366 REPORT — 1886. 



A state of equilibrium will be attained when tlie velocity of reaction is 

 notliing. If then in originally equalled 1, and a quantity x of the body AB has been 

 transformed, the final state will contain 1 — .r, n -x, q + x, p + x, equivalents of the 

 bodies A B, CD, A D, B, respectively. The equation expressing equilibrium 

 will thus be — 



{l-x)(n-x)aB = {p + x){q + x)0y (2) 



or, if p and q are zero, a case often realised in practice — 



(l-.r)(M-.r)aS = .r-^y (2a) 



Now introduce the following definition : — . . . Two electrolytes like A B 

 and CD, vvhich have no common ion, are to be called conjugate; and two like 

 A B and AD, or A B and B, are to be called opposite. Equation (2) expresses 

 the fact that an equilibrium occurs between the system of two conjugates, AB and 

 CD, and the system of their two opposites, AD and CB, which are conjugate to 

 each other. From that system is formed this system, and vice versa ; wherefore 

 equilibrium occurs, because the number of circular currents in which both systems 

 are engaged is the same in the two cases. This is precisely the signification of 

 equation (2). This equation immediately shows that, 



(23) As soon as the relative quantities of the ions, A B C D, are given, the 

 final result is independent of their original form of combination, 

 whether A B and CD, or A D and C B, or any other form. 



This proposition is sufficiently natural to need no proof. Moreover, it has been 

 verified by the work of MINI. Guldberg and Waage and Ostwald. 

 Solving equation (2) we get 



^_ abin + \ )+^y{ q +p) / U a8(n+ 1) + ^y {q + p)\^ aB .n- 0y .q p\ 



^" 2{l3y-ad) - V IV 2(/3y-a8) J jSy-ad ) ^ ^ 



or for the special case when q and p are zero — 



aHn^-l) . , /f/ a8(« + l) y a^ . n ] 

 2(/3y-aS)- V tV2(/3y-aS)/ /3y-aSJ * " ' ^ ■' 



.V = — 



The sign of the radical is always the same as that of /3y — aS. 

 If it should happen that /3y = aS the above solution foils, but, returning to (2), 

 we see that in this case — 



.. = _Jirii^. _ (3b) 



q+p+n+l 



so X is always unambiguously known. 

 Differentiating equation (2), we get- 



dn 



d{a8) _d(0y)_ dq _ dp 



n-x a d /3y g + x p + x 

 ^•^• = 1 ^ 1 ^ 1 ^ 1 W 



q + x p + x 1 — .r M - X 



If, now, a, fi, y, 8, are the coefficients of activity of four bodies, AB, AD, 

 CB, CD, and if the product, aS, for two conjugate bodies is much greater than 

 that, j3y, for the two opposite bodies, one finds realised a case of very great im- 

 portance — namely, the equilibrium of four bodies, acid, base, salt, and water. 

 According to equation (2), if the original quantities mixed, of acid, base, and 

 water, are 1, n, and p equivalents, there are formed x equivalents of salt and of 

 water, where — 



(^ + .t)x = °-(l-,r) (n-.r) (5) 



