152 
PROFESSOR CAYLEY’S SECOND MEMOIR ON THE 
(2Z) 2{(2, 1)— (T, 1,_1)2 — (2, l)(2m-4)} 
+ {3(1, 1, 1)-(1, 1, l)(2m— 5) — (I, 1, l)(2m— 5)} 
+ Supp. (1,1,1) 
(Z) { (4) — (4)(2m— 4) — (I, 3)} 
+ Supp. (4) 
(Z) 2{(4)-(3 L l)-(2-2)} 
+ {(3, l)-(3, l)(2m— 5) — (1, 1, 2)} 
+ Supp. (3, 1) 
(Z) 3{(4)-(2,2)-(3,I)} 
+ {2(2, 2)— (2, 2) (2m— 5)— (1, 1, 2)} 
+ Supp. (2, 2) 
(Z) 2 { (3, 1)— (2, 1, 1)2— (2, 1, 1)2} 
+ {(2, 1, 1)— (2, 1, l)(2m-6)-(*I, 1, 1, 1)3} 
+ Supp. (2,1, 1) 
(Z) 4 { (4) — (1^3) — (4)(2m — 4) f 
+ {(1, 3)-(T, 3)(2m— 5)— (T, 3)(2m — 5)} 
+ Supp. (r, 3) 
(Z) 3{(3, 1) — (T, 1, 2) — (3, l)(2m— 5)} 
+2{2(2, 2)-(I, 1, 2)— (2, 2)(2m— 5)} 
+ {2(1, 1, 2)-(I, 1, 2)(2m— 6)— (I, 1, 2)(2m-6)} 
+ Supp. (T, 1, 2) 
=(1,1, 1)2D; 
=4(4)2D ; 
= 3(3, 1)2D ; 
= 2(2, 2)2D; 
=2(2, 1, 1)2D ; 
=(1, 3)2D; 
= (I, 1, 2)2D; 
(Z) 2{(2, 1, 1)-(I, 1, 1, 1)3— (2, 1, l)(2m— 6)} 
+ {4(1, 1, 1, 1)— (T, 1, 1, l)(2m 7)-(I, 1, 1, l)(2m— 7) } 
+ Supp. (T, 1, 1, 1) =(1, 1, 1, 1)2D. 
110. I content myself with giving the expressions of only the following supplements. 
Supp. (4Z)(1) =m[2( .)"(/)]+*(■ )• 
Supp. (3Z)(2) =K 2( : )-( • /)]+M • /)• 
Supp. (3Z)(1, 1)= ( %nn — %n 2 — n-\-ncc )( :) 
+(2m 2 — imn — 2m+2w+(m— ^)a)( - /) 
+ (-m 2 +m )(//). 
