CURVES WHICH SATISFY GIVEN CONDITIONS. 
157 
o) +208m + 208w+a( +12m+12w— 132) 
( 2 ) — 434m— 434w+a( §m 2 +6mw+fw 2 — ^m— ^w+291)— fa 2 
(3) — 50m— 23n+a( -|m 2 — x fm— +*+ 33) 
w +108m+ 81%+os( — m 2 — 4mw — % 2 + 7 m+-^ L w— 54) + 3a 2 
(s) + 168m+168w + a(— m 2 — 2mn— +i 2 + 25m+- 2 %— 138) + fa 2 . 
Verification is (-i+i+2)4 + (^+ ^-7)2-50-23 + 3(1 4-(^+i)2 + 33)=0. 
118. Fifth equation : 
4(5) 
+ (8, 2) _ 
+ )Supp. (2, 3)— *(2, 3)( 
+ (2, 3)(2m+w— a) 
- ( . 1, 3) 
— 60m— 60w + a( 36) 
+120m+120w+a(— 4m— 4w— 78) + 3a 2 
w 2 + 8m— w+a( — 3) 
— 8m 2 — 12m%— 4w 2 — 12m— 6w+a( 10m+7w+ 6) — 3a 2 
+ 8m 2 + 12mw+3w 2 — 56m— 53w + a(— 6m— 3w+39). 
Verification is 2+8— 1 + 3( — 3)=0. 
119. Sixth equation : 
3(4, 1) 
— 24m 2 — 60m%— 24w 2 +312m+312w 
(0 
+2(3, 2) 
+240m+240w 
(2) 
+2(2, 2, 1) 
+48m 2 +108mw + 48w 2 — 936m— 936w 
(3) 
+ {Supp. (2, 2, 
1)— *(2» 2, 1)} 
+ 12m 2 + 6mw— 6w 2 — 60m— 6% 
(4) 
+ (2, 2, l)(2m+w — a) 
+ 12m 2 + 18 mn-\- 6w 2 +108m+ 54 n 
(5) 
— 2( • 2, 1, 1) 
— 48 m 2 — 72mn— 24w 2 +336m+336% 
(6) 
(i) 
+ a( 
+18m+18w— 198) 
(2) 
+a( 
- 8m- 8rc— 156)+a 2 ( + 6) 
(3) 
+ a( 
— 16m— 16w+654)+a 2 ( m+%— 24) 
(4) 
+ a( mn — 8m— 2w+ 30) 
+a( 2m 2 + 3wm+w 2 — 36m— 21w— 54)+a 2 (— m— w+15) 
(6) +a(— 2m 2 — 4mw— w 2 +50m+29?z— 276)+a 2 ( + 3). 
Verification is (12+6-6)2-60-6 + 3(4-(8+2)2+30)=0. 
120. Seventh equation : 
2 ( 3 , 1 , 1 ) 
+( 2 , 1 , 1 , 1 ) 
+ {Supp.(2, 1, 1, l)-*(2, 1,1,1)} 
+(2, 1, 1, l)(2m+w— a) 
-( • 1 , 1 , 1 , 1 ) 
\m 3 n + mV 
•§-m 4 + + 3m V + fmw 3 + fyt* 
fm 3 n — 4m V — fmw 3 — 
0 ) 
( 2 ) 
(3) 
0) 
(5) 
