925 



For t = the line, which represents this conrse, deviates from 

 the true curve. The iniportaiil agreement existing between Einstein's 

 theory and the experiment now makes us presnme, that the true 

 }v{t) — t curve and the curve accordirig to Einstein onlj deviate 

 from each other for short times after the departure of the particle 

 with the velocity j\, that so the maximum in the true curve lies 

 close to t=zO, and tiiat from this maximum onward it descends 

 pretty well exponentially according to Einstein's curve. It goes 

 without saying that these are only assumptions, which a calculation 

 of the true ro{t) curve must |)rove from the molecular theory. We 

 are however of opinion that it is worth while to point to this 

 possible interpi-etation of Einstein's master-stroke in the theory of 

 the Brownian motion. 



§ '>•. Van der Waals' theory further rests on the tliesis that the 

 magnitude 



\w{i}){t-d^)dd- (3) 



ro{t) 



is essentially negative, if only t be not taken to small. 



Perhaps it is not quite superfluous to demonstrate after what 

 precedes, that this thesis is not right; expecially as an integral of 

 the same kind used by one of us maybe tieated in the same way ^). 

 i When ?/'(/') is a function determined by chance, of which the 

 character is not dependent upon the time, we can i-epresent it for 

 a long ■ interval by a FouRiER-series, the coefficients of the Foukier- 

 series determine the nature of the accidental character '■'). If so 



/ 2nnt 2jxv 



w{t) = Hn ( An sin -— - I Bn i'OS ~~^ t 



when nit) = 0, we must have B^ := 0. 



The calculation of (3) becomes simple, when we apply that 



1) Compare L S. Ornstein. On the Brownian motion. These Proc. XXV, 

 1917. p. 96. 



') When we have to do with a function of accidental character, even then 

 the conduct of this function may very well depend upon the time. If we consider 

 e.g. the length of the path in Brownian motion, we get for all times a = 0, but 

 ^^ = bt, for the velocity however we have r = <>. v~ is constantly independent of 

 the time. Kor the force something analogeous as for the velocity ought to be 

 assumed. By going further into the mechanism of the motion, this can be rendered 

 plausible. 



60 



[Proceedings Royal Acad. Amsterdam. Vol. XXI. 



