(577) 
(ayx, -{- ast) =") and (be, L been) = i 
a group of rays 
(en, + eg) = 0 
It is now at once evident that this is only possible when the first 
two equations have the following form 
agrar — agter = 0, a" — ara,” = 0, 
so that we have 
ate,” — Agg = 0. 
Out of 
ara” — a,*x,” + 2 (agra — A7”) = 0 
and 
art aa,” Ala — 00) = 0 
follows 
(aan ad) CEE —,"@,") pee (arta a. Par") (a@y".vy"—a,"a,") —0 
or in transparent notation 
(aa), #7," 2" + (aa), v,"2," + (aa),7,"7,"— 90... . . (8) 
The tangents in 0, are represented by 
(aa), vt + (aa)ger ” = 0. 
If wy = ke, is the equation of one of these tangents, then the sub- 
stitution in the equation of the Cy, evidently furnishes ‚2 = 0. In 
each of the n-fold points each tangent has thus (2 + 1) points in 
common with the corresponding branch. 
For each value of 4 we find a figure consisting of 3n lines (of 
which however only 3 or 6 are real, according to » being even or 
odd) and (n? + 3) points (of which 4+ or 7 are real). *) 
1) We have in particular for 73 a configuration (125, 9,). From this ensues, 
by the way, that of the configuration (9,, 125) corresponding dually to it only 3 points 
and 4 lines can be real. From the above itis evident that the 12 lines of the (94, 123) 
can be represented by 
Ei —0, == 0 
Ea ane 0, En O | and Ei =— gk, == ils, where 3 — i! is. 
The three lines & = Eg = &, & = Fo = PE, Fo =e, = ef, contain together the 
9 points. They are also indicated by 
Lj + La + de == 0, Li a EXy + 23 = 0, Li |- "Xo =} eLs = 0. 
The 9 points lying also on 2,27; =0, they are the base-points of the pencil 
(a + ay + Hg) (+ La 7g) (@ + 27g + ed) + M My HqXy = 0. 
And so here we have found back the canonical equation of Cs. 
39 
Proceedings Royal Acad. Amsterdam. Vol. XI. 
