PROFESSOR CAYLEY ON THE SEXTACTIC POINTS OF A PLANE CURVE. 567 
the right hand side is 
'3m — 7 
which is 
if for a moment 
=H 
3m — 7 
HA , 
HjU, , Hv 
X , 
Y , Z 
i— 1)A, 
(m-l)B, (m— 1)C. 
x , 
V 1 , 
X, Y, 
Z 
A, B, 
C, 
x=(3', . ..XA, B, CX«, h, g), 
Y=(3', ..XA, B, C 
z =(3', • • XA, B, CX?,./, c). 
50. Hence observing that these equations may be written 
X=(9T, . . -XA, B, CXc>,.A, B,B, B,C), 
Y=(sr, . . XA, B, CXB,A, B,B, B,C), 
Z = (&', . . -XA, B, CXB 2 A, B,B, B g C), 
and that we have 
B = 
A , 
f* » 
B z 
A, 
B, 
c, 
we obtain for H Jac. (U, H, V, H) the value 
=H 
m — 1 
^ 7 (a', . . OCA, B, CXBA, BB, BC), 
or throwing out the factor H, we have the required result. 
Article Nos. 51 to 53 . — Proof of identity used in the fourth transformation , viz., 
Jac./U, V, H)H=-E^, 
or say 
Jac. (U, H, V)H=(B& . . -XA', B', C') 2 . 
51. We have 
V = (($, % v), (% IS, tffk, y, v), (<§, f, CX^, 0X^« ^ ^«)> 
and thence 
B . V =((B$, B Jh B a (§X^ *), BJ6, BjfXA, (*> d*CX*> (*, V )J$« \ d«). 
and 
(3,. V)H=((3.a, 3,®, 3.©X^ f*> *)> ( 3 .fe 3,4fXA, ,), (3,®, 3,#, 3,CX>-, f*. »)XA', B', O 
