1025 
Hence it is apparent that S’ and 7” must be situated at the same 
side of R’ as P’; consequently A’ must be situated as is indicated 
in (9). In order to find still the position of S’ and 7” with respect 
to one another, we eliminate S from (7) and (8); we find: 
SQ Piies 18 Pee TE i KAT) 
consequently : 
OPTS ek” enke eee Mou gay’ (ita) 
Hence it is apparent that SS’ must be situated between R’ and 7”, 
so that the diagram is defined. When we eliminate 7’ from (7) and 
(8), we find: 
EON TSP nk Ves te os (12) 
consequently : 
GERRON Gane «Mele <n) ee Cla) 
which is in accordance with the position of the curves in the diagram. 
Consequently we find: when the relations (7) and (8) exist between 
the five phases, then we obtain a ?,7-diagram, which can be repre- 
sented symbolically by (9). The curves form three bundles, viz. one 
threecurvical bundle (7”S’R’) and two onecurvical bundles, viz. the 
curves P’ and Q’. Consequently the diagram belongs to type HI 
(fig. 6(I})]; therefore, the five phases form the anglepoints of a 
biconcave quintangle. 
Now we take as example a system of five components, so that 
we can represent no more the position of the phases with respect 
to one another, unless in a space of four dimensions. When we 
know however the compositions of the seven phases P, Q, R, S, 
T, U, and V, which occur in a septuplepoint, then the reactions, 
which can occur in the 7 monovariant systems are known. When 
we assume that the reaction between the phases of the equilibrium 
PARIS 
Q+2R+3S=T+U+44V ... . (13) 
and the reaction between the phases of the equilibrium Q’: 
2P+RAT=S+2U4+V... . (Ad) 
We find for the reaction between the phases of the equilibrium 
R’ by elimination of R from (13) and (14): 
Q+58+38U=4P437T+4+2V... . (45) 
It follows for the reaction of the equilibrium S’ that: 
Q+6P+5R+27T=7TU+7V... . (16) 
for the reaction of the equilibrium 7” that: 
Q+2P+3kR+28S=3U+5V ... . (47) 
for the reaction of the equilibrium U’ that: 
er) 
ep) 
Proceedings Royal Acad. Amsterdam. Vol. XVIII. 
