(313) 



Tf a Q' of the net is to be loiiched by the conjugate piano .t, then 



/?y «y — rqi — y^ | 



mnst lie satisfied. 



We lind here a reUilion 



D. (rf, i?, y) = 0, 

 ^\•hi('il is lioniog'eneons and of degree 7 in ((, (■?, y. If we regard 

 these parameters as honiogeneous coordinates, this relation represents 

 a cnrve of degree 7 possessing Jiodes in the points'./ ((? = (), y ^O^i 

 and B (« = 0, y =: 0). 



6. For the conies passing tliroiigli point '''(■''i, //i, -i) ^vo have 

 the relation 



^'A («> t^> y) = ''-1 ?Y + Hi «y — ~i «(-^ — y' = '>• 



It is represented l)v a conic passing throngh A and />. 



Besides ^-i and 7i the anxiliar curves I)' and J/'^ ha\-c ten points 

 in common. So throngh 7' pass the planes of ten conies each degene- 

 rated into two right lines {on = 10). 



That the points ^1 and 7> mnst not he taken into consideration is 

 shown as follows : For a = 0, y =: we find 1> = and // = : 0, 

 thus the pencil of planes around OX; of these tangent planes of 

 course oidy one is conjngate to B = () and the conic determined 

 by it does not form a pair of lines generally. 



(.)ut of the relation ^) 



S^av = 2ïjfi -[" ^H' 4" "^f*' 

 ensnes, as fti? = 6, dft = 10 and (i^ = 2, 



till = 0. 



This could be foreseen, for the cones of \Q'^] form a system gc'; 

 the uuml)er of tliose cones touched by the homologous [danes -t 

 is thus finite and all twofold symbols in which i/ ap[)ears have there- 

 fore the \alue zero. 



7. The right lijie ./' = 0, // = is cut by the conies for which 

 we have 



«,:fc + y-^=:U ami ,/,, -^ + 2r/,, r + J,^ -. 0, 



1) Compare my coiumuuicaliuii in liiese Froceedings, p. :2Gi. 



21* 



