‚=P ko: (a’—b’) (a’?—c’), 
I= BK, : Wa?) Oe), 
ANO s\(C*—a;)\(c? be). 
By polarisation with respect to each of the ellipsoids the complex 
is thus transformed in itself. This agrees with a well known property 
of the tetraedal complex. 
7. The footpoints of the normals are then arranged in an involutory 
quadratic correspondence, which transforms a right line into a twisted 
cubie, thus the tetraedal complex into a complex of twisted cubies 
which all pass through the points O, X,, Y,, 7. Let us now regard 
in general the transformation 
Bie! == 07, | yy AEN ooo (15) 
It substitutes for the ray of the complex indicated by (2) the 
twisted curve 
hj a a ; b? B: A Gn 
(c? + u) 2, i 
2 = ———_—_ Ve z 
(EH), ST Ey ’ 
If we still put 
2 2 2 
a Y 
— = 2, EE (16) 
vy 9. sl 
then this curve is indicated by 
Vn 2 n3 
Da a re b Yo. vie eae 
atu b? Hu : ctu 
So it is the curve w? belonging to the “focus” P,, which corre- 
sponds in the transformation to the footpoint P, of the normal. 
The complea of normals is thus transformed into the complea of 
the curves ow’. 
In connection with this the cone of the complex of 7, passes into 
the locus of the curves @’ containing the point /,, thus ($ 3) into 
the cone of the complex of P,. Indeed the equation (7) does not 
change in form if we apply the relations (15) and (16). 
8. If the vertex of the cone of the complex moves along the 
right line / represented by 
he As Pee anal ais Ae dt 
TT eene ; 
U == 
REED TE 
then the cones form a system with index two represented by 
LUO EN 0; 
where 
