\ iba Ie 
Consequently (15) passes into: 
Ela a, Jee. Hap) =P (appa +... ante). . « (16) 
in which a > 3. 
As neither @, nor 8, nor the reaction-coefficients may be = 0, 
(11) and (12) can, therefore not be satisfied. 
When we give another value to g, then we come to the same 
conclusion. Hence it follows, therefore, that the occurrence of two 
groups is not possible. As further we may easily prove that three 
and more groups may occur indeed, we may consequently conclude : 
“each series consists of three or more groups”. 
Now we take in (1) for a,a,... the series: 
AlB |B |S |e | 7 | D 2 an 
tr ges ENE nt pases, | —— a ate | Po naa 
This series consists of four positive groups, which are indicated 
by A, B, C, and D and of three negative groups, which are indi- 
cated by FR, S and 7’; for the sake of clearness these groups are 
separated from one another by vertical lines. Going from the left 
to the right, we number in each group the curves: 1, 2,..., con- 
sequently A,A,..., B,B,... 
When we deduce from (1) and (2) with the aid of (4) the n+ 2 
reaction equations, then we find the series : 
Oes Fr, allt. 
oe ae aed ee ee 
a iyi ae he ee EE 
and at last: 
ed eel 0 
These series represent the signs of the coefficients of the reactions, 
which may occur each time between 7 -+ 1 phases; they indicate, 
however also which curves are situated at the one and at the other 
side of the curve, which is represented by O; the curves with the 
positive sign are situated viz. at the one side, those with the nega- 
tive sign at the other side of the curve 0. 
Now we find easily that the P,7’ diagramtype can be represented 
by fig. 3(V) and that with each group of signs in (17) a bundle 
in the P,7' diagrain corresponds, which contains just as many curves 
as the group contains signs. We shall refer to this later. 
We have assumed in series (17) an odd number of groups, when 
we add another negative one, then arises the series : 
+ aa | 
A gl ee EN be KONE tE) 
En Ranges 
