(, 509 ) 



of llio ^ '' OIK' Linos Jo [toiiit I*", wliilsl \\\v second coiilains a |)air 



ol' llie /'..,; Ix^sidos llic poiiils 7 ", 7"" coiijiipilc lo 7", so llial 7" 

 a|i))oars in hut one uroii]) of llic ('orrcspoiKlciicc (7". 7'"). So ihc 



dii-rcliiiu' conic <ƒ.,, is al llic same time tlic dircclimi' cui'N'c for the 



t'nndameidal in\'oiulion /''.,. composed of linear triplets 7", 7'", 7"". 



The taii,uents oni ol' a po'nt /'' of the ( '■' to </., will coincide onh' 

 in the cast' that I*" is situated on the lanu'ent in P' to ( '■' . h'l'oni 



this follows that <ƒ.-,; touches the cnrxc ('■' in {ix^^ points; it is easA' 

 to see that these points are the coincidences of the cori'espondciu'e 

 (2, 8) in wliicli a ponit /"* coi-responds to a |>oint 7'. besides tlic 



tangents in these poiids to he counted donhle ^ '■' and r/., jiave six 

 tangents moi-e in common, which are determined hy the coiiicidences 



of 7''.,. and 7%,.,. 



.']. The cuhic curves connecting three triplets of the F.. with 

 the six points />/. detei'mine a [)encil of cnr\es determining the 



groups of this in\"olution. X pair of the 7'",^. consisting of the jxtints 

 //., 7J'., the cuhic [)encil (^'') Aviil contain a curv(^ havijig in 1).^ 

 a node ; hut from this follows that the remaining cur\es must touch 



each other in 7>-, so also in 1),,. 'J'he tri|)let of the /%,.,, of which 

 the hearer /,. passes through />,, determines in the pencil (^'•') a 



degenerated curve consisting of /,. and the conic /i.,.,,., through the 

 points />^/,. (/• = J , 2, 3, 4, 5). A secoiid degenerated curve consists 

 of the conic /■i2S4(! J^ikI '^ ^"^y ^:. through /J.. From this ensues that 

 tlie Jiinth l)ase-[)oint of (^'■') lies iji the point of intei'section of /. and 



^„ wdiilst /'loajs is tonched in />>. hy ^. and /•i234fi in /J,. l)y ^,, ; it 

 goes without saying that in />. and />,. all curves of (C'') have the 

 lines t. and /, as tangents. 



4. We consider the two fundamental involutions l\^ and 7%,., 



hesides the in\'olulions /,„ and /•-„ determined hy lliem and we 

 inquire after the meaning of the common tanuents of the directing 



conies y^,^ and <^5„. 



The in\olutions 7\,,5 and F-^^ have besides the pair of points D\, 



