[341 
ON THE SEXTACTIC POINTS OF A PLANE CURVE. 231 
(J) 
h') 
the inverse 
and thence 
(3m -6)0 (O H) = (3m - 7) 0^ - 0^i, 
11= (5m 2 — 18m + 17) (4m — 9) Jac. (77, V ,77)77 
+ 2 (5m —9) (m-2) (4m —9) Jac. (77, V77, H) 
+ (m - 2) j(5m 2 - 18m + 17) 0^ + ^y ~ 0'P 1 J- = 0. 
22. Now 
^ = (Sl, 33, (S, g, @, 5', CJ, ^ = (2l', 33', (S', ©', B, C)\ 
and writing for shortness 
EV =(021,..\A’, B\ CJ, FV =(2lB', CT$dW, 033', 0(S'), 
^ = (021', ./p, B, G') 2 , ^ = (21'. .pi, B, 77$02i, 033, 0®), 
(we might, in a notation above explained, write 77+ = 7N/ —10+-, and in like 
manner E i F 1 = d s l r 1 u, Tk/r, = 10+p, then we have 
0+ = /i’g/ + 2^1, 0+, = /7+, + 27 7 +,. 
We have moreover 
Jac. (77, V H, H) = — 77+,, | joosi, Nos. 47 to 50. 
Jac. (77, V , H) H — — 77+, ) post, Nos. 51 to 53. 
23. The just-mentioned formulae give 
n = - (5m 2 - 18m + 17) (4m - 9) EV 
-2(5m - 9)(m - 2) (4m - 9) ■”^~ 1 
+ (m — 2) (5m 2 — 18m + 17) (77+ + 277+ ) 
(5m — 9) (m — l) 2 (m — 2) 
+ 
3m- 7 
(^i + 2FyJr 1 ), 
that is 
I I = — (3m — 7) (5m 2 — 18m + 17) 
+ 2 ( m — 2) (5m 2 — 18m +17) 
(5m — 9) (m — l) 2 (m — 2) 
3m-7 
2 (m — 1) (m — 2) (3m — 8) (5m — 9) 
3m- 7 
to 46),