**Proposition 4.2**: *If S is the complement of a line l in then C(V,S) admits only linear flocks.*

*Pf*: Let F be a flock of the cone C(V,S). Let be a plane in F, other than (if it is in F). The projection of S from V into is the complement of the line* l'*, which is the intersection of with the plane determined by V and *l*. Any other plane of F must meet in this line *l'*, thus F is a linear flock.