1888.] Dr Muir on a Class of Simple Alternants. 
305 
A(0 1 2 8; 1) = 
A(0 1 3 8) 
A(0 1 2 7; 2) = 
A(0147)-A(0237) 
A(012 7;l,l) = 
+ A(0 2 3 7) 
A(0 1 2 6; 3) = 
A(01 56)-A(0246)+ A(1236) 
A(012 6j2,l) = 
+ A(0246)-2A(1 236) 
A(012 6; 1,1,1) = 
+ A(1 2 3 6) 
A(0 1 2 5; 4) = 
-A(0156) +A(1 245) 
A(012 5;3,l) = 
-A(0345)-A(1 245) 
A(012 5;2,2) = 
+ A(0345)-A(1 246) 
A(012 5; 2,1,1) = 
+ A(1 2 4 5) 
A(0 1 2 4; 5) = 
- A(0 1 4 7) + A(0 2 4 6) - A(1 2 4 5) 
A(012 4; 4,1) 
-A(0246) + A(0345) + A(1 245) 
A(0 1 2 4; 3,2) 
- A(0 3 4 5) + A(1 2 4 5) 
A(012 4; 3,1,1) 
- A(1 2 4 5) 
A(012 4; 2,2,1) 
A(0 1 2 3; 6) 
- A(0 1 3 8) + A(0 2 3 7) - A(1 2 3 6) 
A(012 3;5,l) = 
-A(0237) + A(1 2 36) 
A(012 3;4,2) = 
+ A(1 236)-A(0345) 
A(012 3; 4,1,1) = 
-A(1 2 3 6) 
A(012 3;3,3) = 
+ A(0 3 4 5) 
A(012 3; 3,2,1) = 
A(012 3j 2,2,2) = 
oT 
(M 
1—1 
O 
C 
A(0237). 
A(0246). 
A(1236). 
A (0 1 2 2 ; 7) 
- 1 
A (0 1 2 2 ; 6,1) 
-1 
+ 1 
A (0 1 2 2; 5,2) 
+ 1 
-1 
+ 1 
A(0 1 2 2; 5,1,1) 
-1 
A (0 1 2 2; 4,3) j 
+ 1 
-1 
-1 
A (0 1 2 2; 4,2,1) 
+ 1 
- 1 
A (0 1 2 2 ; 3,3,1) 
+ 1 
A (0 1 2 2; 3,2,2) 
