930 

 F~:=0 (6/ï) 



kT 



f- 



F{^F{^+xp)dip = ~^=,^ (6y) 



provided we start from particles which at the time ^ = 0, have the 

 velocity u„. 



If we accept this set of equations, which kinetically have not been 

 proved, which however contains the inconsistency developed in ^1, 

 we afterwards do not arrive at any contradiction. 



Van der Waals looked for it in the equation arising; when [2) 

 is multiplied by u and the average is determined, he wrote down ') 



du — 



u — = — wu* 

 dt 



which is really incorrect, l)ut he forgot then that Fu is not zero, 

 if we put ourselves on the stand[)oint of the suppositions 6(o, j^^, y) ; 

 as Ohnstein demonstrated on p. J Oil of his paper. If we introduce 

 for uF the value found there the equation adopts the form 



"du { d\ 



dt ^V 2^/ 



1 . . 

 For times large with reference to ^ this is zeio, whilst it the average 



— (^ 



is determined over all particles it is always zero as m,' = — . 



Now it is supposed in Langevin's proof that .yF=:0. It might 

 be doubted perhaps whether this magnitude is equal to zero"). Yet 

 this is the case. For we have 



d^x dx „ 



de ^ dt ^ 



so 







so 



1) Langevin has not developed any reasonings that could give rise to the sup- 

 position that he puts Fu = 0. 



2) On the fact that x F = rests the very simple theory which Langrvin gave 

 of the Brownian motion. 



