( 529 ) 
So the developable referred to is of degree six; so six is the 
rank of R, . 
By solving «, y, 2 out of (3) and its first and second differential 
coefficients according to ¢ we find 
c= 28( 9#2-+1) 
1—-2y=sP(5+a°,. De) PME 
z=2t (5E +1) 
from which ensues that the curve R, is of degree five. So, instead 
of 5, 2(5—1), 3(5—2) or 5, 8, 9, the characteristic numbers of R, are 
5, 6, 5. 
In passing we can remark here, that the- normal plane 
2880 —3iyta=108+147%+3888+t . . . . (5) 
of the curve &, in the point t is parallel, as it should be, to the 
plane of curvature 
B8—SPxtdty —2z=0 
of the skew parabola in the point ¢. The equation (5) being of degree 
seven in ¢, the locus F',, belonging to R, as original curve, is of 
class seven. This agrees with the general result obtained in the pre- 
ceding paper. For the number 3n—2, here 13, must be diminished 
by four on account of the particularity sub ®) and by two on account 
of the particularity sub’). For, » being a constant, the quintic 
equation »y=0O has five equal infinite roots; moreover the three 
equations @',;=0, a',=0, a's =0 have the factor 15¢2+-7 in 
common, in connection with which the curve #’s proves to contain 
two conjugate complex cusps. 
2. The method followed here for n= not being so easy to 
apply to the space S,, we shall try to find another way, where that 
drawback does not present itself. To do so we must recall in 
mind the proof of the theorem formerly used, according to which 
the envelope of a space with n—i dimensions, of which the equa- 
tion, linear in the coordinates x; (‘= 1, 2,... n), contains a para- 
meter t to degree k, has the characteristic numbers 
Be Me Bly i) B(E—2), en Oe (n—1) (k—n + 2), 
where it is taken for granted that & >n—2, as otherwise the last 
