1906-7.] Dr Muir on Minors of a Product-Determinant. 
87 
«1 
a 2 . 
A 
fa 
• • • /s 
m 3 
m 4 
ra 5 
*1 
b 2 . . 
. b 5 
ffi 
92 
• • • ' 9i 
n z 
n 4 
c 2 . . 
• % 
K 
^2 
■ ■ ■ h 
r 4 
h 
k 2 
■ ■ ■ h 
h 
h 
S 5 
h 
h 
■ ■ • h 
h 
h 
h 
to be expressible as bipartites whose law of formation agrees, and is seen to 
agree of necessity, with that specified in the simpler case. Hence we con- 
clude that every minor of the product-determinant equal to A t A 2 . . . A z , 
say the r-line minor situated in rows a , /3 , y , . . . and in columns 
a, /3', y , . . . is expressible in the same form as the elements of that 
determinant , that is to say, in the form of a bipartite, the elements of 
which are- in order the r-line minors form, able from rows a, /3 , y , . . . of 
A x , from A 2 , A 3 , . . . , and from columns a, f3', y', . . . of A 7 . 
{Issued separately May 29, 1907.) 
