238 



or what is the same thing 



u) denoting, as usual, an unreal nth root of unity. And if 

 we put 



we shall have 



Y=(i + «,)2/, + (i + <.^)y....+(i + «-••>„ 

 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 9i~ic 

 equation 



y"—ny + (^^ — 1)^ = 

 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 <^n"-^ V n d 2w— 1-1"-^ „_, 



L duA -^ Lw—l du n — ij -^ 



by simply writing - and ^^ 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, 

 w=3, w=4, ??=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 



{^-i)(p-l). 



D(D-l) 



e^^=:0; 



