(20) 
common with &;. Moreover any given right line through P deter- 
mining only one conic Q of 4/3, the planes of the conics Q on 
1J; must form a pencil; the planes of the above mentioned degen- 
erated conic Qy pass through p, so p is the axis of the pencil. 
The remaining ten right lines of Z/; are evidently unisecants of 73. 
8. The axis p determined by P cannot belong to a second sur- 
face J/;, for the five trisecants resting on p determine together 
with p the bisecants intersecting each other in P. 
If P lies on R,, p is quite undeterminate. 
The point P being taken on a trisecant t, through that point two 
bisecants pass forming with ¢ conics Qs; the axis p coincides with 
t, which follows as a matter of course from this, that 17; becomes 
the surface ./; belonging to ¢. 
9. If P describes the right line a, the locus of the axis p is 
a cubic scroll A3, of which a, is the linear director. For if P' 
and P" are the points common to a and Q,, then this conic lies 
on the surface 17; and J/;' belonging to P’ and P"; so its plane 
contains the corresponding axes p' and p”. 
To Az evidently belong the five trisecants resting on aj; in the 
points common to A; and these trisecants PR; is cut by A3. They 
moreover meet the double director ag of As. 
These trisecants lie at the same time on the scroll As’ having ag 
as linear director; on this surface a, is the double director. 
The right lines a, and ag correspond mutually to one another. 
If a, is itself an axis, each plane through this right line contains 
only one axis p differing from a,. In that case the surface A3 be- 
comes a scroll of CAYLEY and a, coincides with a. 
In the correspondence (a), az) each axis is consequently assigned 
to itself. This also relates to all trisecants, as each of these must 
be regarded as an axis of each of its points. 
10. The five trisecants cut by a, and by ag also lie on the 
surface 1’, determined by @,; so this contains the right line az as well. 
Therefore both axes p' and p’ lying with a, in a plane @ cut 
each other in the point 9 common to a, and the conic Q, deter- 
mined by a. 
From the mutual correspondence between a, and ag we conclude 
that I, also contains all the conics Q,, the planes of which pass 
through az. Five bisecants belonging to Z's rest on ag. 
If according to a well known annotation we call the five tri- 
