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when A’ is made to move along a right line @ drawn through B. 
From this ensues in connection with the preceding : 
The locus of the vertices of cones of complea possessing a nodal 
edge is a cone A of order n (38n—1) having A as verter and 
passing twice through each edge Ab. 
§ 3. If P moves along the plane @ then the cone of the complex 
(P) consists of the plane @ and a cone of order n cut by @ along 
the right lines ACh. So a is a principal plane and at the same time 
part of the singular surface. 
The plane @ belongs to this too. For, if P lies in 8 then the rays 
connecting P with the points of the ray a corresponding to the 
curve $" drawn through P belong to the complex. All the remaining 
rays of the complex through P lie in 8. So 8 is an n-fold principal 
plane and the singular surface consists of a simple plane, an n-fold 
plane and a cone A of order n(3n — 1). 
The complex possesses (77 + n + 2) single principal points, namely 
the point A, the n? points Bj and the (n +1) points Ct 
$ 4. The nodes of curves c’ belonging to a net lie as is known 
on a curve Hf of order 3 (p— 1) the Hessian of the net, passing 
twice through each base-point of the net. This property can be 
demonstrated in the following way. 
We assume arbitrarily a right line /anda point M. The er touching 
lin L, cuts ML in (p— 1) points Q more. As the curves passing 
through J/ form a pencil, so that 2(p— l) of them touch /, the 
locus of Q passes 2(p— 1) times through M; so it is of order 
3(p—1). Through each of its points of intersection S with / one 
ce passes having with each of the right lines 7 and MS two points 
in common coinciding in S; so S is a node of this cp. 
Consequently the locus of the nodes is a curve of order 3 (p — 1). 
If / passes through a base point B of the net then the pencil 
determined by J cuts in on / an involution of order (p — 1). This 
furnishing 2 (p — 2) coincidences L, the locus of Q is now of order 
(Bp — 5) only. So B represents for each right line drawn through 
that point two points of intersection with the locus of the nodes, 
consequently it is a node of that curve. 
If / touches in B, the curve c,? having a node in B, and if one 
chooses J/ arbitrarily on this curve, then the curves of the pencil 
determined by M have in B, a fixed tangent and 2, is one of the 
coincidences of the involution of order (p — 1). The locus of the 
nodes has now in B, three coinciding points in common with /; 
consequently it has in 5, the same tangents as c‚!. 
