CURVES WHICH SATISFY GIVEN CONDITIONS. 
163 
( 2 ) 
( 2 ) 
(5) 
(4) 
(3, 1) 
P =2S 
Q =2r 
J [=t(m— 3) supra] ; 
R =x(m— 3) 
m 2 — m+8ft+a( — 3); 
ft 2 +8m— ft+a( — 3); 
— 3 mn + 9ft+a(fti— 3). 
(4) 
( 2 ) 
(4) 
N[=/ supra] ; 
0[=/c 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. 
N = — 3 m + a 
— 3m+a (first equation). 
2 J= — 6m 2 + 18m +a(2m-6) 
+ R= — 3 mn + 9 n +«( m— 3) 
— 6m 2 — 3mft+18m+9ft+a(3m— 9) (second equation). 
6K= 
3ft 2 +24m— 
•3 ft+«( 
-9) 
+ L= - 
-3ft 2 
-|— 9ft -j- ct(n • 
-3) 
+ 3N= 
- 9m 
+«( 
3) 
-1-20= 
■6ft+a( 
2) 
15m 
+a(ft- 
-7) (th 
ird equation). 
E= 
\m 2 n 
— 
2m 2 - 
•|mft 
+ 4ft 2 + 2m— 
16ft q-a( 
-fft+ 6) 
+ F = 
m 3 
- 
4m 2 + 
8 mn 
-j- 3m — 
24ft+a( — 
3m 
+ 9) 
+2G= 
2mft 2 +16m 2 — 
2mft 
— 8ft 2 — 64m + 
■ 8ft + a( — 
6m 
+24) 
+ D = - 
-fm 3 
+ 
— 18?ft 
+ a(im 2 — 
-fm 
+ 6) 
+ 3J = 
- 
9m 2 
+2 7m 
+ «( 
3m 
- 9) 
+ J' = 
— 3ft 2 -J- 
9ft + a( 
ft- 3) 
-|m 3 - 
+2mft 2 + 
— 7ft 2 — 50m— 
■23ft + a(-|m 2 — 
- + 33) 
(fourth equation). 
2 A 
MDCCCLXVIII. 
