We investigate in this paper a certain special family of quadric varieties, that is of in [R]. Now among the more important properties of a quadric in [R] is that it possesses a system or systems of “ generators,” i.e., the quadric may be taken as the locus of certain families of subspaces, the behaviour of these depending on the parity of R. If R is even, a quadric V2n–1 in [2n] contains a single family of [n—l]'s, so it seems likely that in discussing special families of quadrics in [2n] an important type will be obtained by constraining the quadric to pass through a number of [n — l]'s.