868 
We take a ternary system with the components water and the 
two salts Z and A which are not volatile, in which of the salt Z 
yet also the hydrate Z.n H,O oceurs, which we shall represent 
bY Zradtigl): 
Suppose, the invariant equilibrium 
LA Zi + Lat G 
occurs in the binary system WW + Z at the temperature 77 and 
under the pressure Py. The liquid Lg is represented in fig. 1 by 
the point d between WW and Z,: of course we might as well have 
taken ¢ between Z and Z,. When we add the salt A to this equi- 
librium, then the equilibrium 7+ 74,+ 1+ G arises; the liquid 
L proceeds then a curve dh m (fig. 1). It is evident that 7’ and P 
change along this curve d/m from point to point. 
Now we assume that in the point m the added salt A dissolves 
no more, so that at 75, and under /?,, the invariant equilibrium: 
Z+4,+Ath, + G 
is formed. A similar case is found e.g. in the system: water + 
Na,S0, + NaCl. In the binary system: water + Na,SO, viz. at 
32°.5 the equilibrium 
Na,SO, + Na,SO; .10 HO + LE 4G 
occurs, On addition of NaCl at 17°.9 arises: 
Na, SO, + Na,SO,.10 H,O + Nat L + G. 
As the gas-phase G is represented in fig. 1 by the point I, the 
phases Z, Z, and @ are situated on a straight line. Z, Z, and G 
are, therefore, the singular phases, A and L,, the indifferent phases 
of the equilibrium : 
Lt ZH AH 1, + G. 
Consequently from the invariant point start the singular equilibria: 
(W)=Z7+44+G4 [Curve (J/) in fig. 2| 
(A) =7+2Z4,+ LH G [Curve (A) = md in fig. 2 and md in fig. 1] 
(L)=Z+2Z,+A+G [Curve (L) = mt in fig. 2| 
and further the equilibria: 
(4) = Zn AH LAG [Curve (Z) = rm in fig. 2 and rm in fig. 1] 
(Zn) = 4 + AH LH G [Curve (Z,) = mb in fig. 2 and mb in fig. 1] 
(== Li AH L [Curve (G) in fig. 2] 
Let us first consider the binary system W-+ Z, in which at 
Tj and under Pa the invariant equilibrium 
ZZ, tee 
yecurs. From the invariant point d (fig. 2) start the equilibria: 
