423 



From this relation it ensues that y = p -\- q. 



Consequently the image of n^ if a curve a"+i^ + '/ iqA'', Bi'+'/, inG). 



The combination with the image of /? produces a control; from 

 which it appears that the curves a and h have promptly n {q — J) 

 points in common, apart from the principal points, 



10. If we write in the results arrived at, ?i = l, ^ = 3, p^i, 

 we obtain the representation of tlie cubic surface to which we 

 referred in ^ 1. The directrices of the linear congruence (1,3) are 

 then a twisted curve «' of fP" and one of the bisecants of a* lying 

 on <P\ 



Tlie image of a plane y'' is then a cWSA*, 7i^). If the six bisecants 

 mentioned above are indicated by bk, and if b^ is the directrix of 

 tlie (1,3), the five straight lines Cik are represented by points. 



The image of «' is a curve a' (3/1, B\ 56') the image of b^ a 

 curve // (3^', ^', 5C) ; these curves have, as they ought to have, 

 two more points in common, which are the images of the points of 

 support of the bisecant b^. 



It is easy to determine from these data the images of the remaining 

 21 straight lines of *P\ 



