SURFACES OF DISCONTINUITY 609 



ponents in it DrUa^', Drrib^', . . . Dnig^', Dnih^', ■ . ■ The change 

 does not in the first instance involve an alteration in t, nor in 

 the position or size of Ds; but Drria^' is changed to Dma^", etc., 

 and Dri^' to Dri^"; in short, the single accent indicates the initial 

 state, the double accent the state after change. Of course the 

 changes of mass in this small portion of the film must be drawn 

 from (or passed into) the remaining portion of the system, i.e. , 

 the rest of the film and the homogeneous masses. Similarly 

 as the total entropy must remain constant the rest of the 

 system must experience a change of entropy equal to Drj^'—Drj^". 

 The homogeneous masses are assumed to be relatively so great 

 that these small changes in them do not practically affect 

 the values of the potentials Ha, f^b, ... of the components a, h, 

 . . . which are both in the volume phases and the surface phase, so 

 that no accenting is required in writing them. A similar remark 

 applies to the large remaining portion of the film. However, 

 as regards the g, h, . . . components which only occur at the 

 surface, the value of the potentials will alter in Ds from /Xg', 

 Hh, ... to Hg", fjLh", . . . , but for the rest of the film they will 

 remain at their original values fig', nh, . . . for the reason already 

 specified, viz., that the changes of masses and entropy in this 

 part of the film are relatively too insignificant to effect a change 

 in the potentials. It is very important to keep in mind the fact 

 that it is assumed that there are components in the surface 

 which are not in the homogeneous masses; otherwise the discus- 

 sion of this particular special case would be pointless. The new 

 condition of the portion Ds of the film is supposed to be one 

 which is still consistent with equilibrium between it and the 

 neighboring homogeneous masses. (This of course places the 

 limitation mentioned above on the generality of the investiga- 

 tion. It will be quite definite in its answer concerning instabil- 

 ity, but leaves a possibility of failure to lead to a definite conclu- 

 sion concerning stability.) In consequence, the energy of the 

 small portion, Ds, of the film will be De^", where D^" is the same 

 function of the variables t, D-q^", Dnia^", etc., and Ds, that 

 Z)es' is of t, Drjs', DiUa^', etc., and Ds. The energy of Ds is 

 therefore increased by Dt^" — D^'. The energy of the rest 

 of the system is increased by an amount which is equal to 



