401 
The simplest way to state this rule is in my opinion as follows. 
The region that does not possess metastable prolongations of three- 
phase lines in the P,T-projection is that of coevistences of phases of 
consecutive concentration. 
Perhaps the clearest way to set forth the meaning will be by 
means of fig. 2. 
If we produce the four stable three-phase lines through the 
quadruple point, as has been done in fig. 2, it appears that no 
metastable prolongations occur in the region between S + L, + L, 
and L,+L,+G. The region in question indicates the coexistence 
of S+L,, L,+h, and L,+G. These coexistences refer every 
time to two phases consecutive in concentration, i. e. if the four 
phases are arranged according to their z-values, the succession is 
SL,L,G. That this is really the case in fig. 2, is clear since it 
dp \ . ok a. 
has been assumed there that (2) is positive, that by L, the liquids 
a), 
were denoted which lie on the lefthand of the longitudinal plait, and 
that the first component appears as solid substance. 
8. To prove the rule in question we will indicate the phases 
arranged according to their «-values in the quadruple point, by 1, 
2, 3, and 4, so disregarding altogether what state of agregation 
the phases possess. The four three-phase lines 1 +243, 14244, 
143844 and 23844 divide the space round the quadruple 
point in the P,7-projection into four parts, which every time indi- 
cate pressures and temperatures of two-phase regions. We know 
besides that every three-phase line forms the boundary of three 
two-phase regions, and so that on one side of the three-phase line 
one, on the other side two regions occur, where every time a com- 
bination of two of the three phases are in equilibrium. In the first 
place it is now clear that none of the two-phase regions can have 
an angle at the quadruple point which is greater than 180°. If this 
were so we should be able to produce one of the bounding three- 
phase lines through the quadruple point. This metastable prolonga- 
tion would then lie in the region where two of the three phases 
could coexist in a stable way; then, by the side of these two the 
third could also occur stable on the three-phase line, which is 
evidently impossible, because the prolongation represents metastable 
states. 
Every quadruple point which contains a two-phase region with 
an angle that is larger than 180° is therefore impossible. If we take 
this into account, the thesis in question can be simply derived. For 
this purpose we first take the coexistence of the phases with the 
