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3. Tlie null points of tlie planes passing tlirougli the point P, lie 

 on a surface (P)^ For P is the null point of one definite plane of 

 the sheaf and on a straight line / through P there lie the null 

 points of three planes through /. 



The intersection of the surface {Py and {QY consists of the curve 

 /' corresponding to PQ, the straight lines a and b, and a curve 0' 

 which is the locus of the singular points S and which passes evi- 

 dently through the 5 base points Cj. 



Three surfaces {0)\ {Py and (Qy have in the first place the 

 curve (}' in common. The points which they have further in common, 

 are apparently the points of intersection of (0)" with the curve ^' 

 corresponding to PQ. To them there belong the 12 points S on A' 

 and the 2x3 points A and B on A'; the remaining two are the 

 null points of the plane OPQ. 



4. Any plane « through a is singular ; it contains a plane pencil (^) 

 and each ray t cuts the conic 0' (§ 1) in two null points. Analog- 

 ously the planes (i through b are singular. 



Also the ten planes a each containing three base points 6', are 

 singular. For in <t,,, there lies a pencil of conies of which each 

 individual is combined with the straight line C^ C^ to a curve (>' ; 

 they cut the straight line t in öj,, in an involution of null points. 



The surface (P)" contains the conies «' and fJ' lying in the planes 

 Pa and Pb, and tlie intersection p of these planes. The straight line 

 p is singular in this respect that it is a null ray for each of its 

 points. The singular null rays p form the bilinear congruence with 

 the director lines a and b. 



Also the ten straight lines Ck Ci are singular; for through each 

 point on such a straight line rjd there passes one straight line t, 

 while rki may be considered as a tangent. 



9* 



