MATHEMATICS 353 



G. T. Bennett {Proc. Lond. Math. Soc, 20, 1921, 59) discusses 

 the three-bar sextic curve. 



H. Hilton {Proc. Lond. Math. Soc, 20, 1921, 93) writes on a 

 plane curve of order n having a multiple point of order n—i, 

 and a conic of 2M-point contact ; and also on some special 

 types of quintic and sextic curves {Rend. Palermo, 44, 1920, 



340- 



By means of the quadratic transformation F. D. Murnaghan 



{Amer. Math. Monthly, 28, 1921, 203) investigates a certain cubic 



twisted cubic curve which is associated with the tetrahedron 



in much the same way as the Kriepert hyperbola is with the 



triangle. 



Two tetrahedra are said to be conjugate if the faces of one 

 are the polar planes of the vertices of the other with regard 

 to a quadric ; when this is so, four faces of one meet four faces 

 of the other in four lines belonging to the same system of 

 generators of a quadric, whence the German description 

 " hyperboloide." Two tetrahedra which are conjugate in 

 four ways are fundamental for the quartic surfaces studied by 

 Schur (see Jessop, Quartic Surfaces, p. 193). A. Baruch {Rend. 

 Palermo, 44, 1920, 261) investigates such tetrahedra, showing 

 that from the first pair two other tetrahedra may be constructed 

 so that each of the four is conjugate to any other in four ways. 



A, Emch {Amer. Math. Monthly, 28, 1921, 46) gives an 

 account of a method for the construction and modelling of 

 algebraic surfaces by considering them as generated from two 

 projective pencils ; in particular he applies the method to a 

 quintic surface with a nodal quartic curve and to a cubic cyclide. 



An equation ^aik, Xix\ =0{i, k = i,2,2,4) gives a correla- 

 tion between two spaces ; the classification of such correlations 

 is, of course, a generalisation of the classification of quadrics ; 

 it is undertaken by K. Kommerell {Math. Zs., 10, 1921, 217). 



The property that if two triangles are inscribed in a conic 

 their sides touch a second conic and there is a third conic to 

 which they are both self-polar may be generalised to a property 

 of two tetrahedra and a twisted cubic (Hurwitz) and in fact to 

 a property of two {n + i) -gons inscribed in a curve of order n 

 in space of n dimensions. H. S. White {Trans. Amer. Math. 

 Soc, 22, 1921 , 80) gives a proof of the general theorem, depend- 

 ing on a special (2,2) correspondence. 



Hurwitz in 1887 showed the existence of " singular " corre- 

 spondences on an algebraic curve (sufficiently specialised), which 

 need two equations to express them. V. Snyder and F. R. 

 Sharpe {Trans. Amer. Math. Soc, 22, 1921, 31) give examples of 

 such correspondences between two curves, obtained by ruled 

 surfaces through the curves. 



C. Rosati {Rend. Palermo, 44, 1920, 307) also considers 



