162 
PROFESSOR CAYLEY’S SECOND MEMOIR ON THE 
127. Referring to Nos. 41 to 47 of the First Memoir, for convenience I collect the 
capitals which belong to a single curve, giving the values in terms of m, n, a as follows. 
( 1 ) 
( 2 ) 
( 4 ) 
( 3 ) 
( 1 , 1, 1, 1 ) 
A =£$(&_ 1) —lm 3 + 2 m 2 n - im 2 — 2 mn+ 8rc 2 + \m- 2 n 
+ <*(-§ m 2 + | m- 6n+ f)+f,; 
B =h(n— 4)(m— 4) = \m 3 n — 2m 3 --|m 2 w+4mw 2 + 10m 2 — 14mw— 16w 2 — 8m +64 
+ «( — f mn+ 6 m+ 6w— 24); 
C =r.i(m-4)(m— 5)= YmV + 2m 3 -im 2 w-|mw 2 -18m 2 + £ww + 5rc 2 + 40m- 5 
+ a(— fm 2 —15); 
D =/.-|(m— 3)(m— 4) = — fm 3 +-^m 2 —18m 
+ «( |m 2 - \m + 6). 
(2, 1, 1) 
( 3 ) 
E =&(w-4) 
= 
\rtfn 
- 
2m 2 - 
|mw+ 4ft 2 + 2m— 16: 
+«( 
— fw+ 6); 
( 3 ) 
F =2&(m— 3) 
= 
m 3 
- 
4m 2 + 
8m% + 3m— 24 
+*( 
— 3m +9); 
(6) 
G = 2r(m— 4) 
= 
mft 2 + 
8m 2 — 
m»- 4ft 2 — 32m+ 4 
+ a( 
- 3m +12); 
(2) 
D[=i.£(m-3)(m-4) 
swprai] ; 
(1) 
H =hz 
= 
— fm 2 ft 
+ 
fmft— 12ft 2 
+ «( 
— -^m+^ft )-fc; 
(2) 
I =x(n— 3)(m— 4) 
= 
— 3mft 2 
+ 
9mft+-12ft 2 -36i 
+*( 
mw- 3m— 4ft + 12); 
( 5 ) 
J =i(m— 3) 
= 
- 
3m 2 
+ 9m+a(m-' 
( 2 , 2 ) 
(9) K = r 
(3) L =z(n — 3) 
(1) M 1) 
^w 2 + 4m— ^+a( — f); 
— 3w 2 +9w+a( n—S); 
fw 2 -+-ftt+a( — 3ft— ^) + ^a 2 ; 
