( 494 ) 
Consequently the invariant 
8 (ab)? (ac)? (be)? + 6 (ab)* 2 — 3a? be 8 
disappears when the four lines af =0 contain two pairs at right 
angles. 
11. Ternary forms can be represented by cones the top of which 
is situated in the origin of three axes of coordinates perpendicular 
to one another. 
Here too it is evident that by a rotation of the axes of coordi- 
nates the symbolical coefficients a of the form 
at = (ay aj + ag 12 + ag a3)” 
undergo the same substitution as the coordinates. 
So the comitants 
at oe tah, MH tof + A3 I3s 
(rn Ya — 291)? + (#2 ¥3 — 43 Yo)? + (a3 41 — A Y3)"s 
| Tj Lg H | 
el Ya Y3 
| 21 22 23 | 
furnish the invariant symbols 
das ty (ar ba)? + (ag bg)? + (a3 bj) 
and 
(abc) © 
For quadratic cones we immediately find the orthogonal invariants 
dg = 4)] 4+ Ag + las 4 B (ay; dzg — a2) and (abe)? = = = 41 433 A323 « 
