[MILLER & KENRICK] IDENTIFICATION OF BASIC SALTS 37 
The first theorem does not exclude the possibility of the coexist- 
ence of n-+-1 or even n-+2 phases under certain conditions of temperature 
and pressure; but if the experiments be carried out at atmospheric 
pressure in a thermostat set for some temperature below the boiling- 
point of the solution, the chance of meeting with such special conditions 
is negligible. 
These theorems, which were reached by Gibbs in 1876, in the 
course of an abstract thermodynamical study of the conditions of 
equilibrium in heterogeneous systems, have often been verified; their 
importance, however, as furnishing a means—often the only means— 
of discovering the chemical individuals in ill-defined muddy precipi- 
tates, is only now beginning to be generally realized. 
Applied to a particular case, fcr instance the formation of basic 
salts by the action of water on the chloride of antimony or on the nitrate 
of bismuth (temperature and pressure fixed as above), the theorems 
affirm : 
(i) That if the system, which consists of three components (see 
below), has arrived at equilibrium, not more than three phases can 
coexist. Of these the solution forms one, the precipitate consequently 
must be either one single homogeneous substance (one phase), or a 
mixture of two phases—for instance, of two basic salts, or of one basic 
salt with the oxide. | 
(ii) That if the observed difference in composition between two 
precipitates, formed by the action of different quantities of water on 
the same salt, is due to their being mixtures of the same pair of basic 
salts in different proportions, the composition of the mother-liquors 
will be the same in the two cases. 
The possible cases are thus divided into three groups:— 
1. The solutions are identical in composition in different experi- 
ments, while the composition of the precipitate varies.—The 
precipitate is a mixture of two phases. 
2. The solutions differ in composition, but the precipitates have 
the same composition.—The precipitate is a single chemical 
compound. 
3. Both solutions and precipitates vary.—The precipitate is a 
single phase of variable composition, a “solid solution.” 
If it were possible to represent the compositions of the solutions 
by abscissæ, and those of the precipitates by ordinates, the results of a 
series of experiments could be represented by a curve; perpendicular 
lines would then correspond to case 1 above, horizontal lines to case 
2, and slanting lines to case 3. In a three-component system this is in 
general not possible. In many cases, however, a pair or pairs of com- 
