636 RICE 



ART, L 



The geometry of the figure is not so simple now, and we cannot 

 make a direct calculation of W as on page 261. The device 

 which Gibbs uses is stated with such conciseness in the sentences 

 toward the bottom of page 263 that the implications involved 

 in them had better be more fully expounded. If the state 

 indicated did form in a natural way, it would happen in some 

 such fashion as this. Beginning at an initial stage of tem- 

 perature and potentials to, mio, M20, . . . for which 



. (TBcito, Mo) PA(to, /Xo) + (TAcito, JUq) Vsito, Mo) 



Pc{to, Mo) = — ^ > 



we would gradually alter the temperature and potentials in 

 such a way as to make pc(t, n) grow larger than the value of 

 the corresponding expression on the right-hand side when (t, fj.) 

 is substituted for (^0, Mo). Notice that this would probably 

 involve a gradual change in the curvature of that portion of the 

 surface not embraced by the lens of C, as pA(t, m) — Pait, m) and 

 (TAsit, m) would probably change in value as t, mi, M2, • • • change 

 in value. The process would end up in the condition and size 

 indicated in the figure. Now to judge if this would happen 

 naturally we need not consider so complicated a change. We 

 have only to conceive any reversible process in which the system 

 begins as imagined with the lens of C formed, and ends up in a 

 final state in which A and B are separated by a surface having 

 the same curvature, but with no lens there. That is, in the final 

 state the temperature and potentials would be the same as they 

 are at the end of the process which is supposed to have formed 

 the lens originally. This is the process conceived by Gibbs, 

 and what we have to do is to determine the sign of the energy 

 change in this conceived process. During it the pressure in A 

 and in B, as well as the surface tension between A and B, will 

 remain at one set of values ; i.e. , Pa, Pb, (Tab will be constant during 

 the process. We are also to conceive that between A and C and 

 between B and C are membranes which gradually contract, keep- 

 ing at constant tensions which are equal to the values of 

 (Tac and aBc in the initial state of this process, i.e., when the lens 

 of C exists in its fully formed state. These membranes are not 



