(fourth equation) 
[407 
282 
(3, 1) 
SECOND MEMOIR ON THE 
(2) 
P = 28 
= m 2 — m + 8n + a ( 
-3); 
(2) 
Q =2t 
= n 2 + 8m — n + oc ( 
-3); 
( 5 ) 
J [= ¿ (m — 3) supra] ; 
(4) 
& 
II 
1 
05 
= — 3 mn +9 n + a (m 
-3). 
(4) 
(4) 
N[= t supra]; 
(2) 
0 [=k supra]. 
128. I make the following calculations, serving to express in terms of Zeuthen’s 
Capitals, the terms in { } contained in the twelve equations respectively. 
iV = — 3m + a. 
— 3m + a (first equation). 
2J = — 6m 2 + 18m + a(2m — 6) 
+ R = — 3mn + 9?i + a ( m — 3) 
— 6m 2 — 3mn + 18m + 9n + a (3m — 9) (second equation). 
6K = 
3w 2 + 24m — 3n + a ( 
-9) 
+ L=- 
3?i 2 
+ 9 n + a (n 
-3) 
+ 3iY= 
- 9 m + a ( 
3) 
+ 20 = 
— 6n + a ( 
2) 
15m +a(w 
— 7) (third equation). 
E = 
^m 2 u — 
2m 2 — 
|mn + 4>i 2 + 2 m — \Qn + a. ( 
-fn+ 6) 
+ F = 
m 3 
- 
4m 2 + 
8mw + 3m — 24n + a ( — 
3m 
+ 9) 
+ 20 = 
2mn 2 + 16m 2 — 
2mn — 8n 2 — 64m + 8n + a ( — 
6m 
+ 24) 
+ D = - 
- |??i s 
+ 
'Qni 2 
— 18m +a(^m 2 — 
\m 
+ 6) 
+ 3 J = 
- 
9m 2 
+ 27m + a( 
3m 
- 9) 
+ J' = 
— 3n 2 + 9 n + a( 
n — 3) 
— 
\m 3 
+ \m 2 n + 2 mn 2 + 
%g-m 2 + 
tymn — 7w 2 — 50m — 23 n + a (|m 2 — 
-%n+ 33)