On the Velocity of Reaction before Complete Equilibrium. 51 



(vol. iii. p. 109). On p. 110 of the same volume he dis- 

 tinguishes the different kinds of equilibrium in respect t > 

 stability (having regard to the absolute values of the vari- 

 ations ■ : it is sufficient and necessary 



for stable equilibrium that (A^) e <0. i. e. (Ae),, >0 ; 



for neutral equilibrium that (Ai7) e = 0, i.e. (Ae^^O ; 

 while in general (An) e ^.O, i.e. (Ae)^__0 ; 



for unstable equilibrium that (A?7) e >0, i. e. (Ae),,<0 ; 

 while in general (Arf) e <0, i. e. (Ae), >0. 



A more detailed consideration and proof of the above 

 theorem is given in the same chapter. On page 116 Gribbs 

 gives us "the conditions relating to the equilibrium between 

 the initially existing homogeneous parts of the given mass ** 

 thus : — " Let us first consider the energy of any homogeneous 

 part of the given mass and its variation for any possible 

 variation in the composition and state of this part. (By 

 homogeneous is meant that the part in question is uniform 

 throughout not only in chemical composition but also in 

 physical state.) If we consider the amount and kind of 

 matter in this homogeneous part as fixed, its energy e is a 

 function of its entropy 77 and its volume v, and the differentials 

 .of these quantities are subject to the relation 



d€ = tdr)— pdv, 



t denoting the (absolute) temperature of the mass, and p it* 

 pressure. For tdrj is the heat received, and pdv the work 

 done by the mass during its change of state. But if we 

 consider the matter in the mass as variable, and write 

 nil, m 2 . . . m n for the quantities of the various substances 

 S], S 2 . • . S» of which the mass is composed, e will evidently 

 be a function of 77, r, m x , m 2 . . . w u , and we shall have for the 

 complete value of the differential of e 



d€ = tdr)—pdr + p 1 dm 1 +fj, 2 dm 2 ... +fi n dm n , . (12) 



fi x , fi 2 . . . l*n denoting the differential coefficients of e taken 

 with respect to m u m 2 . . . m n ." Gibbs then passes to hetero- 

 geneous systems (p. 118) :-****• We* will now suppose that the 

 whole mass is divided into parts so that each part is homo- 

 geneous, and consider such variations in the energy of the 

 system as are due to variations in the composition and state 

 of the several parts remaining (at least approximately) homo- 

 geneous, and together occupying the whole space within the 

 envelope. We will at first suppose the case to be such that 

 the component substances are the same for each of the parr-, 

 each of the substances S l5 S 2 . . . S„ being an actual com- 

 ponent of each part (/. e., each of the masses mi, m 2 . . . m„ in 



E2 



