I 



476 . Mr. S. H. Bur bury on certain 



function and — negative. It does not matter, as regards 



jrj" 



the question of reversibility, whether —=- is necessarily 



cit 



negative, or only more likely at each stage of the process to 



be negative than to be positive. It is enough if a distinction 



exists between the forward motion in which —r- is negative, 



and the backward motion in which -=r- is positive. In this 



distinction consists the irreversibility. But the distinction 

 must exist at every stage of the process at which H exceeds 

 its minimum. 



4. The best known of these theorems is Boltzmann's H 

 theorem in the theory of gases, wherein it is proved that his 

 function H continually diminishes till a certain state is 

 reached, which involves the equal partition of energy. 



So Herr Planck in his treatise liber irreversible Strahlungs- 

 vorgdnge proves that a function L, the entropy of his system, 

 necessarily increases till a state is reached analogous to the 

 equal partition of energy. But in Planck's theorem we have 

 to do, not with molecular motions each evidently reversible, 

 but with electromagnetic vibrations in aether, about which we 

 cannot say with the same certainty that they are reversible 

 separately. At present I propose to deal only with Boltz- 

 mann's theorem, as a type of theorems founded on molecular 

 motions certainly reversible. 



The Directing Condition. 



5. All the molecular motions being reversible, the fact that 



H > H cannot alone make -^ negative. For we may reverse 

 all the velocities, and that reversal in continuous motion 

 changes the sign of — without altering the value of H — H . 

 Some further condition is therefore required to determine 

 the sign of -t~. This we may call the directing condition. 



6. The directing condition being defined, there arises the 

 question whether or not it exists ia fact. If it does, the 

 diminution of H is an irreversible process. If not, the process 

 is not proved to be irreversible. Boltzmann's condition in 

 his Theory of Gases is that the motion is, and continues to 

 be, " molecular ungeordnet." That, if it can be defined, may 

 be the most general form of the condition. For my present 



