1896 - 97 .] Dr Muir on Bordered Skew Determinant . 
359 
= m + 
WbM s 
+ 
2«i I 
m h 1 
h 2 
ft 
k 2 
a i 
+ 
m2 
1 a l a 2 
a 3 
ft 
@2 
7l 
(10 terms) 
2 (5 terms) 
= ft- 
18. If E 5 be compared with the last of the expansions given in 
§ 9, it will readily be seen that every term of the former is included 
in the latter. It follows from this that the terms of S 5 + B 5 are all 
terms of the skew determinant of the 6th order given in § 9. So 
far as S 5 is concerned, this is clear otherwise ; the new point is 
that all the terms of 
\ ticy /ft ll g 
are terms of 
h l h 2 h 3 h i Ji 5 
1 a 4 a 2 a 3 a 4 
ft 
— k-^ 1 a 4 a 2 a 3 a 4 
— a l 1 (3 1 (3 2 (3 3 
k 2 
— k 2 — aj 1 /?2 /? 2 /? 3 
~ a 2~P\ 1 7l 72 
^3 
-k s -a 2 -(3 1 1 y x y 2 
~ a 3 — /? 2 — 7i 1 Sj 
ft 
- & 4 — a 3 — [3 2 ~ Ji 1 S 4 
- a 4 - f3 3 - y 2 - 8 1 1 
ft 
— /c 5 — a 4 — (3 3 — y 2 “ 1 
19. On looking at the third of the identities in § 17, it is easily 
seen where certain of the terms on the right-hand side come from, 
viz., 
m and m | a 4 a 2 a 3 2 
Pi P2 
7i 
7777 
from the skew determinant, and - 1 from the bipartite. Leav- 
ic-Jb.yk^k^ 
ing these out, we have remaining, as the essence of the identity, 
\ ti 2 \ 
• 
a l 
a 2 
a 3 
“ a l 
• 
ft 
P 2 
“ « 2 “ 
-ft 
© 
7\ 
- a 3 - 
-ft- 
-yi 
• 
k 2 
h 
k t 
= 2a x i m h l h 2 
Jb 1 k 2 
a l 
m W + a 2 2 + + Pi + ft 2 + 7i 2 ) + 
