A new type of reluctance machine is described in which, briefly, the radial poles of a conventional machine are replaced by circumferential segments. Working from the flux distribution in the air gap, general equations for the synchronous performance of reluctance machines are developed. These are used in a comparison of the new and conventional machines, and it is shown that the new machine has torque and power-factor characteristics which are superior to those of the conventional one.The air-gap flux distribution in the new machine exhibits unusual characteristics, and to discuss them precisely the ideas of m.m.f. have to be abandoned, those of magnetic potential being employed instead. Expressions are developed for the direct- and quadrature-axis reactances, and values computed from these are found to be in good agreement with values measured for a range of experimental machines.Though attention is devoted chiefly to fixed, normal-frequency operation, consideration is also given to machine performance under varying-frequency and direct-current conditions. In particular, it is shown that, under d.c. or low-frequency conditions, the output torque is directly proportional to the difference between the direct- and quadrature-axis reactances.Additionally a new method for the experimental determination of the axis reactances of salient-pole machines is described. This is based upon the theory of the impedance and current circle diagrams of reluctance machines which are also developed.