566 PROFESSOR CAYLEY ON THE SEXTACTIC POINTS OE A PLANE CURVE. 
where the second line is 
= -y Jac. (U, B,H, d,H)-M Jac. (U, b s H, dJEI), 
or writing (A', B', C') for the first differential coefficients and (a', V, c', f, g\ h!) for the 
second differential coefficients of H, this is 
=-y 
■y 
A, B, C 
+z 
A, B, C 
a', h', g ! 
9\ /', o’ 
V, v, f 
a', h', g’ 
= -*/(C', Jf', C'XA, B, C)+*«', 33', Jf'XA, B, C). 
The first line is 
A, 
B, 
C 
A', 
B', 
C' 
a'. 
A', 
9' 
= A(B7/ - C'h') + B(C 'a' - Mg') + C(A'A' - B V), 
or reducing by the formulae, 
(3m— 7)(A', B', 0)=(a!x^h!y-\-g’z, tix+Vy+fz, g’x+fy+c’z), 
this is 
=sM - 7 {H-®y+®z)+*{-tfy+®z)+c(-®y+f'*)\ 
=ii=7 {-?(«’. «'X A > B, C)+ Z (»', S', Jf'XA, B, C)}. 
Hence we have 
Jac.(U, H, a„H)= 3 A 6 ( 1 +aMf) < -?(«'. JT. «PXA. B , C)+ 2 (S', S', Jf'XA, B, C)} 
=3^7 { C'XA, B, C) +z(®'3', Jf'XA, B, C) } ; 
and in like manner 
Jac. (U, H, B,H)= 
3m — / 
1 
Jac. (U, H, 3,H)=^ 
49. And we thence have 
{-*(£', W, C'XA, B, C)+4<g', Jf', C'XA, B, C)}, 
{-<!', 33', Jf'XA, B, C)+2/(a', 1', C'XA, B, C)}. 
Jac. (U, H, VH)=^ 
(^ 5 1,CX^^,0 , Jf , (C, Jf,CX^> ^ v ) 
(9T, 1', C'XA, B, C), (!', 33', Jf'XA, B, C), (C', Jf', C'XA, B, C) 
x , y z, 
or multiplying the two sides by 
H, 
a, A, g 
K i, f 
9> f> 0 
