Sandström's (1908, 1916) pioneering experiments led to the conclusion, later referred to as Sandström's 'theorem', that differential heating and cooling cannot drive a sustained circulation when the source of heating is at or above the level of the cooling source. This principle is incorrect on theoretical grounds and is contradicted by modern laboratory results for the particular case of differential heating and cooling along a single horizontal boundary of a box. However, the 'theorem' has remained common currency. In order to explain the contradiction and explore the fundamentally important concepts involved, we re-create the original experiments of a century ago. Heating and cooling sources were sited at opposite ends of a box of water similar to that used by Sandström, with the heat source placed above, below or at the same level as the cooling source. We note the unsuitable design of the apparatus, but nevertheless find that the results are robust to changes in thermal insulation. We observe a substantial, persistent circulation in all cases. The results are inconsistent with the often-quoted original report. We conclude that Sandström's 'theorem' has no basis and cannot be used to discount the forcing of a deep convective overturning in the oceans by the meridional gradient of surface temperature or buoyancy fluxes.