( 665 ) 



Consequcnth/ the scroll of the trnnsversnh of quadniplet^ of tin 

 involution is of order — (/) — 1) {p — 2) {p — 3) (4 n — 9). 



Each ])i'ineipal point and each principal plane of r bears 



1 



- (p — 2)(2> — 3) right lines of this scroll. 



6. If p" possesses also a single directrix e all principal planes of 

 r pass through e and the complex is in itself dual. 



1 



If p" has a nodal curve rf of order - {n — 2) (?z — 1) each gene- 

 ratrix / i-ests in {n — 2) points on 6, and is thus cut by {n — 2) 

 right lines /'. By this the generatrices are arranged in a symmetric 

 correspondence of order (n — 2), having with 1,, given on q" in 

 common (n — 2) [p — 1) points H. So the complex has again 

 (71 — 2 j {p — 1) principal points and as many principal planes. 



In like manner the order of P remains the same. But now the 

 curve of the complex can break up on account of its plane contain- 

 ing two or three principal points by which two or three pencils 

 are separated. Besides « can contain still a right line /. So here 

 the degenerations of («) are dually opposed to those of the cone (^). 



(February 21, 1906). 



