1899 - 1900 .] Dr Muir on Determinant Minors. 153 
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5 ” 4 
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1 8 
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6~3 
7 ~ 2 
8~1 
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5 ~ 4 
6 ~ 3 
7 ”2 
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6 ~ 3 
7 ~ 2 
8 _ 1 
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and the general theorem is 
If the symbol 
n + 1, n + 2, . . n-ju+1, . . . , 2n I 
n + 1 , n + 2, . . . , n + /x , . . 2n| 
stand for the sum of the n determinants whose column-indices are 
in every case n + 1 , n + 2, . . . , 2n and whose row-indices are the 
same except that for one of them there has been substituted its defect 
from 2n + 1 ; and if 
* 
I n + 1, n + 2, . . . , n-/>i+l, . . . , 2n 
|n + l, n + 2, ...,n + /4 , . . . , 2n 
be taken to indicate that in the determinant 
In + 1, n + 2, . . ., n-/A+l, . . . , 2n 
|n + l, n + 2, . . n + /A , . . . , 2n 
each element 
P 
of the p th row is to be diminished by the element 
2n + 1 - a 
2n + l-/2 
; then , 
