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The simple circuit of a rectangular-hysteresis-loop core driving an inductance is discussed. Cores may be used as saturable transformers, the power transfer being inhibited by the application of a steady bias. Methods of pulse modulation requiring current in a recording head of either direction require two cores associated with each head if this property is used for selection. The operation of the two-core circuit is discussed. The introduction of a non-linear resistor enables the same head to be used for recording and reading. Details are given of the construction of a switch matrix for head selection in the main store of an electronic digital computer.