[MILLER & KENRICK] IDENTIFICATION OF BASIC SALTS 39 
The precipitates produced by the action of water on the nitrate of 
Bismuth are all of the general formula Bi,0,, mN,O,, nH,0; the com- 
position of the solutions also may be expressed in terms of the same 
substances, Bi,0,, N,0,, and H,0, which are henceforward termed the 
“components” of the System. The compositions of the precipitates and 
solutions might be expressed in terms of other groups of three, — 
elements, compounds, or mixtures—but three at least are necessary, and 
more than three are superfluous; if for example the elements Bi, N, H, 
and O, be selected, and the quantities of three of them in the solution 
be known, that of the fourth can be calculated from the stôchiometric 
relations. 
The condition sine qua non for the application of the Phase Rule 
is that equilibrium be reached with respect to all reactions that occur 
in the system. There is only one sure sign of the attainment of equi- 
librium, namely, that the compositions of precipitates and solution 
are found to be independent of the order in which the components were 
mixed,—the composition of the precipitate must be the same whether 
Bi(NO,), be mixed with water, or Bi,0, with dilute nitric acid, provided 
only that the same quantities of the three components be employed in 
each case. In other words, the quantities of the three components 
(together with the temperature and the pressure) are sufficient to 
define the state of the system. 
Now, it can be shown by a simple MED cel argument: that if 
A, B, C, and D, be any four phases whatever, formed from the same 
three components, it is possible either 
(1) to mix three of these, e.g., A, B, and C, in such proportions 
that the components are present in the mixture in the same propor- 
tions as they are in D, or 
(ii) to prepare a mixture of A and B, and another of C and D in 
such proportions that the quantities of the three components are the 
same in both mixtures. 
In other words, it is possible with these four phases to build up two 
systems identical with respect to the amounts of each of the three com- 
ponents, but differing in the nature and composition of the phases 
composing them, and the condition that the state of the system should 
be completely defined by the amounts of the components (and tempera- 
ture and pressure) can be fulfilled only if one of these alternative 
systems changes spontaneously into the other ; that is, if reactions 
between the phases 
A+B+C0=D AD Der) 
1 Van der Waals, quoted by Roozeboom, Rec. Trav. Chim. Pays-Bas 6 
265. (1887.) 



