1031 
7. Septenary systems [seven components, nine curves|. It is 
evident that we may now distinguish four principal types, viz. a 
partition over 9, 7, 5, or 3 bundles. We find the following seventeen 
types of diagrams. 
ges ak ene 
DEE aig en Mie TR, oie, a a Deeg een Ye 
Len to ee ge Ee 
Sa a An Re ee ey EN OS eo ae 
er ee Br eh a oh fk Bh TD ak ep One 
Meee ee Pa de 8, Oa So tee ing tS a, 
Consequently we find one diagram with 9, four diagrams with 7, 
five with 5 and seven with 3 bundles. 
It is evident that we may find in the same way as above also 
the types of P,7-diagrams for systems with more than seven com- 
ponents. After the previous deductions it is quite unnecessary to 
further discuss this matter. 
Now we shall still briefly discuss the occurrence of symmetry in 
the P,7-diagrams. We call a diagram a symmetrical one, when all 
bundles contain an equal number of curves. Consequently we may 
distinguish different cases of symmetry, viz. with onecurvical, two- 
curvical, threeeurvical bundles, ete. 
Symmetry with onecurvical bundles is only possible as the num- 
ber of bundles is always an odd one, when the P, 7-diagram contains 
an odd number of curves. Consequently it can occur only in systems 
with an odd number of components, therefore in systems with one 
component [fig. 1 (D], with three components |fig. 2 (II)|, with five 
components [fig. 1 a], with seven components [the diagram 
1+1+1+4+1+1+1++41), etc. 
As the number of bundles is always an odd one, (27 + 1) and 
three at least, symmetry with twocurvical bundles is only possible 
when the P,7-diagram contains an even number of curves (47 + 2), 
six at least. Consequently it can occur only in systems with 4n 
components, therefore in systems with + components (fig. 2 (HI), 
in systems with 8 components, etc. 
As the number of bundles is 2n + 1, symmetry with threecurvical 
bundles is only possible in diagrams of systems with 3 (2n +1) — 
2=6n-+1 components. In a system with seven components the 
diagram is, therefore: B, + B, + B, 
