394 



ii = O liave for coordinates y,, — 2y,,?/,,0 and 0,y^, — 2y,,«/,. The 

 polar line of // is therefore represented bj 



jr.. n,, jr., jr.. jr.. jt. 



'«4 



Hence 



This complex has ^V, and C', as cardinal points, <o^ and to, as 

 cardinal planes. 



The complex cone of :c tonches 0^0, at (>,, 0^0, at (>,. Tiie 

 polar line of y lies in the plane 5 if the equation 



5i (2i/, '•'■,— .'/i.V,-i's) f s,y,y,'V, + s,,'/,.'/,^-, + §4(2i/.X— ^,.'^.^•,) = o 

 is satisfied by all values of .r, and .«,. From this follows that the 

 complex rays in § are represented by the points of the cubic which 

 is defined by the cones 



(The ciiord O^O^ does not belong to the image). 



The congruence (2,2) which the complex has in common with 

 the axial complex with directrix ffj. = 0, ^,=0, has for image the 

 quadratic surface the equation of wliich is 



where (rt/t6/) = akbi — dibic- 



