( 596 ) 
So in connection with (7) we find by elimination of the quantities 
= zr the relations 
18 tm = 3 (ap + %)—8t — 2t, 
18 jm=6 yp +8244 oe eT 
6 2m = 3 ep — ty 
proving what was asserted. 
However the two point-fields (P) and (JZ) are not in perspective. 
For on the line of intersection of the planes a and « not a single 
point corresponds to itself. For the conditions *p= @m yp) = Ym, 
zp = 2m involve 
(St + 1) 3 ty? +4 ty 
En eee ee pee 
15 12 3 
and this point is not situated in the normal plane of t. So the 
connecting lines PM of the corresponding points P and M of a 
and ge form a system of rays (3, 1). 
3. Relation between the spacial systems (P) and (M). To a point 
P taken arbitrarily five points correspond. For, if P is given, 
the five conormal points, the normal planes of which intersect in P, 
are given and any point of this quintuple may be regarded as the 
above given point tj. 
To investigate how many points P correspond to any point M, 
we deduce the equation of the plane w belonging to the normal 
plane z of the point tj. The plane w bisecting the distance of the 
points to, ts orthogonally, it is represented by the equation 
(el? FGH (et = (et)? Hy + (ei, 
which reduces itself in connection with (7) to 
38 —8—6z2P42(1—8y)h42(e—82)=0 « (11) 
As t presents itself to degree five in this equation, any given 
point M is centre of five spheres of JOACHTMSTHAL and so a quintuple 
of points P corresponds to this point M. So we find : 
“The relation of the spacial systems (P) and (M/) is a corres- 
pondence (5,5)”. 
