1032 
It is apparent from these considerations that symmetry is possible in 
every system, of which the number of curves is equal to or a multiple, 
of 3, 5, 7...(2n +1). In systems, in which the number of curves 
is 4, 8, 16...2" therefore in systems with 2, 6, 14...(2"—2 
components, symmetry is never possible. We see the confirmation 
of this for systems with 2 components in fig. 2 (I), for those with 
6 components in the deduced types of diagrams. 
In connection with the deduction of the types of the P,7-diagram 
discussed above, of course the question arises: the ?, 7-diagram-ty pes 
deduced above, may they all really exist; or in other words: is it 
possible to find for every P,7-diagram-type of a system of 7-com- 
ponents, really „+ 2 phases of such a composition that they lead 
to that P,7-diagram? We can also put in short this question in 
this way: does a definite type of concentration-diagram belong to each 
of the P,7-diagram-types, deduced in the way treated above? We 
may show that this is the case indicating in which way we can 
find with each given P,7-diagramtype a corresponding concentration- 
diagram. 
A, AA For this we take fig. 3; this repre- 
sents a P,7-diagram of n + 2 curves, 
which are divided over different bundles 
(A); (B), (C).... Although in, this 
4 figure all bundles, except (A) and (£) 
are drawn onecurvical, yet we assume 
in our considerations that they are all 
morecurvical. We call the curves of 
bundle (A), going from the left towards 
the right (A,),(A,),(A;)...; those of 
Fig. 3. bundle (4), also going from the left 
towards the right (B,),(B,),...; the same applies to the curves of 
the other bundles. We call the x + 2 phases occurring in the invariant 
point. WAA, A, ANMB BRE ORO Re ete: 
Now we shall deduce the reactions, which may occur between 
those phases. Previously we have seen that they are completely 
defined, when we know two equations of reaction. In order to 
determine these reactions, we start from the reactions which answer 
the position of the curves with respect to curves (A,) and (f,); we 
call those curves the position-curves. [Of course we may choose for 
this every two arbitrary curves]. 
We find from fig. 3 for the reaction of the phases with respect 
to curve (A,): 
