PEOFESSOE CAYLEY ON THE SEXTACTIC POINTS OF A PLANE CIJEVE. 559 
We have 
Cj.2 1 2-^ 
B 4 U=7-— ^ |B 2 H+B 2 H -jK® SVH, 
4 6 J 1 m — 1 m — 1 5 
B 3 U=t— — TT g BH, 
3 (m—iy ’ 
b 2 u= 
3 2 
(m— l) 2 
H, 
B 2 H=B 2 H, 
3,H= i ^ T (-3» l +6)3<l>-<t.3H+ ^ 
for which values see Appendix , No. 58. And hence the expression sought for is 
+ 2(m— 1)BHB 2 H 
+2H((-3m+6)HB<b-$BH+S(B . V)H)}, 
which is 
|(m— 1)3H3,H 
+ (m-l)3H3"H 
+ (-6m + 12)H ! 34i-3H<I>3H} 
+(^{2H(3.V)H-13HVHi. 
But we have, former memoir, Nos. 21 & 25, 
B 2 H= — ( ---~ 6) Hd> - — VH, 
m — 1 m — 1 
so that the foregoing expression becomes 
3 2 
= (^ip{-(8m-16)MBH+pBHVH 
(3m 6)(3m _?) H ^ H 6m_14 QBH 
m— 1 1 m— 1 m — 1 
- 3H$B XI - (6m - 1 2)H 2 d O } 
+^ i? {2H(3.V)H-f3HVH}. ; 
or finally 
B 4 UB,H+ 2 B 3 UB 2 H+ 2 B 2 TJB 3 H 
= (i 3 Tj 4 {(- 6 m s + 18 m- 12 )H s 3 <I>+(- 17 m , H- 60 m- 55 )H 4 > 3 H} 
+ ^=Ij- 4 {( 2 ro- 2 )H( 3 .V)H+( 8 m- 16 ) 3 HVH} 
(» • V)H, 
