484 Mr. S. H. Burbury on certain 



probable in this sense than the reversed state in which 



—■ — is positive. But when/ r F / =/F in all cases, which we may 



call the normal state, then the direct and the reversed state are 

 equally probable. If, therefore, the last external disturbance 



which has happened to the system be recent, -=— is probably 



negative. The physical importance of this result seems to me 

 to consist in the fact that to any system in nature external 

 disturbances are always happening, and they come generally 

 at haphazard without regard to the state in which the system 

 finds itself for the time being. And therefore the last dis- 

 turbance generally is recent. But a process of this kind is 

 not an irreversible process. 



24. I think the conclusion to be drawn is that the H theorem 

 does not prove, and we have at present no proof, that in 

 our test system of elastic spheres the diminution of H is 

 irreversible in the same sense as loss of kinetic energy by 

 friction. 



Nevertheless, without being irreversible, the process has a 

 certain physical significance. Let us draw the curve for 

 which t is the abscissa and H the ordinate. When II is very 



small, F'/' = F/ nearly, in all cases ; -r- therefore, and also 



— =-, is very small. Therefore the curvature is very small. 



When H differs much from its minimum, the curvature is 

 generally considerable. It follows that on average of infinite 

 time, H will have nearly its minimum value. Deviations will 

 occur, but there is no proof that with increasing time they 

 become less frequent or less important. There is no ultimate 

 state into which the system subsides by an irreversible pro- 

 cess ; but there is a state in which on average of infinite time 

 it will be. And this we may call, as we have already called 

 it, the normal state. 



25. The question whether in an undisturbed system the 

 condition of independence can exist may be expressed in the 

 following form : — Let S be the principal function of the 

 motion. Then if x ly y^ z u x 2 , y^ z i be the coordinates of two 



spheres at time t, their momenta are 3—, -7- &c. If then 



the points # l5 y Y , z x and a? 2 , y. 2 , z 2 are very near each other, 



nave a nd _ any tendency to be of the same sign ? The 



(lOQ\ U.OC2 



condition of independence, if complete, asserts that they have 



