441 
EXPRESSED IN TERMS OF THE ROOTS OF (px, fv. 
going demonstration, that the weight of [which means a„ a, being 
the coefficients of a?”"'', x^~^ in and h^, of the same in <p] has been correctly taken 
to be r+A- in respect of the roots of /“and (p conjoined. 
Art. (20.). If now we proceed in like manner with the general case of m=n-\-e, it 
may be shown, in precisely the same way as in the preceding article, that the most 
general value of any conjunctive of /and p will be a linear function of (e) functions, 
x’' + a -1-^2 ...+«„ 
-4-a2..2;”“^+ ... -l-a„..r 
x”' ' + ai.<r’"“^+&c. -\-a„x^~\ 
and of the (w) functions, 
&c. &c. 
n-lK-i.X” ‘+«-iK 2 •••+«-lK„, 
and that consequently, if the degree of such conjunctive in x be {n—i), it will be of 
the lowest weight when it is a linear function of the entire (e) upper set of functions, 
and (i) of the lower set ; and consequently, the coefficient of the highest power of x 
in such conjunctive will be the determinant 
oK-i 
oK, 
0K3.. 
...„K,... 
iK. 
:K2 
:K3.. 
.K,,. 
2K. 
2K2 
2K3.. 
...2K,... 
-.K. 
.-:K2 
.-.K3.. 
..-:K2... 
1 
a, 
a,.... 

1 
a,... 
a,.... 
1 ... 
a,.... 
1 . ... a„ 
the weight of which is evidently that of 
ol^l X iK .2 X 2K3 ••• X ;_iKj X 
i. e. 1+3+5 + .. .-{-(2^ — \)-\-e.i 
i. e. i*+ef, or ^(e+^), which is (w— if t=n—i. 
3 M 2 
