( 314 ) 



thus 



^'-, («, il y) ^ <h, r - ^d,, ai^r + d,, «' ^' = 0. 

 The curve ^V' repre.seiitiii;j; tliis relalioii hus evidently nodes in 

 A and B. 



By connecting jV ' with M' i\n{\ D' we lind anew jLir = 6 and 

 farther 



tSv — 27. 

 The pairs of lines of the congruence form a skew surtace of 

 degree 27. 



(S. To lijid the characteristic numbers containing the symbol q 

 we considei- the pairs of points which the conies of the congruence 

 have in common with the i)lane z = i. They are indicated by 



fy.r -f- ay II — «,:? + y% 

 So for tiie conies touchiu'»' ~ ^ 1 



a,^ - r 



h\ {a. ,1 y) = 0, 



which is represented by a cur\e /»*" having .1 and JJ for nodes. 

 By combining /^ and //, J/'"' and \' wv tind successively 



do r= 84, H() 1= 8, I'Q := 22. 



From this ejisues thai the skew surface of the pairs of lines has 

 a double curve of degree 17 and that the conies touching a given 

 plane (in i)articular thus the parabolae of the congruence) form a 

 surface of degree 22. 



Out of the relations 



3r' =: rfr + ^l^v and 8o' =r 2öq -\- '2(iq 

 we finally tind for the missing characteristic numbers 



v' = n and q' — 28. 

 So the conies cuttinu" a tixed riulit line form a surface of order 17. 



