924 



reet result. Besides the negative conclusion that the tlieorj of v. d. 

 Waals ought to' be rejected some positive result can be deduced 

 from our calculations. 



The formula (1) is just as much a matter of course as it is right ^) 

 and consequently there must be a mistake in the supposition 

 Xgiu{t) = 0, while there can be no difficulty for anyone in seeing 

 that everything is all right when this magnitude can become negative 

 for fixed values of t. We shall in this paragraph use the average 

 .according to (a). As ./•, has been given once and for all, the above 

 reasoning shows, that tv{t) for certain values of t must possess the 

 opposite sign ol .f, '). Now van der Waals has rightly drawn 

 attention to it, that according to statistical mechanics for t = 0, io{t') = 0. 

 Besides it is evident, that foi- i infinite the average value of iv{t) 

 undergoes no influence from .r, and therefore must be zero. The 

 course of iü{t) may consequently be imagined in a way as represented 

 by the accompanying figure (where .r, has been supposed positive). 



Of course the curve may be more complicated for example io{t) 

 might oscillate round the axis. If now we calculate iv{t) according to 

 the Einstein-Langevin formula, we tind, if we take into consideration 

 that F{t) is equal to zero : 



w{t) = — ^x-{- F{t) = — ^e-^<- X, 



1) From the formula (1) v^re can deduce the relation A- = bi if we introduce 

 suppositions, it is however impossible to find the value of h, without penetrating 

 into the mechanism of the Brownian motion. 



*) There are cases, when this is not so necessary according to what precedes, 

 but if io is more than the equipartition value, it is certainly the case. 



