Bulletin of the Calcutta Mathematical Society March 1941

We now state and prove that the necessary and sufficient condition that the conics determined by the sets of points it and uf - should intersect in a point nn the cubic is that the sixth point of intersection 'with the cubic of either conic be a point of inflexion ; when the condition is satisfied then the other conic also passes through the same point of inflexion and the relation between the [...] For the two double points are the projections of P and P which are the points in which the line PdP meets that quadric of the pencil which passes through P. Similarly the pairs of points in which the join of the double points of 7/ meets the pairs of bitangents of if from V'1 Vf2 Vf„ and Vi4 also belong to the stated involution. [...] Let V and VG be the united elements of the involution determined by the pairs of points in which the line P Pi meets the quadrics of the pencil fixed by r. Then evidently V' and Vi„ of the previous article are the projections of 175 and Vc. [...] PROJECTION OF THE GENERATORS OF A QUADRIC 29 Then the conics in which the plane V2V V4 meets the quadrics of the pencil belong to the pencil of conics determined by the points X4. [...] (d) If 7 degenerates into two conics meeting in K1 and K2 then all the quadrics of the pencil have the same tangent planes at K1 and K.. In this ease also there are only two cones belonging to the pencil of quadrics their vertices P1 and 2 being the united elements of the involution fixed by the pairs of points in which the quadrics of the pencil are met by the line of intersection of the commo