From a thin-film persistent-supercurrent memory cell is abstracted a particular theoretical model which is discussed exactly and in detail. The behavior predicted is in good agreement with that of experimental devices built to be as closely like the model as was possible at the time. Partly because of the simplicity of the analysis and the rather complete understanding thus gained, this model may prove to be useful for the design of large-scale memory and computing systems. For a single cell, a memory cycle time of 5 millimicroseconds should be achievable, and for a large memory perhaps 10 millimicroseconds.