1129 
21 —k (7—k)—4k(EK—1) or 4 (T—A (6—/DM. 
These straight lines are bitangents of the curve (pl, 
The following table contains for the null system Ns 2 the number 
of singular null points, the number of singular null rays s Ear 
an /, of null points) and the number of singular null rays s* (con- 
taining an J, of null points). 
k Ss Cs 
DER re 0 
1 15 6 
2 10 10 
3 6 12 
4 3 Iz 
5 | 10 
6 0 6 
i 0 
The curve (P)!-& has an (8—A)-fold point in P, consequently 
lies on 2(9—4%) of its tangents ¢ The base tangents, therefore, 
envelop a curve of class 2 (9—A). 
The curve (P)®, belonging to N33, has in each of the / singular 
points S a point of inflection, with stationary tangents PS ($ 6). 
§ 8. The net [c°] distinguishes itself from a general net [ec] in 
this, that in the latter no figures appear composed of a straight line 
and a ct, In connection with this the null system NM3 3,2), which 
is determined by the points of inflection, has in general no singular 
rays. 
If the point / is made to describe the straight line p, its null 
rays 2 envelop a curve of class 3 (n—l1). The curves belonging 
to p and q have besides the three null rays of the point pg, more- 
over (97? —18-+- 6) tangents in common; they are here the null 
rays 7, which have one null point in p and another in g. Their 
number is therefore at the same time the order of the curve a 
described by the null points of the straight lines 7, of which a null 
point lies in p. 
The intersections of aw with p form three groups. In the first 
place each of the 3(m—2) null points of p is a (3 —-7)-fold point 
of a, A second group consists of the intersections of p with the 
