( 15 ) 



So these quadratic skew sin-nices of Avhicli the first evidently 

 passes tlii-diiirli A'" coiilaiii tlic xcrliccs (tC tlic coiiiiih'.ictinis harimi 

 a cnsi)ld(il (nhje. 



^>. V{n' llic |)(»iiils /* of Ihc A'^ litis cour of course «Ic^^cucralcs 

 iulo the piauo (•oiiuccliuii' /' wiili ilic lau^cul />' iu liic coujiil:;iIc 

 jtoiiil P' aiul a (|ua(lralic coue loiu-liiii,ii- llial piano. 



For points on llie ri|nht lines / and /// the coniplexconc niusi con- 

 sist of a plane counled doulile and llic >iu,ulc plane ./■,=:l) or./'=:(). 

 For, each ray in a and ,>' helonus lo tlie conijtlex, whilst all ri;:hl 

 lines restin^»- on / and m are double rays of the complex. Indeed ihe 

 sid)stitulion v/j = 0, //,=:() in the e(piation of the complex ^^ives 

 the relation .i\ (//„ ■i\— i/i .''.,)■' := 0.. 



For |)oints on one of the lan^ents ft and Atlie complexcone ltreai<s 

 lip into the j)lane « or /? ajid ijito a (juadratic c(»ne touchinn- ii. 



For a point of the intersection of a and ^i we find a de.ireneralion 

 into three planes. 



For the complexcurves analogous consid(M-ations hold n(„,(I ; <.. o. i|„. 

 complexciirve de<^enei-ates into tiiree pencils of rays when the plant» 

 passes through AB. 



7. The complexcoiie degenerates into a [»1ane and a (piadralic 

 cone if the vei-tex lies in « or in ii or on the surface of the tanucjits 

 of A'\ In the former case a or ,? helon^i^ to it; in the latter tiie plane 

 throu,ii;li the vertex P and the conjugate tangejit />'. 



To investigate whether there ai-e more points foi- which such a 

 degeneration takes place, we su[>[»ose that the eipiation of ihe inlei- 

 section of the complexcoiie with .i\ = 0, thus that 



is dedncible to the form 



Then the following conditions are to he salislied: 



^'22'".-.+2A.,,f,=:3//i//,, A3,fi+2/^j3c-, — —2!i^y^, ^'.i. '•-.+-''' •..'•.■,= —'^V, .'/.;. 



Let us in the lirsi place put A,,=:3U and r, = y.,, then 2/y,, is 

 equal to — //, and 'Ih^^ eipial lo //.,. Further we (ind //„=:—//, amJ 

 c'j =1 — ij^. xlfter some deduction we get as only condition 



