1677 
Er) KAn + Anm _ mn — 1. Ann (6) 
1 
ar), KAVA AV, mnAN LSV 
by which is defined the direction of curve (Ff) in the invariant 
point. In the same way we find the directions of the other curves. 
Between all reactions in which 7 + 2 phases take part there are 
two special ones, viz. the isovolumetrical and the isentropical 
reaction (conf. communication I). At a reaction between the phases 
in the first the volume remains unchanged, in the second the 
entropy remains unchanged; in this latter case, therefore, heat is 
neither added nor withdrawn. We can easily deduce those reac- 
tions from (2) and (5). In order to find the isovolumetrical reaction 
we subtract the reactions from one another after having multiplied 
(2) by OV, and (5) by AV;; in order to find the isentropical 
reaction we subtract the reactions from one another, after having 
multiplied (2) by Ay, and (5) Ay,. Let us write the isentropical 
reaction : 
a,f, + a,F, +... + ante Fate = 0 AV 0 ee) 
and the isovolumetrical reaction : 
DE, +BB... + bate Fuse = 0 Os Aa (8) 
Hence follows: 
(Aa, +b,) F, + (Ae, +5,)F,+...=0 aAaAV ; Ay. . (9) 
When we give to 4 such a value that 4a, + 6, =0, then (9) 
represents the reaction which may occur between the phases of the 
equilibrium (#,) and the change in volume and entropy belonging 
to this reaction. Hence follows: 
()= i a of (5) ey ae (10) 
aia bs ‘ AAV b AV aan ; AV 
it 
In the same way we find: 
Od Ay b, (dE An t 
==) =) = al — | ZE — et. 
a. Nad}. AV Gg\ alu. AV 
Hence it appears that between the direction-coefficients of the 
tangents to the curve (Ff)... in the invariant point the following 
relations exist: 
b, = b, dk dP\ An A 
atom ere a as 
From (11) follows the direction of each of the curves in the 
invariant point; this is however not yet sufficient to find the P,7- 
C 
dP 5, : 
diagram. When (=) is e.g. positive, then this means that the 
