Anglin — On some Theorems in Determinanfs. 



651 





«', 



h\ . 



. . I 



«!, 



h, . 



. . I 



1, 



1, • 



. . 1 



= (ahc . . . l)hn 



(2) 



4. We now propose to obtain corresponding results in the cases of 

 2, 3, 4, , . , and m - 1 general indices. 



In the case of two general indices, it may be shown by (2') that 



a". 



&c. 



= a" ihcd . . .1) //p-„+2 - &c. 



Now it may readily be shown that 



{B) 



hn referring to I, c, d, . . . I. 



Hence, the right-hand member of the above equation becomes by 



a", 



a, 



&c. 



';)-m+2 



which, by (2), 



i.,i 



{abc . . . I) 



&c. 



>-«i+i> 



1, 



p-m + 2, p-m+l 

 n-m + 2, n-m+1 



(3) 



