944 Dr. S. A. Shorter : Contribution to the 



From equations (1) and (2) we can readily deduce the 

 equations 



M w„ +M '!5o +M >!& = • • • < 3 > 



dF , T,, BFj dF 2 



: 2 2 P 



Since d 2 3> d 2 <fr 



BMiBM, ~ SMjSM ' 



we have c)F, 3F 2 



SF 2 5F 

 5M„-?)M 2 • 



BF 3F, 



M »w 2 +M 'ts 2 +M w 2 =0 -- • • (5 > 



clM, - BM ( 



(6) 

 (7) 

 (8) 



Now the chemical potentials are homogeneous functions of 

 M , Mi, and M 2 of zero degree, and hence can be written in 

 the form fi{s u s 2 , p, 6)(i=0, 1, 2), where 5 1 = M 1 /M and 

 5 2 = M 2 /M . From the above equations we can readily deduce 

 the equations 





Vi . - y. 



+ s 2 ^=0, (9) 



OSi OS l ^dSi 



^+sM+sM=0, .... (10) 



0«2 0«2 0«2 



d« 2 — b«i 



(11) 



Consider two homogeneous systems, the one containing 

 masses M + 8M , JM^ + SMj, M 8 + SM 8 , and the other masses 

 M -SM , Mx-SMj, M 2 -SM 2 o£ the components O , C l9 and 

 C 2 respectively. Unless the equations 



M - Mi - M 2 K ^> 



are verified, the two systems will differ in composition, and 

 if they are placed in communication with each other, dif- 

 fusion will occur and finally a homogeneous system will 

 result. This irreversible process must result in a diminution 



