The problem of circulating corrosive liquids assumes a major importance in nuclear-engineering practice, where the standards of safety and reliability which are imposed demand sealed circulating systems. One method employs a completely enclosed centrifugal pump driven by a squirrel-cage induction motor in which the rotor is separated from the stator by a thin cylindrical corrosion-resistant shell which is situated in the air-gap of the machine and effectively forms part of the retaining wall of the circulating system. A precise assessment for design or development purposes depends on a knowledge of the power losses in the stationary shell and it is a solution of this eddy-current problem which is developed in this paper.Arguments more appropriate to field theory than to circuit theory lead to a classical boundary-value problem which takes into account the nature and thickness of the shell and the length of overhang, and provides formulae for current densities, flow lines and dissipated power in terms of ordinary machine parameters and the dimensions and electrical constants of the shell. Theoretical and practical results are compared and shown to be in close agreement. Some of the graphical results display a pronounced slot effect and suggest methods for making a more detailed investigation.The theory can be extended to correspond to a composite shell of complex structure and it has some bearing on the principles employed in drag-cup motors, to which it could be applied.