98 DEVELOPMENT OF A CERTAIN INFINITE DETERMINANT ARISING IN [2 

 We have already considered the following 



(16). 



We must therefore now consider 



(6) = (12) = (17) involving a"b, 



(7) = (13) = (21) 5 6, 



(8) = (14) = (23) 6", 



(30) ,, c\ with two constituents of the diagonal, 



(20), (28) ,, ctbc, with constituent 2 of the diagonal, 



(24), (29) ,, abc, ,, ,, 3 



(18), (27) ,, :l c, with no constituent of the diagonal, 



(19), (22) 3 & ! , 



We thus omit (25), (26), (31), (32) each of which is of the eighth 

 order in a ; further it is easily seen that no new element involving five 

 constituents not of the diagonal is of as low order as a 6 except terms 

 compounded out of (6), (7), (8) in the forms 



(33) -231f)4 involving a*b, 



(34) -31254 a'b, 



(35) 32154 aV, 



the constituents 5, 4 being not necessarily drawn from rows consecutive 

 to the rows 1, 2, 3. 



Consider the terms (6), 231, and (7), 312. 



These will be equal to one another, and their sum 



The sum of these terms 



/>\ j /w\ 



(6) and (7) = - -7 



<l( 

 Now consider the terms (33), -23154, and (34), -31254. 



