486 Proceedings of Royal Society of Edinburgh. [sess. 
It is known, however, that in the simpler case of equilibrium 
between the undissociated portions of a strong acid or of a salt and 
its ions, the law of mass action in its original form is not valid ; no 
dissociation constant is obtained, according to Ostwald’s well-known 
“ dilution law,” which is simply the law of mass action applied to 
the equilibrium in question. As the equilibrium, the nature of 
which it is here sought to determine, is that existing between a 
strong acid, its neutral and its acid salt, it was therefore improbable 
that it would follow as a consequence of this law, and a brief in- 
spection of the figures calculated from the experimental results 
justified this conclusion. In order to represent the equilibrium 
between the ions and the undissociated portion of a highly dis- 
sociated electrolyte, empirical formulae have been proposed, as 
modifications of Ostwald’s expression, by Rudolphi (Zeit. johysik. 
Chem., xvii. 385), van’t Hoff (i ibid ., xviii. 301), and others. In 
the same manner, the expression for the equilibrium under con- 
sideration may be made more general and quite empirical if we 
write it thus : — 
{dH^l-aJfx {aM 2 S0 4 (l-a 2 )}" = K.aMHS0 4 .(l -a 3 ) 
where m and n are unknown exponents. The expression given 
above is a particular case of this more general equation, where m 
and n are the same and equal to 0‘ 5. 
In what follows, an experimental method is described by means 
of which the concentrations of the acid, neutral sulphate and acid 
sulphate were determined, while the values of (1 - cq) (1 - a 2 ) and 
(l-a 3 ) were calculated from Kohlrauch’s measurements of the 
electrical conductivity of acids and salt solutions. ( Wied . Ann., 
1885, xxvi. 196.) It was then possible, by comparison of the 
results obtained for the various solutions, to find the values of the 
exponents m and n, as well as the mean value of the constant K. 
The expression was then completely determined. Its accuracy was 
tested by using it to calculate the percentage of free acid in the 
various solutions, the values so obtained being then compared with 
those actually observed. 
