474 
the directrix d; consequently Bj is a double principal point of the 
complex }7'}’. 
The plane pencil which is the image of a ray in §,,,, bas one 
ray in the axial complex; hence the complex {¢'}’ contains the ten 
fields |Biim|. It contains also the ten bilinear congruences with the 
directrices 641, P'mnr- 
Of the scroll (£)* representing a ray ¢,, four rays rest on d; the 
complex {£}’ contains therefore the field {t,|, which has to be 
counted four times. 
The quadratic cone associated to a singular ray s (§ 5), has two 
generatrices in common with the axial complex; hence the con- 
gruence (5,8) of the rays s belongs twice to {7'}’. 
