1896-97.] 
Dr Muir on a certain Eliminant. 
363 
as it were, quadrisecting the latter by a vertical and a horizontal 
line, and folding the second or third quarter over on the first ;* so 
that, in fact, it may be written 
a b c d e f 
9 
abode 
9 f 
abed 
JJL 
9 f e 
a b c 
ft 
9 f e d 
a b 
9 f e d c 
a 
g f e d e b 
if the symbol ]=[ be taken to mean that each element of the one 
determinant-form is to be increased by the corresponding element 
of the other. The removal of the linear factor and the reduction 
of the determinant to the next lower order results in the curious 
theorem— 
a b c d e f 
9 
abode 
9 f 
ah o d 
44 
9 f e 
a b o 
TT 
9 f e d 
a b 
9 f e do 
a 
g / e d c b 
= (a + b + c + d + e +/+ g) 
abode 
-9 
abed 
~9 ~f 
a b c 
-9 ~f -e 
a b 
-9 ~f ~d 
a 
0 
1 
1 
1 
1 
1 
The second of the two determinants differs from the first merely 
in having minus signs where the latter has plus signs, and the 
analogous theorem in regard to it is 
* See the theorem regarding centro-symmetric determinants in Scott’s Text- 
book, pp. 68, 69 ; or Muir’s, pp. 183, 184. The original source is Zehfuss, 
Zeitsch. f. Math. u. Phys., vii. pp. 438, 439, where, however, the case for odd- 
ordered determinants is quite erroneously stated. 
