DIFFUSION AND ENTROPY OF GASES 607 



that phenomenon is as consistent with the motion being periodic 

 as with its being asymptotic — i.e. irreversible. For if periodic, 

 any point in the path may be described in either of two direc- 

 tions, tj^pically the paths may be ABCA, or ACBA, By the 

 way in which we make the experiment, we determine the 

 direction to be that in which the initial motion is towards more 

 uniform mixture, say ABCA, if B denotes the initial, and C a 

 state of more uniform mixture than B. That is because initially 

 the two gases are at rest relatively to one another. As an 

 example, suppose a semicircular smooth tube in a vertical plane 

 with its middle point as base, and in it a heavy particle. The 

 particle, if free to move, and placed at rest at a point above the 

 lowest, will begin by moving downwards. But it will oscillate 

 about the lowest point, and will not move irreversibly to the 

 lowest point. The reason why it begins by moving downwards 

 is because it starts /rc'w rest. For precisely the same reason the 

 two gases, each at rest relatively to the other, begin by moving 

 towards the more uniform mixture. But there is no proof that 

 the motion is irreversible. 



21. It is true no man has ever observed them to begin to 

 separate. But to make this evidence of the irreversibility, it 

 would be necessary to continue the experiment for a time at 

 least equal to half the period, if the motion be periodic. And 

 not only that, but also to completely protect the system from all 

 disturbances from without during the whole time. Has this ever 

 been done ? And as regards external disturbances, can it be 

 done ? If practically it cannot be done, then it may be that in 

 any experiment that can practically be performed, the motion 

 will appear to be irreversible, because the external influences 

 prevent it from being periodic. But then they also prevent 

 the argument from being applicable. 



22. If the diameters of the molecules were so small that no 

 collisions occurred, the motion must be periodic. Can it be 

 proved that collisions convert it into an irreversible motion ? 



23. I think we unconsciously derive the idea of the motion 

 being irreversible from Boltzmann's H Theorem, which is 

 supposed to prove that an irreversible motion of a gas is 

 possible, and that, I think — although the weight of authority 

 against me is immense — rests on " a misuse of the theory of 

 probabilities." 



We suppose that at an initial instant the co-ordinates and 



