1899-1900.] Dr Muir on Determinant Minors. 
149 
I «A c g I • ffs ~ KVrb/s + I a A c s I 'fn + \ a A c 7\‘ e 8 
— | & 4 & 6 c 8 | • e 7 + | a^btjCg | • e 6 — | a^) 8 e 7 | • d 8 4- | a> 5 b 6 c 8 1 • d 7 
— | $ 5 & 7 Cg | * + | $6^7 C 8 I * ^5 J 
where the first factors of the ten terms of the expansion are the 
three-lined determinants formable from the rectangular array 
a 4 a 5 a Q a 7 a 8 
and the second factors are the remaining non-zero elements 
d^ d 7 
e 6 e 7 e 8 
f 7 fs 
g 8 - 
(8) Now, on referring back, it will be found that this kind of 
expansion is exactly similar to that which appears on the right- 
hand side of the new general identity of § 4. This latter in the 
special case of § 3 may consequently be written — 
12 3 4 
12 3 5 
12 3 6 
1 2 3 71 
ft 
5 6 7 8 
4 6 7 8 
+ 
4 5 7 8 " 
4 5 6 8| 
4_5 4 6 4_7 4 8 
5~4 6 ~ 4 7 ~ 4 8 ~4 
5_6 5 7 5_8 
6~5 7 ~ 5 8 ~ 5 
6 7 6 8 
7 ~ 6 8 ~ 6 
7_8 
8 7 
