406] ON THE CURVES WHICH SATISFY GIVEN CONDITIONS. 225 
(1*1, 1) 
(.•.)= n + 2m — 3, 
( :/) = 2n + 4m — 6, 
( • // ) = 4n + 4m — 6, 
(///) = 4n + 2m —3; 
(1*1, 2) 
( : )= «-4, 
( • / ) = 2a — 8, 
( // ) = 2a — 4; 
(1*1, 1, 1) 
( : ) = 2m 2 +2mn + £// 2 — 8m — f/i + 13 — fa, 
( • / ) = 2m 2 + 4//m + // 2 — 8m — 7/i + 18 - 3a, 
( // ) = m 2 + 4mw 4 2n 2 — 4m — 8?i + 12 - 3a; 
(1/d, 3) 
( • ) = — 4m — 3/i — 5 + 3a, 
( / ) = — 8m — 8n — 6 + 6a; 
(Ld, 1, 2) 
( • )= 4m + 8?? + 44 + a(2m + n— 17), 
( / ) = 20m+ 16w + 42 +a (2m+2?i-27); 
(1*1,1,1,1) 
( • ) =|m s +2m 2 /i+ m/i 2 +|w 3 —5m 2 — 9mn—2n 2 +^ j m+^-n—57 + a(— 3m—|/i+^.) r 
( / ) =^ 8 +2m 2 w+2m/i 2 +^/i 3 —fm 2 —10mw—4n 2 —-^m+^/i—54+a(—3m—3w+-^)r 
(2/d) 
( .••) = !, 
( :/) = 2, 
(•//) = 2, 
(///) = i; 
(2d, 1) 
( : ) = 2m + n—o, 
( • / ) = 2m + 2w — 6, 
( // )= m+2w — 4; 
(2/d, 2) 
( • ) = «-7, 
( / ) = «-6; 
c. VI. 
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