A variational expression is constructed for the drag on a sphere of radius a that moves with speed U [Lt ] Ωa along the axis of a container of rotational speed Ω and length h [Gt ] a with E = v/Ωa2 [Lt ] 1. Two complementary approximations, based on the asymptotic solutions in the limits δ = Eh/2a ↑ ∞ and δ ↓ 0, and a variational interpolation between these approximations are compared with the numerical results of Hocking, Moore & Walton (1979). The limit δ ↓ 0 is singular, and the variational principle fails in that limit in the sense that the error in the drag is of the same order as the error in the trial function rather than of second order therein; nevertheless, the variational interpolation is in error by less than 0·1% for δ > 0·003 and by less than 1% for all δ. The variational formulation may be of interest in other contexts.