( 16 ) 

 or 



O/l//.— //.//.)' == -lO/i.'/a— //,') (//^//i— //.')• 



that is the rcric.i' of the cimi plc.rconc hcloiuis to tlir siii-focc of tdixjcnts. 

 If wc piil r'i = O, \v(' llipii arrive aftoi' o.\clii(liii,ü' //,=() and 

 il^^O (for wliicli the iiidieated de<j,eiierati(m always takes place) 

 at the (hml)h' coiiditioii 



that is at Ihe puiiils of ir. 



S. Lel lis suppose that the taiiiïeiits of Ii^ are an'aiiji:ed in the 

 triplets of a J'. To determine the (k^gree of the complex of the eoMimon 

 transversals <»f the |)airs of tangents we can also set alxmt as fol- 

 lows. In an ai'hitrarv pencil we consider the coi'respondeiice of two 

 rays ,v and s' , which are cnt by two tangents helojiging to J\ 

 To the coincidences of this correspondence (H, 8) hehuig the fonr 

 ravs resting on the donhle rays (iJ>,L\d of ./•' ; the others are nnited 

 in pairs to six rays, each resting on two tangents of a tri[)let, .svW/i/r 

 coiDftlex is of (/('(/ire (i. 



To find the degree of the congrnence of the right lines, each resting 

 on the three tangents of a gi"on|), let ns considiM- the i-ays they have 

 in common with tlic^ analogous c(tngrnence Itelonging to a second ./■\ 

 If I'l, r., is one of the toiii- common pairs of \\\c two involntions, 

 and /•., and // successively the tangent foi-ming with i\ and r. a 

 group, the ccnnmon transversals oi' j\, r.^, r.^ and r./ helojig to the two 

 congruences '). Evidently they can lia\e no other rays in commoji 

 than those eight, which are indicated by these; consecpiently the con- 

 gruence is of ordei- two. 



The com|)lexcone of an arbitrary point /' has as ain)ears from 

 the above, firo tliirefold e(i(/('s\ as it has to be rational, it has 

 moreo\ei" fo/rr doiihlc ('(((ji's. 



If P lies on the snrface of tangents of IT, this cone degenerates 

 into the system of jilanes which connect I* with the two tangents 

 conjugate to /y and a biquadratic cone with threefold edge. 



9. The (piadratic sci-oUs determined l»y the tri[)lets of tangents, 

 evidently form a system of surfaces two of which pass through any 

 point and two of which touch any ])lane. This system is thus 

 represented in point- or tangential coordinates by an equation of the 

 form 



-) This consideration leads to no result if we consider a rational skew curve 

 of higher order. 



