248 
341] ON THE SEXTACTIC POINTS OF A PLANE CURVE, 
then the three equations are 
- 2 (m - 1) (to - 2) Ff, = (3to - 6) (3 to - 7) HEH - (3 to - 7) 2 E9, 
- (to - l) 2 AW = (3to — 7) (3to — 8) 031? 
+ (3to - 6) (3to - 7) HFIi - 2 (3to - 7) (3to - 8) JW, 
- 2 (to - 1) ^ = 2 (3to - 7) 03# - 2 (3to - 7) F% 
whence, adding, we have 
- (to -1) 2 (AW X + 2F%) = - (3to - 7) 2 (AW + 2iY) 
+ (3to - 6) (3to - 7) {03# + H (AO + AO)}, 
(that is 
- (to -1) 2 3W x = - (3to - 7) 2 3W + (3to - 6) (3to - 7) 3 . OAT, 
which is right). 
And by linearly combining the three equations, we deduce 
(3w — 6) (3to — 7) HEU — — 2 (to — 1) ( m — 2) F¥ 1 + (3to - 7) 2 AW, 
(3to - 7) 03# = - (to - 1) AW X + (3to - 7) AW, 
(3to - 6) (3to - 7) #AO = (to - 1) (3to - 8) AW Z + (3to - 7) (3to -8) AW- (to - 1 ) 2 AW Z , 
which are the formulae, ante, No. 24. 
Article Nos. 47 to 50.—Proof of an identity used in the fourth transformation, viz., 
Jac. (V, VH, 
or say 
Jac. (U, H, V#) = (31', ./p, B, GJdA, dB, 3(7). 
47. We have 
V = (31,. .$>, /x, 3j/, d z ) 
= ((31, £, @$>, fji, V), (£, 23, $$>, /X, y)> (@, g, (£$>, /X, ^$3*, 3^, 3 Z ); 
or, attending to the effect of the bar as denoting the exemption of the (31, ..) from 
differentiation, 
Jac. (U, II, V#) = (31, £, ®$>, fi, v) Jac. (U, H, 3 X H) 
+ (f), 33, /4, v) Jac. (U, II, dyH) 
+ (®, /x, v) Jac. (U, #, 3 Z H). 
31—2