76 BUTLER ART. D 



same condition, as initially, of having the greatest entropy 

 consistent with its energy." Now the change we suppose to 

 take place cannot be infinitely slow, except at particular mo- 

 ments, so that we may choose a time at which it is proceeding 

 at a finite rate. We will consider the change which occurs in a 

 short interval of time after the chosen time. No change what- 

 ever in the state of the system, which does not alter the value of 

 the energy, and which commences in the same state which the 

 system has at the chosen time, will cause an increase of entropy. 

 "Hence, it will generally be possible by some slight variation in 

 the circumstances of the case" (e.g., by a slight change of pres- 

 sure or temperature or of the quantities of the substances) to 

 make all changes in the state of the system like or nearly like 

 that which is supposed actually to occur, and not involving a 

 change of energy, to involve a necessary decrease of entropy, 

 which would render any such change impossible." "If, then, 

 there is any tendency toward change in the system as first 

 supposed, it is a tendency which can be entirely checked by 

 an infinitesimal variation in the circumstances of the case. 

 As this supposition cannot be allowed, we must believe that a 

 system is always in equilibrium when it has the greatest en- 

 tropy consistent with its energy, or, in other words, when it has 

 the least energy consistent with its entropy." 



The essential steps of this argument may be recapitulated 

 as follows. A system having the greatest entropy consistent 

 with its energy must be in equilibrium, because 



(a) if it were not in equilibrium a change must take place, 



and except at particular moments must take place at a 



finite rate; 

 (/3), but it is shown that in such a case, the change can be 



entirely checked by an infinitely small modification of 



the circumstances of the case; 

 (7), therefore, an infinitely small modification makes a finite 



difference in the rate of change, which cannot be 



allowed. 

 We may observe that the statement that the hypothetical 

 change cannot be infinitely slow is an essential part of the 

 argument. For, if the change which is supposed to occur were 



