Anglin — On some Theorems in Determinants. 

 where the symbol {cilcd) denotes 



647 



d^, ¥, (P, (P 



or, P, 0', d' 



a, I, c, d 



1, 1, 1, 1 



or the product of the differences of a, h, c, d, taken two at a time ; and 

 where in the determinants on the right-hand side of the equations the 

 elements are in reality A's, but for convenience the suffixes only being 

 written. 



And further, in the case of five letters, a, b, c, d, e, it is deduced, 

 with the aid of the preceding results (3), (4), and (5), that h,. denoting 

 the sum of the homogeneous products of a, h, e, d, e, and their powers of 

 n dimensions, 



a", h'% c", d", e" 



a^, ¥, c", d^, e^ 



or, P, c^, d'^, e- 



a, I, c, d, e 



1, 1, 1, 1, 1 



{abcde) hn 



(6) 



a^\ 







a% 



&c. 





a\ 





= {abcde) 



a, 







1, 







a% 







a% 



&c. 





a\ 





= {cibcde) 



fl, 







1, 







r - Z, r -4 



n- 3, w - 4 



(7) 



s - 2, 5-3, 5-4 

 r-2, r-3, r - 4 

 n- 2, n- 8, n- A 



(8) 



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