THEIR APPLICATION TO THE SCLUTION OF EQUATIONS. 219 
is a moderate expression to say that, by making pro- 
ducts instead of powers of linear functions of the roots 
the basis of the theory, the difficulties of the calculation 
are diminished by one-fifth. The cyclical symbol (%’), 
again, combining five terms in one, diminishes by four- 
fifths the four-fifths that remain. So that altogether more 
than five-sixths of the labour disappears. And since there 
is no six-valued function of five letters of less than four 
dimensions, it is improbable that any view of the subject 
can lead to a simpler reducing sextic than that in 0. 
VOL, XV. GQ 
