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of intersection of s with the corresponding ray ¢; on the rays s’ 
conjugate to the m rays ¢ passing through JS’ this point of intersection 
falls in S', so that the locus of the point (s', 7) must pass 1 times 
through S'; the curve is therefore of order (n +1). 
The cone (P) of the complea is of order (n +1) and of class 2n 
and has an n-fold edge PS. 
§ 2. If the point S’ lies on the envelope t, two of the n rays t 
passing through S’ coincide, so also two of the tangent planes through 
2S to the cone (P). 
The locus of the points P for which two tangent planes through 
the n-fold edge of the cone of the complex coincide is the cone = of 
order 2(n—1) projecting the envelope t, out of S. 
The 8(7— 2) cuspidal edges of © contain the points P, for which 
three of the tangent planes of (P) coincide along the n-fold edge. 
The 2 (27 — 2) (n—s) double edges of © form the locus of the points 
P, for which two pairs of tangent planes of P coincide along PS. 
The cone = is a part of the singular surface of the complex; 
the remaining parts are planes. 
To these belongs in the first place the plane o. Each right line of 
o is cut by m rays ¢, can thus be regarded n times as ray of the 
complex. Consequently 6 is an n-fold principal plane. In connection 
with this the cone of the complex of a point P assumed in 6 
degenerates into m planes coinciding with o and into the plane 
through P and the right line ¢ corresponding to the ray s deter- 
mined by P. 
On the contrary r is single principal plane, for each of its right 
lines rests on but one ray s. The cone of the complex of a point P 
lying in r degenerates into t and into the planes through P and 
the m rays s corresponding to the right lines ¢ through P. 
Finally there are still (n +1) principal planes y,,(k=1 ton HD), 
each connecting two homologous rays s,¢. For the points of the 
line of intersection of o and + are arranged by the projective systems 
(s) and [4], in a (1,7) correspondence; in each of the (n-+-1) points 
of coincidence CC} two homologous rays meet. In connection with 
this the cone of the complex of a point P assumed in one of these 
principal planes degenerates into the combination of this principal 
plane with a cone of order #, for of the projective systems (s’) and 
[t|, lying in t two homologous rays coincide. 
§ 3. The curve of the complex (a) in the arbitrary plane a is of 
class (2 + 1) and has the line of intersection (o sr) as n-fold tangent; 
