682 



Fig. 1. 



a and h are fulfilled and that still u^ and ?/, have continually 

 opposite signs, so that the integral (3) becomes negative. 



§ 4. Now we have : 

 4 u,u. 



{u,-\ u;)^-^u,-u,)\ 



(4) 



The sign of u^ w, is determined by which term is the greater 

 of the two. 



When the motions of the pair of points obey the eqnipartition 



theorem, u^u^ is just equal to zero. (See the appendix). 



From the above it is evident that a motion of the pair of points 

 is possible, in which they remain close together and at the same 

 time travel through great distances, while still at Qxevy moment 

 the velocity a^ is "independent" of u^. The paradox mentioned in 

 §§ 1 and 2 proves thus to be apparent only. Therefore there is no 

 objection against Einstein's assumption that a suspended sphere during 

 its Brownian movement imparts its motion to the surrounding jiuid in 

 the same loay as in the case of a systematic motion under the injiu- 

 ence of a constant force. 



§ 5. In the positive proof however that Einstein's assumption 

 follows from the fundaments of statistical mechanics we meet with 

 the following difificulty: Let us demand, (to stick to our example), that 

 the inequality u^^, <C ^i <C ^*i8 + ^ exists 



1^*^ at the instant t^ ; 



2"^^ also during the interval from t^ — r till t^ ; and let us ask 

 what can be said of the occurrence of different values of u^. In 



