The purpose of this note is to bring to attention a result which seems to have been long forgotten — indeed it may never have been widely known — and to present a parallel new result.

The ‘long forgotten’ result is that, for a simple cantilever thin walled torsion tube of area A(y) the torsional deflection θ at the tip when subjected to a torque T(y) is a minimum, for constant tube weight, if the skin thickness t(y) is proportional to , where y is the spanwise co-ordinate.