THERMODYNAMIC AL SYSTEM OF GIBBS 103 



Sh, Si, etc., which can pass through the diaphragm, is constant, 

 i.e., 



dmh' + 87nh" = 0, dm/ + 6m /' = 0, etc., (86) [75] 



but the quantities of those components, Sa,Sb, etc., which cannot 

 pass through the diaphragm must be constant in each fluid, 

 i.e., 



8ma' = 0, 8ma" = 0, dnib' = 0, 8mb" = 0, etc., (87) [74] 



and the volume of the fluid mass on each side of the diaphragm 

 must be constant, i.e., 



8v' = 0, bv" = 0. (88) [73] 



The general condition of equilibrium (64), which takes the form 



t'bt]' — p'bv' + Ha'dMa + Hhbrrih . . - + Hh'bmi,' + Hi'dnii . . . 



+t"8v" - p"8v" + ^a"8ma" + fJLb"8mb" . . . 



+ fjiH"8mH" + tii"8mi" ... ^0, 



will now give the following particular conditions: 



(1) t' = t", (89) [76] 



(2) m;/ = m;.", m/ = Mi", etc., (90) [77] 



if Sh, Si, etc., are actual components of both fluids; but it is 

 not necessary that 



V' = V", (91) 



or 



tia' = Ma", Mb' = Mb", etc. (92) 



Thus the values of the potentials of components which are 

 present on both sides of the diaphragm and which can pass 

 through it must be equal, but it is not necessary that the pres- 

 sures, or the values of the potentials of those substances to 

 which the diaphragm is impermeable, shall be the same in the 

 two fluids. 



