554 PEOEESSOE CAYLEY ON THE SEXTACTIC POINTS OE A PLANE CUEVE. 
and thence 
11= (5m 2 — 18m+17)(4m— 9) Jac. (U, V , H)H 
-j-2(5m-9)(m-2)(4m-9) Jac. (U, VH, H) 
+ ( m _2)|(5rn 2 -18m+17)B^+ (m ~3^ y r — 
22. Now 
*=(& 35, €, jr, <B, 1IA', B', C') 2 , %=(%, 33', €', f, <&, fc'*A, B, C) 2 , 
and writing for shortness 
E'F = (B0, . .JA, B‘, C') 2 , F'F =(a, . -IA, B', C'^B^', B$', BC'), 
E^ 1= (Ba', . oca, b, c) 2 , F^^car, . oca, b, cxaa, bis , bc ), 
(we might, in a notation above explained, write E'F=B' v P'h, F'4 r =^B'4 r u, and in like 
manner ET'^B'^u, FSE r 1 =^BM' g), then we have 
d^=E^+2F>p, B^r 1= E^ 1 +2F^ 1 . 
We have moreover 
Jac. (U, VH, H) =-^Et 7 E'F,, 1 post, Nos. 47 to 50. 
Jac. (U, V , H)H=— E'F , J post, Nos. 51 to 53. 
23. The just-mentioned formuke give 
II = -(5m 2 -18m+17)(4m-9)E'F 
— 2(5m— 9)(m— 2)(4m— 9) 3 ” FM^ 
+(m— 2)(5m 2 — 18m-F17)(E' v F +2FT r ) 
that is 
+ 
(5m— 9) (m— l) 2 (m — 2) 
3m — 7 
(E^ 1 +2F^ 1 ), 
n = -(3m-7)(5m 2 -18m+17) E'F 
+2(m— 2)(5m 2 — 18m+17) FT' 1 
(5m-9)(m-l) 2 (m-2) 
■*" 3m- 7 1 
2(m — l)(m — 2) (3m— 8) (5m— 9) _ - 
3m— 7 * V| 
or, as this may also be written, 
(3m— 7)U=— (5m 2 — 18m-f-17){— 2(m— 1)( m— 2)FT r 1 -f (3m— 7) 2 E4 / } 
— (5m— 9)(m— 2) { (m-l)(3m-8)F'F 1 +(3m-7)(3m-8)F^-( m-l) 2 E« 
+(25m 2 -103m+106)(m-2){ -( m-l)F^+ (3m-7)F^ }• 
