570 PEOFESSOE CAYLEY ON THE SEXTACTIC POINTS OF A PLANE CUE YE. 
and I notice that we have 
ru=2d>, VU~H, □U=3H, 
5 TO— 1 5 5 
V^= O, V 2 U=Hd> , V.3 = 0 , 
the last of which is proved, post No. 65 ; the others are found without any difficulty. 
56. I form the Table 
3,11=0, 
a;u=^U 
1 TO— 1 
_ TT toU , , . 
S 2 U =s3T (-4>) 
a;u=- = ^r3<i> 
1 TO— 1 
$ 2 
3 2 
+ 
(TO- If 
$ 2 
(H), 
+ 
s 2 
+ 
+ 
(to— l ) 2 
3 2 
(3H), 
a 1 a s u=o, 
3;U=^(4-) +^(-H<K), 
3^=-?^™+-^ VH, 
2 TO— 1 TO — 1 
and assuming U=0, 
(^ip( i»+£vH), 
VH 
3?H=3 2 H= — (3m ^ ){ ^Z 7) a 
(to — l ) 2 
(to— l ) 2 
(3 W =OH jr= aHVH-^ *, 
which are for the most part given in my former memoir ; the expressions for b 2 U, d 3 U, 
which are not explicitly given, follow at once from the equations 
(3 2 +3 2 )U=0, (B 2 +2B 1 3 2 +3 3 )U=0; 
those for chd 3 U, d 2 U, and d 4 U are new, but when the expressions for chd 3 U and B 2 U are 
