  This is an English translation of Anders Wiman's classical paper "\"{U}ber
die Anwendung der Tschirnhausen Transformation auf die Reduktion algebraischer
Gleichungen" from 1927. The original work first appeared in the 1927
extraordinary edition of Nova Acta Regiae Societatis Scientiarum Upsaliensis.
In this paper, Wiman gives an argument that the general polynomial of degree
nine can be solved using one algebraic function of four variables and accessory
irrationalities of degree at most five. However, his argument assumes certain
intersections in affine space are generic without proof.
