517 
NaCl + Na,SO, + Na,SO,.10 H,O + solution + vapour 
the equilibrium : 
M — Na,SO, + Na,SO,.10 H,O + vapour 
is also constant singular. 
In a quadruplepoint 
Keer ii he 
in which Z is a liquid, which has casually the same composition 
as the solid phase (or a vapour) H, the equilibrium: 
Mee 
is variable singular. In the quintuplepoint: 
pT a Se an i a Oa a 
the equilibrium : 
M=Z,+L24+G 
is variable singular, when we imagine in fig. 1 (VIII) the liquid ZL 
in the point d. 
It is evident that between the two species of singularity a great 
difference exists. By a fit choice of the components we may obtain 
easily constant singular equilibria; the occurrence of variable singular 
equilibria is however very casual. As those species have also 
different properties, we shall discuss them separately. 
17. The occurrence of two indifferent phases; the equilibrium M 
ts constant singular. 
The two indifferent phases /, and #4 may either have in (1) 
the same sign or not. When they have in (1) the same sign, then 
they have it also in (5); when they have in (Ll) opposite signs, then 
this is also the case in (5). This is, however, also the case in each 
other reaction-equation. When we deduce from (1) and (5) another 
reaction-equation by multiplying the first one by # and the second 
one by /, then the coefficients of the indifferent phases /’, and F441 
become : 
(A+ dua, and (& + lwa, 1. 
Hence it appears, therefore: when in a reaction-equation the in- 
different phases have the same or the opposite sign, then they have 
it also in all other reaction-equations. [They have it, therefore, also 
in the isentropical and isovolumetrical reactions]. 
So, in order to decide whether the indifferent phases have the 
same sign, or not, it is only necessary to know, therefore, one single 
reaction. 
When we imagine in fig. 1 (VIII) Z, in tbe point of intersection 
of the lines GZ, and Z,Z,, then G and Z are the indifferent phases. 
