Frederick C. Ferry. 



II. The Cubic Scroll of the First Kiud. 



The equation of the cubic scroll of the first kind in 

 homogeneous coordinates is 



x^s — y^z = 0. 



Let this surface (or its equation, as the case may demand) be 

 designated by 2. The double director is given by x = 0, 

 y = 0; the linear director by z = 0,s = 0; any generator 

 by y = XX , s = z-z ; all generators intersect both directors, 

 joining the points of a system on the linear director to the 

 points of a homographie system in involution on the double 

 director. The tvs^o pinch points are given by 



x=:0,y = 0,z=:0 and x = 0,y = 0,s = 0. 



Any plane through z = , s = meets 2 in a pair of 

 generators and touches the surface in the two points where 

 these generators meet the linear director; the two geuerators 

 cut out by the plane z = coincide, as do the two generators 

 cut out by the plane s;=0 also; thus the planes z = and 

 s = respectively are tangent to 2 all along these pairs of 

 generators; i. e., the two pinch point generators in each case 

 coincide, while from all other points on the double director 

 the two generators are distinct. 



