CURVES WHICH SATISFY GIVEN CONDITIONS. 
287 
*(3, 2) = ac (— 9 + a) = « (3 {n — 3) + ac — 1 + 1 ) 
= SL + 2M + 0 
k (3, 1, 1) — k (^m 2 + 2mn + \ri 2 — -C 3 -m — -^-n + 27 — |a) 
= H + 2/ + D' + J' 
Referring to 
(third equation). 
(fourth equation). 
viz. k 1 H = 
/c* 1 .21 = 2mn 
k-'.D' = 
ac" 1 J' = 
— bm + 4 n 
— 6 m — 8n + 24 
— \n + 6 
n — 3 
— —CC 
^m 2 + 2mn + \n? — — ^-n + 27 — |a 
«(2, 3) = k (2/cl, 3) 
ac (2, 2, 1) =/c(2/â, 2, l) + *(n-3) 
= ac (2*1, 2, 1) + /' 
ac(2, 1, 1, 1) = *(2*T, 1, 1, l) + /c.K»-3)(»-4) 
= *(2*I, 1, 1, 1) + D' 
(fifth equation). 
(sixth equation). 
(seventh equation). 
(eighth equation). 
AC ( 1, 4) = AC (1 Acl, 4) + AC 
= ac (1*1, 4) + 0 
*(1,1,3)+ AC (2, 3) + AC 2(4, 1) 
= AC (IacI, 1, 3) + *(2)cI, 3) + *(ra-3) 
+ ac (2*1, 3) 
4- ac (2m + 2)i — 6) 
= ac (IacI, 1, 3) + 2ac(2ac1, 3) + 2R + 8J 
AC (I, 2, 2) = ac (IacI, 2, 2) + * {3 (n-3) + * - 1} 
= ac (IacI, 2, 2) + 3L + 2M 
AC(1, 1, 1, 2) + ac (2, 2, 1) 
= ac(1*1, 1, 1, 2) + AC(2*1, 2, l)+/c{i(n-3)(n~4)+8 + 2w-3m-4} 
+ *(2*1, 2, 1) + * (w 3) 
= *(1*1, 1, 1, 2) + 2* (2*1, 1, 2) 
+ D' + tf+27 + /' 
(ninth equation). 
(tenth equation). 
(eleventh equation).