124, Mr. S. H. Burbury on Diffusion of 



velocity reversed, and owing to these reversals the mean x 

 velocity of all the oxygen molecules is zero. A short time 

 after removal of the partition, those oxygen molecules which, 

 but for the removal, would have had their x velocities u 

 changed to —u, will still retain their original x velocity u. 

 So by removing the partition we have in effect given to the 

 oxygen gas a mean momentum towards the (originally) 

 nitrogen half of the cylinder, and to the nitrogen gas an equal 

 mean momentum towards the oxygen half. 



We thus determine the direction in which the cycle, if 

 there be a cycle, is described. 



In the limiting case of molecules having infinitely small 

 diameters, so that collisions will not occur, it is evident 

 that the motion must be cyclic. But it will be argued that 

 the cyclic motion is destroyed by the collisions which actually 

 occur. Before considering the general effect of this, we may 

 note the application of it to the inference (2), which I under- 

 stand Bryan to draw, namely, that the diffusion process, if 

 irreversible, must on that account be attended by gain of 

 entropy. May we not reason thus : The gain of entropy due 

 to all the collisions is the sum of the gains of entropy due to 

 the collisions separately. Therefore it is zero, because each 

 separate collision is a reversible process attended by no gain 

 of entropy? Is not the implied assumption that if the 

 diffusion is an irreversible process, it must on that account 

 involve gain of entropy, erroneous ? 



As to the general question of irreversibilit} 1 -, let the two 

 diffusing gases be equal in quantity, and both at the same 

 pressure and temperature. And let their respective densities 

 at any point at any instant be denoted by p and p' . Let 



the integration being throughout the containing vessel. 

 Then also 



dt -J 



dt 



It can then be proved on practically the same assumptions as 

 those which are necessary in the proof of Boltz mann's H 

 theorem, though not by identically the same method, that 



— is on average negative, so that K diminishes until it 



dt & ° J 



acquires its minimum value zero when p = p' everywhere. 



The necessary assumptions are, in Boltzmann's language, 

 " dass die Bewegung molecular vmgeordnet isfc und fur alle 

 Folgezeit bleibt." I have tried to give a definition of the 



