Molecular Thermodynamics. 609 



We mav write, more briefly, 



^=2n 1 (0 1 -R log Cl ) +n£<t>Jf x ( Cl c 2 ), . (5) 



where every <£>' as well as every <f> is of the form 



(6; 



$ s = (const.) jtu + 1 ^— 



so that 



£*—£. ••••.. (7) 



|^=^ = | ; .... (8) 

 where 



= 2%£i + ^2^/ a: (CiC2 . . . «) (9) 



The formal convenience of this use * of Q will appear 

 clearly below. 

 Now from (5) 



or writing, for convenience, 

 we obtain 



while from (9) 



3 J=*.-Rlog«. + 20x'[F I+ g], . . (ii) 



--:* + M F * + il • • (12) 



+s *'E?- 4 -l3 • • < 13 > 



and from (3) 



We may now consider the general system of any number of 

 components in any number of phases from the " molecular " 

 point of view. 



Any infinitesimal change in the molecular constitution of 

 the system can be represented by %&n la , where 8ni a represents 

 an increment of the number of molecules of the species (1) in 



* Planck writes Q for what will be SQ in this paper. 

 Phil. Mag. S. 6. Vol. 43. No. 255. March 1922. 2 R. 



