Frederick C. Ferrv. 



second and third orders. In a later publication^) this same 

 mathematician considered the geometry on the cubic scrolls 

 in particular, giving a mode of representation of the points 

 on the surface by parameters (entirely similar to the method 

 given by Cayley^) for the points of the quadric surface); 

 any curve on the cubic scroll is then given by a homogeneous 

 equation in three parameters. The equations connecting the 

 singularities of the cones standing on these curves were 

 obtained and the asymptotic curves briefly considered with 

 regard to their directions at the pinch points. An outline 

 of a classification of the curves on the cubic scroll according 

 to the deficiencies of the corresponding plane curves was 

 given by the same author in a note-^) published in 1869. 

 By another method Voss*) in 1874 considered the asymptotic 

 curves on the cubic scroll of the first kind and the ruled 

 quartic surfaces on which these curves lie. 



Noether^), in his monumental treatise on twisted curves, 

 gave a general investigation of the properties of the curves 

 which are the intersections of surfaces and treated in par- 

 ticular the curves on the general cubic surface; but did not 

 consider the special case of the cubic scroll. Halphen ^) about 

 the same time, in his able memoir on the classification of 



^) Ueber die Steinersche Fläche. Kronecker J., LXVn, 1 — 22. 



^) On the curves situate on a surface of the second order. 

 Phil. Mag., 1861, 35—38. 



^) Bemerkung über die Geometrie auf den windschiefen Flächen 

 dritter Ordnung. Klein Ann., I, 634 — 636. 



*) Zur Theorie der windschiefen Flächen. Klein Ann., Vni, 

 54—135. 



^) Zur Grundlegung der Theorie der algebraischen Eaumcurven. 

 Berlin, 1883. 



^) Sur la Classification des Courbes algébriques. J. de l'Ec. Pol., 

 LH, 1882. 



