■2C,2 
^IISS C. A. SCOTT PLAXE CUBICS. 
Note added Februaiiy 19, 1894. 
[It may be proper to give the point equation of the Cayleyan, the cubic being in 
the form here considered, 
{x -{■ y zf — (^\xyz = 0. 
The line equation of the Cayleyan is 
(!' + '>?' + = 0 • 
eliminating I' from this and 
+ yW + = 0 
we obtain a cubic equation in ; y', 
^'3Y3 _p sew (XY^ + ^px'zW + Ste [X^Y + '2py'ze + ^'®X3 = 0, 
where 1L=- z — y',Y — z — x. 
The discriminant of this, equated to zero, gives the reciprocal to (i.). 
With the ordinary notation for the coefficients of the cubic equation, the result is 
ahl^ + 4oc^ — Qo.hcd + iWd — 3h^c^ = 0, 
\vl)ich may be written 
aW + ac3 _p _ 3 ^ 
Writing for a, h, c, d their values, we have 
ahP + = SXWo + 6pz~X^Y^ {xX + y'Y) 
+ Uph'^X^Y'^ {x'^X- + q_ g^s^'e q. j/sys). 
= XW3 + pz'-^XY {xX + y Y") 2p~xy'z\ 
Substituting, and noticing that 
.t'X - yX = z' {x - y'), 
and that therefore a factor ph'^ divides out, we have the reciprocal to (i.) in the form 
