1687 
ua F, Hua, +... pal + npeanpeFne=—=0 0; An (22) 
We take a, and w‚a, positive and we assume that the order of 
succession of the phases is chosen in such a way that the condition 
hy Ue > ea Bt OT inte Oe aw EN) 
is satisfied. 
Now it appears from our previous considerations that we know 
the P,T-diagram completely, viz. the directions of the curves in the 
invariant point, ete, when we know, besides the reactions (21) and 
(22) also the changes of volume and entropy 4V and Aj occurring 
with those reactions. 
The isentropical reaction (21) alone is not sufficient to find the 
P,T-diagram, it is indeed sufficient, however, for defining the P,7- 
diagramtype; this follows viz. at once from the series of signs of 
this reaction. It is apparent from our previous considerations, that, 
when the last group of this series of signs is negative, we have 
to consider it as forming with the first a single group only. In 
the series of signs (19) the phases of A and 7’ form, therefore, one 
single group only, which consists of the sub-groups A and 7. 
It is apparent from the following that the series of signs of the 
isentropical reaction, defines the P,7-diagramtype. Above we have 
found viz.. that the number of bundles of curves is equal to the 
number of groups of signs and that each bundle contains as many 
curves as the group of signs contains phases. Further it was apparent 
that the bundles in the P,7-diagram and the groups in the series 
of signs have the same order of succession, if only we take in the 
series of signs, going from left to right, first the positive — and 
afterwards the negative groups. [In the series of signs (19) this 
order of succession is, therefore A+ 7. B, C, R and S, which is 
in accordance with the figs. 1, 2 and 3}. 
The series, which indicates the signs of AP has always either 
the same or the opposite signs of the series of signs of the isen- 
tropical reaction. Hence it follows that all curves, that have the 
same signs in the isentropical series of signs, also go in the same 
direction of pressure. In series of signs (19) the phases of groups 
B, C and the sub-group A have all the same sign; the corresponding 
curves must go, therefore, all in the same direction of pressure, 
starting from the invariant point; in figs. 1 and 2 they go towards 
lower pressures, in fig. 3 towards higher pressures. The same is 
true for the curves of groups A, S and the sub-group 7. It is 
apparent from all this that the series of signs of the isentropical 
reaction (21) defines still somewhat more than only the type of 
