564 ON POLYZOMAL CURVES. [414 
205. Y. v7=Vro=Vn = \/p; order of tetrazomal is = 5; orders of trizomals = 3, 2; 
same as Y. supra. 
YI. VZ + Vp = 0, Vm + Vw = 0, aVZ + Z>Vm4-cV?i + cZVj3 = 0; order of tetrazomal 
= 5; orders of trizomals are 3, 2. 
We have here 
= ^± d vz; 
Vm x = Vm + ,y/k~[ b ^ m > 
= Vra + /y/c n/m, 
or writing the values of Vm x , in the form 
Vm + ,y/^ ^ Vm, 
= — Vm + ,y/^ ^ Vm, 
cid 
then observing that as before l = ^ m, if to fix the ideas we assume 
equations are 
Vz; = 
the 
a ~t d VZ and similarly VZ 2 = a "t"- d VZ 
Vm, = Vm+^VZ, 
d 
Vm 2 = Vm — g VZ, 
V?? 1 = — Vm + |jVZ, 
Vw 2 = Vm — - Vz, 
whence 
VZj + Vm x + V/ij = 0, VZ 2 - Vm 2 - Vm = (). 
We have moreover 
it aa + iZd /, 
a VZj = — — VZ, 
and thence 
so that 
b Vm x + c Viij = (6 — c) Vm + ^ j~ CC ^^ 
a VZ^ + Z> Vmj + c Vftj = (a — d) VZ+ (b — c) Vm = 0, 
: Vmj : Vn x = 6 — c : c — a : a — b; 
is thus a conic, and it has been seen that the other 
the corresponding trizomal 
trizomal is a cubic.