608 RICE ART. L 



considered, we are regarding the energy as expressible in the 

 same functional form of the altered values of the variables, and 

 this implies that such other states are states of equilibrium. 

 In consequence, this method limits us to the consideration of 

 the stability of the initial state with reference to the neighboring 

 equilibrium states, but not with regard to all neighboring states, 

 among which may be non-equilibrium states. In the purely 

 dynamical problem, all states of the system, equihbrium or not, 

 have their potential energy expressible in terms of the coordi- 

 nates; but in the thermodynamical problem all the states of 

 the system cannot have their energy expressed in terms of the 

 variables. Indeed certain values of the variables inconsistent 

 with equilibrium may "fail to determine with precision any 

 state of the system." The question of instability would of 

 course offer no difficulty in this case. If near the equilibrium 

 state in question there exist one or more other equilibrium states 

 which under the usual conditions possess less energy, the origi- 

 nal state is certainly unstable; that requires no consideration of 

 non-equilibrium states. However, although there may exist 

 neighboring states of equilibrium which might prove, on investi- 

 gation by the method outlined, to be states of greater energy, 

 we cannot be so definite about the original state being one of 

 stable equilibrium; for the method does not preclude the pos- 

 sibility of the existence of non-equilibrium states of smaller 

 energy. Having drawn the reader's attention to this matter, 

 which we shall take up later, we proceed to a commentary on 

 the subsection. 



40. Stability of a Plane Portion of a Dividing Surface Which 



Does Not Move 



At the outset Gibbs deals with the problem of stability with 

 the limitation that the dividing surface film is plane and uniform 

 and is not supposed to move. He directs attention to the 

 possibility of a small change taking place in the variables which 

 specify a small portion of the fihn, and which are a small group 

 of the entire collection of variables specifying the whole system. 

 Denote the small part of the film by Ds; its variables are the 

 temperature t, its entropy Dt]^', and the masses of the com- 



