1898 - 99 .] 
becomes 
Dr Muir on a Per symmetric Eliminant. 
545 
+ K a ~\ 
- K a ~\ 
+ 
which vanishes, because the two coefficients of every power of 
X n cancel each other. 
4. Distinguishing the chosen element by placing a dot over it, 
we may write this identity shortly in the form 
of § 2 ; and this means that the latter can, by a mere rearrange- 
ment of its terms be expressed as a sum of n different multiples of 
zero. 
5. The same superfluous provision for evanescence appears in 
another mode of establishing the identity 
^(A-ijAg, . . . . , A„) — • 0 . 
Now, it is easily seen that 
jPi<£(A.;i,A,2) • • • j • ■ • > "b + y? n <^)(Aj,A 2 , . . . , A, 4 
is the same as the general expression 
® a ^05— ~b 
S 1 *2 % = 0 . 
s 2 s 3 s 4 
For, on substituting the equivalents of the s’ s, we change the deter- 
minant into 
