407] 
CURVES WHICH SATISFY GIVEN CONDITIONS. 
289 
Supp. (T, 1, 1, 2) = k (1/d, 1, 1, 2) + 2k (2«1, 1, 2) 
+ 7T+27 + D' + J' 
+ (m-f)(3P + 37 T +6D + 2D + 77+27+5/) 
-2E-2F- D-£D+£/r+f/--^/+2D'-/' 
(eleventh equation). 
Supp. (I, 1, 1, 1, 1)= «(Ld, 1, 1, 1, 1) + 2k (2ici, 1, 1, 1 )+D' 
+ (m - f) (d + 2D + 4 C + 3D) 
-fd-fD-fC-2D-D'. 
(twelfth equation). 
132. Hence finally, merely collecting the terms, we have the following expressions 
of the Supplements in the twelve equations respectively. 
Supp. (5) 
Supp. (4, 1) 
Supp. (3, 2) 
Supp. (3, 1, 1) 
Supp. (2, 3) 
Supp. (2, 2, 1) 
Supp. (2, 1, 1, 1) 
Supp. (T, 4) 
Supp. (T, 1, 3) 
Supp. (I, 2, 2) 
(first equation), 
(second equation), 
(third equation), 
(fourth equation), 
(fifth equation), 
(sixth equation), 
(seventh equation), 
(eighth equation). 
= E+O 
= 2J+2R + J' 
= 6K + 47 + 2M + SN + 30 
= D + P + 7 7 +2D + 7T+27 + 3/+D' + 2/' 
= *(2d, 3) + Q 
= *(2/d, 2, l) + 3D + 7 + 4/+3/' 
= k(2k1, 1, 1, 1) + D + 4D+ 4D + 2D' 
= «(1/cl, 4) + (4m — 7)N + (2m — 1) 0 
•= «(l«i, 1, 3) + 2«(2«l, 3) 
+ (2m-6)P + (2m-5)Q+(5m-10)/+(4m-8)D+4/' (ninth equation). 
= «(LH, 2, 2) 
+ (9m— 18)K+3mL+(m+2)M+(2m—6)iV r +(m— 3)0 (tenth equation). 
Supp. (I, 1, 1, 2) = «(Ld, 1, 1, 2) + 2k (2k\, 1, 2) 
+ (2m — 5) D + (3m — 9) E + (3m — 9) F+ (6m — 15) G 
+ ( m — 1) TT + (2m — 1)7 + (5m — 15) /+ 3D' (eleventh equation). 
Supp. (I, 1, 1, 1, 1)= * (1/d, 1, 1, 1, 1) + 2k (2/d, 1, 1, 1) 
+ (m — 4)d + (2m — 7)D + (4m— 12) G + (3m— 10) D, (twelfth equation). 
where I recall the remark, ante, No. 126, that in each equation the Capitals belong 
to the system obtained by diminishing the barred number by unity and removing the 
bar; (4) for the first equation, (3, 1) for the second, and so on. 
C. VI. 
37