414] 
ON POLYZOMAL CURVES. 
491 
48. The result just obtained of course implies that when as above 
aU+hV + cW + dT = 0, - + ^ + - = 0, 
a b c 
the trizomal curve ViZ7 + VmF + *JnW = 0 can be expressed by means of any three of 
the four zomals U, V, W, T, and we may at once write down the four forms 
■ . vi ■ VI ■ VS)(*>■■>*.'"••4-»■ 
VI ■ ■ • V • ■ 
I m /1 
V b 2 ’ “ V a 2 ’ 
/ Id Jmd / nd 
V abc ’ V abc * V abc ’ 
the last of which is the original equation \/lU + VmF + s/nW = 0. It may be added 
that if the first equation be represented by Vw^Fq-*Jn 1 W+ \ZpxT= 0,—that is, if we 
have 
md 
abc 
wd 
abc 
and therefore 
Vmi= V / 5' = 
“■ + ^+£ = ¿('1 + ™ + ^, =0; 
\a D C / 
b c d be la b 
or if the second equation be represented by *Jl 2 U+ */n 2 W + \/p i T = 0,—that is, if we 
have 
V " I = V / a"” ^“Vsfc' 
and therefore 
-+ —+ nr = 0; 
a c d 
or if the third equation be represented by Jl 3 U + m a V + Vp 3 T = 0,—that is, if we 
have 
and therefore 
¿8 m 3 » 3 _ 
"i i_ » J 
a b cl 
62—2