492 ON POLYZOMAL CURVES. 
[414 
then the equation of the trizomal may also be expressed in the forms 
( 
• J 
Vm! , 
Vp! 
— ViB], 
• J 
/pibc 
V ad ’ 
/Wjbd 
"V ac 
- Vn a , - 
/pxbc 
'V ad ’ 
• ) 
/ mjed 
V ^b~ 
- Vpi, 
/Wjbd 
V AwT’ 
/m x cd 
“V “lb - ’ 
• 
• > 
/»2ac 
“V bd~’ 
/w. 2 ad 
V "b3" 
V5 , 
• ; 
vV , 
Vp 2 
A) 2 ac 
V bd ’ 
— Vw 2 , 
• > 
/led 
V ab 
Ai 2 ad 
“V be” ’ 
-VS, 
/Led 
V ab * 
• 
Vp, ) (VCT, VF, VÌF, VT) = 0, 
and 
/p 3 ab 
V cd 
• -v^ d 
VI 
V 
TOj 
V 
^3 
/m,ad /ibd /— 
V ir- -VÌ5-* • 
49. These equations may, however, be expressed in a much more elegant form. 
Write 
a' = —- b' = — —— 
(£78) ’ (7 Sa ) ’ 
c — d 
C ~(8a/3y ~ (a/37) ’ 
where, for shortness, (^78) = (/3 — 7) (y — 8) (5 — /3), &c.; (a, /3, 7) being arbitrary quantities 
or, what is the same thing, 
Assume 
a : b : c : d = a'(/3y8) : -b'(y8a) : c'(8a/3) : -d'(a/3y). 
I : m : n = pa! (fi — y) 2 : <rb' (7 — a) 2 : tc (a — /3) 2 ; 
then the equation - + ^ + - = 0 takes the form 
cl D C 
p (fi 7) (® S) + O’ (7 et) (fi 5) + t (oc fi') (7 8),