The paper deals with the problem of designing interpoles for d.c. machines so as to obtain a prescribed constant distribution of current between brushes and commutator—for example, a uniform distribution. The procedure is to consider the hypothetical condition in which the current distribution is the prescribed one, the brush contact characteristic being known, and to distinguish the components of e.m.f. that are then induced in the meshes formed by the commutating coils. For the prescribed distribution to be the actual one, these component e.m.f.s must sum to zero.If the net mesh e.m.f.s cannot be made zero at all times during commutation, their evaluation provides a basis for determining the actual distribution of current, the net e.m.f.s being sources of ‘circulating currents’ superposed on the prescribed distribution. The paper is mainly confined to the problem of evaluating the e.m.f.s, the calculation of consequent circulating currents being the topic of a companion paper. Variations from the prescribed contact characteristic may also be considered as a superposed disturbance, but this aspect is not discussed here in detail. The chief aim is to make possible the recognition of various causes of circulating currents, and to suggest means for reducing them. A difference from previous publications on this complex electromagnetic problem is that the slotted construction of the armature has been fully taken into account, and it is shown that this may greatly affect the waveforms of component e.m.f.s, especially those due to flux crossing the air-gaps.