1466 
By elimination of 2, 4’, 2" we find from this 
a | azcrey | + B | beeaey | = 0, a lagere | + 3 | bjeze | = 0; 
for brevity each determinant of the form a, c',c", is represented by 
its first column. Elimination of @, 8 produces now the relation 
|agcaty| |byeze, | == lagere) | | bxexey| epoca oe (0) 
from which it ensues that the bisecants of the curves o° form a 
cubic line complex, to be indicated by I”. The point C is evidently 
principal point of T°, the planes of the six conics 9° are principal 
planes. 
As a straight line passing through C' is bisecant of two curves 
o°, the complex cones of T* are rational; the edge passing through 
C' is the double line of the cone. 
The quartic cone formed by the tangents out of C at ®° is evi- 
dently the locus of the vertices of the complex cones with a cusp- 
idal edge. 
For a point P of ®* the complex cone degenerates into the quadratic 
cone, which projects the curve g° laid through P out of that point, 
and a plane pencil, formed by the bisecants, which the remaining 
curves send through P. 
If P lies on a singular bisecant fr, the plane pencil consists of 
chords of the conic 9°, whereas ft is common bisecant for the 
remaining curves. 
For a point of 9%, the complex cone consists of three plane pencils. 
§ 5. From (5) it ensues that the plane 7 of the pencil formed 
by the bisecants which the curves 9* send through the point P (not 
situated on an /;), contains the point C, which was to be expected. 
This plane may be called the null-plane of P; its intersection with 
DP? will be indicated by 2°. 
The complex curve in MZ consists of the pencil with vertex Pand 
the twice to be counted pencil with vertex C, for any ray passing 
through C meets 2* moreover in two points which belong to 
two different curves 9’. 
Let w* be the intersection of #* with the arbitrary plane W. By 
the curves 9° the points of w’ are arranged in the triplets of an 
involution /*, which has the complex curve of I” as curve of 
involution. This involution is generated by the intersection of three 
projective pencils of quadries, which have as equations 
a (axc'x—a'gcx) + B (bxc'z—b'zez) = 0, ete. . … . : (7) 
Every two pencils produce a figure of order four, composed of 
the surface ®* and one of the planes c, c', c’. The base of each 
