



quite irregular, so that F=^0. The determination of the average is 



to be understood in this way that it is lo be taken at a given 



moment for particles which all have had (he same velocity u^ a 



time before. 



Now we are able to integrate the equation (1), if we introduce 



w 



— r= /?, we have 



m 



t 



M = u, e-/3' + e-pi lel^i F{i)dt (2) 





 where u^ is the velocity at the time t = 0. 



If then we determine the average of this equation in the way 

 indicated, the result is 



u :=z u^ e-t^<- (3) 



or expressed in words: when we start from a great number of 

 particles of given velocity, the average velocity decreases in the 

 same way as with large spheres; the damping coefficient also is 

 deduced in the same way from radius and coefllicient of friction 

 of the fluid. Let us now calculate also the average of ihe square 

 of Ihe velocity. For this we find : 



1) Lord Rayleigh, Pliil. Mag XXXIl, p. 424. 1S94. Papers ill. Dynamical 

 problems in illustration of the theory of gases. 



') Dr. A. Fokker, Over de BROWN'sclie beweging in hot stralingsveld. Diss. 

 Leiden, pg. 528, 1913. 



') M. Planck, Ueber einen Satz der Slatistisclien Dynamik u.s.w. Berl. Ber. 

 p. 324. 1917. 



7 



Proceedings Royal Acad Amsterdam. Vol. XXI 



