GotigeEp> 
ViI—Least Roots of Equations. By J. Dovctas Hamitton Dickson, B.A., 
F.R.S.E., Fellow and Tutor of St Peter’s College, Cambridge. 
(Read 26th March 1877.) 
(.) Let Fi) = 1, + ba4+...+ 6,2" = 0 be an equation whose roots are 
all real and different ; then 
GZ) _ g(7) 
eee ee 5 f ° (1) 
where ¢(v) =1+a7+...+ a,#", and 2 indicates summation for all the 
roots of F(v) = 0, of which 7 is a root: 
Let also 
Baa A, FAe +. FAME ee 
then 
It+ae+ae7+..jJ=(1+ba2+be'+...)(A, + Aaet...), 
and equating coefficients of like power of z , 
De tO AG oe OLA cg bus 
eer ot) OLN 5) eg 
UN ee tas 
whence 
+A,0, =a, 
+ x, p—1 = G1 
ae | i : a(S) 
T pti 
the suffix number indicating the order of the determinant. 
VOL, XXVIII, PART I. 
