( 492 ) 
(ry)? + Aal = 0 
are determined by 
- en 
or by dy a = 0. 
In connection with this consideration the covariant of Hesse 
(a b)? az Be 
furnishes two lines forming the threefold elements of a cubic invo- 
lution of which a? = 0 is a group. 
T 
The lines of HESSE are orthogonal, when the invariant (ab)? a, 
is equal to zero. 
The lines a, a?=0 are orthogonal when the covariant aaa, dis- 
appears, i. e. when we have 
Yr: Ya = aq da: — Aj Ga 
By substitution into by 22=0 we find that the pair of rays 
in question is indicated by 
(ab) aq 0? = 0. 
The lines of Hesse are the double elements of the involution 
(a b)? az by = 0. 
If yj:ya is replaced by ez cc: — ej ce, it is evident that the covariant 
(a 6)? (bc) ce az 
determines the ray conjugate in this involution to the ray aa a, = 0. 
Evidently the orthogonal pair of rays of this involution is 
indicated by 
(ab)? az (6 2) = 0. 
