(571 ) 
By this three conies 9,,6,,7, through O, and QO, are determined 
containing in succession the quadruplets of points 
Mahe, bikes Uta. Gant ems 
Fei: Pity ijs Er; 
Fate 1) Maple ey: NE 
On these too the pencils (O,) and (V,) arranged in (2, 2) determine 
involutory (2,2), which then again are connected with fundamentat 
involutions on C,. The pairs of such an involution lie on rays through 
the pole ZS, 7 of O,O, with respect to the corresponding conic 
9, OG, T,. This pole is the point of intersection of two double tangents ; 
this follows amongst others from the fact, that the point of contact 
of each tangent of the C, drawn from F must lie on the conic 9, 
and must be a coincidence of the involutory (2,2); the number of 
these tangents amounts thus to four, so that the remaining tangents 
out of A must coincide two by two in two double tangents. 
For further particulars about the properties which can be deduced 
from these observations | refer to my paper mentioned above and to 
the paper named in it published in “N. Archief voor Wiskunde, XIV.” 
4. We shall now suppose that 0, and 0, are bijlecnodal points. Let 
us choose the point VY, in such a way, that the tangents in ©, and 
in O, are separated harmonically by O,0,,0,0, resp. by O,0,,0,0,, 
then the equation of C, has the form 
Ba, — GET —a,?a,72,7 + b,0,2,0," + 5,2,2,° + b,2,2,° + C°, = 0. 
If O, and QO, are to become biflecnodal points, then we shall every 
time have to find‘when substituting 7, + ar, and z,= + 4,2, 
that z,* —0. For this is necessary 6, = 4,5, = 0 and 6, + a,b, = 0, 
ns), Os aud ba) *). 
So we have to deal with the equation 
DE, — Aw U — wt He, =0. 
If we write for this ° 
(w,* ae ats’) (w,” TER ao.) sie (c* a= a,*a,") a," — 0, 
and if we put moreover 
C= ie ed 
it is evident that C, can be generated by the projective involutions 
of rays 
bh The six points 7189, 8,72, Sila, 482, 472, Mil lie on a conic; for, through 
111g) S1S2, tylg passes the line h. 
2) We find moreover that C, cannot have at the same time a flecnodal point 
and a bifleenodal point. 
