(317 ) 



"characterized by the particularity that each of the two points 

 "7/1 , L^ counted four times represents a quadruple of it. The oscu- 

 "lating spaces belonging to the points of any quadruple intersect in 

 ''a point A of LiL^. And if this quadruple describes /^ , the point 

 "^ generates on Li L^ a series of points in projective correspondence 

 "with li." 



Moreover we easily find ') : 



"If J[ and A' are two points of the line L-^L^ harmonically sepa- 

 " rated by Lj and Z-g, the quadruple of /^ belonging to A has the 

 "combination of ij and ig with the quadruple of Jj, belonging to 

 "^1' for its sextic covariant T. And combination of the quadruples 

 "belonging to yl and ^' generates an involution of the eighth order." 



The indicated h is represented by the equation 



so it is characterized by the particularity that each of the two points 

 L^ and L^ counted eight times represents an octuple of it. 



4. We now pass to the space 5" and there we determine the 

 locus of the planes having three points Zj L^ L^ in common with 

 the normal curve Q, 



A» 



of that space.. This is obtained by eliminating the six quantities 

 Aj, Aj, Ag, pi, p2i Pi between the seven relations 



'■t = Pi h'' + P2 h^ + ;^3 ^-3^ 



(5) 



where k must take the values 0, 1, . . . 5, G. In quite the ?ame way 

 as above we find here the curved si)ace >^^■' with five dimensions of 

 the fourth order represented by 



— 0. 



In fact, the form T of .r/ ± xJ is x^ x^ (.t'l* =F «2*). 



