404 
PROFESSOR CAYLEY ON THE PROBLEM OF 
There is a division by 2 on account of the symmetry. 
Case 51. a=c=e=J$=D=x. By reciprocation of 50, 
No. is = X 3 ( + 1) 
+X 2 ( 2a?-14a* + 28a;- 11) 
+X(-10a; 3 +70a; 2 -116a;- 8) 
+ 12a; 3 — 76a; 2 + 64a; 
+f(-6X-4a;+42). 
There is a division by 2 on account of the symmetry. 
Case 52. a—c—e— B=D = F=a;. 
Functional process, by taking the curve to be the aggregate of two curves, say =x-\-x'. 
The enumeration of the cases is conveniently made in a somewhat different manner 
from that heretofore employed, viz. we may write 
x or x 1 
II 
x 1 or x 
II 
Case 
times 
all 
none 
(52) 
1 
a 
residue 
(50) 
3 
B 
55 
(51) 
3 
a , c 
55 
(46) 
3 
B, D 
55 
(47) 
3 
a , D 
55 
(48) 
3 
a , B 
55 
(49) 
6 
a, c , e 
B, 1), F 
(43) 
1 
a, B, F 
c , e , D 
(44) 
3 
a, B 1) 
o , e, F 
(45) 
6 
32; 
and the functional equation then is 
<p(x+x') — <px—<px' 
= 3F 
' a; 3 ( + l)i 
x\ 2X 3 -14X 2 + 28X-11) 
• x (— 10X 3 +70X 2 — 116X — 8) ■ 
+ 12X 3 — 76X 2 + 64X 
. +£( — 6a; — 4X +42) . 
+ •• 
(50) x 3 
