( 598) 
T, = + Zeil 22e =0 
3 
Bitte eee ea ee 
where v? stands for 2° + y° + 2? — w?. Reducing ts? Ty — t° 7, = 0 
and 4,2 7, — t,2 Ts = 0 by means of the relation 3t,t,= 1, we find 
‚in ¢, as variable 
3 (1 — 27 0%) 2 + 542% 4+ 270° 4+ 18y —7=0 
i 
a + (14 — 270) tj + 6(82—2) =O 
and so after elimination of ¢; we obtain the equation 
3(1—27 v), 542 , 27 +18 y—7, 0 ; 0 
0 ‚ &(1—27 v), 54 Z ‚ 27v+18 y—-7, 0 
0 5 0 ‚ 8s — 274 , 54 2 ‚ 27vF18y =), 
3 , 0 F 1-27? , 6(8z2—2) , 0 
0 ; 3 ; 0 ; 1-270? , 6(8z2—2) 
which is really of degree ten. For by developing we find 
ee Ne et mee eee hey fe Op 
Of this curved space the sphere, according to which the hyper- 
cone v=, + ye + <2 — wg = 9 intersects the space at infinity, is 
a fivefold surface, ete. 
In passing we remark that the plane (11) envelops the developable 
of which the rational skew curve of degree five represented by the 
equations 
Gx=t(18t*+ It — 1) 
2 — 84) = st (15? — 1) 
22 t(l0 PU) 
is the cuspidal edge; as follows from the common factor 30 — 1 
of the derivatives of z,y,z according to t this curve has two real 
cusps, etc. 
5. The normal curve Nn of S*. If we represent the curve by 
the equations 
