558 PEOFESSOB CAYLEY ON THE SEXTACTIC POINTS OF A PLANE CTTEYE. 
and thence *2 
^jy 4 (18m 2 -66m+60)HO 
+ (S?iy4(-10m+18)VH 
+K?iy | ( Q ) ! 
whence operating on each side with B n =5, we have 
(3;+10a>3,+63';3 J +123 1 3*)U= j-4 ( 1 8 m ! - 6 6m + 6 0 ) ( H3 41 + <63H ) 
+(^ir4(- 10m + 18 )(( 3 - v ) H + 9VH > 
+(^ir 3Q - 
We have besides (see Appendix, Nos. 69 to 74), 
3?3,U= pli)3{(3m-6)H3<I>+(-m+3)<l>SH} 
3 ^ U = (^?ip(-H3<I>+<I>3H); 
and thence 
(43;3,+33,3|)U= ~y 3 {(90m-21)H3®+(-m+9)®3H} 
+ (^{-4(3.V)H> ; 
and adding this to the foregoing expression for 
(h?+10B^ 2 +6B^3 + 12B 1 B 2 )U, 
we have 
(d\ + lOBft, + 105 2 5 3 + 155 £*) U= 
^Ay,{(27m ! -96TO+81)H3<I>+(17m 2 -56»i+51)<I>3H} 
+ (^T)i {(-14m+22)(3 . V)H + (-10m+18)3V . H} 
ci4 
-J-7 — ~va5Q. 
1 (to — l ) 4 
32. Calculation of 
5 4 U5 1 H+25 3 U5 2 H+25 2 U5 3 H. 
