[341 
(a.v)#, 
341] ON THE SEXTACTIC POINTS OF A PLANE CURVE. 
But we have, former memoir, Nos. 21 and 25, 
d 2 H = -H<$>VH 
m — 1 m — 1 
?rH=- ( 3m ~ 6 > ^ _7) wii- ^ a, 
(m — 1)- (m — 1) (m — l) 2 
so that the foregoing expression becomes 
= (S^ f_(8m ~ 16)OT5ir+f&si;rvif 
- ( - 3m 6) (S ” 1 7) ffd>air+1 4 &3irv h — T iiair 
m — 1 m — 1 m — I 
— — (6m —12) tf 2 03>} 
A s 
+ № <? ■ V) H - m7.H\; 
or finally 
0 4 Udjl + 20 3 Ud,H + 20 2 Ud 3 H = 
7 ——{(— 6m 2 + 18m — 12) H 2 d<& + (— 17m 2 + 60m — 55) HQdH) 
(m — l) 4 1 
+ {(2m - 2) H (0 . V) H + (8m - 16) dH'V H) 
(m —l) 4t 
33. Calculation of dJJd 3 U. 
This is 
^ 4 
(m — 1) 
HdH. 
237 
Article Nos. 34 and 35.—The Jacobian Formula. 
34. In general, if P, Q, R, S be functions of the degrees p, q, r, s respectively, 
we have identically 
t-. /-* n „U = Q, 
pP, 
qQ, 
rR, 
sS 
d x P> 
dxQ, 
d x R, 
d x S 
d y P, 
d y Q, 
dyRy 
d y S 
dzP, 
d z Q, 
d z R, 
d z s 
or, what is the same thing, 
pP Jac. (Q, R, S) — qQ Jac. (R, S, P) + rR Jac. (S, P, Q) -- sS Jac. (P, Q, R) — 0.