516 
other, without other phases participating in this reaction, conse- 
quently they must have the same composition. 
This is the case when in the quadruplepoint two modifications of 
a same substance occur e.g. red and yellow Hq/, or ice and water- 
vapour or, when e.g. naphtaline and a vapour, which consists of 
naphtaline only, oceur. This is also the case, when a liquid has 
casually the same composition as a hydrate or as a vapour, etc. In 
the concentration-diagram those two singular phases are represented 
by the same point. 
When in a ternary system two indifferent phases occur, then 
the singular equilibrium J/ consists, therefore, of 3 phases. Those 
three singular phases must have, therefore, such a composition that 
one of them can be separated into the other ones; consequently 
in the concentration-diagram those three phases are situated on a 
straight line. 
This is the ease when in the quintuplepoint occur e.g. the phases: 
watervapour + Na,CO, .10H,O+ Na,CO,.7H,9O or: watervapour 
+ Na,SO,.10 H,O + Na,SO, or when a liquid has casually such 
a composition that it may be separated into two other phases, ete. 
When in fig. 1 (VIII) ZZ, and Z, are situated on a straight line, 
then G and £ are the indifferent and 4,Z, and Z, the singular 
phases; when JZ is situated casually on the line GZ, then Z, and 
7, are the indifferent — and Z,, L and G the singular phases. 
When in a quaternary system two indifferent phases occur, then 
the singular equilibrium „MZ consists, therefore, of four phases. Those 
four singular phases must have, therefore, such a composition that 
between them a phase-reaction is possible; consequently they must 
be situated in the concentrationdiagram in a plane. When in 
the figs. 1 (IID, 3 (ID, 5 (III) and 7 (III) eg. C and # are the 
indifferent phases, then A,5,D and / are the singular phases and 
those must be situated in a plane. 
Further we shall see that it is necessary to divide the singular 
equilibria Jf into two groups. When all phases of the equilibrium 
M have a constant composition, then we call J/ “constant singular” ; 
when one or more of those phases have, however, a variable 
composition, then we call M “variable singular”. 
In a quadruple-point with the phases: 
HgI, red + Hgl, yellow + F+ F, 
the equilibrium 
M= Hyl, red + Hgl, yellow 
is therefore, constant singular. In the quintuplepoint : 
