100 

 Because for u" we set 



_ / ï^" V 1 1 r I 



?/' = I M. COS D ^ -| siji Qt ] -\ I 'f (c) sm Q {t — t) dh,] . ( 1 1) 



V Q J 9 U \ 







For the integral, if again vve make a double integral of it and 

 if we introduce the constant 6 



+ 00 



6 -^- At» (£)»'($ + xY)<hY (12) 



00 



we can write 



or 6t 



— I sin* o it — ^) d^ = 1- periodical terms. 



9 J 2()» ' ^ 







Thus we find 



- 6t 



u* = — -[-periodical terms (l-'') 



This formula shows that u'' increases indefinilely with the time, 

 while it is evident according to statistical mechanics that ?<" must 



approach — . 

 m 



Consequently if the equation (9) is treated as a diffeiential equation 

 we arrive at results which are not right '). 



§3. Miss Dr. Snkthlage and Prof. Dr. J. v. d. Waals Jr. have observed, 

 that the theory of the Browiiian motion must be in accordance with 

 a general theorem of statistical mechanics. For the case that we 

 consider a particle, that under the influence of the impacts of the 

 molecules of the liquid executes a movement, the force which the 

 molecules exercise does not depend upon the velocity, but only upon 

 the coordinates. Consequently the product of force and velocity must 

 on the average be zero, as well in a canonical as in a microcanonical 

 as in a time ensemble. Now they are of opinion that Einstein's 

 formula comes into conflict with this. I shall demonstrate that this 

 is only the case to a certain extent. 



If we assume in a canonical (or micro-canonical ensemble) all 

 systems selected in which ihe velocity of our particle at a point of 

 time is equivalent to ?i, and if then we follow this group of particles. 



^) An analogous question is treated by M. Planck (Ann. der Phys. 1912. Bd. 

 37 p. 462) where it is demonstrated that the energy of a resonator subjected to 

 tlie irregular field of black radiation increases in proportion to the time; the f of 

 Planck agrees here with v. d. Waals' u. 



