184 



GUGGENHEIM 



ART. E 



Tj of each phase and by taking for granted the condition for 

 thermal equiUbrium (1) [19]. 



With this choice of independent variables the characteristic 

 function is yp defined by 



\p = e — tt]. 



(7) [87] 



Its dependence on the independent variables t, v, mi, nh, . . . m„ 

 is given by 



d\p = —r]dt — pdv + fiidmi + tiidm^ . . . + Undrrin. (8) [88] 



The condition of membrane equilibrium takes the form 



subject to 



dmh + dmh" = 0, 

 dmi + dm/' = 0, 



(9.5) [75] 



Substituting from (8) into (9.1), and using (9.2), (9.3), (9.4) and 

 (9.5), we obtain 



(hh' - Hh")dmH' + (m/ - nHdrrii' + ... - 0. (10) 

 If mh, mi, ... are independently variable it follows that 



lih = fJ'h , 



I // 



/it - V-i , 



(11) [77] 



