128 



6. If we consider N' as tlie null-point of i\ there arises a null- 

 sijstem with tiie characteristii' numbers n =z \ , /J=:3, y^4 (^5). 



If »' continues to pass tiirongh a point P, the locus of N con- 

 sists of a surface [Pf and the four pencils of rays round the points 

 Ck in the planes Ckb (^ 2). 



if r revolves round the straight line /, r describes a curve X' and 

 the four singular rays through Ck which rest on /. 



The surfaces (Pf and {Qy have in common the curve X' corre- 

 sponding to PQ, and the 18 singular straigth lines 64 6^/ and Ck Bi. 



With a q' [Pf has in common the 3 points of which the planes 

 of osculation pass through P; the remaining 12 common points lie 

 in the cardinal points C; these are ihei'efore triple points of (P)'. 

 The planes of osculation in Ck envelop accordingly a cone of the 

 third class. 



