rOE AN EQUATION OE ANY OEDEE. 
in 
where the coefficients are such that and by equating to zero the determinant 
formed with these coefficients, we have the result of the elimination. 
In the present case, writing for a moment and in like 
manner ^^(s'+\/^)=A', cp^{s'=\/d)=B', we have 
x’ /'A I -D\ «(A— B) „ A— B 
Fs'=:)i(A'+B')-^^A;^. Gs'=^' 
A/fl 
VS ’ 
and therefore 
FsGs'— F5 'Gs=w 
( A + B) ( A' - B') - ( A - B) (A' + B') {s - s') ( A - B) ( A' - B'; 
or reducing and dividing by s — s', 
FsGs'-Fs'Gs 
=2w 
AB'-A'B , (A-B)A'-B' 
«— «' ■■ \/S(s—s') ' 0 
Hence, substituting for A, B, A', B' these values, we have the expression 
{s-s') v/a 
v'S)-f\{s— \^l)} {<p^{s' + v'e)— 
+ 
which is of the form 
( fto.o, «0.1 • • ao.«-2ls, 1)" '(5,1)™ ' 
1,0 
and equating to zero the determinant formed with the coefficients, we have an equation 
in 6 which is the equation of differences of the given equation (pv=(). For instance, if 
the given equation is (pv=(a, b, c, dy^v, 1)^=0, then we have 
8^^(s-f"\/ ^)— 6-\~ci6^ 8d-}-12c\X 6-\-^bd ^3^5, 1)^ 
=(A, B, C, DXs, l)^ 
^<p\{s—\/l)={a,2h—a\/l, ic—Ab\/^-\-aO, M—12c\/l-\-^b6—a6^1js, 1 )-’ 
= (A, B', G, D'Xs,l)- 
and the function in s, s' is 
3(AB'-A'B)sV^ 
+ 3(AC' -A'C)ss'(s+s') 
+ (AD'-A'D)(s"H-ss'4-s'"} 
-f 9(BC'-B'C)ss' 
+ 3(BD'-B'D)(s+s') 
_-f3(CD'-C'D) 
+y(A-A', B-B', C-C', D-D'Js, 1)^(A-A', B-B', C-C', D-D'Xs', 1)\ 
Q 2 
6 
aG 
