610 RICE ART. L 



t8r]' 4- tia'^rria + Hh'^rrih . . . + ixg'hvfhg' + lihhmh + . • . 



where 677', 5ma', etc., are the increases of entropy and of the 

 masses of the various components in the rest of the system. 

 But we have seen that these increases are Dtf' — Drj^", 

 Dma^' — Dnia^", etc. Hence the increase in the energy of the 

 rest of the system is 



tiDri^' - Dr,s") + tiJ{Dm.^' - Drua^") . . . 



+ tio'il^m/ - Dm/') + . . . (24) 



The increase in energy of the whole system is therefore 

 D^" - D^' + tiDri^' - Dr}S") + fiaiDma^' - Dnia^") . . . 

 + IX,' {Dm/ - Dm/') + ... 



where we have dropped as unnecessary the accents over Mo, 

 Hb, . . . , the potentials which do not alter between the first and 

 second state. Now by [502] applied to the small portion of the 

 film, which it will be remembered is in an equilibrium condition 

 in both states 



De^' = t D/ + 0-' Z)s + yiaDma^' ... + fx/ Dm,^' + . . . , 

 De^" = t D/' + (t"Ds + tioDm/' ... + iiJ'Dm/' + . . . , 



where a' and a" are the values of the surface tension in the small 

 portion in the two states. Hence we easily see that the increase 

 in energy of the whole system is equal to 



ia" - <j')Ds + (m/' - n,')Dm/' + (m." - HK')Dm/' + . . . (25) 



This is the expression which occurs just a little below the middle 

 of page 241, stated for a small portion of the film Ds. If this 

 is a positive quantity for all changes, infinitesimal or finite, the 

 system is stable. To discuss instability we must consider two 

 different cases. The expression (25) may be negative even 

 when Dwo*', . . . Dmg^', . . . differ by infinitesimal amounts 

 from Dma^", . . . Dmg^" , . . . and therefore nj, tih, . . . o-' differ 

 by infinitesimal amounts from Hg", nh", . . . <r". If this be so, 



