352 SCIENCE PROGRESS 



that the seven conies arising thus from seven hnes have three 

 common points. 



A. Kieier (Vteriel jakrsschrift Zurich, 67, 1922, 15-19) deals 

 with the problem of finding a plane such that the orthogonal 

 projection on to it of a given tetrahedron shall be a triangle 

 and its orthocentre. 



H. J. van Veen (Proc. Amst. Acad., 35, 1922, 52-60, 61-6) 

 examines the axes of the quadrics of revolution which pass 

 through 4, 5, 6, or 7 given points. If 4 points are given the 

 axes form a complex of order 3 ; if 5, a congruence of order 

 7 and class 2 ; if 6, a ruled surface of order 6 ; if 7, there are 

 4 quadrics of revolution. 



G. Corte {Rend. Lincei, 64, 1921, 459-62) gives an algebraic 

 interpretation of the principle of duality applied to formulse of 

 incidence. 



L. Berzolari {Rend. Lincei, 31, (i), 1922, 421-5, 446-50) 

 investigates the complex of the fourth degree, all of whose 

 cones have three generators which are both double and 

 inflexional. It originally arose from the consideration of 

 twisted cubics which are invariant for a certain group of collinea- 

 tions, or more simply from three linear complexes which are in 

 involution two by two. 



P. Tortorici {Rend. Napoli, 28, 1922, 51-4) proves analytic- 

 ally a theorem given by Segre, that if a rectilinear congruence 

 with ruled focal surfaces establishes a correspondence between 

 the asymptotic curves of one focal surface and the generators 

 of the other, the first focal surface must be a quadric. 



In 1908 Re3^e showed that the congruence of twisted cubics 

 through 5 points can be represented by the rays of a sheaf ; 

 J. de Vries {Proc. Amst. Acad., 35, 1922, 22-6) examines 

 another congruence of cubics which by a cubic transformation 

 can be represented by the rays of a bilinear congruence ; it 

 consists of the cubics through two fixed points having three 

 fixed chords, and has already been dealt with in another way 

 by Stuyvaert (1902). 



The projective differential geometry of plane curves was 

 founded by Halphen and developed by Wilczynski ; G. Sannia 

 {Rend. Lincei, 31, (i), 1922, 450-4) develops the theory more 

 simply by means of the absolute differential calculus with one 

 variable ; he keeps a complete analogy with the metrical 

 theory by defining projective arc, curvature and normal. 



M. J. Conran {Proc. L.M.S., 21, 1922, 191-213) investigates 

 the differential geometry of twisted curves in elliptic space ; 

 he obtains analogues of the Frenet-Serret formulae in the form 

 of eighteen equations between the line co-ordinates of the 

 tangent, principal normal and binormal, and their derivatives 

 with respect to the arc ; he defines two curves which corre- 



