CURVES WHICH SATISFY GIVEN CONDITIONS. 
169 
*(1, 1, 1, 1, l) + *(2, 1, 1, 1) Referring to 
=*(LH, 1, 1, 1, 1)+ *(>1, 1, 1, 1) 
+ *(2*1, 1, 1, l)+z.}(n-3)(n-4) 
=*(1*1, 1, 1 , 1 , 1)+2*(2*1, 1 , 1 , 1) + D' .... (twelfth equation) 
131. Hence, substituting in the expressions of the several Supplements, we have 
Supp. (5) 
= 0 
+N 
(first equation) 
Supp. (4, 1) 
= R+J' 
+2J+R 
(second equation 
Supp. (3, 2) 
= 3L + 2M+0 
+6K+L+3N+20 
(third equation) 
Supp. (3, 1, 1) 
= H+2I+D'+J' 
+E+F + 2G+D + 3J+J' .... 
(fourth equation) 
Supp. (2, 3) 
= *(2*I, 3) 
+Q 
(fifth equation) 
Supp. (2, 2, 1) 
= *(2*1, 1, 1)+J' 
+ 3G+I+4J+2J' 
(sixth equation) 
Supp. (2, 1, 1, 1) 
= *(2*1, 1, 1, 1,)+D' 
+B + 4C + 4D+D' 
(seventh equation) 
Supp. (I, 4) 
= *(LH, 4) + 0 
+(m-|)(4N+0) 
-iN+|0 
(eighth equation) 
Supp. (I, 1, 3) 
= *(la, 1, 3) + 2*(2*l, 3)+2R + 3J' 
+(m-2)(2P+2Q+5J+4R) 
— 2P— Q-2R+J' . . . 
(ninth equation). 
Supp. (1, 2, 2) 
= *(LH, 2, 2)+3L+2M 
+ (m-2)(9K+3L + M+2N+0) 
+ 3L+2M-2N-0 . 
(tenth equation). 
