( 575 ). 
As it is touched in O, and Q; by the lines 
Yots 4 y;t, =O and voer, — a,7y,2¢, = 9; 
we find that 
Vita — U YY TD — A YY Tg + c*y, wv,” = 0 
represents a conic 13 touching the polar curve in O, and Qs. 
If (y) lies on C,, then 
HY — GY Ys) TAN Ya Heys = 0, 
i. e. (y) also belongs to #,. The tangent (y) to 1, has as equation 
Vai eo Y2%,) x (az Q Has Yi YsUs—Ys (0 Yot Has yow) +207 y,*a, = 0. 
As when (z) and (4) are exchanged it determines the polar curve 
1, it represents at the same time the tangent in (4) to C,. 
In each of its points C, ts touched by a conic which touches the 
polar curve of that point in the biflecnodal points. 
The curves C, and 4, have two more points in common. If / is 
their connecting line, then the pencil determined by C, and 4, + / 
contains a curve composed of 4, and a second conic. From this 
ensues: Zhe points of contact of the sin tangents out of a point of C, 
can be connected by a conic. 
8. The projective involutions of rays (O,) and (O,) have as 
double rays 
N= Ds, Be OF 
Ho. Ten 
Pean 0. 
B= 0; a = 0, 
and eae! 
Mt Oe eet Oe 
When the double rays 0,0, and 0,0, are conjugated to each 
other, their point of intersection becomes a third double point of C,. 
This takes place when we have 
Seca seats 
— + —=0, or = 0. 
a, 
£ 
The C, is then represented by 
Gt. BE dd = 0. 
So it has three bifleenodal points. As is evident from the above 
we can describe in this C, oo quadrangles having the three double 
points as diagonal points. 
The double tangents of the first group are now replaced by the 
tangents in VO, (§ 4). In each of the bifleenodal points the tangents 
are harmonically separated by the lines to the remaining two 
double points. 
The C, with three bifleenodal points have been extensively treated 
by Lagurrrn (Nour. Ann. 2° série XVII, 1878) and by Scuoure (Archiv 
der Math. und Phys. 2° Reihe, H, Il, IV, VI, 1885— 87). 
