1904-5.] Vanishing Aggregates of Determinant Minors. 857 
and applying theorem V. we have, making a = /3= 1, 
or 
134 
467 
1341 
467 ! 
136 
447 
146 
347 
+ 
137 
446 
147 
146 
347 
+ 
147 
346 
167 
344 
346 
Starting with the aggregate 
1234 
= 0. 
( 11 ) 
2 
5678 
= -2 
1236 
4578 
or 
1234 
1235 
1236 
+ 
1237 
1238 
5678 
4678 
4578 
4568 
4567 
and applying theorem IV. we have, making a — 1, 
1235 
5678 
1236 
4678 
1237 
4578 
1238 
4568 
1239 
4567 
( 12 ) 
Theorem V. is not applicable in this case. 
5. It has been shown that 
n-k 
9 
(V) 
•2 (- 1 )* 
i x =i 
/2n\h$2n\ k\n-k\ 
\ a a i\ ) 
(2 n \k\n-k\ 
V a 
/2 n-k\ 
\h+2g) 
= 2 (-ir’Ph 
where P,, denotes the product of the two aggregates : 
(T) 
Z ^ 1 )’ 3 
* 2=1 
2n\k\h\2n\k\h + 2g\g 
a /3 a i x ic A 
/2n—2g—h—Tc\ 
V n—h—g ) 
x-vr* 
2n\k\h + 2g\g\ 
CL 1%) 
2n\k\h\2n\k\h + 2g\n-k- g 
a fS a i Y i z 
f2n | k | h + 2g \ n - k - g 
V a 
v~9\ 
^3 / 
If the determinant from which these minors are taken be 
axisymmetric, then these aggregates vanish. 
'2n\ V 
If in this relation some of the numbers in 
be put equal 
Metzler, l.c., paper I. theorem (2). 
