1271 



because it is very well adapted to help us to forin a true conception 

 about the forces that appear in the Brownian movement, l^et us 

 consider a sphere of finite dimensions immersed in a viscous liquid, 

 and fastened to a cord. By means of this cord the sphere can be 

 moved in the .i' direction both in positive and in negative sense. 

 Let us now assume that a force F{t) is applied, the value of which 

 is tixed without our taking the velocities acquired b}' the sphere 

 into account. We may e.g. imagine that the value of i^ for different 

 moments is determined bj soiue lottery or other, and that i^ further 

 satisfies the conditions mentioned on the preceding page. 



The equation of motion of the sphere will then be: 



du 

 dt ^ 



Ornstein integrates this equation and shows that Fu =: iiii*. 



Though the value of F has been fixed independently of ?/, yet 

 F and u are statistically not independent of each othei'. And this 

 is owing to this that the velocity u is not independent of the force 

 F, which has given rise to it. 



When we now again return to the Brownian movement, the 

 force F will no longer be exerted by pulling a cord, but by colli- 

 sions of molecules. But for the rest everything remains the same. 

 We may, indeed, assume a friction, also counteracting the momen- 

 tary velocity. And there may be reason to do so, just as was the 

 case for the larger sphere attached to a cord. But then the motive 

 force F does not satisfy the condition Fu = 0, as is generally 

 assumed, but we may put: 



F= ^ ^u + F' with F« = 0, 

 so that the force of friction — i^x, may not be introduced, without 

 the introduction of another force -|- jin that again neutralizes it. 

 The only remaining force F' is then independent of u. 



