[341 
341] ON THE SEXTACTIC POINTS OF A PLANE CURVF. 235 
>plying this 
factors, we 
so that the sextactic points are the intersections of the curve 
U — cc 3 + y s + z 3 + Qlxyz = 0, 
with the curve 
(y 3 — z 3 ) (z 3 — x 3 ) (x s — if) = 0. 
expression 
+ 2l 3 ) xyz), 
Article Nos. 31 to 33.—Proof of identities for the first transformation. 
31. Calculation of (97 + lOS^ + 10373 3 + 153i97) U. 
Writing 3 in place of D, we have (former memoir, No. 20) 
(9/ + 69 a 2 9 2 ) U=. ( 23 ,H m + 8m “ 6 H® - 2 * Vi/). 
(m — If \ m — 1 m-1 J 
But 
23 ,H= 6m ~ 12 If® ^ - ViT, | 
m l m l j former memoir, 
= (8m - 6) (3m - 7) m _ *Ln | Nos. 21 and 22; 
(m - l) 2 (m - 1)- (m — 1) ) 
and thence 
(37 + 63 1 2 3o) 17 = > ■— (18m 2 — 66m + 60) H® 
+ j——77, (— 10m + 18) V H 
{m - 1 ) 4 v 7 
whence operating on each side with d u =9, we have 
(3. 5 + 10373, + 6373s + 123x37) U = —^p- 4 (18m 2 - 66m + 60) (Ho® + ®oH) 
+ ( ~i). (- lo»» ■+ is) ((a. v > h+a v h\ 
We have besides (see Appendix, Nos. 69 to 74), 
373s U = , {(3m — 6) Ho® + (— m + 3) ®oH) 
(m — 1 )■ 
30—2