( 631 ) 
with @ and 8 we find 
By Py 3 —= Uy Pig — Ve * Pas, 
Yr? Pre = Ya Pas = Ys * Pas 
After substitution, and elimination of 2, we find an equation of 
the form 
Pos (A Pia H As Pas + %s Poa)” =P is (0, Pig + Os Pas + Do Poa) 
by which the exponent between brackets reminds us that we must 
think here of a symbolical raising to a power. 
If in pru= ee y,—#, ye we put the coordinate x, equal to zero, 
we find for the intersection of the cone of the complex of Y on 
the equation 
(Ys Ca — YoU) (4, 2) + a, %, + a, &,)” = (y, U — Yi, Xs) (b, 7, Hb, «4-6, wo)”, 
or shorter 
5 . . je Nm 
NEN bn — Yet, a+ Io (2, ar — a, 7) = 0. 
This proves anew, that the intersections of the cones of the complex 
form a net. 
Mathematics. — “On nets of algebraic plane curves”. By Prof. 
JAN DE VRIES. 
If a net of curves of order m is represented by an equation in 
homogeneous coordinates 
gr az + yy be + ys cr = 0 
to the curve indicated by a system of values y,:y,:7, is conjugated 
the point Y having y,, y,, y, as coordinates and reversely. 
A homogeneous linear relation between the parameters vj then 
indicates a right line as locus of Y, corresponding to a pencil com- 
prised in the net. 
To the Hessian, H, passing through the nodes of the curves belonging 
to the net, a curve (2) corresponds of which the order is easy to 
determine. For, the pencil represented by an arbitrary right line /y 
has 3(n—1)* nodes. So for the order n” of (Y) we find n"=3(n—1)?. 
If one of the curves of a pencil has a node in one of the base- 
points, it is equivalent to two of the 3(n—1)* curves with node 
belonging to the pencil. Then the image /y touches the curve (Y) 
and reversely. 
Let us suppose that the met has 6 fixed points, then H passes 
