(528 ) 
where t is again the parametervalue of the “point ¢” of the curve. 
The quintie v of the preceding paper being unity here, vy =O 
considered as an equation of degree n has here n infinite roots, from 
which ensues that the » points at infinity of the curve coincide in a 
single point, the point at infinity of the «,-axis. As an introduction 
to the general case of an arbitrary x, let us first however consider 
the case n= 3 of the skew parabola. 
1. If to avoid indices we write for the rectangular coordinates 
of a point of S, as is customary 2, y, z instead of 2), #9, #3, the 
skew parabola is represented by 
rbi nt ae ae) 
The equation of the normal plane in the point t is 
a—t + 2t(yt?) + 3? (et?) =O, 
or classified according to t 
80 + 28 — Jet? + (1—2y)t —#=0. .. (3) 
This equation being of degree 5 in ¢, five normal planes of the 
skew parabola pass through any given point and so the locus &, is 
of order five, as was formerly found. 
The equation of the developable enveloped by the series of normal 
planes is found by eliminating ¢ out of (3) and its differential coeffi- 
cient according to t. This is immediately reduced to the elimination 
of ¢ between the two cubic equations 
4 48 —92? +4(1-2y)t —5x=0 
135 28+ 12 (10 y—7) 2 +8 (25 x—8)t+4(1—2y) =0 
by which is found by means of the wellknown method of elimination 
de, —92 , 4-8y , PE MD 0 j 0 
OMAP 4 ; —92z , 4—8y , —5x , 0 
ORE 0 fi f : —92 , 4-8y, TL 
tel tad'y VEL ent gen Mans aN ears 
Oe, 1352 , 120y—84, 75x—24, 4—8y , 0 
: 1852 © 120y—84, 75xu-—24, 4—8y 
