136 
Dr Muir on Permanents and Determinants. [sess. 
The effect of the change is the same as if the two lines had been 
retained, but the second read from right to left. The % it will he 
noted, does not tolerate any permutations of suffixes separately 
from the letters to which they are attached in the typical term, 
the entities which are subject to combination being a 19 b 2 , c s> 
d 4 , .... viewed as wholes. Thus, a typical term in the next case 
being + + 
! I • I C B^4 e 5 1 > 
the first factors of the remaining terms of the same kind are got 
by taking the other pairs obtainable from a v b 2 , c 3 , d 4 , e 5 , viz., 
the pairs 
g£]C 3 , a x d 4 , a x e 5 , b 2 c 3 , b 2 d 4 , b 2 e b , c 3 d 4 , c 3 c 5 , d 4 e b ' } 
and the full aggregate of terms indicated by 
+ + 
2 ! a x b 2 1 1 e B d 4 e h ! 
is 
+ + + + + + 
a x b 2 j | c»d 4 e b I + | a x c ?> 1 j b 2 d 4 e 5 1 + | a x d 4 1 . | b 2 c 3 e b ] + .... 
With this explanation the general theorem may be put in the 
form 
a x b 2 c 3 d 4 e b ... - 2«i I b 2 c z d 4 e 5 • • • I 
+ + 
+ 2 I a x b 2 1 1 c B d 4 e b . . . : 
+ + 
- 2 I a x b 2 c 3 1 . | d 4 e b | 0. 
