238 
ov what is the same thing 
(l + w )yi + (1+ w2 )y* ••• + (;+ w ")y»' 
to denoting, as usual, an unreal nth root of unity. And if 
we put 
0,Oi — — f- tv, o.) — — f- w, ■ • • o — — -4- w *, 
1 n 1 n n 1 
we shall have 
Y = (;+»>■ +(;+*’>- +(;+”">• 
and 
*(Y) = 0, 
which establishes the proposition. It hence appears that the 
argument in which the statement above amended occurs, 
% does not require any further modification. 
The general form of the differential resolvent for the n-ic 
equation 
y" — ny -f- (« — 1 ) # = 0 
given in my last communication to the Society (see pp. 199-201 
of the Proceedings), may be deduced from Mr. Cayley’s equa- 
tion (p. 193, ibid.) — 
r d i ’ ,-1 r 
' n d 
2 n — 1"| 
.n — \ U du 
n — 1 J 
w’-’y, 
by simply writing - and 
n — 1 
in place of a and u re- 
spectively. But I think it right to mention that the form 
was suggested to me by induction from the particular cases, 
n=3, n— 4, n— 5. In fact, I found by direct calculation that 
the several symbolical forms of the differential resolvents are 
as follow, viz. : — For the cubic the resolvent is 
e' 20 y=0; 
y 
D(D-l) 
