1896-97.] Dr Muir on a certain Eliminant. 
361 
a b 
c 
d 
e 
/ 
g 
9 
• 
<9 
9 • 
. a 
b 
c 
d 
e 
f 
g 
. 
e 
9 • 
• • 
a 
b 
c 
d 
e 
f 
g 
e 
• 
• 
a 
b 
c 
d 
e 
/ 
g 
9 • 
• 
. 
a 
b 
c 
d 
e 
f g 
• • 
• 
* 
. 
a 
b 
c 
d 
e / 9 
g f 
e 
d 
c 
b 
a 
• 
9 
a 
• 
g 
/ 
e 
d 
c 
b 
a 
8 
• 
• 
. 
9 
f 
e 
d 
c 
b 
a 
• 
9 • 
9 
g 
f 
e 
d 
c 
b 
a 
• • 
» • 
. 
• 
g 
f 
e 
d 
c 
b a 
9 9 
• 
• 
g 
f 
e 
d 
c l 
a 
we notice at once 
that, by reason of 
the centro-symmetry 
determinant resolves into 
a 
b 
c 
d 
e 
f+g 
a 
b 
c 
d + g 
e+f 
. 
• 
a 
b + g 
c+f 
d + e 
a 
. 
g 
a+f 
b + e 
c + d 
a 
g 
f 
e 
a + d 
b + c 
9 
f 
e 
d 
c 
a + b 
and 
a 
b 
c 
d 
e 
f-g 
9 
a 
b 
c 
d- 
-g 
e-f 
9 
9 
a 
b-g 
c - 
f 
d- e 
9 
. 
- 
g 
a-f 
b- 
e 
c-d 
« 
-9 
•/ 
- e 
a - 
■d 
b- c 
-g 
-/ 
e 
-d 
c 
a-b 
• 
Of these it is clear that 
a+b+c+d+e+f+g and a-b+c- d+e-f+g 
are respectively factors, the cofactors being 
abed e 1 
abed e - 1 
. a b c d+g 1 
a b c d- g 1 
. a b+g e+f 1 
a b- g c-f -1 
. g a+f b+e 1 
~g a-f b-e 1 
. g f e a+d 1 
• ~g ~f ~ e a-d - 1 
g f e d c 1 
i 
- g -f — e -d - e 1 
YOL. XXI. 29/3/97 2 A 
