Gases as an Irreversible Process. 125 



expression " molecular ungeordnet," namely this : — The 

 chance that any molecule at any instant shall have assigned 

 velocities is independent of the velocities and positions of 

 all the other molecules for the time being. This I call 

 condition A. That, if it be accepted, is, so long as it remains 



true in fact, a sufficient foundation for the proof that — — , or 



7T7- (it 



~rr, is on average negative. But the state of things thus. 



assumed to exist cannot possibly continue to exist indefinitely 

 in a system completely isolated, that is completely protected 

 from external disturbance. With my definition, therefore, 

 the proof fails altogether that H or K continues irreversibly 

 to diminish if the system be isolated. 



If my definition be not accepted, will anybody make a 

 better one ? I think if he does he will find that "molecular 

 ungeordnet " represents a state of things which, like my 

 condition A, cannot possibly continue to exist indefinitely in 

 the isolated system. 



The Loschmidt objection, that if you were to reverse all the 

 velocities, the system would retrace its course, applies only to 

 the isolated system, and as applied to the isolated system is in 

 my opinion a conclusive objection to the theorem that the 

 diminution of H or K is in that system irreversible. 



The defence of the theorem which has met with wide 

 acceptance, is that the reversed motion, although possible, is 

 infinitely improbable compared with the direct motion. But 

 if Maxwell's law prevails — and it cannot be denied by advo- 

 cates of the H theorem — any set of velocities and the reversed 

 set are equally probable. 



If on the other hand the system be not isolated, but subject 

 to disturbances, Loschmidt's objection is not true in fact. 

 For on reversal of the velocities, the system would not retrace 

 its course, beyond the point at which the last disturbance 

 occurred. It may therefore be true that if disturbances are 

 always occurring, e.g. if you keep stirring the mixture, II or 

 K will go on diminishing to minimum. 



I venture to suggest the following as the true theory. The 

 motion is in theory cyclic — i. e. reversible — in both cases, the 

 H theorem and the diffusion — that is it is cyclic provided 

 that the system be completely isolated. But that condition of 

 complete isolation is impossible to realize in nature. How 

 for instance can you prevent the gas in a closed vessel from 

 being affected by vibrations coining from the surrounding 

 medium ? That is a sufficient reason why we can never 

 expect the cyclic motion of two diffusing gases to become 



m37 



