681 



filled with a gas which is in inolecular-statistical equilibrium. Its 

 raolecules collide both with m^ and m^. 



Considering a corresponding canonical ensemble, the expression 



const, e ^^T dx^dx^du^du^ (2) 



(where x^, x^, u^ and u^ are the coordinates and velocities of the 

 two particles, and <?> {x^, xj is the potential energy of the force 

 holding them together) gives the number of individuals of the en- 

 semble for which x^, x^, u^ and u^ have their values between 

 specified infinitely close limits. For given values of x^, x, and especi- 

 ally also of Wj (2) gives the same number of individuals in the 

 ensemble for equal and opposite values of u^ i. e. : equal and 

 opposite values of u^ are still equally probable, u^ is ''independent" 

 of ^^l. On the other hand the Brownian movement will in the 

 course of time cause great displacements along the X-axis. At the same 

 time the points will remain close together in virtue of the inequality 

 (1). This is the paradox mentioned at the end of § 1. 



§ 3. Let us first leave aside the molecular-statistic side of the 

 problem and put the following purely kineniatical question. During 

 a long time O the two points m^ and ni^, may be conducted along 

 the A'-axis in an arbitrai-y way, only restricted to the conditions that 



a. the inequality (1) shall remain valid; 



b. the distance between the final and original positions of the pair 

 of points may be great compared with D. This implies that m^ 

 ,, accompanies" m^. Now we ask: does this imply that always the 

 mean with respect to the time 





(3) 



will be positive, or is it possible that the integral can be zero or 

 eventually even negative? 



The sign of the integral (3) indicates in a natural way in how 

 far the two points move more in the same oi- in opposite directions. 

 But we can point out that for the above described motion of the 

 pair of points ;?«,, m^ the inequality (3) need not be fulfilled. This 

 will become evident by an example of a case for which the integral 

 becomes negative. In fig. 1 the two zigzag lines represent a possible 

 a;, /-diagram of the two points rn^, m,. We see that the conditions 



