93J 



T 



F» = [x, -f ^* (!—«-(»')] /' + i?' p-z^^rf^ (e^^ 



F{,i)dy 



The first term is zero according to 6(3, for the second term we 

 can write by partial integration 



- -F{t)e-^' fe^-nv) dy - F {t)jF{,j) dy. 

 



The two last integrals are equal, as F{t) F{ti) is ditterent from 

 zero only if i] lies in the immediate neighbourhood of t. The value 



of both integrals, as proved in Ornstein's paper, is — . 



Thus it becomes clear that there is no question of inner contradic- 

 tion, and that only the supposition about W{t) — incorrect through 

 the times of commencement — is an error in the theory of Einstein 

 and Langevin. As we showed in § 1 of this paper the value which 

 according to Einstein's formula is obtained for the average force at a 

 given velocity at the time zero W{t) only deviates for a verj' short time 

 from the real value of this magnitude. The fact that Einstein's for- 

 mula leads to results which agree well with reality support the 

 supposition that the relation 



W{t) = — ^x, e-i^i 



holds with a very good approximation already a very short time 

 after the moment in which all emulsion-particles possess the velocity 

 x^. The true kinetic theory of the Brownian motion will [)erhaps be 

 able to give an account of this fact. 



Institute for Theoretical Physics. 

 Utrecht, Sept. 1918. 



