e. H. SISAM — ON ALGEBRAIC HYPERCONICAL, ETC. 481 



si ha successivamente 



^dP = ^'dp-V'dpl^''dP^[^ 



dp) ' 



Sostituendo nella (e), poi nella (b) e tenendo conto della (a) 

 si ha la formula (1). 



È poi chiaro che dalla (1) si ricava il limite del rapporto 

 di due elementi di area in Xqp e Xv^, nei punti Pqp, Pvp. 

 Torino, Febbraio 1911. 



On Algebpaic Hyperconical Connexes in Space of r Dimensions, 



By C. H. SISAM (Urbana, III., U. S. A.). 



1. The term " algehraic hyperconical connex in space of r 

 dimensions „ will be used in this paper to denote the entity de- 

 termined by the pairs of points in S^ whose coordinates satisfy 

 an equation 



m n 



(1) F{xo ...X,; «/o . . . y,) = , 



where F{xy) is a polynomial, homogeneous of degree m in 

 the coordinates of the point (x) and homogeneous of degree n 

 in the coordinates of the point («/), and satisfying the condition 

 that, if the point (x) is fixed, F{ì/q . . .y^) ='^ is the equation 

 of an hypercone with vertex at (x). 



In ^3, this entity has been studied by Masoni (*). Ft will be 

 shown (Section 2) that , if m >• n , F{xy) = determines the 



(*} Masom, * Rendie. dell' Accad. delle Scienze di Napoli „, voi. XXll 

 (1883), pp. 145-164. — See also the recension of Segre in " Jahrbuch der 

 Fortschr. d. Mathem. ,, Bd. 16, p. 724. 



